EM2 Teach Grade 1 Module 6 UTE by General

What does this painting have to do with math? American realist Edward Hopper painted ordinary people and places in ways that made viewers examine them more deeply. In this painting, we are in a restaurant, where a cashier and server are busily at work. What can you count here? If the server gave two of the yellow fruits to the guests at the table, how many would be left in the row? We will learn all about addition and subtraction within 10s in Units of Ten. On the cover Tables for Ladies, 1930 Edward Hopper, American, 1882–1967 Oil on canvas The Metropolitan Museum of Art, New York, NY, USA Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48 1/4, W. 60 1/4 in (122.6 x 153 cm). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists Rights Society (ARS), NY. Photo credit: Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY

Great Minds® is the creator of Eureka Math®, Wit & Wisdom®, Alexandria Plan™, and PhD Science®. Published by Great Minds PBC. greatminds.org Copyright © 2021 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Where expressly indicated, teachers may copy pages solely for use by students in their classrooms. Printed in the USA 1 2 3 4 5 6 7 8 9 10 XXX 25 24 23 22 21 ISBN 978-1-63898-398-9

A Story of Units®

Units of Ten ▸ 1 TEACH

Module

1 2 3 4 5 6

Counting, Comparison, and Addition

Addition and Subtraction Relationships

Properties of Operations to Make Easier Problems

Comparison and Composition of Length Measurements

Place Value Concepts to Compare, Add, and Subtract

Attributes of Shapes · Advancing Place Value, Addition, and Subtraction

Contents Part 1: Attributes of Shapes Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Why. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Topic B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Composition of Shapes

Achievement Descriptors: Overview . . . . . . . . . . . . . . . . . . . . . 12

Lesson 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Topic A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Attributes of Shapes

Lesson 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Name two-dimensional shapes based on the number of sides.

Lesson 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Sort and name two-dimensional shapes based on attributes.

Lesson 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

Create composite shapes and identify shapes within two- and three-dimensional composite shapes. Create new composite shapes by adding a shape.

Lesson 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 Combine identical composite shapes.

Lesson 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Relate the size of a shape to how many are needed to compose a new shape.

Draw two-dimensional shapes and identify defining attributes.

Lesson 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Name solid shapes and describe their attributes.

Lesson 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Reason about the functionality of three-dimensional shapes based on their attributes.

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Topic C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Halves and Fourths

Resources

Lesson 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Observational Assessment Recording Sheet . . . . . . . . . . . . . . . . . . . . 240

Reason about equal and not equal shares.

Lesson 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

Achievement Descriptors: Proficiency Indicators. . . . . . . . . . . . . . . . 234

Sample Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

Name equal shares as halves or fourths.

Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

Math Past. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

Partition shapes into halves, fourths, and quarters.

Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248

Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 Relate the number of equal shares to the size of the shares.

Lesson 14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 Tell time to the half hour with the term half past.

Lesson 15 (Optional). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Reason about the location of the hour hand to tell time.

Module Assessment (Part 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

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Part 2: Advancing Place Value, Addition, and Subtraction Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 Why. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252

Topic E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 Deepening Problem Solving

Achievement Descriptors: Overview . . . . . . . . . . . . . . . . . . . . 254

Lesson 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316

Topic D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Count and Represent Numbers Beyond 100

Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328

Lesson 16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

Lesson 22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342

Count and record totals for collections greater than 100.

Represent and solve add to and take from with start unknown word problems.

Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274 Read, write, and represent numbers greater than 100.

Lesson 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 Count up and down across 100.

Lesson 19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 Write totals for collections larger than 100 shown in various groups of tens and ones.

Represent and solve put together and take apart word problems. Represent and solve add to and take from word problems.

Lesson 23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 Represent and solve comparison word problems.

Lesson 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370 Reason with nonstandard measurement units.

Lesson 25 (Optional). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 Solve nonroutine problems.

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Topic F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 Extending Addition to 100

Resources

Lesson 26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

Observational Assessment Recording Sheet . . . . . . . . . . . . . . . . . . . . 482

Make a total in more than one way.

Lesson 27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

Achievement Descriptors: Proficiency Indicators. . . . . . . . . . . . . . . . 476

Sample Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484

Add two-digit numbers in various ways, part 1.

Terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

Lesson 28. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

Math Past. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

Add two-digit numbers in various ways, part 2.

Lesson 29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 Add tens to make 100.

Lesson 30. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448 Make the next ten and add tens to make 100.

Lesson 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 Add to make 100.

Mathematician Sketches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Works Cited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Credits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Acknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

Module Assessment (Part 2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471

Before This Module

Overview

Grade K Module 2

Part 1: Attributes of Shapes

Students identify, name, and describe squares, rectangles, and triangles by using defining attributes such as the number of closed, straight sides and the number of corners. They are exposed to trapezoids and rhombuses. They also describe the faces of solid shapes and discuss functionality. However, triangular prisms are new to grade 1. In kindergarten, students construct solid and flat shapes by using sticks, and they draw flat shapes by using a straightedge and dot paper. Students compose two-dimensional and three-dimensional shapes and identify the smaller shapes used in the compositions.

Topic A Attributes of Shapes Students begin their study of geometry by describing and naming two-dimensional flat shapes by using defining attributes. At first, they count the number of sides on shapes to sort them into these categories: triangles, quadrilaterals, pentagons, and hexagons. They see that two shapes with the same number of sides that look different can still be given the same name. Students draw, name, and describe shapes (triangles, rectangles, squares, rhombuses, trapezoids, and hexagons) by using defining attributes such as square corners, parallel sides, and side lengths. Students describe and name three-dimensional solid shapes, including cubes, cones, cylinders, rectangular prisms, triangular prisms, and pyramids. They look at the faces they see in unfolded nets to describe the solid shapes the nets will become. They also notice how a solid shape’s attributes (its faces, edges, and corners) impact its functionality (like whether it rolls or stacks).

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Topic B Composition of Shapes Students decompose and compose flat and solid composite shapes in increasingly complex ways: • They identify shapes within a composite shape. • They name composite shapes using defining attributes. • They create composite shapes by combining shapes. Geometric composition is an important concept because it deepens understanding of part–whole relationships in other areas, such as composing 10 ones to make 1 ten, decomposing 8 into 2 and 6, partitioning a whole into halves, or recognizing that a clock is partitioned into hours and minutes. After students compose a shape in a variety of ways, they compare the number of shapes they used. They realize that the smaller the shapes they use to make a composed shape, the more shapes they need to make the composition.

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Topic C Halves and Fourths In topic C, students continue to compose and decompose shapes and relate their work to basic fractions. They partition shapes in a variety of ways and determine if the parts are equal shares of the whole. They conclude that equal parts (or shares) are the same shape and size. Then students partition circles and rectangles into 2 and 4 equal parts and name the shares as halves, fourths, and quarters. They identify 1 share as 1 half or 1 fourth of the whole and verbalize how many equal shares compose the whole (2 shares or 4 shares). Students also determine that the more shares you partition a shape into, the smaller the shares get. Finally, students connect their understanding of halves to telling time. They reason about the phrase half past and relate it to a half-circle. They recognize that half past can also be stated as a time, such as 2:30, because the minute hand has gone halfway around the clock. In optional lesson 15, students also analyze the movement and location of the hour hand, noting that it will be halfway between the 2 and the 3 at 2:30.

After This Module Grade 2 Module 3 Students begin using the number of angles in a shape as a defining attribute of flat shapes. They use the number of faces, edges, and vertices as defining attributes of solid shapes. Fraction work expands from working with halves and fourths to include thirds. Students refine their understanding of equal shares as they see that equal shares are the same size, but not always the same shape. Grade 2 students relate fractions to telling time by using the language quarter past and quarter to.

Why Part 1: Attributes of Shapes How do attributes of shapes help students name and describe them? Grade 1 students expand their knowledge of defining attributes, or the mathematical characteristics of a shape, to describe flat shapes with increasing precision. They use attributes, such as the number of straight sides and whether the shape has equal-length sides, parallel sides, or square corners, to sort a variety of shapes into different categories. They find that the fewer attributes a shape category has, the more shapes that fit into that category. In contrast, the more attributes a category has, the fewer shapes that fit into that category. Students see that the same shape can have more than one name or fit into more than one category, depending on the attributes they are considering. This concept connects to students’ experience of naming and representing numbers in various ways.

Triangle

Quadrilateral

• Triangle–A triangle is any closed shape with 3 straight sides. In later grades, students use attributes, such as angles, to name specific triangles. Grade 1 students see a variety of triangles and may notice specific attributes, but the name triangle stays consistent. • Hexagon–A hexagon is any closed shape with 6 straight sides. Students identify a variety of hexagons in grade 1, not just regular hexagons with 6 equal side lengths and 3 pairs of parallel sides. • Quadrilateral–A quadrilateral is any closed shape with 4 straight sides. The following shapes can be called quadrilaterals: rectangle, square, trapezoid, and rhombus. Grade 1 students do not work with parallelograms or kites.

Hexagon

Rectangle

Trapezoid

Square

Rhombus

• Trapezoid–A trapezoid is any closed shape with 4 straight sides and at least 2 parallel sides. A square and a rectangle may be called a trapezoid. • Rectangle–A rectangle is any closed shape with 4 straight sides and 4 right angles. A square can also be called a rectangle. • Rhombus–A rhombus is any closed shape with 4 straight sides of equal length. A square can also be called a rhombus. • Square–A square has 4 right angles and 4 straight sides of equal length. No other shapes can be called a square. 10

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Students describe and name both exemplar and variant shapes. Exemplars are the shapes students typically visualize. They are often symmetrical with a horizontal base. Variants are less frequently encountered in children’s books and media. To name these shapes, students must pay close attention to their defining attributes. When asked to sort shapes or to identify a specific shape within a set, students are shown some nonexamples, or distractors. Obvious distractors do not look much like the exemplars and are easier for students to categorize as nonexamples on sight. Difficult distractors look more like the exemplars, but they do not have all the defining attributes of the target shape. They require students to attend to defining attributes with more precision.

TRIANGLES

RECTANGLES Examples

Exemplars

Variants

Nonexamples

Obvious Distractors

Difficult Distractors

Examples

Exemplars

Variants

HEXAGONS

Nonexamples

Obvious Distractors

Difficult Distractors

Examples

Exemplars

Variants

Nonexamples

Obvious Distractors

Difficult Distractors

Achievement Descriptors: Overview Part 1: Attributes of Shapes Achievement Descriptors (ADs) are standards-aligned descriptions that detail what students should know and be able to do based on the instruction. ADs are written by using portions of various standards to form a clear, concise description of the work covered in each module. Each module has its own set of ADs, and the number of ADs varies by module. Taken together, the sets of module-level ADs describe what students should accomplish by the end of the year. ADs and their proficiency indicators support teachers with interpreting student work on

Observational Assessment Recording Sheet Student Name

Grade 1 Module 6

Part 1: Attributes of Shapes Achievement Descriptors

Dates and Details of Observations

1.Mod6.AD1

Tell time to the half hour, including using the term half past.

1.Mod6.AD2

Identify the defining attributes of two-dimensional shapes and three-dimensional shapes.

1.Mod6.AD3

Draw two-dimensional shapes that have certain defining attributes.

1.Mod6.AD4

Compose two-dimensional and three-dimensional shapes to create a composite shape.

1.Mod6.AD5

Partition circles and rectangles into 2 or 4 equal shares and describe the shares by using the words halves, fourths, or quarters.

1.Mod6.AD6

Draw or write to show that decomposing the same whole into more equal shares creates smaller shares. PP Partially Proficient

Notes

P Proficient

HP Highly Proficient

• informal classroom observations (recording sheet provided in the module resources), • data from other lesson-embedded formative assessments, • Exit Tickets, 242

• Topic Tickets, and

This page may be reproduced for classroom use only.

• Module Assessments. This module contains the six ADs listed.

1.Mod6.AD1

1.Mod6.AD2

1.Mod6.AD3

Tell time to the half hour, including using the term half past.

Identify the defining attributes of two-dimensional shapes and threedimensional shapes.

Draw two-dimensional shapes that have certain defining attributes.

1.Mod6.AD4

1.Mod6.AD5

1.Mod6.AD6

Compose two-dimensional and three-dimensional shapes to create a composite shape.

Partition circles and rectangles into 2 or 4 equal shares and describe the shares by using the words halves, fourths, or quarters.

Draw or write to show that decomposing the same whole into more equal shares creates smaller shares.

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The first page of each lesson identifies the ADs aligned with that lesson. Each AD may have up to three indicators, each aligned to a proficiency category (i.e., Partially Proficient, Proficient, Highly Proficient). While every AD has an indicator to describe Proficient performance, only select ADs have an indicator for Partially Proficient and/or Highly Proficient performance. An example of one of these ADs, along with its proficiency indicators, is shown here for reference. The complete set of this module’s ADs with proficiency indicators can be found in the Achievement Descriptors: Proficiency Indicators resource. ADs have the following parts: • AD Code: The code indicates the grade level and the module number and then lists the ADs in no particular order. For example, the first AD for grade 1 module 6 part 1 is coded as 1.Mod6.AD1. • AD Language: The language is crafted from standards and concisely describes what will be assessed. • AD Indicators: The indicators describe the precise expectations of the AD for the given proficiency category.

2 AD Code Grade.Module.AD# EUREKA MATH

AD Language

1 ▸ M6

1.Mod6.AD2 Identify the defining attributes of two-dimensional shapes and three-dimensional shapes. Partially Proficient Identify the number of sides or corners on a twodimensional shape. Circle all the shapes with 4 sides.

Proficient Identify parallel sides and square corners for twodimensional shapes and the shapes of the faces for three-dimensional shapes. Circle the shape that has 4 sides and 1 pair of parallel sides.

Highly Proficient Identify equal side lengths for two-dimensional shapes.

AD Indicators

Circle the shape with 4 equal sides.

Circle the shape with all square faces.

Topic A Attributes of Shapes Students begin their grade 1 study of geometry by describing and classifying shapes. They analyze two-dimensional flat shapes to distinguish between defining and nondefining attributes (e.g., a shape having 3 straight sides can define a triangle, but a shape being green does not mean it is a triangle). Students count the number of sides on shapes to sort them into the categories of triangles, quadrilaterals, pentagons, and hexagons. They see that two shapes with the same number of sides that look different can still be given the same name.

Students use other defining attributes like square corners, parallel sides, and side length to name, draw, describe, and sort triangles, rectangles, squares, rhombuses, trapezoids, and hexagons. Students may name shapes differently depending on whether they are looking at just the number of sides or they consider other attributes too. For example, any shape with 4 sides can be called a quadrilateral, but sometimes more specific names like rectangle, square, trapezoid, or rhombus can apply. For each two-dimensional shape type, students see examples and nonexamples. Examples include variants, or atypical examples that may be unfamiliar to them. Nonexamples include distractors to help students clarify the attributes of a specific shape. 14

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Students also analyze three-dimensional solid shapes, including cubes, cones, cylinders, rectangular prisms, triangular prisms, and pyramids. They reason about the flat shapes they see in unfolded nets and make predictions about which solid shape the nets will make when they are built. Students build the shapes to test their predictions. Through this work, students understand that they can recognize and describe solid shapes by looking at their faces. They also notice how a shape’s attributes impact its functionality. They manipulate a variety of solid shapes to understand both how the shapes move and the functions they perform (e.g., rolling, stacking). Students relate these qualities to the shape’s faces, edges, and corners.

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Progression of Lessons Lesson 1

Lesson 2

Lesson 3

Name two-dimensional shapes based on the number of sides.

Sort and name two-dimensional shapes based on attributes.

Draw two-dimensional shapes and identify defining attributes.

3 Sides

Triangle

4 Sides

Quadrilateral

I counted 4 sides on these different shapes. They are all called quadrilaterals.

This shape is a rectangle. It has 4 square corners and 2 pairs of parallel sides.

I can draw a trapezoid. There are no square corners. There is 1 pair of parallel sides.

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Lesson 4

Lesson 5

Name solid shapes and describe their attributes.

Reason about the functionality of three-dimensional shapes based on their attributes. EUREKA MATH2

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Which one do you want to blow on in a race?

I see rectangles and triangles. I think this shape will be a prism. It has 5 faces.

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A sphere rolls because it does not have faces or edges. A pyramid would be better to stack on the top of a tower.

LESSON 1

Name two-dimensional shapes based on the number of sides.

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Circle all the shapes with 4 sides.

Lesson at a Glance Students count the number of sides on shapes and use that information to sort them into four categories: triangles, quadrilaterals, pentagons, and hexagons. Students see that shapes that look different but have the same number of sides share a name. This lesson introduces the academic verb sketch.

Key Question • What can we notice about a shape to help us name it?

Achievement Descriptor 1.Mod6.AD2 Identify the defining attributes of two-dimensional

shapes and three-dimensional shapes.

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Agenda

Materials

Lesson Preparation

Fluency

Teacher

The Shape Cut and Shape Sort removables must be torn out of student books (one Shape Sort removable consists of two pages). Each pair of students needs one of each removable. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 5 min

35 min

• Cut and Sort

• Computer or device* • Projection device* • Teach book*

• Count, Trace, and Draw to Name

Students

• Problem Set

• Shape Cut removable (1 per student pair, in the student book)

Land

10 min

• Shape Sort removable (1 per student pair, in the student book) • Scissors • Glue (one container per student pair) • Crayon • Dry-erase marker* • Learn book* • Pencil* • Personal whiteboard* • Personal whiteboard eraser* * These materials are only listed in lesson 1. Ready these materials for every lesson.

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Fluency

10 5

Happy Counting by Ones from 100–120 Students visualize a35number line while counting aloud to build fluency counting within 120. 10

Invite students to participate in Happy Counting. Let’s count by ones. The first number you say is 100. Ready? Signal up or down accordingly for each count.

100

101

102

103

102

103

104

105

Teacher Note

104

105

106

107

108

109

110

109

Continue counting by ones to 120. Change directions occasionally, emphasizing crossing over 110 and where students hesitate or count inaccurately.

By the end of grade 1, students should be able to fluently count to 120, starting at any number less than 120. Consider having students practice Happy Counting to 120 often as time allows.

Show Me Attributes Students use body movements to show geometric attributes to prepare for naming and describing shapes. Let’s use our hands and arms to show words we use to talk about shapes. Show students the body movements for corners, straight, curved, closed, and open.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 1

Corners

Straight

Closed

Curved

Open

I’ll say a word. You use your body to show the word. Ready? Show me closed. Show me open. Show me straight. Show me curved. Show me corners. Alternate playfully among the different attributes.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 1

Choral Response: Shapes and Attributes Students identify two-dimensional shapes and their attributes to prepare for extending their knowledge of two-dimensional shapes from kindergarten. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display the picture of the triangle. How many sides does the shape have? 3

Teacher Note In kindergarten, students identified squares as rectangles too. Validate that both responses are correct. If students do not know the name of a shape, provide it and have students repeat it chorally.

What is the name of the shape? Triangle Language Support

Repeat the process with the following sequence:

Consider using strategic, flexible grouping throughout the module.

4 sides rectangle

6 sides hexagon

3 sides triangle

4 sides square

3 sides triangle

• Pair students who have different levels of mathematical proficiency. • Pair students who have different levels of English language proficiency.

6 sides hexagon

4 sides rectangle

4 sides square

6 sides hexagon

As applicable, complement any of these groupings by pairing students who speak the same native language.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 1 10

Launch

5 35

Students discuss the defining attributes of a triangle. Display the picture of10a tricycle, triangle, and triceratops. What are each of these objects called? Triangle, triceratops, tricycle There is something these three objects have that is the same. What is the same about a tricycle, triangle, and triceratops?

Language Support Recognizing the prefix tri- (meaning three) can help students understand how words can tell us about the objects they represent. Write each object’s name on the board. Draw a box around the prefix and share that tri means three.

The tricycle has 3 wheels, the triceratops has 3 horns, and the triangle has 3 sides. They all have 3 of something. That is why their names sound similar. Display the triangle. Let’s count the sides of the triangle. (Model tracing the sides of the triangle while leading the choral count.) 1, 2, 3 Turn and talk to your partner. How do we know this shape is a triangle? Listen for responses that mention that the shape is closed and that it has 3 straight sides. Lead a brief discussion to confirm that these are the defining attributes of a triangle as you point them out in the picture. Triangles must be closed and have 3 straight sides. Display the three nonexamples of triangles, one at a time.

Teacher Note Students will see examples and nonexamples of two-dimensional shapes. Examples may include variants, or atypical examples, which may be unfamiliar to them. Nonexamples include distractors to help students clarify the attributes of a specific shape.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 1

Ask students whether they are triangles and have them share why they think so. If students do not know they are not triangles, provide an accurate response. The blue shape is not a triangle. It has 4 sides, not 3 sides. The filled-in shape is not a triangle. It has a curved side. The 3 black lines do not make a triangle. This shape has 3 sides, but 1 side is open. None of these shapes are triangles. Transition to the next segment by framing the work. We can count the straight sides of closed shapes to help us name them. Today, we will find out the names of more shapes. 10 5

Learn Cut and Sort

35 10

Materials—S: Shape Cut removable, Shape Sort removable, scissors, glue

Students sort shapes by the number of sides and name each category. EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 1 ▸ Shape Cut

Partner students and make sure that each pair has the Shape Cut removable, the two-page Shape Sort removable, and scissors.

UDL: Action & Expression

Partner A cuts the Shape Cut removable on the dotted line and gives one piece to partner B. Make sure the Shape Sorts pages are side by side where both partners can reach them.

Offer alternative materials if using scissors presents a fine motor challenge for students. For example, allow students to draw the shape or build the shape with craft sticks.

First, cut on the black lines. Then cut out each of the four shapes. Use the gray parts to cut your own shapes with 3, 4, 5, or 6 sides.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 1

Direct partners to sort their shapes. Work together to sort the shapes. Count the number of sides on each shape. Place the shapes where they belong on the Shape Sort. When students finish, display an accurate Shape Sort. EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 1 ▸ Shape Sort

3 Sides

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 1 ▸ Shape Sort

5 Sides

4 Sides

Promoting Mathematical Practice As students sort shapes according to the number of sides, they look for and make use of structure. It is important for students to understand that some structures, like the number of sides, define a shape’s type, while other structures, like the size of the shape, do not.

6 Sides

Teacher Note Triangle

Quadrilateral

Pentagon

Hexagon

(Point to the word Triangle.) We know that closed shapes with 3 straight sides are called triangles. Hold up a shape from the Triangle category and have the class count the sides chorally.

A common misconception is that all hexagons are regular and have equal sides and angles. Hexagons can take many forms, including those that are concave with points (or corners) that point inward. Regular Hexagon (Exemplar)

Check your work to be sure the shapes in this group are triangles. Show thumbs-up when you are ready. (Point to the word Quadrilateral.) All closed shapes with 4 straight sides are called quadrilaterals, although sometimes we know them by other names. What can we call all shapes with 4 sides?

Hexagons (Variants)

Quadrilaterals Hold up each shape from the Quadrilateral category and have the class count the sides chorally. Have students check their work. Repeat the process with the pentagons and hexagons.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 1

Consider having students glue their shapes on the Shape Sorts and displaying them.

Teacher Note

Count, Trace, and Draw to Name

This lesson exposes students to the terms quadrilateral and pentagon, but students are not expected to master them.

Materials—S: Crayon

Students name the defining attributes of shapes in a given category. Have students turn to the shapes chart in their student book. Show the chart and point to the triangles. Why are these shapes triangles? They all have 3 straight sides. And they are all closed. Tell students to write the number of sides and use a crayon to trace a triangle of their choice. Students may notice that the shapes have the same number of corners as sides. If so, have students count the corners of some shapes to confirm their observation. Repeat the process with the quadrilaterals, pentagons, and hexagons. Students may share other names for quadrilaterals.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 1

Name

1. Write the number of sides. 2. Trace the shapes. 3. Draw a shape.

Sides

Name

Triangles

Quadrilaterals

Pentagons

Hexagons

Language Support

Shapes

This is the first use of the word sketch as an academic verb in the curriculum. Guide students to gain more understanding of the word by explaining the similarities between sketching and drawing.

Invite students to draw more shapes that belong in each category. Have them count the sides of the shapes they draw.

Explain that sketching is for practicing or quick work. It is similar to drawing. When we sketch, we do not create finished artwork that takes longer to complete.

When we draw shapes, we may not make them perfectly. That is okay. When we draw something quickly and it is not exactly like the object, we sketch it.

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. Directions may be read aloud.

5 EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 1 35

Land Debrief

5 min

Objective: Name two-dimensional shapes based on the number of sides. Gather students and display the four shapes. Use the Which One Doesn’t Belong? routine to engage students in discussion. Study the shapes. Find a reason why one of the shapes does not belong with the others. Allow quiet think time, then have partners turn and talk. Point to each shape and invite students to explain their thinking. Ask questions that encourage naming the shape and connecting the name with the number of sides. Students might make the following observations, although it is not necessary for the class to generate them all:

Teacher Note Marilyn Burns’ The Greedy Triangle connects well with the concept presented in this lesson, which is that shapes are named according to the number of sides they have. The book also shows shapes in the real world. Consider using the book as a read-aloud before or after this lesson. Students may sketch the shapes as they are presented in the book or build them with craft sticks.

• The hexagon doesn’t belong because it has 6 sides and it has a corner pointing in. • The circle doesn’t belong because it does not have straight sides. It is curved. • The triangle doesn’t belong because it only has 3 sides. • The square doesn’t belong because it has more than one name (e.g., quadrilateral, square, rectangle). It also has 4 sides, and the sides are all the same length. The triangle is red, and the hexagon is not colored in. Does the color of a shape or whether it is filled help us name the shape? Why? No, color does not help. Different shapes can be the same color. A shape can be any color. Or filled in or not filled in. What can we notice about a shape to help us name it? We can count the number of sides to help us name it. Copyright © Great Minds PBC

1 ▸ M6 ▸ TA ▸ Lesson 1

EUREKA MATH2

Prepare students for the next lesson by pointing to the square. Today, we learned that a shape with 4 straight closed sides is called a quadrilateral. Sometimes shapes have more than one name. What is another name for this shape? Square Rectangle We can count the sides of a shape to name it. In the next lesson we will discover other ways to name shapes.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 1

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Name

1 ▸ M6 ▸ TA ▸ Lesson 1

EUREKA MATH2

4. Draw a shape with 3 sides. Sample:

1. Circle the shapes with 3 sides.

5. Draw a shape with 4 sides.

2. Circle the shapes with 4 sides.

Sample:

6. Draw a shape with 6 sides. Sample: 3. Circle the shapes with 6 sides.

PROBLEM SET

LESSON 2

Sort and name two-dimensional shapes based on attributes.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2

Name

Count.

corners

sides

Lesson at a Glance Students identify the attributes of various quadrilaterals and test different shapes to see whether the sides are parallel and the corners are square (right angles). They use their knowledge of attributes to sort and discuss a variety of shapes. The terms parallel, rhombus, trapezoid, and square corner are introduced in this lesson. There is no Fluency component in this lesson. This allows students to spend more time exploring shape attributes.

Key Questions • What are different ways to describe a shape? • How can we describe this shape?

Circle.

Square corners

Parallel sides

Yes

Achievement Descriptor 1.Mod6.AD2 Identify the defining attributes of two-dimensional

shapes and three-dimensional shapes.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 2

Agenda

Materials

Lesson Preparation

Launch

Teacher

• The removables Shape Attribute Sort and Square Corners and Parallel Sides must be torn out of student books. Shape Attribute Sort must be placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Learn

5 min

40 min

• Square Corners • Parallel Sides • Simon Says: Shape Attributes • Half-Circle, Quarter-Circle • Problem Set

Land

15 min

• Square pattern block • Square Corners and Parallel Sides (digital download) • Craft sticks (2) • Chart paper

Students • Craft sticks (2) • Square pattern block • Square Corners and Parallel Sides (in the student book)

• Prepare the anchor chart that will be used in the lesson (see image in Land). • Copy or print Square Corners and Parallel Sides to use for demonstration.

• Shape Attribute Sort (in the student book)

1 ▸ M6 ▸ TA ▸ Lesson 2

Launch

EUREKA MATH2

5 40

Students identify and discuss the attributes of quadrilaterals. Gather students and 15 display the four quadrilaterals. Engage students in the alike and different routine. Although color and orientation are attributes of the shapes, ask questions that help students identify mathematical attributes, such as the number of sides and corners. Students do not need to generate all of the sample responses. What is the same about these shapes? They all have 4 straight sides. They are closed. They have 4 corners. If students do not mention corners, ask them to count the corners of the shapes, then show how many corners each shape has by using their fingers. All of these closed shapes have 4 straight sides and 4 corners. What can we call all of these shapes? Quadrilaterals Quadrilaterals have 4 sides and 4 corners. What is different about each of these quadrilaterals? The blue one is long. It is a rectangle. The red one is pushed in on the sides. The yellow one has pointy corners like a diamond. The green one is a square. 32

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 2

Explain to the class that squares are special rectangles because all the sides are the same length. All these shapes are quadrilaterals because they have 4 sides and 4 corners. But each shape has its own name too. We can use those names to help us talk about how the shapes are different. Write the names under each shape.

Point to each shape and read its name. Ask students to repeat the shape names chorally. Transition to the next segment by framing the work. These shapes have the same number of sides and corners. Today, we will look closely at how their sides and corners may be different.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2 5

Learn

40 15

Square Corners Materials—T/S: Square pattern block, Square Corners and Parallel Sides

Students identify square corners (right angles) in shapes and use them as a defining attribute. Make sure students have the Square Corners and Parallel Sides removable. Show a copy of the removable. Invite students to look at the rectangle, then show a square pattern block. A square has 4 straight sides that are the same length. It also has 4 corners. Place the pattern block on a corner of the rectangle. If a square fits perfectly in a shape’s corner, we can call the corner a square corner. We can sketch a little square on the shape to show it is a square corner. Demonstrate sketching a small square in one corner of the rectangle. Then have students place their square on each corner of the rectangle. Tell them to sketch a small square in the corner if it is a square corner.

Teacher Note In kindergarten, students learned that a square is a special rectangle. A rectangle has 4 square corners, and a square has 4 square corners and 4 sides that have the same length. A rhombus also has 4 sides that are the same length. A square is a kind of rhombus that also has square corners. Knowing the relationship between a rhombus and a square is not necessary in grade 1. By the end of the lesson, students should recognize that both types of shapes have 4 sides that are the same length.

How many square corners does a rectangle have? 4 How do you know they are square corners? The block fits in the corner perfectly. Repeat the process with the square.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 2

Any shape that has 4 square corners can be called a rectangle. So, a square is also a rectangle because it has 4 square corners. Why can we say a square is also a rectangle?

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2 ▸ Square Corners and Parallel Sides

Because it has 4 square corners Just like the number of sides can help us name a shape, so can square corners. Invite students to test the rhombus and trapezoid for square corners. Do the rhombus and the trapezoid have square corners? How do you know? No, their corners did not fit the square perfectly.

1 ▸ M6 ▸ TA ▸ Lesson 2 ▸ Square Corners and Parallel Sides

17 EUREKA MATH2

To help students internalize the term parallel, have them hold their arms as shown in the photo. Have students say the term. Repeat the process, with students holding their arms vertically.

The rhombus and trapezoid have 4 sides, but they do not have square corners. Tell students to test the hexagons. Transition to the next segment by inviting students to turn and talk to a partner about their findings.

Parallel Sides Materials—T/S: Craft sticks, Square Corners and Parallel Sides

Students identify parallel sides of shapes as a defining attribute.

Ask students to keep their Square Corners and Parallel Sides removable and then distribute craft sticks. Use the rectangle to model and explain how to test for parallel lines as students follow along.

Explain that, like a pair of mittens or a pair of socks, parallel sides come in pairs.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2

Notice that our sticks do not touch. Imagine that these sticks stretch out very far on both ends. Would they touch then? No. When two sides that are across from each other never touch, we call them parallel. What do we call sides across from each other that never touch? Parallel Guide students to test the vertical sides of the rectangle. Are these sides parallel? How do you know? Yes, the sticks do not touch. A rectangle has 2 pairs of parallel sides. (Point to the vertical and horizontal parallel lines.) Have students use their craft sticks to test the square for parallel lines.

UDL: Engagement After students find parallel sides with craft sticks, invite them to highlight the parallel sides.

What do you notice about the parallel sides on a square? A square has 2 pairs of parallel sides, just like a rectangle. Both squares and rectangles have 4 sides, 4 square corners, and 2 pairs of parallel sides. What is different about these shapes? The rectangle is longer.

Students may also use pattern blocks to help them identify parallel sides.

All 4 sides of the square are the same length, but the sides of the rectangle are not all the same. Have students test the rhombus, trapezoid, triangles, and hexagons for parallel sides. Discuss the results. Students should find the following: • The rhombus has 2 pairs of parallel sides. • The trapezoid only has 1 pair of parallel sides. • The triangles do not have parallel sides. • One hexagon has 3 pairs of parallel sides and the other has 2 pairs.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 2

Simon Says: Shape Attributes Materials—S: Shape Attribute Sort, square pattern block, craft sticks

Students identify shapes according to their attributes. Consider inviting students to stand during this part of the lesson. Make sure they have a personal whiteboard with the Shape Attribute Sort removable inside. Display the set of shapes.

Promoting Mathematical Practice

Invite students to play a version of Simon Says. As Simon tells them to, they should circle shapes that fit the stated attribute(s). In this version of the game, students continue to play even if they make a mistake. They may use craft sticks and square pattern blocks to help them make their decisions.

Students look for and make use of structure when they sort and name shapes based on the stated attributes. Students may name shapes differently depending on whether they look at just the number of sides or consider other attributes too.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2 ▸ Shape Attribute Sort

Simon says circle all the quadrilaterals, or shapes with 4 sides.

For example, any shape with 4 sides can be called a quadrilateral. When students identify the shapes with 4 sides and 2 pairs of parallel sides, they can all be called quadrilaterals, or they can be called by more specific names like rectangle, square, or rhombus.

Students circle the rectangle, square, rhombus, and trapezoid. (Point to the triangle and hexagon.) I didn’t see anyone circle these shapes. Why not? They are not quadrilaterals. They do not have 4 sides. Copyright © Great Minds PBC

Have students erase. Simon says circle all the shapes with 4 sides and 4 square corners.

However, students are not expected to classify shapes in a hierarchy. For example, they are not expected to understand that all rectangles are also trapezoids.

Students circle the rectangle and square. (Point to the rhombus.) Why didn’t we circle the rhombus? It does not have 4 square corners. (Point to the trapezoid.) Why didn’t we circle the trapezoid? It does not have 4 square corners. Have students erase. Simon says circle all the shapes with 4 sides and 2 pairs of parallel sides. Students circle the rectangle, rhombus, and square. Copyright © Great Minds PBC

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2

(Point to the trapezoid.) Why didn’t we circle the trapezoid? It has only 1 pair of parallel sides, not 2. That’s right, this trapezoid has 1 pair of parallel sides. Have students erase. Simon says circle all the shapes with 4 sides that look like they are the same length.

Language Support To help students internalize the terms rhombus and trapezoid, display images of all the quadrilaterals with their names.

Students circle the rhombus and the square. Everyone circled the square because we know the sides of a square are the same length. We can circle the rhombus too. Just like a square, a rhombus has 4 sides that are the same length. (Point to the rectangle.) Why didn’t we circle the rectangle? The sides are not all the same length. Have students erase. Simon says circle all the shapes with curves. Students circle the circle, half-circle, and quarter-circle. Let’s look at these shapes more closely and name them.

Half-Circle, Quarter-Circle Materials—S: Shape Attribute Sort

Students discuss the attributes of a quarter-circle and half-circle and compare them to the attributes of a circle. Display the quarter-circle and tell students to point to the shape on their Shape Attribute Sort. What do you notice about this shape?

Have students point out the rhombus and then the trapezoid. Summarize the attributes discussed in this lesson: • The rhombus has sides that are the same length. (Consider letting students measure the sides of a rhombus with centimeter cubes.) • The rhombus does not have square corners, but it has 2 pairs of parallel sides. • The trapezoid does not have square corners (a different trapezoid may have a square corner). • The trapezoid has 1 pair of parallel sides.

It has 1 square corner. It is curved. It has 2 straight sides. The sides are not parallel. 38

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 2

Display the circle with the quarter-circle overlay. Point to the quarter-circle. This shape is a quarter-circle. What is the name of the shape? A quarter-circle Display the half-circle. Tell students to point to it on their Shape Attribute Sort. We found another shape that is curved. It is called a half-circle. What is the name of this shape?

Teacher Note Curved lines in a shape are not called sides, although students may refer to them that way. Redirect students to say, “curved part” or “curved line.” The terms quarter and half are more explicitly discussed in topic C as part of students’ exploration of halves and fourths.

A half-circle Display the circle with the half-circle overlay. Point to the half-circle. Does the half-circle have any square corners? No. Display all three shapes. Ask students to name each shape chorally.

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. Directions may be read aloud.

5 EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2 40

Land Debrief

10 min

Materials—T: Chart paper

Objective: Sort and name two-dimensional shapes based on attributes. Gather students and display the chart with six shapes. Point to the shapes one at a time and ask the following question. How many ways can we describe these shapes? Invite students to think–pair–share. Write their ideas on the chart. It is not necessary for the class to generate all the possibilities in the following sample, but ask questions to encourage students to share as many geometric attributes as possible. For example: • What names can you think of for this shape? • What do you notice about the sides of this shape?

Teacher Note Consider extending practice with naming shapes and attributes of shapes by having students do one or more of the following activities: • Go on a shape hunt around school or at home. • Create a class shape museum by bringing in items or images from home. • Cut out shapes to create shape collages. Invite students to label or write about their work.

• What do you notice about the corners of this shape?

Shapes in the real world are often imperfect examples. Ask students why an object or picture reminds them of a shape and have them tell why it may not be a perfect example of the shape’s attributes.

Leave the chart posted for students to reference.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 2

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Teacher Note This chart is not meant to define shape type by attribute, but to help students name and notice attributes of particular shapes. Students may notice attributes specific to the shape shown, but they may not be characteristic of all shapes of that type. For example, they may correctly share that this right triangle has a square corner, even though that is not an attribute of all triangles. Likewise, the number of square corners or pairs of parallel sides in a hexagon or trapezoid can vary depending on the specific shape.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2

Name

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2

Count.

1. Count.

sides

corners

Does it have square corners?

Does it have parallel sides?

Yes

Count.

sides

corners

Does it have square corners?

Does it have parallel sides?

Yes

sides

corners

Does it have square corners?

Does it have parallel sides?

Yes

2. Circle all the shapes with parallel sides.

3. Circle all the shapes with square corners.

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 2

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 2

4. Draw a shape with parallel sides. Sample:

Draw a shape with a square corner. Sample:

5. Match the shape with its name.

rectangle trapezoid rhombus square

What is the same about all these shapes? Write or draw your answer. Sample:

They have 4 sides.

PROBLEM SET

3 EUREKA MATH2

Name

LESSON 3

Draw two-dimensional shapes and identify defining attributes. 1 ▸ M6 ▸ TA ▸ Lesson 3

Draw a trapezoid. Sample:

Lesson at a Glance Students analyze shapes used in a floor plan. They name each shape and discuss its attibutes. Then they use dots, cubes, and a straightedge to draw shapes precisely. There is no Problem Set in this lesson. This allows students to spend more time using their tools to draw a variety of shapes.

Key Questions • How does what we know about a shape help us to draw it? • Which tools are helpful for precisely drawing shapes?

Achievement Descriptors 1.Mod6.AD2 Identify the defining attributes of two-dimensional

shapes and three-dimensional shapes. 1.Mod6.AD3 Draw two-dimensional shapes that have certain defining

attributes.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 3

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Assemble cups or resealable plastic bags with 8 centimeter cubes for each student. Save them for use in future lessons.

Launch Learn

10 min 10 min

30 min

• Draw Shapes • Design a Floor Plan

Land

10 min

• Dot Shapes (digital download) • Craft sticks (2) • Centimeter cubes (8)

Students • Craft sticks (2) • Centimeter cubes (8) • Dot Shapes (in the student book) • Dot Paper (in the student book)

• Copy or print Dot Shapes to use for demonstration. • Dot Shapes and Dot Paper must be torn out of student books. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 3

Fluency

10 10

Happy Counting by Ones from 100–120 Students visualize a30number line while counting aloud to build fluency counting within 120. 10

Invite students to participate in Happy Counting. Let’s count by ones. The first number you say is 107. Ready? Signal up or down accordingly for each count.

107

108

109

110

109

110

111

112

113

112

113

114

115

114

115

116

Continue counting by ones to 120. Change directions occasionally, emphasizing crossing over 110 and where students hesitate or count inaccurately.

Show Me Attributes Students use body movements to show geometric attributes to develop fluency with shape terminology. Let’s use our hands and arms to show words we use to talk about shapes. Show students the body movements for straight, corners, square corner, and parallel.

Straight 46

Corners

Square Corner

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 3

I’ll say a word. You use your body to show the word. Ready? Show me straight. Show me parallel. Show me corners. Show me square corner. Alternate playfully among the different attributes.

Choral Response: Shapes and Attributes Students identify two-dimensional shapes and their attributes to develop fluency with naming shapes. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display the picture of the rectangle. How many sides does the shape have? 4 How many corners does the shape have? 4 What is the name of the shape? Rectangle

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 3

Repeat the process with the following sequence:

3 sides 3 corners Triangle

4 sides 4 corners Square

Teacher Note

3 sides 3 corners Triangle

5 sides 5 corners Pentagon

Validate all correct responses when there is more than one name for the shape. • The orange rectangle is also a quadrilateral. • The red square is also a rectangle and a quadrilateral. • The blue trapezoid is also a quadrilateral.

6 sides 6 corners Hexagon

4 sides 4 corners Trapezoid

5 sides 5 corners Pentagon

Launch

30 Students identify shapes and name their attributes.

Display the Classroom Floor Plan. 10 Explain that a floor plan is a picture that shows where furniture is placed in a room or space. Then have students turn to the Dot Paper in their student book. Felipe is a teacher. He made this floor plan of how he would like his classroom to look next year. What do you notice? Expect students to share a variety of observations. Use the key to help them name and identify each shape. Have students point to the shape and share its attributes, such as the number of sides and whether it has equal side lengths, square corners, or parallel sides. Consider referring to the shape chart the class made in lesson 2. For example, ask the following questions. Felipe used shapes to represent different items in the classroom. (Point to the rhombus in the key.) He used this shape to represent a pillow. 48

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 3

Teacher desk Student desk

Pillow

Chair

Table

Rug

What shape is it? How do we know? It’s a rhombus. It has 4 sides. It looks like the sides are the same length. (Point to the trapezoid in the key.) Felipe used this shape to represent student desks. (Point to this shape in the floor plan.) What shape is it? How do we know? It’s a trapezoid. It has 4 sides. Two sides are parallel.

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1 ▸ M6 ▸ TA ▸ Lesson 3

Continue with the remaining shapes. Then introduce the idea of drawing shapes precisely. Felipe drew the shapes carefully using what he knows about each shape. It helps to use tools when we want to draw shapes carefully. What kind of tools do you think Felipe used? Maybe he used a pencil, something to make straight lines, and something to measure. Transition to the next segment by framing the work. Today, we will use tools and what we know about shapes to draw them carefully. 10 10

Learn

Teacher Note This lesson creates an opportunity for students to recognize an application of geometry. Consider leading a discussion about jobs that include drawing shapes. Mention jobs that require the person to create designs, blueprints, or floor plans. Such jobs may include architects, interior designers, landscape designers, artists, or engineers.

30 10

Draw Shapes

Materials—T/S: Dot Shapes, craft sticks, centimeter cubes

Students draw shapes and discuss their defining attributes. Make sure students have a copy of Dot Shapes as well as 8 centimeter cubes and two craft sticks. Show Dot Shapes.

EUREKA MATH2

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Let’s use two tools to draw each shape in Felipe’s floor plan. We’ll use a craft stick as a straightedge and the dots on the paper as corners. (Point to the purple dots.) Think about a way to connect the dots so that they make a closed shape. Use your finger to trace your idea. What shape do you think the connected dots make? Why? I think they make a triangle because the shape has 3 corners and 3 sides.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 3

Demonstrate using the craft stick as a straightedge to make a right triangle as students follow along. What do you notice about this triangle? It has 3 corners and 3 sides. It has a square corner. Repeat this process with the hexagon, trapezoid, and rectangle. Be sure the following attributes of each shape are discussed. If students do not recognize parallel sides or square corners, have them use craft sticks to extend parallel lines and centimeter cubes to test corners. • Hexagon: 6 sides, 3 pairs of parallel sides • Trapezoid: 4 sides, 1 pair of parallel sides • Rectangle: 4 sides, 4 square corners, 2 pairs of parallel sides Continue with the square and the rhombus, making sure the following attributes are discussed. After drawing the square and the rhombus, guide students to use centimeter cubes to measure all 4 sides to confirm that they are equal in length. • Square: 4 sides of equal length, 4 square corners, 2 pairs of parallel sides • Rhombus: 4 sides of equal length, 2 pairs of parallel sides

Teacher Note As with rhombuses and hexagons, students may draw a variety of trapezoids on their own such as:

Help students compare the rhombus and the square. How is this rhombus the same as the square? They both have sides that are equal length. They both have 2 pairs of parallel sides. How is this rhombus different from the square?

Any shape with 4 sides and at least 1 pair of parallel sides can be called a trapezoid. Therefore, squares, rectangles, and rhombuses are special types of trapezoids. Classification of trapezoids is not expected in grade 1.

The rhombus does not have square corners.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 3

Any shape that has 4 sides of equal length and 2 pairs of parallel lines can be called a rhombus. So, a square can be called a rhombus. Why can we say that a square is also a rhombus? Because it has 4 equal sides and 2 pairs of parallel lines A square is a special rhombus because it also has square corners. Invite students to use their tools to draw any closed shape with straight sides in the space without dots. Ask them to think about the attributes of the shape they choose to draw. Without dots, students will approximate parallel sides and square corners. Precision is not expected. When they finish, invite one or two students to share and discuss their process. Lead the discussion by asking the following questions. How can we use what we know about a shape to draw it? We can think about how many sides the shape has. If we know a shape has square corners or parallel lines, we can draw them. Which tools are helpful for drawing shapes carefully? Why? A straightedge is helpful for making straight sides. A straightedge can help you make square corners and parallel sides.

Promoting Mathematical Practice

Centimeter cubes help you measure sides to be sure they’re the same.

Students model with mathematics when they use shapes to create a floor plan.

Design a Floor Plan Materials—S: Dot Paper, craft stick, centimeter cubes Teacher desk Student desk

Students create a floor plan by using shapes.

Pillow

Chair

Table

Rug

This requires students to model abstractly in two ways:

Display Felipe’s Classroom Floor Plan and leave it up for reference during this segment.

• Students reason only about the shape of objects, disregarding other qualities, such as color or texture.

Make sure students have Dot Paper, a craft stick, and centimeter cubes.

• Students understand that they can use shapes to represent much larger objects and that they can represent a room on paper even if the actual room they are modeling is larger than the paper.

It’s your turn to make a floor plan of a room. You can choose any room you would like to. You will use your tools to draw a few shapes that show what you would like in the room. 52

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 3

Turn and talk to a partner and discuss how you can use shapes to design a room. EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Dot Paper

Provide students with the following directions. Draw some shapes on the Dot Paper with your craft stick to make a floor plan. If you have time, make a shape key.

Teacher Note When students use Dot Paper to draw shapes, the length of any diagonal side will not be a whole number. If a student tries to measure these sides to verify that they have drawn, for example, a rhombus, encourage them to be as precise as they can without being exact. For example, they may say, “All of the sides are a little less than 2 centimeter cubes long, so I think this shape is a rhombus.”

As time allows, invite students to show their designs. 10 Encourage them to use shape names and attributes as they explain their work. 10

Land Debrief

5 min

Objective: Draw two-dimensional shapes and identify defining attributes. Display the Classroom Floor Plan.

Differentiation: Support Some students may need more practice with drawing shapes before transitioning to dot paper. Use the second Dot Shapes removable in the student book as an alternative activity to making a floor plan.

I am making a classroom floor plan too. This is what I’ve drawn so far. Give students a moment to notice and wonder. I want to add a trapezoid desk here. (Point to the empty space.) What do I need to think about when I draw a trapezoid? You need 4 sides and 4 corners. Make sure 2 of the sides are parallel. Use a stick to make straight sides. Draw a trapezoid. Engage students in the process by inviting them to share directions. While drawing, revoice the attributes of the trapezoid (4 straight sides, 1 pair of parallel sides).

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EUREKA MATH2

How does what we know about a shape help us to draw it? We can think about how many sides the shape has to help us draw it. If we know a shape has square corners or parallel lines, we can draw them. Which tools are helpful for drawing shapes carefully? Why? A craft stick is helpful to make straight or parallel sides. Dots are helpful because they can help you make the outline. Centimeter cubes are helpful because then you can measure sides or check corners.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

LESSON 4

Name solid shapes and describe their attributes.

EUREKA MATH2

Name

1 ▸ M6 ▸ TA ▸ Lesson 4

1. Color the faces on a cube.

Lesson at a Glance Students identify and name six solid shapes: cubes, cylinders, cones, square pyramids, rectangular prisms, and triangular prisms. Students describe the flat shapes they see on nets, or unfolded solid shapes, to make good guesses about which solid shape the net will become when it is folded. Students work with a partner to describe solid shapes, guess what unfolded solid shapes will become when folded, and fold nets into solid shapes. This lesson omits the Problem Set to allow more time for students to explore solid shapes.

2. Color the faces on a triangular prism.

Key Question • What are some ways to describe a solid shape?

Achievement Descriptor 1.Mod6.AD2 Identify the defining attributes of two-dimensional

shapes and three-dimensional shapes.

3. Draw an X on the faces that are not on a cylinder.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 4

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Tens and Ones removables and the Solid Shapes removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. Consider saving the Tens and Ones removable for use in lesson 5.

Launch Learn

10 min 10 min

25 min

• Mystery Shape • Which Solid Shape Is It?

Land

15 min

• Geometric solids • Solid Shapes removable (digital download) • Chart paper

Students • Tens and Ones removable (in the student book) • Solid Shapes removable (in the student book) • Geometric solids

• Copy or print the Solid Shapes removable to use for demonstration. • Create two sets of six stations. Each station needs one unfolded 3-D net and one corresponding container (cube, cone, cylinder, rectangular prism, triangular prism, square pyramid). Keep one of each solid figure for use in the lesson. Place each solid at the correct station. After finishing the stations, collect a cube, cone, cylinder, triangular prism, and rectangular prism for use in Land. • Prepare the anchor chart that will be used in the lesson (see image in Land).

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Fluency

10 10

Happy Counting by Ones from 100–120 Students visualize a25number line while counting aloud to build fluency counting within 120. 15

Invite students to participate in Happy Counting. Let’s count by ones. The first number you say is 111. Ready? Signal up or down accordingly for each count.

111

112

113

114

115

114

115

116

117

118

119

120

119

118

119

120

Continue counting by ones to 120. Change directions occasionally, emphasizing crossing over 110 and where students hesitate or count inaccurately.

Whiteboard Exchange: Tens and Ones Materials—S: Tens and Ones removable

Students decompose a two-digit number into tens and ones to build an understanding of place value. Make sure students have a personal whiteboard with a Tens and Ones removable inside. After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the number bond.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 4

Write the total, 14, in the number bond.

Break apart 14 into tens and ones. Fill in the number bond.

Differentiation: Support

10 4

Display the completed number bond with parts 10 and 4.

How many tens are in 14? 1 ten

tens

ones

14 has 1 ten and how many ones? Fill in the blanks. Display the completed blanks: 1 ten 4 ones.

1 0 4

Since we only have 1 ten, we need to cross off the s. Repeat the process with the following sequence:

Students might write 0 tens and 14 ones as their answer. Validate this response, then encourage students to visualize separating the Hide Zero cards into tens and ones. Consider modeling one or two problems with the demonstration set of Hide Zero cards if students need more support.

106

Choral Response: Shapes Students identify three-dimensional shapes to prepare for extending their knowledge of three-dimensional shapes from kindergarten. Display the cone. What is the name of this shape? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. If they do not respond correctly, state the name and have students repeat it chorally. Cone Repeat the process with the following sequence: Cube

Cone

Cylinder

Cube

Sphere

Cylinder

Cone

Cube

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Launch

25 solids Material—T: Geometric

Students identify solid shapes. 15 Gather students with their student books. Have them open their books to the solid shapes chart. Display the image of a square and hold up a cube. Invite students to turn and talk to compare the shapes.

EUREKA MATH2

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Name

Solid Shapes cube

How are these shapes the same and how are they different?

rectangular prism

One is a flat square and one looks like a box. The box has lots of squares.

cylinder cone

(Point to the square.) What is the name of this flat shape? It’s a square.

triangular prism pyramid

A cube is a solid shape. Solids are tall, deep, and wide. (Gesture to show height, depth, and width.) (Point to the flat surfaces on the cube.) Many solid shapes have faces. What shape are the faces on a cube? They are squares. We can tell this solid shape is a cube because all the faces are squares. Tell students to find the cube on the solid shapes chart. Display the picture of the farm.

Teacher Note Polygons are closed shapes with all straight sides. Curved shapes are not polygons. A solid shape made up of only polygonal faces is called a polyhedron. Cubes, square pyramids, rectangular prisms, and triangular prisms are polyhedrons. Cylinders, cubes, and cones are not polyhedrons because the curved part is not a polygonal face.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 4

Where do you see a cube in this picture? How do you know it is a cube? The bottom part of the little house is a cube. I know it’s a cube because it has squares. The walls of the doghouse remind us of a cube. (Outline the cube in the picture.) One at a time, hold up and name the other solid shapes (square pyramid, rectangular prism, triangular prism, cylinder, and cone). Ask students to repeat the names and identify each of the shapes on their chart. Then have them think–pair–share about where they see that solid shape in the farm scene. Outline each solid shape as students name it. Triangular prism is new to grade 1. When you hold up that shape, introduce it. This shape is a triangular prism. It has triangles and rectangles as faces and looks like the roof of the barn. Transition to the next segment by framing the work. Today, we will look carefully at these solid shapes and think about different ways to tell about them.

UDL: Engagement At another time of the day, consider providing students with a choice by having them build a farm with the solid shapes in the grade 1 materials kit or the kindergarten materials kit. Ask students to describe the buildings to a partner by using the names of the shapes or their attributes (faces, corners, edges). Having students engage with the material in a variety of contexts helps make the content more relevant to them.

10 10

Learn

25 15

Mystery Shape Materials—T: Cube, Solid Shapes removable; S: Solid Shapes removable

Students identify flat shapes on a net to guess which solid shape the net makes when it is folded. Make sure students have the Solid Shapes removable inserted in their personal whiteboards. Show a Solid Shapes removable and demonstrate as students follow along. Hold up the net for the cube.

Promoting Mathematical Practice As students try to guess which solid shape each net will make, they look for and make use of structure. Students can use the structure of the faces that make up each solid shape to inform their guess. Help students consider their guesses carefully by drawing attention to the faces they can see in the net. For example, if a student is trying to determine what shape the cone’s net will be, ask “What faces do you see? Do any of the solid shapes also have one face that is a circle?”

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This solid shape is unfolded. What shape will it be when we put it together? Circle your idea on your whiteboard. Ask students to share their choice and reasoning. As needed, help the class name solid shapes as they refer to them. Demonstrate folding the net. Place the shape in the cube container. What solid shape did we make? Circle your answer on your whiteboard.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 4 ▸ Solid Shapes

What shape will it be? Circle.

rectangular prism

cone

triangular prism

cube

cylinder

pyramid

triangular prism

cube

cylinder

pyramid

What shape is it? Circle.

rectangular prism

cone

Circle the face shapes. Write the number of faces.

circle

square

triangle

rectangle

Many students circled the cube. How do you know this solid shape is a cube? 6

All the faces are squares. This is a cube because it has square faces. Circle the shape of the faces on your whiteboard. Let’s count all the faces. We’ll start with the sides and then count the top and bottom. Have students count chorally as you point to each of the 6 faces. Ask students to write the number of faces on their whiteboard. Now it’s your turn. When you see an unfolded shape, notice which flat shapes you see. Use the flat shapes to help you guess what solid shape the paper will become.

Which Solid Shape Is It? Materials—S: Solid Shapes removable, geometric solids

Students independently interact with nets of solid shapes and identify the faces.

EM2_0106SE_A_L04_removable_solid_shapes.indd 37

13/04/21 12:41 AM

Differentiation: Challenge Have students count and record how many edges and corners each shape has. Students may or may not count the apex of the square pyramid as a corner or may mistakenly describe the line where circular bases meet curved parts as edges. Any of these practices is acceptable in grade 1, given students’ developing knowledge of geometry.

Organize the class into two equal groups. Place student pairs at each station. Ask students to complete the same activity from the previous segment. After 1–2 minutes, prompt students to rotate to the next station. Students do not need to rotate through all six stations. Help students recall the process they used in the Mystery Shape activity: • Go to a station and look carefully at the unfolded solid shape. • Make a good guess. What solid shape will it be? Record your guess on your whiteboard. 62

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 4

• Fold the shape and put it in the container. Partners, plan to take turns doing this. • Circle the solid shape on your whiteboard. • Notice which flat shapes you see on the faces. Circle them on your whiteboard. • Count the faces and record how many are on your whiteboard. • Erase your whiteboard, take the shape out of the container, and unfold it for the next pair of students. As you listen to students discussing the nets and shapes, encourage them to use attributes to describe them and make their choices. Use the following questions and prompts to assess and advance student thinking: • What faces do you see on this solid shape? • Fold the shape10and place it in the container. What solid shape is it? How do you know?

Teacher Note Students may not use precise names for the solid shapes. Listen for students to describe a shape’s attributes, then provide them with the shape name. Also, expect some students to count the curved surfaces of the cone and cylinder as faces even though they are not. Gently correct them by saying that curved parts are not faces, like the curved lines of flat shapes (e.g., a circle) are not sides.

• How else can you describe this ___ (name of shape)? 10

UDL: Engagement

Land Debrief

10 min

Materials—T: Chart paper, geometric solids

Objective: Name solid shapes and describe their attributes. Gather students, hold up one solid shape at a time, and ask them the following question. How many ways can we describe this shape? Invite students to think–pair–share. Write their ideas on the chart. It is not necessary for the class to generate all the possibilities in the sample, but ask questions to encourage students to share as many mathematical attributes as possible. For example, ask the following questions:

As students work at stations, foster collaboration by structuring peer interactions for success. Consider the following suggestions: • Provide sentence stems to support dialogue such as: “I see a (flat shape). I think this shape will be a .” • Define responsibilities for each partner, such as who gets to fold the shape first and when to switch so the other partner folds. • Review the goals and directions as needed. • Set a timer to signal the rotations.

1 ▸ M6 ▸ TA ▸ Lesson 4

EUREKA MATH2

Consider leaving the chart posted for student reference.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 4

Hold up a cube and a rectangular prism. What is the same about a cube and a rectangular prism? They have 6 faces. What is different about a cube and a rectangular prism? The rectangular prism is longer. The cube has all square faces. The rectangular prism has all rectangle faces. As time allows, extend students’ thinking by exploring edges and corners. Solid shapes have edges and corners. (Hold up a cube and point to an edge.) The lines where you folded the shapes are called edges. The places where the edges meet are called corners. Have students think–pair–share about whether a cube and a rectangular prism have the same number of edges and corners. Ask them to share their reasoning. Confirm students’ thinking by inviting them to count the edges and then the corners chorally.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

LESSON 5

Reason about the functionality of three-dimensional shapes based on their attributes.

EUREKA MATH2

1 ▸ M6 ▸ TA

Name

1. Which faces do you see on the shapes? Circle them below.

Lesson at a Glance Students discuss the attributes of objects that are shaped like spheres, such as balls or globes. Students reason about attributes to compare solid shapes. They notice which attributes cause solid shapes to roll and stack, and they discuss how a shape’s attributes affect how it functions.

Key Question • Which solid shapes roll and stack? Why?

Achievement Descriptor 1.Mod6.AD2 Identify the defining attributes of two-dimensional

shapes and three-dimensional shapes.

2. Draw any shape with parallel sides. Sample:

How many sides?

Draw any shape with square corners. Sample:

How many sides?

4 47

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Tens and Ones removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance, to have students prepare them during the lesson, or to use the ones prepared in lesson 4.

Launch Learn

10 min 10 min

30 min

• Which One? • Problem Set

Land

10 min

• Balls (2)

Students • Tens and Ones removable (in the student book) • Which One? recording sheets (one per student pair, in the teacher edition) • Geometric solids

• Gather two small balls, such as tennis balls, to use as spheres in stations. • Create stations. Copy or print each of the 12 Which One? recording sheets from the teacher edition. Place them around the room. Each recording sheet asks a question about two specific geometric solids. Place the solids that correspond with the recording sheets at each station. • Set aside one square pyramid and one ball for demonstration and then place them at the correct station.

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1 ▸ M6 ▸ TA ▸ Lesson 5

Fluency

10 10

Whiteboard Exchange: Tens and Ones Materials—S: Tens and30 Ones removable

Students decompose a two-digit number into tens and ones to build 10 an understanding of place value. Make sure students have a personal whiteboard with a Tens and Ones removable inside. After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the number bond.

Write the total, 11, in the number bond.

Break apart 11 into tens and ones. Fill in the number bond. Display the completed number bond with parts 10 and 1.

1 tens

ones

How many tens are in 11? 1 ten 11 has 1 ten and how many ones? Fill in the blanks. 1 ten 1 one Display the completed blanks with 1 ten 1 one. Since we only have 1 ten and 1 one, we need to cross off the s in both places. Repeat the process with the following sequence:

105

115

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5

Choral Response: Shapes and Attributes Students identify three-dimensional shapes and their attributes to develop fluency with describing and naming shapes. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say and show the answer.

Teacher Note The question “What shape is the face?” should be omitted when describing the sphere.

Display the cone. Does the solid shape have flat faces, curves, or both?

Teacher Note

Both What shape is the face?

More than one response may be correct for some shapes. For example, the pyramid has triangular faces and a square face. To alleviate confusion, consider pointing to the shape or part of the shape as you ask the question. For example, point to a triangular face on the pyramid and ask, “What shape is this face?” Then point to the square face on the pyramid to elicit that it is a square.

Circle What is the name of the shape? Cone Repeat the process with the following sequence:

Flat faces Squares Cube

Both Circle Cone

Both Circles Cylinder

Flat faces Squares Cube

Flat faces Triangles and rectangles Triangular prism

Both Circles Cylinder

Flat faces Rectangles Rectangular prism

Flat faces Triangles and a square Pyramid

Curves Sphere

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Launch Materials—T: Ball

10 30

Students describe the attributes of a sphere. 10

Display the image of the globe without telling about it. Give students quiet time to view the image. Invite students to notice and wonder about the sculpture. A sculpture is a piece of art that is not flat. It is a solid shape because it is tall, wide, and deep. What do you notice and wonder about this sculpture? It looks like a circle. I think it’s the Earth. This is a sculpture of a globe. A globe is made to look like Earth. A globe is a solid shape. Let’s see which other objects are the same solid shape as this globe. Display images of round objects, one at a time. Tell students to show thumbs-up when they see a picture of an object that is the same solid shape as the globe. If they make a mistake, explain why the object is not the same solid shape as the globe. Students do not need to use the word sphere yet.

Teacher Note This sculpture is called the Unisphere. It was designed to be the centerpiece of the 1964–1965 World’s Fair held in Queens, New York. The base, rings, and continents are made of about 900,000 pounds of stainless steel. In the sculpture’s final form, the three rings represented the orbits around Earth taken by the first Russian cosmonaut, the first American astronaut, and the first communications satellite. Peter Muller-Munk Associates designed the sculpture and the American Bridge Company made it. The sculpture was built in only 110 days.

Hold up a ball. How can you describe this solid shape? It’s a ball. It’s round. It is curved. Have students turn and talk to a partner about the ball. Have students answer these questions.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5

When you play games like kick or catch, why is it helpful that balls are round? A ball rolls when it goes on the ground, so you can kick it back and forth. You can catch a ball because it’s not pointy.

UDL: Representation

The globe and the ball are each shaped like a sphere. Spheres are round, solid shapes. They do not have flat faces and they are curved. (Hold up the ball.) What do we call this shape? A sphere Transition to the next segment by framing the work. Today, we will notice and wonder about what spheres and other solid shapes can do. 10

As students decide whether each shape they see is solid, they may have difficulty discerning between flat and solid shapes in the pictures. Consider supporting students by providing actual objects that are similar to the objects in the pictures. For example, show students a marble and a globe and discuss how they have similar attributes.

Learn Which One?

30 10 EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Station Demo

Materials—T: Ball, square pyramid; S: Which One? recording sheets, geometric solids

Which one do you want to blow on in a race?

Students reason about how the attributes of solid shapes affect how they function. Gather students and display the Which One? graph. Imagine we have a race to see how fast we can move one of these solid shapes across the room by blowing on it. Which one do you want to blow on in a race, a tennis ball or a pyramid? Turn and talk about your choice.

This page may be reproduced for classroom use only.

After students have talked, have them raise their hands to choose a shape. Record responses as X’s on the graph. Invite students to find the total number of choices for each shape. Then blow on each shape on a flat surface to move it.

EUREKA MATH2

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What happened? When we blow on the pyramid it doesn’t go very far or move straight. The ball rolls. A sphere rolls but a pyramid does not. Why? The pyramid has flat faces and pointy parts. The sphere is curved. Continue by having students work in pairs at the stations. Consider pairing strong readers with emerging readers. • Pairs rotate to each station for about 1 minute.

Differentiation: Support Support students with the graphs by asking guiding questions, such as the following: • Have you seen something like this before? • How can you show your choice? How do you know?

• Student pairs read the question and discuss their choice using the solid shapes provided at each station. • Each student records their choice on the graph or chart. Circulate and invite students to touch and manipulate the shapes as they discuss their answers with their partners. Encourage students to use geometric language such as faces, edges, curves, and corners. Use the following questions and prompts to assess and advance student thinking: • What do you notice about the solid shapes? What faces do you see? • How do you think the solids will move? Why? • Which parts of the shape make it better for rolling, standing on, or playing catch with? • How does turning the shape make it easier to roll, stand on, or play catch with? Have the last pair at each station find and record the total choices for each question. Then have the class take a gallery walk to look at the final graphs and charts. Consider saving the graphs and charts and having students analyze them at another time.

Promoting Mathematical Practice Students attend to precision when they name the attributes of shapes to explain their preference at each station. A student using precise language might say they would rather stand on the triangular prism because it has two flat faces: one they can put on the ground, and one they can stand on. Allow students to be creative while still using precise language. Perhaps a student would rather stand on the cone because they want to practice balancing on the point, or perhaps they prefer to throw the triangular prism because the rectangular faces make it shaped like a football.

10 EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5 30

Land Debrief

5 min

Objective: Reason about the functionality of three-dimensional shapes based on their attributes. Display the image of the three-dimensional sculpture. Do you think we would be able to create a sculpture just like this? Why? No, the sphere and cylinder would roll. No, the pyramid would not stay up like that. Display the block towers. Ask students to show thumbs-up if they think they could make towers like this. Which shapes stack well? Why? The cube and rectangular prism work well for stacking. They have flat faces, so they don’t roll away. Which shape rolls and stacks well? Why? The cylinder rolls because it has a curve. It works well for stacking because it has 2 flat faces.

Teacher Note Students may state that dice can roll although they are cubes without any curved surfaces. If so, ask students if a cube rolls as well as a cylinder, sphere, or cone.

Which shapes are good to use as the top of a tower but would not work well at the bottom of a tower? Why? The cone or pyramid would work for the top because they can stack on top of other shapes. You can’t put anything on top of them because they are pointy. Which solid shapes roll? Why? The sphere, cone, and cylinder can roll because they are curved. Copyright © Great Minds PBC

1 ▸ M6 ▸ TA ▸ Lesson 5

EUREKA MATH2

Confirm that solid shapes move differently and can be used in different ways. Ask students to pick a favorite shape from the shapes displayed in the towers. Have them turn and talk about why they like that shape the best.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Name

1 ▸ M6 ▸ TA ▸ Lesson 5

1. Circle the shapes that roll.

2. Circle the shapes that stack.

3. Circle the shapes that do not roll.

4. Circle the shape that rolls but does not stack.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

1. Which one do you want on the top of a tower?

cube

square pyramid

Make a tally mark.

This page may be reproduced for classroom use only.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

2. Which one do you want to stand on?

rectangular prism

square pyramid

Make a tally mark.

This page may be reproduced for classroom use only.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

3. Which one do you want to roll in a race?

cone

cylinder

Color 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

4. Which one do you want to play catch with?

hexagonal pyramid

hexagonal prism

Color 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

5. Which one do you want on top of a tower?

rectangular prism

cone

Draw an X on 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

6. Which one do you want to stand on?

triangular prism

cube

Draw a J in 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

7. Which one do you want to roll in a race?

hexagonal prism

cylinder

Make a tally mark.

This page may be reproduced for classroom use only.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

8. Which one do you want to play catch with?

triangular prism

triangular pyramid

Make a tally mark.

This page may be reproduced for classroom use only.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

9. Which one do you want on top of a tower?

pentagonal prism

triangular pyramid

Color 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

10. Which one do you want to stand on?

pentagonal prism

pentagonal pyramid

Color 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

11. Which one do you want to roll in a race?

sphere

hexagonal pyramid

Draw an X on 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2 1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Stations

12. Which one do you want to play catch with?

sphere

pentagonal pyramid

Draw a J in 1 space.

This page may be reproduced for classroom use only.

EUREKA MATH2

1 ▸ M6 ▸ TA ▸ Lesson 5 ▸ Which One? Station Demo

Which one do you want to blow on in a race?

This page may be reproduced for classroom use only.

Topic B Composition of Shapes In topic B, students decompose and compose flat and solid composite shapes. Students combine two or more shapes to make a composite shape. They simultaneously see the individual parts and the whole shape the parts make. This is similar to combining 10 ones to make 1 ten. Students put together composite shapes to make new shapes. Students work with composite shapes in increasingly complex ways: • They identify shapes within a composite shape. • They identify composite shapes within a larger composite shape. • They name composite shapes based on their defining attributes. • They create composite two- and three-dimensional shapes. • They add a shape and recognize patterns in the resulting composite shapes. • They combine composite shapes to make a larger composite shape. Rectangle

The snowflake is made of triangles, hexagons, and other shapes.

I see a hexagon made of 4 squares. It has 6 sides.

I can compose a hexagon many ways. I see composed shapes.

I composed a cube out of 8 smaller cubes.

Each time we add a shape, there is a pattern in the resulting composite shapes: hexagon, rectangle, hexagon, rectangle.

Hexagon

We combined composed rectangles to make new shapes.

EUREKA MATH2 1 ▸ M6 ▸ TB

These lessons refer to composite shapes as composed shapes for ease of language, since students are already familiar with the term compose from their work with numbers. After making a composite shape in a variety of ways and reasoning about the number of shapes used to make the shape, students substitute one shape for a congruent composite shape. For example, they replace a trapezoid in a composite shape with three triangles and reason why it took more of the triangles to make the composite shape. Students develop and test a conjecture: the smaller the shape, the more of them they need to make the same composed shape. Although students do not yet have technical understanding of area or fractions, they can intuitively understand and explain that smaller pieces take up less space than larger pieces.

3 blocks

5 blocks

EUREKA MATH2

1 ▸ M6 ▸ TB

Progression of Lessons Lesson 6

Lesson 7

Lesson 8

Create composite shapes and identify shapes within two- and threedimensional composite shapes.

Create new composite shapes by adding a shape.

Combine identical composite shapes. Rectangle

Hexagon

We composed a rectangle out of 2 triangles. We combined our rectangles to make new composed shapes. I made a snowflake out of shapes. I see a hexagon composed of a square and a trapezoid. The tower is composed of a pyramid and a rectangular prism.

When we add a square to the hexagon, it becomes a rectangle.

EUREKA MATH2 1 ▸ M6 ▸ TB

Lesson 9 Relate the size of a shape to how many are needed to compose a new shape.

The first lion is composed with 6 shapes. The second lion is made with 14 shapes. The triangles are smaller than rhombuses or hexagons, so it takes more of them to make the lion.

LESSON 6

Create composite shapes and identify shapes within two- and three-dimensional composite shapes.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 6

Name

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 6

3. Find triangles made of 4 triangles. Sample:

1. Find small triangles. Sample:

How many did you find? How many did you find?

4. Find triangles made of 8 triangles. Sample:

2. Find triangles made of 2 triangles. Sample:

How many did you find? How many did you find?

10 53

EXIT TICKET

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 6

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 6

Lesson at a Glance Students study various composed shapes, including those in artwork, and recognize that larger shapes can be composed of other smaller shapes. They make this discovery in both flat shapes and solid shapes. Students create their own composite two- and three-dimensional shapes. This lesson revisits the term compose.

5. Trace other shapes.

There is no Problem Set in this lesson, and additional time is provided for students to complete the Exit Ticket.

Key Question

What other shapes did you find? Sample:

square

• How can smaller shapes be used to compose a larger shape?

Achievement Descriptor 1.Mod6.AD4 Compose two-dimensional and three-dimensional

shapes to create a composite shape.

EXIT TICKET

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 6

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Snowflake Puzzle removables must be torn out of student books. Consider whether to prepare these materials in advance or to have students tear them out during the lesson.

Launch Learn

10 min 15 min

20 min

• Geometric solids

Students

• Composite Squares

• Plastic pattern blocks

• Composite Solid Shapes

• Centimeter cubes (8)

• Assemble bins of pattern blocks to place in workspaces for small groups of students to share. Each bin should contain about 100 blocks.

Land

• Snowflake Puzzle (in the student book)

• Students will reuse the 8 centimeter cubes they used in lesson 3.

15 min

• A teacher demonstration in Learn requires using solid shapes to build the following composed shapes, which are all displayed together for students to see. Set aside the necessary shapes.

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 6

Fluency

10 15

Whiteboard Exchange: Tens and Ones 20 a two-digit number into tens and ones to build Students decompose an understanding of place value. 15

Display the number 12 with the blanks beneath it.

How many tens are in 12? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

1 ten

ten

ones

12 has 1 ten and how many ones? Write how many tens and how many ones. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the completed blanks: 1 ten 2 ones. Repeat the process with the following sequence:

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110

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EUREKA MATH2

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Show Me Shapes Materials—S: Pattern blocks

Students identify flat shapes to build fluency with analyzing and identifying two-dimensional shapes from topic A. Make sure each student has pattern blocks. Each student will need a trapezoid, square, hexagon, blue rhombus, and triangle. Spread out your shapes so you can see them all. Find the shape with 3 corners and 3 sides. Hold your shape close to keep it a secret. Stand up. Wait until most students stand up with the shape.

Teacher Note

Show me the shape. (Holds up the triangle) Have a seat and get ready for the next one. Find the shape with 6 corners and 6 sides. Hold it close and stand up when you find it.

• What is the name of the shape? • How many corners does the shape have?

Show me the shape.

• How many sides does the shape have?

(Holds up the hexagon)

• How do you know the shape is a triangle?

Repeat the process with the following sequence: Find the shape with a square corner.

Consider providing opportunities for students to name and describe the shapes. Ask questions such as these:

Find the quadrilateral that does not have 4 equal sides.

Find the rhombus.

Find the shapes with 4 equal sides and 4 corners.

Have students set their pattern blocks aside for use in Launch.

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 6

Choral Response: Name the Shapes Students name the two-dimensional shapes used to compose a larger shape, then name the larger shape, to build fluency with analyzing and identifying two-dimensional shapes from topic A. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display the image of the triangle on top of the trapezoid. What shapes did I use to make the bigger shape? (Point to the triangle, and then to the trapezoid.) Triangle, trapezoid Display the composed shape outlined in black. What is the name of the big shape? Triangle Repeat the process with the following sequence:

Rectangle

Hexagon

Rhombus

Pentagon

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 6 10

Launch

15 20

Materials—S: Pattern blocks, Snowflake Puzzle

Students see that larger shapes can be composed of smaller shapes. 15 Display the pattern block snowflake. Turn and talk to a partner. What do you notice about this pattern block puzzle? They used all the different blocks to make it. It looks like a snowflake. It looks like a flower. Let’s think of this as a snowflake made of shapes. When a shape is made from other shapes, we call it a composed shape. Remember, compose is another way to say make or put together. What shapes compose this snowflake? I see some hexagons, rhombuses, squares, triangles, and trapezoids. I wonder if we can find shapes inside this snowflake that are composed of other shapes. Display the hexagonal composition from the snowflake. Look at the outlined shape. How many sides does it have?

Language Support Help students understand the term compose by using it to describe classroom items that are grouped. For example, table groups are composed of desks, and floors are composed of tiles. A composed shape may also be referred to as a composite shape.

6 What do we call shapes with 6 sides? Hexagons What shapes are used to make the hexagon? A square and a trapezoid

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Invite students to identify and describe other composed shapes. Ask students to name the larger shape and the shapes that compose it. Some possibilities include: • Hexagon made from 2 tan rhombuses • Trapezoid made from a blue rhombus and green triangle Distribute a snowflake puzzle. Invite students to complete it together. Ask pairs to talk about which shapes compose the snowflake, and which shapes are composed of other shapes. Consider posting sentence frames, such as the following, to support their conversation. • The snowflake is composed of [shape names]. • I see a [shape name] made of [shape names]. Transition to the next segment by framing the work. Today, we will look at how flat and solid shapes can be composed of other shapes.

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Learn

20 15

Composite Squares Materials—S: Crayon

Students identify composed shapes. Display the squares image and have students turn to it in their student book. Pair students. Have them work together to find as many squares as they can. Ask students to outline the squares they see with a crayon. See some possible student responses in the following chart. Single Squares

Squares Composed of 4 Smaller Squares

Squares Composed of Smaller Shapes

A Square Composed of All the Shapes

Promoting Mathematical Practice Students reason abstractly and quantitatively when they identify two- and three-dimensional composite shapes and the shapes they are composed of. Doing this requires students to recognize the abstract boundary of the shape, ignoring the other shapes inside or outside of it. They attend to the quantitative attributes of shapes, such as the number of sides or corners, to identify and name the shape. Promote this mathematical practice by helping students see both the composite shape and the parts that make it up.

Circulate and listen in to students’ thinking. Lead a discussion about the squares students see, using questions such as the following. Record their ideas by outlining the shapes they describe on the image. Where do you see squares? How many small squares can you find? (Pause for students to count.) 9

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Differentiation: Challenge Consider inviting students to count and record all the possible squares in each image. There are 15 squares total.

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 6

The bigger squares are composed shapes. They are made of smaller squares. Does anyone see a composed square made of other shapes? Do you see composed shapes that aren’t squares? Squares can be used to compose other squares, or even other shapes. Solid shapes can be used to make composed shapes, too. Let’s try making composed solid shapes.

Differentiation: Support Students may identify a rectangle that is not composed of smaller shapes. If this happens, guide students’ thinking by asking them to identify a rectangle that is composed of squares.

Composite Solid Shapes Materials—T: Geometric solids; S: Centimeter cubes

Students build composite shapes composed from solids and reason about them. Ask students to watch as you compose the following composite shapes by using solid shapes:

What did I make? You made towers with solid shapes. You made bigger shapes out of smaller ones. Assist students to identify the solid shapes that make up a few of the composed shapes. Make sure students have the eight centimeter cubes out and a personal whiteboard to work on. Invite students to compose a cube by using the 8 smaller cubes.

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How did you compose a larger cube from smaller cubes? How do you know it is a cube? First I made a square with 4 cubes. Then I stacked another square just like it on top. All of the faces are squares. Have groups of four students combine their cubes to make a larger cube. Invite a pair of students to share how they know they composed a cube. As time allows, encourage groups to compose other solid shapes with 10 their cubes. Students do not need to use all of the cubes. They may build horizontally, vertically, or a combination of both. 15

Land Debrief

5 min

Objective: Create composite shapes and identify shapes within two- and three-dimensional composite shapes. Display The Card Players by Theo van Doesburg. Do not reveal any information about the painting. Provide students with quiet time to view the artwork.

Teacher Note Dutch artist Theo van Doesburg made this painting in 1916–1917. He used a technique new to him, working with blocks of color, to make a scene. He arranged rounded and pointed geometric shapes to complete this scene called The Card Players. Some people see three players sitting and one standing, while others see just two sitting and one standing. This style of art is called Cubism because of its frequent use of foursided shapes. Consider extending students’ study of the painting by having them make a scene by using shapes or pattern blocks.

What do you notice about this artwork? People are sitting at a table playing a game. One person is standing. The artist used different shapes to make the people. There are four cards in the corners with shapes on them.

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Engage students in student-to-student discourse about how the artist uses composed shapes in his art. What shapes do you see? I see triangles and a rhombus. How does the artist use composed shapes? The artist made the card players’ clothes with shapes. The person who is standing has clothes made of different shapes too. The chair and the table are made up of different rectangles. The people’s heads are even different shapes put together. Share the title of the artwork and the artist’s name. Consider sharing details about the artwork from the Teacher Note that may be of interest to students. Display the first enlarged segment of the artwork. In this part of the painting, how did the artist use smaller shapes to compose a new larger shape?

UDL: Engagement As students construct their own composite shapes, they may not make the shape they had planned. Some may feel frustrated. Facilitate personal coping skills by reminding students that when we struggle or make mistakes, we are learning. Discuss strategies for dealing with frustration and persevering, such as the following: • Ask yourself, “What new shape did I make, if any?” • Pause to take deep breaths and feel calm before working again. • Choose a different approach and try again.

He used rectangles, hexagons, a triangle, and quarter circles to make a rectangle. Display the enlarged cards from the artwork. What do you notice about this part of the artwork? There are four cards. There are shapes on the cards. Have students think–pair–share about the numbers on the cards. The shapes on the cards represent numbers. Talk with your partner about how the numbers on the cards could be combined to make a total. I see 4 and 8. That is 12. I see 5, 2, and 5. That is 12. Just like when we combine or add parts to make a total, we can combine, or compose, smaller shapes to make a larger shape. Copyright © Great Minds PBC

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Exit Ticket

EUREKA MATH2

10 min

Provide up to 10 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem. More time has been provided for students to do the Exit Ticket. Students only need to identify composite shapes. They do not need to find them all, and they do not need to complete all of the items.

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LESSON 7

Create new composite shapes by adding a shape.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7

Name

Color in the triangles.

Lesson at a Glance Students compose new shapes by adding one square at a time to a composite shape. They discuss how the new shape is composed, as well as its name and attributes. Students record their work and notice patterns in the compositions.

Key Question • What happens when shapes are added to a composed shape?

Achievement Descriptor 1.Mod6.AD4 Compose two-dimensional and three-dimensional

shapes to create a composite shape. Trace the new shape. What is the new shape?

Sides

4 trapezoid

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 7

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Tens and Ones Sprints must be torn out of student books. Consider whether to prepare these materials in advance or to have students tear them out during the lesson.

Launch Learn

15 min 5 min

30 min

• Sticky notes (12) • Chart paper

• Compose Shapes from a Composition

Students

• Patterns in Composed Shapes

• Tens and Ones Sprint (in the student book)

• Problem Set

Land

10 min

• Sticky notes (10 per student pair)

• Make sets of 10 square sticky notes for each pair of students. Alternatively, students may use square tiles if they are available. • Copy or print the pattern recording table to use for demonstration.

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EUREKA MATH2

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Fluency

15 5

Sprint: Tens and Ones Materials—S: Tens and30 Ones Sprint

Students decompose two-digit numbers into tens and ones to build 10 EUREKA MATH 1 ▸ M6 ▸ TB ▸ Lesson 7 ▸ Sprint ▸ Tens and Ones an understanding of place value. 2

Have students read the instructions and complete the sample problems. Sprint Write the number of tens and ones.

Teacher Note 1. 2.

1 ten 2 ones Some students may respond with 12 is 0 tens and 12 ones. Although this answer is mathematically correct, encourage students to unitize the tens.

40 4 tens 0 ones

Direct students to Sprint A. Frame the task. I do not expect you to finish. Do as many problems as you can, your personal best. Take your mark. Get set. Think! Time students for 1 minute on Sprint A. Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint A quickly and energetically. Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B.

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Celebrate students’ effort and success. Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A. Lead students in one fast-paced and one slow-paced counting activity, each with a stretch or physical movement. Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B. Direct students to Sprint B. Take your mark. Get set. Improve!

Teacher Note Consider asking the following questions to discuss the patterns in Sprint A: • What do you notice about problems 1–5? 6–10? • How do problems 1–5 compare to problems 11–15?

Time students for 1 minute on Sprint B. Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint B quickly and energetically. Count the number you got correct and write the number at the top of the page.

Teacher Note Count forward by ones from 95 to 105 for the fast-paced counting activity. Count backward by ones from 120 to 110 for the slow-paced counting activity.

Stand if you got more correct on Sprint B. Celebrate students’ improvement.

Choral Response: Name the Shapes Students name the two-dimensional shapes used to compose a larger shape, then name the larger shape to build fluency with analyzing and identifying two-dimensional shapes from topic A. After asking each question, wait until most students raise their hands, and then signal for students to respond.

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Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display the image of the two trapezoids. What shapes did I use to make the composed shape? (Gesture to the top trapezoid in the hexagon, and then the bottom trapezoid.) Trapezoid, trapezoid Display the composed shape outlined in black. What is the name of the composed shape? Hexagon Repeat the process with the following sequence:

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Differentiation: Support

Hexagon

Trapezoid

Pentagon

Hexagon

Pentagon

Rhombus

Quadrilateral

If students have difficulty counting the sides of the composed shape, provide pattern blocks. Invite students to build the shape and touch and count the sides.

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 7 15

Launch

5 30

Students analyze a series of composite shapes to notice a pattern. Gather students and 10 display the picture of two gray shapes. Both of these bigger shapes are composed of, or made of, the same smaller shape. What smaller shape do you think they are composed of? Squares, triangles, rectangles Display a square next to the composed rectangle. The composed shapes are made of squares. How many squares do you think make this composed shape? I think it’s 2 squares next to each other to make a rectangle. Display the picture of 2 squares composing the rectangle. What is the composed shape made from 2 squares? A rectangle Display the composed hexagon. How many squares do you think make this composed shape? 3 squares. They made the rectangle, then put 1 more on top to make an L. Display the picture of 3 squares composing the hexagon. What is the composed shape made from 3 squares? How do you know? It is a hexagon. It has 6 sides. Confirm the shape is a hexagon by tracing the shape’s border as students count the sides. Then display the picture of three shapes.

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I see a pattern. 1 square, 2 squares, 3 squares (Point to each shape.) Invite students to think–pair–share about which shape comes next in the sequence. How could we compose the next shape? Why? We could add 1 square because the pattern is to add a square each time. Display the picture of 4 squares composing a larger square. What shape did we compose by using 4 squares? How do you know? It’s a square. It has 4 sides that are all the same length. It has 4 square corners. It has parallel sides. How was a new shape composed each time? (Point to the shapes from left to right.) We added 1 more square. Transition to the next segment by framing the work. Today, we will continue the pattern to see what happens when we add another square to composed shapes.

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Learn

30 10

Compose Shapes from a Composition Materials—S: Sticky notes

Students add a square to a composed shape and identify the new shape. Display the three composed shapes and show the first half of the table. Ask students to turn to the table in their student book. Model how to complete it as students follow along. How many squares compose this shape? (Point to the shape on the left.) 2 Write 2 in the Squares column of the table.

Squares

Shape

Sides

What is the composed shape? A rectangle Write rectangle in the Shapes column of the table. How many sides does the rectangle have? 4 sides Write 4 in the Sides column of the table. Repeat the process for the hexagon and the large square. Then distribute one set of 10 sticky notes to each set of partners. Invite them to duplicate the composed square by using 4 sticky notes, or smaller squares. Then invite students to look at the table again.

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Let’s use the pattern to compose the next shape. How many squares should we use? 5 squares

Promoting Mathematical Practice

The pattern is 2, 3, 4, and then 5. When students recognize patterns in the table and use them to predict, they look for and make use of repeated reasoning.

How many sides will our new shape have? How do you know? The pattern we wrote for the sides goes 4, 6, 4, so I think the next shape will have 6 sides.

Consider asking the following questions:

What do we call a shape with 6 sides?

• What would the next line on the chart look like?

A hexagon

• What shape do you think we would make with 20 squares? How many sides would it have?

Have students compose the next shape by placing a sticky note on the top left or bottom right of the square. Then guide students to record their work in the table. How many squares did we use to compose the fifth shape? 5 squares

Squares

Shape

Sides

How many sides does it have? 6 sides What is the name of the new composed shape? A hexagon We put together the big square and a small square to make a hexagon composed of 5 squares. Invite students to continue making composite shapes by adding one square (one sticky note) at a time. Make sure students record the number of squares, the name of the composed shape, and the number of sides in the chart as they go. If students are unsure about what shape name to use, they may sketch the shape instead.

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Circulate and make sure students continue the pattern when placing sticky notes. See the following examples.

Advance and assess student thinking by asking: • Where does the next square go? Why? • How many squares did you use to make the last shape? How many squares will be in the new shape? Why? • What do you think the new shape will be? Why? • What shapes did you put together to make the new shape? As time allows, invite students to use 10 sticky notes to compose other shapes.

Patterns in Composed Shapes Students identify a repeating and growing pattern in a series of composed shapes. Display the two composed shapes. Invite students to examine how a composed shape changes when a square is added. How does the shape change? A new square fills in the empty spot at the top. The new shape has 8 squares instead of 7. The first shape is a hexagon. The second shape is a rectangle. Revoice student thinking.

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At first there was a hexagon composed of squares. Then a hexagon and a square are composed to make a rectangle. Display the completed table. Lead a discussion about the growing (2, 3, 4, …) and repeating (4, 6, 4, 6, …) patterns. Have students think–pair–share about the patterns they see in the table. Talk with your partner about which patterns you notice.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7

Name

Squares

Shape

Sides

rectangle

hexagon

square

The number of squares goes up one at a time: 2, 3, 4, 5, 6, 7, 8, 9, 10.

hexagon

The number of sides goes back and forth between 4 and 6.

rectangle

There’s a shape and then a hexagon, then a shape and a hexagon, and on and on like that.

hexagon

rectangle

hexagon

rectangle

Why does the number of squares grow by 1 each time? It grows because we add 1 square each time. Each time we composed by lining up a new square next to an old one. Sometimes the new square stuck out and made a 6-sided shape. Other times the new square filled in an empty space and made a 4-sided shape.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex.

Teacher Note Students may notice a pattern in the shape names and that “square” does not fit the rule— rectangle, hexagon, etc. Point out that a square can also be named a rectangle since it has 4 sides and 2 square corners.

Directions may be read aloud.

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Land Debrief

5 min

Materials—T: Sticky notes, chart paper

Objective: Create new composite shapes by adding a shape. Gather students and show 8 sticky notes arranged horizontally on chart paper. What is this shape? A rectangle What shape is the rectangle composed of?

Differentiation: Challenge Invite students to draw their own set of composite shapes by using grid paper. Have them analyze the composition of each new shape by counting the number of sides.

It is composed of squares. Turn and talk to your partner. What will happen if I add 1 square to each short side of the composed shape? Do you think it will still be a rectangle? Invite students to share their thinking. Then add a sticky note to both ends of the rectangle. What happened? It is still a 4-sided shape. It is still a rectangle. It is longer. We composed the rectangle and 2 squares. Now we have a longer rectangle that is composed of 10 squares. We can add many squares to either end of this shape, but it will still be a rectangle. How can we use this rectangle and square to compose a shape that is not a rectangle?

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Invite students to share their ideas and try them with sticky notes on the chart paper. Ask the class to count the sides to determine what new shape is composed. See the examples. What happens when we add shapes to a composed shape? If you add a shape to a composed shape you might make a new shape.

8-sided shape

You might just make the same shape, but bigger.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

8-sided shape

Hexagon

120

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 7

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7 ▸ Sprint ▸ Tens and Ones

Number Correct:

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7 ▸ Sprint ▸ Tens and Ones

Number Correct:

Write the number of tens and ones.

Write the number of tens and ones. 1.

1 ten 1 one

11.

31 3 tens 1 one

1 ten 1 one

11.

1 ten 3 ones

12.

53 5 tens 3 ones

1 ten 2 ones

12.

42 4 tens 2 ones

1 ten 5 ones

13.

75 7 tens 5 ones

1 ten 4 ones

13.

64 6 tens 4 ones

1 ten 7 ones

14.

97 9 tens 7 ones

1 ten 6 ones

14.

86 8 tens 6 ones

1 ten 9 ones

15.

99 9 tens 9 ones

1 ten 8 ones

15.

88 8 tens 8 ones

1 ten 0 ones

16.

100 10 tens 0 ones

1 ten 0 ones

16.

100 10 tens 0 ones

30 3 tens 0 ones

17.

103 10 tens 3 ones

20 2 tens 0 ones

17.

94 9 tens 4 ones

50 5 tens 0 ones

18.

107 10 tens 7 ones

40 4 tens 0 ones

18.

98 9 tens 8 ones

70 7 tens 0 ones

19.

110 11 tens 0 ones

60 6 tens 0 ones

19.

100 10 tens 0 ones

10.

90 9 tens 0 ones

20.

117 11 tens 7 ones

10.

80 8 tens 0 ones

20.

110 11 tens 0 ones

2 tens 1 one

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EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7

Name

1. Color a rhombus.

Color a rhombus.

What is the last new shape?

2. Color a triangle.

Color a triangle.

What is the last new shape?

122

hexagon

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7

3. Color 4 triangles.

Color a rhombus.

Sides

What is the new shape?

triangle

Sides

Color a triangle.

Sides

6 63

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 7

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 7

4. Color in the pattern. How many?

rhombuses

PROBLEM SET

123

8 EUREKA MATH2

LESSON 8

Combine identical composite shapes.

1 ▸ M6 ▸ TB ▸ Lesson 8

Name

Color 1 triangle. What is the composed shape?

Lesson at a Glance Students analyze and identify identical composite shapes within larger composite shapes. They manipulate triangles to compose new shapes. Then students combine their composed shape with a partner’s composed shape and identify the new shape.

Key Question

rhombus

• What happens when you put together copies of the same composed shape?

Achievement Descriptor

Color 1 triangle.

1.Mod6.AD4 Compose two-dimensional and three-dimensional

What is the composed shape?

shapes to create a composite shape.

trapezoid Color 1 triangle.

What is the composed shape?

triangle

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 8

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Hidden Addends Mats must be torn out of student books. Consider whether to prepare these materials in advance or to have students tear them out during the lesson.

Launch Learn

10 minutes 10 minutes

25 minutes

• Compose a Shape

• 100-bead rekenrek • Triangles removable (digital download) • Scissors

• Make a New Composed Shape

Students

• Problem Set

• Eureka Math Numeral Cards (1 deck per student pair)

Land

15 minutes

• Hidden Addends Mat (1 per student pair, in the student book) • Triangles removable (in the student book) • Scissors

• Copy or print the Triangles removable to use for demonstration. • The Triangles removables must be torn out of student books. The 2 triangles must be cut out for each student. Consider whether to prepare these materials in advance or to have students tear them out and cut them during the lesson.

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Fluency

10 10

Counting on the Rekenrek by Tens and Ones Materials—T: Rekenrek25

Students count to a specified number the Say Ten way and then the regular way 15 to build an understanding of place value. Show students the rekenrek. Start with all beads to the right side. Let’s count to 82 the Say Ten way. Say how many beads there are as I slide them over. Slide over 10 beads in each row all at once as students count to 8 ten. 1 ten, 2 ten, 3 ten, 4 ten, 5 ten, 6 ten, 7 ten, 8 ten Slide over 2 more beads, one at a time, as students count to 8 ten 2. 8 ten 1, 8 ten 2

“8 ten 2” Student View

Slide all the beads back to the right side. Let’s count to 82 the regular way. Say how many beads there are as I slide them over. Repeat the process as students count by tens and ones to 82. 10, 20, 30, 40, 50, 60, 70, 80, 81, 82

Repeat the process as students count by tens and ones the Say Ten way and the regular way to the following numbers:

8 ten 6 86 126

9 ten 3 93

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 8

Hidden Addends Materials—S: Numeral Cards, Hidden Addends Mat

Students find the total and say an addition equation or related subtraction equation to build addition and subtraction fluency within 20. Have students form pairs. Distribute a deck of Numeral Cards to each pair. Have them use the following procedure to play. Consider doing a practice round with students. • Partners place the deck of cards facedown next to the Hidden Addends Mat. • Partner A and partner B flip over a card from the top of the pile and place it on a blue rectangle. • Both students say the total. • Partner A says an addition sentence. Partner B says a related subtraction sentence. See the sample partner dialogue under the image.

4 + 9 Partners A and B: “13” Partner A: “4 + 9 = 13” Partner B: “13 – 9 = 4”

• Students discard the card into a separate pile. Circulate during the activity to ensure that students are saying accurate number sentences. If students run out of cards before the time ends, they can switch roles, shuffle the cards, and continue playing.

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1 ▸ M6 ▸ TB ▸ Lesson 8 10

Launch

10 25

Students find smaller composed shapes within a large composed shape.

UDL: Engagement

Display the composite triangle. Form student pairs. Have partners work together to find as many shapes in the picture as they can. Some possible student responses are in the following chart.

If time allows, invite students to create the large composite triangle being displayed. Direct students to start by composing a triangle with pattern blocks (by using the green triangle and red trapezoid). Then have them make three more composed triangles and combine all four to make the larger triangle.

Lead a discussion and record students’ ideas by outlining the shapes they describe on the picture.

I see green Two trapezoids A trapezoid triangles and make a hexagon. and a triangle red trapezoids. make a larger triangle.

Three triangles and three trapezoids make a larger trapezoid.

All the shapes make a big triangle!

Display the smaller composite triangle. What is this shape? Which shapes is it composed of? It’s a triangle composed with a small triangle and a trapezoid. Display the large triangle that contains the smaller composite triangle. I wonder how many smaller composed triangles we need to make the large triangle. 128

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 8

Invite students to share their ideas and encourage them to explain their thinking. Display the image that shows the four triangles in sequence. Give students time to study the image and recognize how the smaller composed triangles compose the large triangle. With each large triangle, have the class count the number of smaller composed triangles.

How many small composed triangles combine to make the large triangle? 4 Transition to the next segment by framing the work. Today, we will use composed shapes like the small triangles to make larger composed shapes. 10 10

Learn

25 15

Compose a Shape Materials—T/S: Triangles removable, scissors

Students manipulate two right triangles to compose new shapes. Make sure all students have two triangles cut out from the Triangles removable. Put your triangles together to see how many shapes you can make.

Promoting Mathematical Practice Using composed shapes to make new, larger shapes can be challenging and gives students an opportunity to make sense of problems and persevere in solving them. These tasks require students to consider the smaller composed shape as a new unit and to manipulate it as a whole rather than as two distinct pieces. Familiarizing students with this kind of geometric thinking, which relies on intuition about physical space, can help them manipulate numerical units of units, which can be less intuitive. For example, this work can help students make sense of hundreds, which are composed of tens, which are in turn composed of ones.

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Allow time for exploration. Encourage students to change the position of the triangles to make new shapes. Advance and assess student thinking by asking the following questions:

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 8 ▸ Triangles

• What does it mean to make composed shapes? • What is the new shape? How do you know? Invite two or three students to share how they composed new shapes (see possible compositions). Then direct students to open the student book to the recording sheet. When we turn, flip, or move the triangles we can make new composed shapes. Model using the triangles to compose the shapes in the book, and have students name the new shapes.

Ask students to record the compositions on the recording sheet by drawing lines that show the two triangles. If students need help identifying where to draw the lines, invite them to use their triangles to make each shape. Although the lines do not need to be precise, students may use a straightedge. EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 8

Name

Draw a line to show 2 smaller triangles.

quadrilateral

triangle

rectangle

130

triangle 73

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 8

Make a New Composed Shape Materials—S: Two right triangles from Triangles removable

Students make composed shapes by combining smaller composed shapes. Let’s make new, larger composed shapes by combining two smaller composed shapes. Use 2 triangles to compose your own rectangle. Place your rectangle next to your partner’s rectangle.

Differentiation: Challenge Students may find they can make additional composed shapes if they do not align the edges exactly. For example, 2 triangles can compose a hexagon like the one below.

What different shapes do you see? How many of each shape do you see? 1 square, 2 rectangles, 4 triangles What is the new shape we composed? A square Invite partners to combine their composite rectangles to make new shapes. As you circulate, assess and advance student thinking by using the following questions and prompts: • How do you make a larger composed shape by using the 2 rectangles? • What different shapes do you see? How many of each shape do you see? • Count the sides. What is the new shape? Rectangle

Hexagon

Invite two or three students to share their work.

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Have students use their 2 triangles to compose a new, larger triangle. Have partners repeat the process with the composed triangle to make a variety of quadrilaterals. Quadrilaterals

If time allows, encourage groups of three or four students to combine composite rectangles or triangles and discuss the new shape they made.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be read aloud.

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10 EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 8 25

Land Debrief

10 min

Objective: Combine identical composite shapes. Display the quilt and invite students to notice and wonder about the artwork. If necessary, stimulate discussion by asking the following questions: • What shapes do you see? • What composed shapes do you see? • Do you see any patterns? Consider sharing details about the artwork that may be of interest to students. Invite students to find repeated composed shapes. Answers will vary. Only two are highlighted in the following sample dialogue. Have students think–pair–share about the composed shapes in the quilt. Talk with a partner. Where do you see a composed shape that is combined with itself to make the quilt?

Teacher Note This quilt, created by Stephen Blumrich, is titled Black Uncle Sam pieced miniature quilt. It features a pattern of repeating composite shapes. Each square contains a figure wearing a top hat. The quilt hangs in the National Museum of African American History and Culture. Also consider quilt related literature such as Sam Johnson and the Blue Ribbon Quilt by Lisa Campbell Ernst, The Quilt Story by Tomie dePaola and Tony Johnston, and The Quilt by Ann Jonas. Faith Ringgold’s painted quilt artwork for the children’s book Tar Beach won both the Caldecott Honor and the Coretta Scott King Award for Illustrations. Consider extending students’ study of the art by inviting them to glue paper shapes on a square to make the same figure or object. Put the squares together to create a class quilt.

Squares put together make a rectangle. The man is a composed shape. How many copies of those composed shapes do you see? 12 What happens when you put together copies of the same composed shape? It makes a new, larger shape.

Exit Ticket

5 min

133

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1 ▸ M6 ▸ TB ▸ Lesson 8

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 8

Name

1. Color 1 square.

Color 2 squares.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 8

2. Color 1 rectangle.

Color 2 rectangles.

Color 4 squares.

What is the last composed shape? It has

134

rectangle

sides.

3. Draw a triangle to compose a square.

rectangle

sides.

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 8

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 8

4. Draw a triangle to compose a rhombus.

5. Draw a triangle to compose a larger triangle.

PROBLEM SET

135

LESSON 9

Relate the size of a shape to how many are needed to compose a new shape.

EUREKA MATH2

1 ▸ M6 ▸ TB

Name

1. Trace a composed shape. Sample:

Lesson at a Glance Students make composed shapes and share solutions. They reason about why the same composed shape requires more of some blocks and fewer of others. They develop and test a conjecture: the smaller the shape, the more of them are needed to compose a new shape.

Key Question • Why does the number of blocks we need to compose a shape change?

Achievement Descriptor How many sides does the composed shape have?

1.Mod6.AD4 Compose two-dimensional and three-dimensional

shapes to create a composite shape.

Circle the shapes that made the composed shape.

2. Draw a triangle to make a composed shape. What is the composed shape?

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 9

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Ready the Hidden Addends Mats.

• 100-bead rekenrek

• Assemble bins of pattern blocks and place them in workspaces for small groups of students to share. Each bin should contain about 50 blocks. Squares and tan rhombuses are not needed for this lesson. Consider removing these shapes from the sets of blocks.

Launch Learn

10 min 15 min

25 min

• Form a Conjecture

• Plastic pattern blocks • Composite Triangle (digital download)

• Test the Conjecture

Students

• Problem Set

• Eureka Math2 Numeral Cards (1 deck per student pair)

Land

10 min

• Hidden Addends Mat (1 mat per student pair, in the student book) • Plastic pattern blocks (about 50 per group) • Composite Triangle (in the student book)

• Copy or print Composite Triangle to use for demonstration. • The Composite Triangle and Hexagon must be torn out of student books. Consider whether to prepare these materials in advance or to have students tear them out during the lesson.

• Hexagon (in the student book)

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EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 9

Fluency

10 15

Counting on the Rekenrek by Tens and Ones Materials—T: Rekenrek25

Students count to a specified number the Say Ten way and then the regular way 10 to build an understanding of place value. Show students the rekenrek. Start with all beads to the right side. Let’s count to 83 the Say Ten way. Say how many beads there are as I slide them over. Slide over 10 beads in each row all at once as students count to 8 ten. 1 ten, 2 ten, 3 ten, 4 ten, 5 ten, 6 ten, 7 ten, 8 ten Slide over 3 more beads, one at a time, as students count to 8 ten 3.

“8 ten 3” Student View

8 ten 1, 8 ten 2, 8 ten 3 Slide all the beads back to the right side. Let’s count to 83 the regular way. Say how many beads there are as I slide them over. Repeat the process as students count by tens and ones to 83. 10, 20, 30, 40, 50, 60, 70, 80, 81, 82, 83

138

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 9

Repeat the process as students count by tens and ones the Say Ten way and the regular way to the following numbers:

8 ten 7 87

9 ten 4 94

9 ten 8 98

Hidden Addends Materials—S: Numeral Cards, Hidden Addends Mat

Students find the total and say an addition equation or related subtraction equation to build addition and subtraction fluency within 20. Have students form pairs. Distribute a deck of Numeral Cards to each pair. Have them use the following procedure to play. Consider doing a practice round with students. • Partners place the deck of cards face down next to the Hidden Addends Mat. • Partner A and partner B flip over a card from the top of the pile and place it on a blue rectangle. • Both students say the total.

4 + 9 Partners A and B: “13” Partner A: “4 + 9 = 13” Partner B: “13 – 9 = 4”

• Partner A says an addition sentence. Partner B says a related subtraction sentence. See the sample partner dialogue under the image. • Students discard the cards into a separate pile. Circulate during the activity to ensure that students are saying accurate number sentences. If students run out of cards before the time ends, they can switch roles, shuffle the cards, and continue playing.

139

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 9 10

Launch

25 blocks, Composite Triangle Materials—T/S: Pattern

Students test different ways to compose a shape by using smaller shapes. 10

Make sure all students have a Composite Triangle removable and pattern blocks. I wonder how many different ways we can compose this triangle with pattern blocks. Give the following directions, and model making a composition if needed: • Use pattern blocks to compose the large triangle. Compose the large triangle in different ways. Change the pattern blocks you use each time you make the triangle. • Record each composition you make by drawing lines on the small triangles at the bottom of the page. Allow 4–5 minutes for exploration. Circulate and observe. See the chart for possible student responses. Assess and advance student thinking by asking the following questions: • How many total blocks did you use? Which blocks did you use to compose the triangle? • Replace one block with a different block. What happens?

Number of Blocks

1 2 3

Teacher Note Students’ recordings do not need to be exact. Focus on the physical manipulation of the pattern blocks. Encourage students to sketch without spending too much time trying to be precise. Recording a composed shape is a precursor to partitioning shapes into halves and fourths.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 9 ▸ Composite Triangle

How many ways?

none none Draw lines to show the blocks you used.

4 5 6 7

8 9

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EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 9

Invite two or three students to share different compositions. As students display their work, ask the following questions. Look at how your classmate composed the triangle. What do you notice? How many blocks did they use to make the triangle? Transition to the next segment by framing the work. The triangle can be composed by using different numbers of blocks. Today, we will see what else we notice about how to compose the same shape in different ways. 10 15

Learn

UDL: Engagement As students use their pattern blocks to compose new shapes, focus on giving mastery-oriented feedback instead of attention to detail like perfectly straight lines. Offer feedback that focuses attention on students’ efforts and strategy use, not on abilities or intelligence. For example, give feedback on the shapes students used correctly to compose the triangle.

25 10

Form a Conjecture Students compare different ways to compose the same shape and reason about the number of shapes they use. Display the first set of composed triangles. Show thumbs-up if you used one of these ways to compose the triangle. What is the same about these two ways? What is different? Both ways use green triangles. One shape has triangles and a rhombus. How many blocks go together to compose the first triangle? 9 How many blocks go together to compose the second triangle? 8

141

1 ▸ M6 ▸ TB ▸ Lesson 9

EUREKA MATH2

Why do you think the first triangle needs 1 more block than the second triangle? The rhombus is like 2 green triangles. Display the second set of two composed triangles. How many blocks go together to compose the first triangle? 5 How many blocks go together to compose the second triangle? 3 Why do you think the second triangle needs fewer blocks than the first triangle? 1 trapezoid is the same size as 3 green triangles. Display the third set of two composed triangles. Point to the shape on the left. This composition uses the greatest number of blocks. How many does it use?

Promoting Mathematical Practice Students look for and make use of repeated reasoning when they conjecture that they need more small shapes than large shapes to compose a new shape. In this lesson, students get repeated experience with seeing and feeling how the size of a shape affects the number needed. This lesson also gives students an opportunity to construct viable arguments when they explain why they think their conjecture is true. Although students do not yet have technical understanding of area or fractions, they can intuitively understand and explain that smaller pieces take up less space than larger pieces.

9 (Point to the shape on the right.) This composition uses the fewest number of blocks. How many does it use? 3 Ask students to think-pair-share about why 9 triangle blocks are needed to compose the green triangle and only 3 trapezoid blocks are needed to compose the red triangle. Triangles are smaller so we need more of them. Trapezoids are larger so we need fewer of them.

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EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 9

Revoice students’ thinking to form a conjecture.

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 9 ▸ Hexagon

Make the gray hexagon with blocks.

Draw lines to show the blocks you used.

Ask students to restate this idea to a partner. Let’s try out our idea with another composed shape.

Test the Conjecture Materials—S: Pattern blocks, Hexagon

Students test their conjecture to confirm that when the shapes are smaller, more of them are needed to compose a new shape. Make sure all students have a Hexagon removable and pattern blocks. Show a composite hexagon. What is this shape? How do you know? It’s a hexagon. It has 6 sides and 6 corners. I wonder how many different ways we can use pattern blocks to compose this hexagon. Allow 4–5 minutes for exploration with pattern blocks. Circulate and observe. See the chart for possible student responses. Assess and advance student thinking by asking: • How many total blocks did you use? Which blocks did you use to compose the hexagon?

Differentiation: Challenge Ask students to attempt to find all the ways to compose the hexagon (or the triangle in Launch). Have them record solutions by using an organized table to confirm they found all the ways.

Number of How many ways? Blocks

• Replace one block with a different block. What happens?

• Did you use more blocks or fewer blocks this time? Why do you think that happened?

3 4 5 6

143

1 ▸ M6 ▸ TB ▸ Lesson 9

EUREKA MATH2

Invite two or three students to share different compositions. Focus students’ attention on confirming their conjecture.

What is the fewest number of blocks we can use to make this hexagon? 1 yellow hexagon What is the greatest number of blocks we can use to make this hexagon? 6 green triangles Display both hexagons. We said if we use small shapes to compose a new shape, we need more of them than if we use larger shapes. Is that true with these hexagons? Why? It’s true. When we use the small triangles, we need 6. But we only need 1 larger hexagon block. Display a hexagon pattern block composed of 2 trapezoids. Suppose we take away 1 trapezoid and replace it with smaller shapes. Will we need more blocks or fewer blocks? Why? You will need more blocks because the new shapes are smaller than the trapezoid. Display both hexagons. What happened? There were 2 blocks and now there are 3 blocks. There are more blocks than before.

144

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 9

Suppose I take away the rhombus and replace it with triangles. Would there be more blocks or fewer blocks? There would be more blocks because it takes 2 triangles to make 1 rhombus. Display all three hexagons to confirm. Then help students summarize their learning. Why do we need more of some blocks to compose a shape? The smaller the blocks are, the more of them you need to compose a shape. Why do we need fewer of some blocks to compose a shape? The larger the blocks are, the fewer of them you need to compose a shape.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be read aloud.

145

15 1 ▸ M6 ▸ TB ▸ Lesson 9 25

Land Debrief

EUREKA MATH2

5 min

Objective: Relate the size of a shape to how many are needed to compose a new shape. Gather students and display the animal puzzle. What do you notice about this shape? It’s an animal. Just like we did with the triangle and hexagon, we can use pattern blocks to compose this shape in many ways. Two students composed it by using different blocks. Logan used the fewest number of blocks. Zoey used the greatest number of blocks. How many do you think each of them used? Turn and talk to your partner to make a good guess. Display sample solutions. Let’s look at Logan’s puzzle. What do you notice? The head is 1 big hexagon. The body and front leg are made of blue rhombuses. There are 6 blocks. Logan’s animal is composed of 6 blocks: 1 hexagon, 3 blue rhombuses, 1 tan rhombus, and 1 square. Now look at Zoey’s animal. What is different? Zoey used different blocks. She used almost all triangles. Zoey used 14 blocks.

146

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The puzzle is the same. Why did Zoey use more blocks than Logan used? Zoey used triangles to make most of the body. Triangles are smaller than the blocks Logan used. Triangle blocks are smaller than hexagon and rhombus blocks. Zoey needed more blocks to compose the shape. Why can the number of blocks we need to compose a shape change? The smaller the block, the more of them we need to compose a shape. The larger the block, the fewer of them we need to compose the same shape.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

147

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 9

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Name

1 ▸ M6 ▸ TB ▸ Lesson 9

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 9

2. Circle the hexagon made with more blocks.

1. Circle the triangle made with fewer blocks.

Make a hexagon that has more blocks. Draw the shapes. Make a triangle that has fewer blocks. Draw the shapes. Sample:

3. Make a trapezoid with blocks. Draw the shapes. Sample:

148

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TB ▸ Lesson 9

EUREKA MATH2

1 ▸ M6 ▸ TB ▸ Lesson 9

4. Make a trapezoid with some new blocks. Draw the shapes. Sample:

How many blocks did you use?

5. Circle the trapezoid that has more blocks. Write why it has more blocks.

The blocks are smaller.

PROBLEM SET

149

Topic C Halves and Fourths In topic C, students explore the foundation of fractions. They continue to compose and decompose shapes and consider whether the parts that make up the whole are equal shares (or parts). Students focus on partitioning circles and rectangles into halves and fourths. At first, students use their intuition to reason about “fair” shares. Then they cut paper, compose pattern block shapes, and analyze partitioned shapes to answer the question, Are the parts equal shares of the whole? They come to understand equal shares as parts that have the same size and shape. In later grades, students learn that equal parts are the same size but not necessarily the same shape. Students fold paper to make an origami owl. They notice how the folds partition the paper into halves and then fourths. Students partition more circles and rectangles into 2 or 4 equal parts and name the shares as halves, fourths, and quarters. After partitioning, they identify 1 share as either 1 half or 1 fourth of the whole. As they analyze partitioned shapes, students verbalize how many equal shares compose the whole—either 2 shares or 4 shares. Students hear a sharing scenario that helps them experience the relationship between the size of a fractional piece and the number of pieces the whole is partitioned into. They discover that the more shares of a whole there are, the smaller the shares become. This correlates with the line of thought from topic b lesson 9 that the smaller the pieces, the more of them that are needed to compose a larger shape. Finally, students connect their understanding of half to telling time. They reason about the phrase half past and relate it to a half-circle. Students observe that the minute hand starts at the hour hand and goes halfway around the clock to show half past. As a result, half past can also be stated as a time, such as 3:30. Students also analyze the movement and location of the hour hand, noticing that it is halfway between 3 and 4 at 3:30.

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1 ▸ M6 ▸ TC

Progression of Lessons Lesson 10

Lesson 11

Lesson 12

Reason about equal and not equal shares.

Name equal shares as halves or fourths.

Partition shapes into halves, fourths, and quarters.

Halves are made up of 2 equal parts, and fourths are made up of 4 equal parts.

I can fold, cut, or draw to partition a shape. When I partition a shape into 4 equal parts, they are called fourths or quarters.

The hexagon is composed of 3 equal parts when the shapes are the same shape and size.

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Lesson 13

Lesson 14

Lesson 15 (Optional)

Relate the number of equal shares to the size of the shares.

Tell time to the half hour with the term half past.

Reason about the location of the hour hand to tell time.

When we share the pizza with more people, the size of 1 share gets smaller.

Half past 6 means 6:30. The minute hand has gone around the clock a half-circle.

The hour hand moves halfway between the two hours. The minute hand goes halfway around an hour.

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LESSON 10

Reason about equal and not equal shares.

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 10

Circle the foods that show equal shares.

Lesson at a Glance Students watch a video that presents a situation about sharing and discuss equal shares in terms of fairness. They find fair ways to share by cutting paper that represents brownies, and then they use equal parts to compose shapes. They reason about different ways to partition shapes and talk about whether the representations show equal shares. The term partition is introduced in this lesson.

Key Question • How do you know if a shape is composed of equal parts?

Achievement Descriptor 1.Mod6.AD5 Partition circles and rectangles into 2 or 4 equal

shares and describe the shares by using the words halves, fourths, or quarters.

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Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Prepare sticky notes by creating sets of 3 for each student.

Launch Learn

10 min 10 min

30 min

• Compose by Using Equal Parts • Partition to Show Equal Shares • Problem Set

Land

10 min

• Plastic pattern blocks • Circle removable (digital download) • Sticky notes (3) • Scissors

Students • Plastic pattern blocks • Circle removable (in the student book) • Sticky notes (3) • Scissors

• Prepare pattern blocks by creating sets that contain 1 hexagon, 2 trapezoids, 6 triangles, and 3 blue rhombuses per student. • The Circle removables must be torn out of student books. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. • Copy or print the Circle removable to use for demonstration.

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Fluency

10 10

Choral Response: Find the Length 30 Students find the length of an object measured in centimeters to build fluency with measurement skills from module 4. 10

Display the picture of the block with the centimeter cubes beneath it. I measured a block by using centimeter cubes and took this picture. How many centimeters long is the block? Raise your hand when you know.

4 cm

Wait until most students raise their hands, and then signal for students to respond. 4 cm Display the answer. Repeat the process with the following sequence: Teacher Note

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5 cm

7 cm

9 cm

13 cm

15 cm

18 cm

11 cm

Consider pausing on one or two of the slides to count the centimeter cubes and verify their lengths. Point out that the color of the centimeter cubes changes after every 5 cubes.

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 10

Whiteboard Exchange: 7 as an Addend Students find a total and use the commutative property to write a related addition sentence to build addition fluency within 20. After each prompt for a written response, give students time to work. When most students are ready, signal for them to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display 1 + 7 = ____.

1+7= 8

Write the equation and then find the total. Display the completed addition sentence: 1 + 7 = 8.

7+1=8

Change the order of the addends to write a related addition sentence. (Point to the addends.) Display the related addition sentence: 7 + 1 = 8. Repeat the process with the following sequence:

3+7

2+7

7+7

5+7

0+7

9+7

4+7

6+7

8+7

Choral Response: Circle, Half-Circle, or Quarter-Circle Students determine if a shape or object is in the form of a circle, half-circle, quarter-circle, or none of these to prepare for reasoning about equal shares and not equal shares. Display the circle. Is the picture a circle, half-circle, quarter-circle, or none of these? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. Circle

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Repeat the process with the following sequence:

Launch

10 30

Materials—T/S: Sticky notes, scissors

Students cut paper10to show equal shares. Gather students and play part 1 of the video, which shows two children sharing a brownie. What did you notice? What do you wonder? One person cuts the brownie to give it to the children, but it was not fair. The child who got the smaller piece feels sad.

UDL: Engagement

I wonder why one brownie was larger than the other. Ask students to think–pair–share about whether the brownie was cut fairly. Listen for students to reason about equality. As you circulate, distribute three sticky notes and a pair of scissors to each student for use after the discussion. Select a few students to share their thoughts about the video.

The video presents a sharing scenario to get students thinking about equal shares by using a familiar context. As needed, create a different scenario to make the content more culturally relevant.

The way the first brownie was cut is not fair. One boy got more. It is not fair because the pieces are not the same size. Ask students to imagine that each of their sticky notes is a brownie. Let’s cut a new brownie for the children in the video. How would you cut it to make the pieces fair? Use your scissors and sticky notes to try different ways of cutting the square brownie. Share your ideas with your partner. 158

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Have a few students who cut their sticky notes into equal shares display their work. If needed, cut sticky notes and show students the different ways to make equal shares. For each sample you show, ask these questions. Is this fair? Why? Listen for responses that mention that the pieces are the same size, or equal. Play part 2 of the video. What happened this time? Is the way the brownies are cut fair now? Why? Yes, they are fair. They are the same shape and size. Display the brownie cut into equal shares. These brownie pieces are fair because they are cut into parts that are the same size. We can call them equal shares.

Promoting Mathematical Practice As students use sticky notes to reason about equal shares of real-world objects, they model with mathematics. Real-world objects like food do not have perfectly straight sides or corners, which makes them more difficult to partition equally. Thinking about which shape an object resembles can help students make sense of how to partition the object. Tell students that mathematicians and other people represent real objects by using shapes all the time. For example, an architect uses straight lines and sharp corners to design a building.

How do we know this brownie is cut into equal shares for the children? Both of their pieces are the same size. Display the brownie that is not cut into equal shares. How do we know these brownies are not fair? The pieces are not the same size. Transition to the next segment by framing the work. Today, we will make equal shares and look for equal parts.

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Learn

30 10

Compose by Using Equal Parts Materials—T/S: Pattern blocks

Students compose shapes to show equal shares. Distribute pattern blocks. Ask students to take out a rhombus. Let’s show equal shares of a shape. Put triangles on top of the rhombus to compose it. Invite a student to share their work. How many equal shares or equal parts did we need to compose the rhombus?

Teacher Note Students relate composing shapes with composing equal shares. When referring to the parts that compose the shape, the terms equal shares and equal parts are interchangeable. In upcoming lessons, students label the equal shares as halves or fourths. They do not need to name the fractional unit in this lesson.

2 How do you know the parts are equal? The triangles I used are the same size and shape. Have students exchange their rhombus for a trapezoid. Use pattern blocks to show that both the rhombus and the trapezoid can be composed of equal parts as students do the same. When we use triangles to compose the trapezoid and the rhombus, the parts are the same size, the same shape, and they cover the whole shape. The triangles show equal shares.

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Repeat the process to compose a hexagon. Have students compose the hexagon by using 3 rhombuses, and then have them compose it by using 6 triangles. After each composition, ask students to show thumbs-up if they think the parts in the composition are equal shares of the whole. Invite a couple of students to justify their thinking. Then demonstrate a composition that does not show equal shares. Cover a hexagon with 4 triangles and 1 rhombus. Show thumbs-up if you think the parts are equal shares of the whole. Show thumbs-down if you think the parts are not equal shares of the whole. Invite one or two students to justify their thinking. Not all of the parts are the same shape, so they are not equal. The triangles are the same, but the rhombus is bigger. They’re not equal shares. Display the set of shapes that shows equal shares.

We show equal shares by composing only with parts that are the same shape and size. Invite students to compose a hexagon with equal shares in a new way (2 trapezoids). Then have students set aside their pattern blocks.

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Partition to Show Equal Shares

Differentiation: Challenge

Materials—T/S: Circle removable

Students determine whether shapes are partitioned into equal shares. Make sure that students have the Circle removable. Guide students to make equal parts by folding the paper vertically. Have them open the paper to look at the fold.

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 10 ▸ Circle

Encourage students to partition other paper shapes, such as squares, rectangles, rhombuses, trapezoids, and hexagons. If students cut them after folding them, they can lay the shapes on top of a nonpartitioned shape to test if they are indeed the same shape and size.

Did we fold the circle into equal parts? How do you know? Yes, because the 2 parts are the same size and shape. Tell students to use a pencil to trace the fold within the circle. Students may use the edge of their book as a straightedge. When we partition a shape, we split it up. We can fold, cut, or draw lines to partition a shape. Point to where we partitioned the circle into equal parts.

Guide students to partition the circle again by folding the paper horizontally. Have them open the paper and trace the new fold. Is the circle partitioned into equal parts? How do you know?

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Name

1 ▸ M6 ▸ TC ▸ Lesson 10

Yes. The 4 parts are the same size and shape. Ask students to set aside the circle and to turn to the pictures of food in their student book. These foods are cut into parts. Sometimes the whole is partitioned into equal parts, and other times it is not. Circle only the foods that are partitioned into equal parts. After students work on their own, invite them to share their work with a partner. Facilitate a class discussion by using the following questions. Which foods are partitioned into equal shares? How do you know all the parts are equal shares of the whole?

Ask students to look at the watermelon, pear, and tomato. 162

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How do you know these foods are not partitioned into equal shares of the whole? The parts of the watermelon are different shapes and sizes. One part of the pear is larger, so it is not an equal share. If two people share the tomato, they would not get the same-size piece.

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

5 min

Objective: Reason about equal and not equal shares. Gather students and display two pies.

Both pies have been partitioned into 2 parts. Which pie is partitioned into equal shares? How do you know? The first pie shows equal shares because the parts are the same shape and size. Copyright © Great Minds PBC

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Which pie would you rather share with a friend? Why? I want to share the first pie cut into equal parts because it is fair. I want the pie that is not cut into equal shares so I can have the bigger piece! Display a pie that has not been partitioned. Extend the discussion by inviting students to brainstorm other ways to partition the pie equally. Record their ideas. An example is shown. How do you know if a shape is composed of equal parts? The parts are all the same shape and size.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

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Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 10

EUREKA MATH2

2. Circle the foods that show equal shares.

1. Circle the shapes that show equal parts.

PROBLEM SET

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EUREKA MATH2

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3. Draw lines to make equal parts. Sample:

4. Draw a shape. Draw lines to make equal parts. Sample:

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PROBLEM SET

LESSON 11

Name equal shares as halves or fourths.

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 11

1. Circle the shape that shows halves.

Lesson at a Glance Students fold origami owls to create, identify, and discuss halves and fourths. Then they identify halves and fourths in partitioned shapes. The terms halves and fourths are introduced in this lesson.

Key Question • How do you know if something is partitioned into halves or fourths?

Achievement Descriptor 1.Mod6.AD5 Partition circles and rectangles into 2 or 4 equal

shares and describe the shares by using the words halves, fourths, or quarters.

2. Circle the shape that shows fourths.

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Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Origami Owl removables must be torn out of student books. The square, circles, and triangle must be cut out accurately. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 5 min

35 min

• Paper Folding: Origami • Halves and Fourths • Problem Set

Land

10 min

• Origami Owl removable (2 copies, digital download) • Scissors • Glue

Students • Origami Owl removable (in the student book)

• Copy or print two copies of the Origami Owl removable. Watch the video and make one origami owl prior to the lesson.

• Scissors • Glue

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Fluency

10 5

Choral Response: Find the Length 35 Students find the length of an object measured in centimeters to build fluency with measurement skills from module 4. 10

Display the picture of the paper clip with the centimeter cubes beside it. I measured a paper clip with centimeter cubes and took this picture. How many centimeters tall is the paper clip? Raise your hand when you know.

3 cm

Wait until most students raise their hands, and then signal for students to respond. 3 cm Display the answer. Repeat the process with the following sequence:

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6 cm

8 cm

12 cm

17 cm

19 cm

21 cm

14 cm

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 11

Whiteboard Exchange: 8 as an Addend Students find a total and use the commutative property to write a related addition sentence to build addition fluency within 20. After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display 1 + 8 = .

1+8= 9

Write the equation and then find the total. Display the completed addition sentence: 1 + 8 = 9.

8+1=9

Change the order of the addends to write a related addition sentence. (Point to the addends.) Display the related addition sentence: 8 + 1 = 9. Repeat the process with the following sequence:

2+8

4+8

8+8

5+8

0+8

9+8

6+8

3+8

7+8

Choral Response: Equal or Not Equal Shares Students determine if a shape or object is partitioned into equal shares and say the number of equal shares to prepare for naming halves and fourths. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display the circle partitioned into halves.

Teacher Note This fluency activity is like Circle, Half-Circle, or Quarter-Circle in lesson 10. Since students recently developed a knowledge of equal shares, this activity asks about equal shares instead of circles, half-circles, and quarter-circles.

Is the circle partitioned into equal shares? Yes.

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How many equal shares? 2 Display the hexagon partitioned into unequal shares. Is the hexagon partitioned into equal shares? No. Repeat the process with the following sequence: Teacher Note

Launch

5 35

Students notice and wonder about artwork that shows a partitioned object. Gather students with10 their whiteboards. Display The Watermelons by Diego Rivera. Do not give students any information about the painting. Invite students to notice and wonder about the artwork.

The Watermelons is Diego Rivera’s last painting. He created it in 1957. He is best known for his large-scale murals that he painted in several cities in both Mexico and the United States. Near the end of his life, he lost the use of his right arm and began making smaller paintings like this one. He is known for vivid colors and lifelike textures, which he achieved by mixing sand into his oil paints. Across the span of his 71 years, he was recognized with solo exhibitions and acclaimed by the world’s most famous museums and galleries.

Then stimulate discussion by asking the following questions: • Do you think the watermelons are cut into equal shares? Why? • Point to a piece of watermelon. How many pieces like this would make a whole watermelon? Why? 172

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Share the title of the artwork and the artist’s name. Consider sharing details about the artwork that may be of interest to students. Transition to the next segment by framing the work. Today, we will look for and name equal shares or parts. 10 5

Learn

35 10

Paper Folding: Origami Materials—T: Completed origami owl, Origami Owl removable, scissors, glue; S: Origami Owl removable, scissors, glue

Students fold an origami owl bookmark and notice halves and fourths. Show students an example of the origami owl bookmark. We will make these owls by folding paper. Take a close look. What shapes do you notice? I see two triangles. The owl is a square (or rhombus).

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 11 ▸ Origami Owl

The eyes are circles. The square is composed of equal parts. What shapes are the equal parts? I see a square made of 2 triangles that are the same size. What do you think we’ll have to do to make the owl? We will have to cut and fold paper. Play the video to preview the steps for folding the owl. Make sure each student has the Origami Owl removable and scissors or the precut shapes from the removable. Demonstrate the following steps as students follow along. Be sure students make tight creases after each fold. Copyright © Great Minds PBC

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Promoting Mathematical Practice Step 1

Put the square white side up and turn it like this. Fold the paper in half by connecting the top and bottom corners. Open it up. Did we fold the square into equal parts? How many? Yes, the 2 sides of the fold (triangles) are the same size. We folded a line right down the middle, so the 2 parts are equal. We folded our paper in half, or into 2 equal parts. Now we have 2 halves. Point to the halves with me. Let’s fold it in half again the other way. Fold the paper in half again by connecting the left and right corners.

As students make equal parts by folding paper, they learn to use an appropriate tool strategically. Drawing equal parts can involve measuring with more precision than many grade 1 students have learned. However, they are able to create equal parts by folding. Grade 1 students are not alone in using paper folding as a mathematical tool. In the book Geometric Exercises in Paper Folding, first published in 1893, the Indian mathematician T. Sundara Row showed that many mathematical constructions that were difficult or impossible to achieve with the compass and straightedge used by ancient Greek mathematicians were more easily produced through paper folding.

Open the whole paper back up. How many equal parts do you see? 4 When there are 4 equal parts, the parts are called fourths. Point to the fourths with me. Have students fold their squares in half again to make the large triangle. Step 2

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Demonstrate steps 3–6: 3. Fold the corners on each side of the triangle up to the top corner, along the center fold. 4. Open the paper back to a triangle. Fold the top corner (first flap only) to the bottom side. 5. Fold a corner on one side of the triangle up, fold again to tuck part of it in, and make a crease. 6. Repeat step 5 with the other corner.

Step 3

Step 4

Step 5

Step 6

Demonstrate how to make the owl’s nose and eyes. Fold the triangle in half. Open it back up. How many halves do you see? 2 How do we know these are halves? There are 2 equal parts. Now fold both circles in half to make half-circles. Fold them in half again to make quarter-circles. Open the circles back up. How many equal parts do you see in each circle? 4

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What do we call 4 equal parts? Fourths Have students draw a dot on the circle at the center point where the two folds intersect. Then have them glue the eyes and nose onto the owl. Model placing the owl on the corner of a page of the student book to use it as a bookmark.

Halves and Fourths Students identify halves and fourths and partition shapes into equal parts.

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 11

Prompt students to open their student book to the foods partitioned into halves and fourths. Invite students to think–pair–share about the foods that are partitioned in half. Which foods are partitioned in half? Circle them. The watermelon, sandwich, hot dog, and apple are cut into halves. They all have 2 equal parts, or shares. Then have students think–pair–share about the foods that are not partitioned into halves. How are the cracker and the pie partitioned? How do you know? They are in 4 equal parts. That’s fourths. Copyright © Great Minds PBC

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Ask students to look at the crackers that are shaped like a square and a circle at the bottom of the page. Draw a line in the square cracker to make halves. Color 1 half of the cracker. Draw two lines in the circle cracker to make fourths. Color 1 fourth of the cracker. Invite a few students who partitioned the crackers differently to share their work. Consider replicating and displaying student work that shows a misconception. Guide the class to correct the work. Conclude the discussion by helping students summarize what they learned about halves and fourths.

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How are halves and fourths the same? How are they different? They both are equal parts of a whole shape. Halves are 2 equal parts in a whole shape. Fourths are 4 equal parts in a whole shape.

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. Directions may be read aloud. Help students recognize the words half, halves, fourth, and fourths in print. Invite students to underline the words as you read them aloud.

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Land Debrief

5 min

Objective: Name equal shares as halves or fourths. Display the picture of shapes. Which shape shows fourths? How do you know? The orange circle shows fourths. It has 4 equal parts. Why doesn’t the blue circle show fourths? It has 4 parts, but they aren’t the same size. Which shape shows halves? How do you know? The yellow rectangle shows halves. It has 2 equal parts.

Teacher Note This is an example of pottery made in 1895 by the Acoma tribe living in New Mexico. This group of craftspeople often experimented with geometric designs as part of their plant and animal motifs.

Why doesn’t the gray rectangle show halves or fourths? It is partitioned into 3 parts, not 2 or 4 parts. How do you know if something is partitioned into halves or fourths? You have to count the parts. If there are 2 equal parts, then it’s partitioned into halves. If there are 4 equal parts, then it’s partitioned into fourths.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

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Consider displaying for students the jug and ask them to look for halves and fourths, such as a square composed of 2 triangles, or a rectangle composed of 4 triangles.

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 11

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 11

EUREKA MATH2

3. Circle the shapes that show fourths.

1. Circle the shapes that show halves.

4. Draw to make fourths.

2. Draw to make halves.

Color 1 fourth.

Color 1 half.

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PROBLEM SET

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12 EUREKA MATH2

Name

LESSON 12

Partition shapes into halves, fourths, and quarters. 1 ▸ M6 ▸ TC ▸ Lesson 12

Draw a line to make halves. Color 1 half.

Lesson at a Glance Students are presented with a sharing scenario and engage in discussion about whether an object is partitioned into halves. They view different pictures of partitioned objects and determine whether they show halves or fourths. The term quarters is introduced in this lesson.

Key Questions • How do you know if a shape is partitioned into halves? • How do you know if a shape is partitioned into fourths (quarters)?

Achievement Descriptor 1.Mod6.AD5 Partition circles and rectangles into 2 or 4 equal

shares and describe the shares by using the words halves, fourths, or quarters.

Draw lines to make quarters. Color 1 quarter.

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Agenda

Materials

Lesson Preparation

Fluency

Teacher

The Partition the Snack removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 5 min

35 min

• Halves and Quarters • Partitioning Shapes

• Demonstration clock

Students • Partition the Snack removable

• Problem Set

Land

10 min

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Fluency

10 5

Whiteboard Exchange: 9 as an Addend 35and use the commutative property to write a related Students find a total addition sentence to build addition fluency within 20. 10

After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display 1 + 9 = .

1 + 9 = 10

Write the equation, and then find the total. Display the completed addition sentence: 1 + 9 = 10.

9 + 1 = 10

Change the order of the addends to write a related addition sentence. (Point to the addends.) Display the related addition sentence: 9 + 1 = 10. Repeat the process with the following sequence:

3+9

2+9

9+9

5+9

0+9

7+9

4+9

6+9

8+9

Counting on the Clock Materials—T: Demonstration clock

Students count by hours or half hours to build fluency with telling time from module 5. Show students the demonstration clock with the hands set to 1:00. What time is shown on the clock? Raise your hand when you know. 182

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Wait until most students raise their hands, and then signal for students to respond. 1:00 Use the clock to say the time as I move the minute hand to count hours. The first time you say is 1:00. Ready? Move the minute hand on the clock in 60-minute intervals to 10:00, pause, and then move back to 1:00. 1:00, 2:00, 3:00, … , 10:00 10:00, 9:00, 8:00, … , 1:00 Now use the clock to say the time as I move the minute hand to count half hours. The first time you say is 1:00. Ready? Move the minute hand on the clock in 30-minute intervals to 6:00, pause, and then move back to 1:00. 1:00, 1:30, 2:00, … , 6:00 6:00, 5:30, 5:00, … , 1:00

Choral Response: Equal or Not Equal Shares Students determine how objects are partitioned to prepare for identifying and partitioning halves and fourths. After asking each question, wait until most students raise their hands, and then signal for students to respond. Raise your hand when you know the answer to each question. Wait for my signal to say the answer. Display the circle partitioned into fourths. Is the circle partitioned into equal shares? Yes.

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How many equal shares are there in the circle? 4 Are the equal shares halves, fourths, or neither? Fourths Display the triangle partitioned into unequal shares. Is the triangle partitioned into equal shares? No. Repeat the process with the following sequence:

Launch

5 35

Students consider if a candy bar is partitioned into halves. Gather students and 10 display the candy bar. Share the following situation. Traun and Senji share a candy bar. They each want half of the bar. This is how they plan to cut the candy bar. Do you think they will each get half? Why? After giving students time to think, lead a class discussion. Support student-to-student dialogue by inviting them to agree or disagree, ask a question to clarify, or restate an idea in their own words. Encourage students to use math language, such as equal share, equal part, halves, and half of.

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The bar is not cut into halves because the 2 parts are not the same size. It’s not fair! One of them would get a bigger piece. Display a candy bar that is not partitioned. How would you partition the candy bar to make halves? Cut it right down the middle. Record students’ ideas. Then invite students to consider how they would share the candy bar with 4 friends and record their thinking. How many equal shares are in a whole candy bar when we partition it into halves? 2 equal shares How many equal shares are in a whole candy bar when we partition it into fourths? 4 equal shares Transition to the next segment by framing the work. Today, we will practice partitioning objects into halves and fourths. We’ll talk about how we know that 10 we’ve made halves and fourths. 5

Learn

35 10

Language Support

Halves and Quarters Students identify whether an object is partitioned into halves or fourths and justify their thinking. Display each of the pictures of partitioned pies. Engage students in a variation of the Take a Stand routine as each picture is displayed. Have students stand if they think the picture shows an object cut into halves. Invite students who stand to explain their reasoning. Copyright © Great Minds PBC

Support student-to-student discourse by pointing out the sentence stems on the Talking Tool. Encourage students to use the sentence stems to build on one another’s ideas. For example, a student might say, “I disagree that this pie shows halves because the 2 parts are not the same size.”

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Language Support The term quarters is a synonym for fourths. Help students remember the terms presented in this topic by making an anchor chart such as the one shown.

Both sides are the same size.

The 2 parts are not the same size.

There are 2 equal parts.

The pieces are not halves because they are not equal shares.

The parts are the same shape. They are half-circles.

The 2 pieces are the same shape and size.

Halves have 2 pieces. This has 4.

They are still halves, just turned.

This shows fourths. Fourths Quarters

The parts are all the same shape. They are quarter-circles.

Halves

Continue to display the pie partitioned into fourths. This pie is cut into fourths. Another name for 4 equal parts, or fourths, is quarters. We can say this pie is cut into fourths, or we can say it is cut into quarters. What is another word for fourths?

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 12

Quarters Notice that when a circle is partitioned into quarters, the parts are called quarter-circles. Direct students to turn to the partitioned shapes in their student book. These shapes might be partitioned into equal parts or they might not be partitioned into equal parts. Have students work with a partner to circle shapes that are partitioned into quarters. Invite students to use the terms fourths and quarters as they work. When they finish, invite students to share their work. Record their thinking.

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13/04/21 1:10 AM

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 12

Which shapes are partitioned into quarters? How do you know? The red rectangle shows quarters because there are 4 parts that are the same size. The yellow square shows fourths because the 4 triangles are equal shares. The purple rhombus shows quarters because the parts are the same shape and size. Which shapes are not partitioned into quarters? How do you know? The pink triangle and the blue circle are not partitioned into quarters because they do not have 4 parts. The green trapezoid does not show quarters because the 4 parts are not all the same size.

Partitioning Shapes Materials—S: Partition the Snack removable

Students partition shapes into halves and fourths. Make sure each partner has the Partition the Snack removable inserted into their personal whiteboard. Model the following directions. EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Partition the Snack

Partner A partitions all of the food pictures, some into halves and some into not halves. Partner B points to each picture and says “Halves” or “Not halves” and explains their thinking. Partners erase their whiteboards.

As students work with a partner to partition the snacks, they have a chance to construct viable arguments and critique the reasoning of others. The assessing and advancing questions in this segment are designed to promote this mathematical practice.

Then partner B partitions all of the food pictures, some into fourths and some into not fourths. Partner A points to each picture and says “Quarters” or “Not quarters” and explains their thinking. Partner A can also say, “Fourths.” Partners erase their whiteboards. Copyright © Great Minds PBC

EM2_0106TE_C_L12_removable_partion_the_snack_studentwork.indd 113

Promoting Mathematical Practice

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03/03/21 6:05 PM

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Allow 1–2 minutes for students to practice with halves, and 1–2 minutes to practice with fourths. Encourage students to find as many ways as they can to partition the foods. Use the following questions to assess and advance thinking:

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Partition the Snack

Language Support Provide sentence frames that help students verbalize their arguments:

• How do you know this is partitioned into halves (or fourths or quarters)?

• This is partitioned into halves because .

• How do you know that this is not partitioned into halves (or fourths or quarters)?

• This is not partitioned into halves because .

• Where do you see a half? Where do you see a fourth (or quarter)? Gather the class. Invite students to choose one food item. Partition your food into halves.

EM2_0106TE_C_L12_removable_partion_the_snack_studentwork.indd 115

Color 1 half. Have students hold up their whiteboards to share their work. Give feedback. Repeat the process with quarters.

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex.

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03/03/21 6:05 PM

Differentiation: Support Support students by providing a straightedge before they partition the items. However, partitioning with precision takes time and practice. Listen for students to simply demonstrate understanding of halves and fourths.

Directions and word problems may be read aloud. Help students recognize the words quarter and quarters in print. Invite students to underline them as you read them aloud.

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5 EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 12 35

Land Debrief

5 min

Objective: Partition shapes into halves, fourths, and quarters. Gather students and display the three pizzas. Invite students to turn and talk about what they notice.

Which pizza is partitioned into halves? How do you know? Pizza B is partitioned into halves. I know because it has 2 equal shares. Point to pizza B. Think about this pizza. How many people can get an equal share? Why? Two people can have equal shares because it is cut in half.

Which pizza is partitioned into quarters? How do you know? Pizza A is partitioned into quarters because it has 4 equal shares (parts). Point to pizza A. Think about this pizza. How many people can get an equal share? Why? Four people can have equal shares because it is cut into fourths.

Point to pizza C. Is this pizza partitioned into halves or fourths? Why? It is not partitioned into halves or fourths because it has 3 parts (shares).

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

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Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 12

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 12

3. Circle.

halves

1. Circle the shapes that show halves.

How many equal parts?

fourths

4. Circle.

halves quarters 2. Circle the shapes that show fourths or quarters. 5. Circle.

halves quarters

190

115

116

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 12

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 12

6. Draw a line to make halves. Color 1 half.

Draw lines to make quarters. Color 1 quarter.

Kit cut a cake.

Wes cut a cake.

Who made equal parts? Circle.

Kit

Wes

Write or draw how you know. Sample:

PROBLEM SET

117

191

LESSON 13

Relate the number of equal shares to the size of the shares.

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 13

Name

Draw halves.

Draw fourths.

Color 1 half.

Color 1 fourth.

Lesson at a Glance Students hear a sharing scenario that engages them in thinking about what happens to equal shares of a whole when the whole is partitioned into more equal parts. They draw to model the story and discuss their observations. Students craft and tell their own equal sharing story.

Key Question • As a whole is partitioned into more equal parts, what happens to the size of the parts? Circle the shape with the smaller shares.

Achievement Descriptor 1.Mod6.AD6 Draw or write to show that decomposing the same whole

into more equal shares creates smaller shares.

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EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 13

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The 7, 8, or 9 as an Addend Sprints must be torn out of student books. Decide whether to prepare these materials in advance or to have students tear them out during the lesson.

Launch Learn

10 min 5 min

35 min

• Equal Shares • Sharing Stories • Problem Set

Land

10 min

• None

Students • 7, 8, or 9 as an Addend Sprint (in the student book) • Pizza removable (in the student book) • Craft stick

• The Pizza removables must be torn out of student books and placed in personal whiteboards. Decide whether to prepare these materials in advance or to have students prepare them during the lesson.

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Fluency

10 5

Sprint: 7, 8, or 9 as an Addend Materials—S: 7, 8, or 935as an Addend Sprint

Students find a part or total of an addition sentence to build addition fluency 10 EUREKA MATH 1 ▸ M6 ▸ TC ▸ Lesson 13 ▸ Sprint ▸ 7, 8, or 9 as an Addend within 20. 2

Sprint Have students read the instructions and complete the sample problems. Write the part or total. 1. 2.

2+7=■ 6+8=■

9 14

Teacher Note

Read the answers to Sprint A quickly and energetically. Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B.

• What do you notice about problems 1–5? 6–10? 11–15?

194

Consider asking the following questions to discuss the patterns in Sprint A:

• What strategy did you use to solve problem 4? For which other problems could you use the same strategy?

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EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 13

Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B. Direct students to Sprint B. Take your mark. Get set. Improve! Time students for 1 minute on Sprint B. Stop! Underline the last problem you did.

Teacher Note Count forward by ones from 100 to 110 for the fast-paced counting activity. Count backward by ones from 110 to 100 for the slow-paced counting activity.

I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint B quickly and energetically. Count the number you got correct and write the number at the top of the page. Stand if you got more correct on Sprint B. Celebrate students’ improvement.

Launch

Language Support

Materials—S: Pizza removable

Students reason about the size of 1 half compared to the size of a whole. 10 Make sure students have the Pizza removable in their personal whiteboards. Display the picture of the man and the pizza. Tell students that the man’s name is Azeez, and he likes pizza. Consider inviting students to show thumbs-up if they enjoy pizza too. Azeez has a whole pizza to share with his family. What are some ways he can cut his pizza to share it?

The word whole is a homophone with the word hole. The words sound the same but have different spellings and meanings. Support the mathematical use of the term whole when working with fractions by facilitating a class discussion, with visuals, to distinguish the different meanings of the terms. Display the term whole and a picture of the pizza. Label the picture whole. Display the term hole and a picture of a hole in the ground and label the picture hole.

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Expect responses to vary. Listen for students to mention partitioning the pizza into halves or fourths. At first, he just plans to share his pizza with his wife. Draw to partition the pizza to show how he could share it equally with his wife. After students draw their partition, display the pizza partitioned in half. This is how Azeez thinks he can share the pizza. What is his idea? He is going to cut it in half to get 2 equal pieces. Ask students to show thumbs-up if they partitioned their pizza into halves. Invite students to revise their work if needed.

UDL: Representation Color-coding is a critical feature of fractional representations. Keeping Azeez’s slice of pizza blue throughout the lesson helps students see the relationship between the number of pieces the whole is cut into and the size of the pieces.

If Azeez cuts it in half, his share would look like what is outlined in blue. What would his share of the whole pizza be? 1 half At first, Azeez has the whole pizza. If he cuts the pizza in half would his share get bigger or smaller? Smaller Why would that happen? It would get smaller because he is sharing it with another person. Invite students to think–pair–share about how the size of Azeez’s slice of pizza will change when the number of people he shares the pizza with increases. Talk with your partner. Suppose Azeez shares the pizza with more people in his family. What will happen to the size of his share? Will it get bigger or smaller? His share will get smaller. Transition to the next segment by framing the work. Today, we will see what happens to the size of the parts when we partition the whole into more and more shares.

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10 EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 13 5

Learn

35 10

Equal Shares

Materials—S: Pizza removable

Students reason about the relationship between the number of equal parts and the size of the parts. Display the picture of Azeez’s family. Azeez’s children smell the pizza and come running into the kitchen. Partition the pizza to show how Azeez could share the pizza equally with his wife and children. After students finish partitioning the pizza, display the picture of the pizza cut into quarters. This is how Azeez thinks he can share the pizza now. What is his idea? He could cut the pizza into fourths to get 4 equal pieces. Ask students to show thumbs-up if they partitioned their pizza into fourths. Invite students to revise their work if needed.

Promoting Mathematical Practice Students use the story of Azeez and his pizza to look for and express regularity in repeated reasoning. Through repeated experience, they notice and explain that the more people Azeez shares the pizza with, the smaller his share gets. This lesson shows the converse of the idea presented in lesson 9. In that lesson, students saw that the smaller the shape, the more of that shape it takes to compose a larger shape. Here students notice that the more pieces a shape is partitioned into, the smaller the pieces become.

If Azeez cuts the pizza into fourths, his share would look like what is outlined in blue. What would his share of the whole pizza be? 1 fourth (or 1 quarter) If he shares the pizza with his wife, his share is 1 half of the pizza. If he partitions the pizza into fourths to share it with his children too, will his share get bigger or smaller? Why? It would get smaller because there are more people sharing the pizza. Display the picture of Azeez’s extended family. Copyright © Great Minds PBC

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Four more people come over. Now there are eight people sharing the pizza.

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Pizza

If eight people share the pizza, what will happen to Azeez’s share? Why? It will get smaller because there are a lot more people getting a share of the pizza. Guide students to partition their pizza into 8 equal pieces. Then display the final pizza. If Azeez cuts the pizza into 8 pieces, his share would look like what is outlined in blue. What would happen if he shares the pizza with more people? His share will get smaller. Display the three pizzas partitioned differently.

127

Which pizza has the largest parts? Why? Pizza A, with 2 pieces, has the largest parts. It is cut in half for only two people. Which pizza has the smallest parts? Why? Pizza C, with 8 pieces, has the smallest parts. It is cut to share with a lot of people. Which pizza would you choose? Why? I want the pizza with 2 pieces so I can have a really big piece. I want the pizza with 8 slices because I like to share with my friends. I want the pizza with 4 slices because I have four people in my family. What happens when we partition a shape into more and more parts? The pieces get smaller and smaller.

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EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 13

Sharing Stories Materials—S: Craft stick

Students partition rectangles into increasing numbers of parts and reason about the size of the parts. Have students turn to the rectangles in their student book. Provide students with a craft stick as a straightedge. Let’s pretend this rectangle is something you can partition and share. Use your imagination. What could the rectangle be? Collect and record students’ ideas. Ideas will vary, but may include a rectangular pizza, sheet cake, lasagna, clay, or paper. As needed, suggest these items to stimulate students’ thinking.

Language Support Consider preparing a list of rectangular items for students to choose from ahead of time. Also consider having images to correlate with each item you could display to help students tell their stories.

Partner students and invite pairs to decide what the rectangle represents. Then share the directions. Tell your own sharing story. Everyone in the story must get an equal share. Draw to partition the rectangles to match the story and the number of equal shares. Then color in 1 part, or share, of each rectangle. EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 13

Name

2 equal shares

4 equal shares

Sample:

3 equal shares

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 13

129

130

equal shares

LESSON

199

1 ▸ M6 ▸ TC ▸ Lesson 13

EUREKA MATH2

Circulate and support students. Ask the following assessing and advancing questions: • How many equal parts should you make? • What part is yours? Is it bigger or smaller than your last part? Why? • For the last rectangle, choose a larger number of shares. How will you partition it? Invite a few students to share their work. Student work may vary. If needed, model how to partition the rectangles and prompt students to revise their work. Guide students to confirm the relationship between the number of parts and the size of the parts. What happens to the size of the shares when a shape is partitioned into more parts? When we partition a shape into more parts, the shares get smaller.

Problem Set Differentiate the set by selecting problems for students to finish within the timeframe. Problems are organized from simple to complex. Directions and word problems may be read aloud.

200

5 EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 13 35

Land Debrief

5 min

Objective: Relate the number of equal shares to the size of the shares. Display the two cookies. What is the same about how these cookies are partitioned? What is different in how they are partitioned? They both have equal shares. One is partitioned into halves. The other is in fourths. One cookie has smaller pieces. When the cookie is partitioned into halves, how many shares are in the whole? 2 When the cookie is partitioned into quarters, how many shares are in the whole? 4 Have students think–pair–share about the shares. Talk to your partner. Which cookie would you want to share? Why? I would choose the one cut in half because I could get a bigger piece. I would choose the one cut into fourths so I could share it with more friends. What would happen to the shares if 20 people wanted some of the cookie? The pieces would be very small! We would need 20 shares. As we partition a whole into more equal parts, what happens to the size of the parts? The parts get smaller.

Exit Ticket

5 min

201

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 13

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 13 ▸ Sprint ▸ 7, 8, or 9 as an Addend

Number Correct:

Write the part or total.

Number Correct:

Write the part or total.

3+7=■

11.

3+9=■

1+7=■

11.

1+9=■

4+7=■

12.

4+9=■

2+7=■

12.

2+9=■

5+7=■

13.

5+9=■

3+7=■

13.

3+9=■

8+7=■

14.

8+9=■

6+7=■

14.

6+9=■

9+7=■

15.

9+9=■

7+7=■

15.

7+9=■

3+8=■

16.

1+■=9

1+8=■

16.

1+■=8

4+8=■

17.

2 + ■ = 11

2+8=■

17.

2 + ■ = 10

5+8=■

18.

0+■=9

3+8=■

18.

0+■=8

8+8=■

19.

■

+ 9 = 15

6+8=■

19.

■

+ 9 = 13

10.

9+8=■

20.

16 = 7 + ■

10.

7+8=■

20.

14 = 5 + ■

122

202

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 13 ▸ Sprint ▸ 7, 8, or 9 as an Addend

124

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 13

EUREKA MATH2

Name

1 ▸ M6 ▸ TC ▸ Lesson 13

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 13

3. Sam cuts 2 equal parts.

Mel cuts 4 equal parts.

1. Color 1 share. Circle the shape with the smaller shares.

2. Color 1 share.

Draw.

Sam eats 1 part.

Mel eats 1 part.

Color his part.

Color her part.

Who ate the bigger part?

Circle the shape with the larger shares.

Write or draw.

Sam ate more.

129

130

PROBLEM SET

203

LESSON 14

Tell time to the half hour with the term half past.

EUREKA MATH2

1 ▸ M6 ▸ TC

Name

1. Circle the times that match the clock.

Lesson at a Glance Students relate the phrase half past to their understanding of half of a circle. They recognize that half past can also be stated as a time, such as 2:30. Students practice reading and matching times to the hour and half hour on digital and analog clocks.

Key Question • What does it mean if the time is half past the hour?

Achievement Descriptor 7:30

8:30

2. Draw to show halves. Color 1 half.

7 o’clock

1.Mod6.AD1 Tell time to the half hour, including using the term

half past 7

half past.

3. Draw to show fourths. Color 1 fourth.

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EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 14

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Match: Time cards must be torn out of student books and cut out. Decide whether to prepare these materials in advance or to have students prepare them during the lesson. The cards will be used again in lesson 15.

Launch Learn

10 min 5 min

35 min

• Demonstration clock • Match: Time cards (digital download)

• Half Past

Students

• Match: Time

• Match: Time cards (1 set per student pair)

• Problem Set

Land

10 min

• Scissors

• Copy or print a set of the Match: Time cards and prepare it to use for demonstration. • Prepare the digital interactive clock for the lesson. 1 minute

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1 ▸ M6 ▸ TC ▸ Lesson 14

Fluency

Ready, Set, Add

35 and say an addition equation or related subtraction Students find the total equation to build addition and subtraction fluency within 10. 10

Let’s play Ready, Set, Add. Have students form pairs and stand facing each other. Model the action: Make a fist, and shake it on each word as you say, “Ready, set, add.” At “add,” open your fist, and hold up any number of fingers. Tell students that they will make the same motion. At “add” they will show their partner any number of fingers. Consider doing a practice round with students. Clarify the following directions: • To show zero, show a closed fist at “add.”

Partners A and B: “6” Partner A: “4 + 2 = 6” Partner B: “6 – 2 = 4”

• Try to use different numbers each time to surprise your partner. Each time partners show fingers, have them both say the total number of fingers. Then have partner A say an addition equation to represent the fingers shown, followed by partner B saying a related subtraction equation. See the sample dialogue under the photograph. Switch roles after each round. Circulate as students play the game to ensure that each student is trying a variety of numbers.

Counting on the Clock Materials—T: Demonstration clock

Students count by hours or half hours to build fluency with telling time from module 5. 206

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 14

Show students the demonstration clock with the hands set to 3:00. What time is shown on the clock? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 3:00 Use the clock to say the time as I move the minute hand to count hours. The first time you say is 3:00. Ready? Move the minute hand on the clock in 60-minute intervals to 12:00, pause, and then move back to 3:00. 3:00, 4:00, 5:00, … , 12:00 12:00, 11:00, 10:00, … , 3:00 Now use the clock to say the time as I move the minute hand to count half hours. The first time you say is 3:00. Ready? Move the minute hand on the clock in 30-minute intervals to 8:00, pause, and then move back to 3:00. 3:00, 3:30, 4:00, … , 8:00 8:00, 7:30, 7:00, … , 3:00

Choral Response: Tell Time Students tell time to the nearest half hour to build fluency with telling time from module 5. Display the picture of the clock that shows 3:00. What time does the clock show? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 3:00

3:00 207

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 14

Display the answer. Repeat the process with the following sequence:

5:00

6:00

9:00

9:30

2:30

8:30

1:00

11:30

12:00

6:30

4:30

Launch

35 meaning of the language half past. Students discuss the

Display the invitation and read it aloud. 10

UDL: Engagement

What is this note about? It is about meeting someone at the park to play. Reread the invitation. What is the important information in the note?

Adjust the context of the invitation to help make the math relevant to students. For example, you may choose to use students’ names in the note or name a local park.

The important information is where to meet, and what time to meet. Have students think–pair–share about the information in the note. Talk to your partner. What does half past 2 mean? It’s around 2 o’clock. It may be after 2 o’clock because it says past.

208

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 14

Transition to the next segment by framing the work. Today, we will look at a clock and figure out what time it is when we say it’s half past 2. 10 5

Learn Half Past

35 10

Students practice telling time to the half hour by using both analog and digital clocks. Display the clock with no hands. What shape is a clock? Circle Display the clock partitioned in half.

11 12 1 2 10 9 3 8 4 7 6 5

What shape is half of a circle? Half-circle Point to the vertical line from 12 to 6. Invite students to point out the half-circles on the clock. Each time the minute hand goes around the whole circle, we count 1 hour. When the minute hand goes around a half-circle, we count half of an hour. Using the digital interactive, show 2 o’clock on the analog clock only. What time does this clock show? 2 o’clock Yes, let’s go past 2 o’clock until the minute hand makes a half-circle and shows half past 2, or half an hour past 2 o’clock.

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Move the minute hand one minute at a time to 2:30 as students chorally tell the time (2:01, … , 2:15). Pause at 2:15 and have students reflect on the movement of the hands. What is happening with the minute hand? What happened to the hour hand? The minute hand is moving past 2 o’clock one minute at a time. The hour hand is moving, too, but slower than the minute hand is moving. What do you notice about the green part? The green part gets bigger as the hands move. The green part is a quarter-circle now. Does the clock show half past 2 o’clock now? How do you know? No, the minute hand hasn’t made a half-circle yet. Repeat the process from 2:15 to 2:30. What do you notice about the hands and the green part now? The green makes a half-circle. The hour hand is between the 2 and the 3. The minute hand is on the 6 now. Does the clock show half past 2 now? How do you know? Yes, the minute hand went past 2 o’clock and made a half-circle. This clock shows half past 2. The minute hand started at 2 and made a half-circle around the clock. That tells us that half of an hour went by. What time does the clock show at half past 2? 2:30 Show 2:30 on the digital clock as well. (Point to the digital clock.) At 2:30 this clock shows 2 hours and 30 minutes. (Point to the 2 and then to the 30.) 30 minutes is the same as half of an hour. 210

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 14

Write half past where students can see it for the remainder of the lesson. The person who wrote the note said half past 2. What time is half past 2? 2:30 Show 3:00 on the analog clock. Talk to your partner. What time do you think it will it be at half past 3? Show 3:30 and ask the class to state the time chorally. Half past 3 is the same as 3:30. The minute hand started at 3 and made a half-circle, or went 30 minutes, around the clock. As time allows, show other times, such as 12:30, and ask the class to chorally state the time both ways: first as 12:30 and then as half past 12.

Match: Time Materials—T: Match: Time cards; S: Match: Time cards, scissors

Students read and match times in various formats to the hour and half hour. Model the following directions for the Match game. EUREKA MATH2

4:30

half past 4

4:30

Name

Write the times your matches show.

Let’s play Match with cards that show time. Place six cards faceup. Place the other cards in a pile and set them aside. Look at your six cards. Working with a partner, find two cards that match because they show the same time. Use the recording sheet in your student book to write that time on the first clock on the recording sheet.

1 ▸ M6 ▸ TC ▸ Lesson 14

: 137

211

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 14

Set aside the matching cards and place two new cards faceup where the other two cards were. Keep playing until you have found all the matches. Partner students and distribute materials to each pair. Have students turn to the recording sheet with the digital clocks in their book. Allow 6–7 minutes for play. As students play, circulate and use the following suggestions to assess student thinking: • Show me a match. What is the time the cards show? • Read this time by using half past.

Problem Set

Differentiation: Support The cards include times to the hour and half hour in variations: analog, digital, and word form. Support the needs of your students by removing some forms from the set as necessary.

Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 5

Land Debrief

5 min

Objective: Tell time to the half hour with the term half past. Show only the analog clock set at 6:00. Have students turn and talk about what time it shows. Pose a misconception for students to consider. I think this clock shows half past 6 because the hands are making a half-circle. Do you agree or disagree? Why? I disagree, because it shows 6:00. I disagree. The hour hand is on the 6, and the minute hand is on the 12. The minute hand needs to be on the 6 to show half past.

212

Promoting Mathematical Practice When students explain why the first clock does not show half past 6, they construct viable arguments and critique the reasoning of others. Consider asking the following questions: • What questions can you ask your friend about why they think the clock shows half past 6? • How do you use the minute hand to know when it is 6 o’clock and when it is half past 6?

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 14

I disagree. The minute hand has to make a half-circle around the clock, not the hour hand. You convinced me! This clock shows 6:00. How can we change it to show half past 6:00? The minute hand should point to the 6, not the 12. The minute hand needs to make a half-circle around the circle.

Show 6:30 on the analog clock. To show half past 6, the minute hand starts at 6 and makes a half-circle around the clock. What time is half past 6? 6:30 Show 6:30 on the digital clock to confirm the time. What does it mean if the time is half past the hour? It means the minute hand has gone around the clock halfway. It is 30 minutes after the hour.

Topic Ticket

6:30

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

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EUREKA MATH2

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Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 14

Name

3. Fill in the blanks.

1. Circle all clocks that show half past 3.

3:00

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 14

7:30 2:00

3:30

11:30 9:00 2. Circle all clocks that show half past 12.

half past

2 half past

7 o’clock

11 o’clock

4. Draw lines to match the times.

6 o’clock

12:00

12:30

6:30

half past 12 half past 6

214

139

140

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 14

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 14

5. Draw or write half past an hour on the clocks. Sample:

PROBLEM SET

141

215

LESSON 15

Reason about the location of the hour hand to tell time. (Optional)

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 15

Name

Circle all clocks that show half past 2.

2:00

Lesson at a Glance Students study time-telling tools from long ago. They look carefully at the shadow on a sundial to help them focus on the hour hand. Using an analog clock, students analyze the movement and location of the hour hand at the hour and half hour.

Key Question

2:30

• How does the hour hand show half past an hour?

Achievement Descriptor 1.Mod6.AD1 Tell time to the half hour, including using the term

half past.

151

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 15

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Set out the Match: Time cards that were cut out and prepared in lesson 14. Partners will use them again in Learn.

Launch Learn

10 min 10 min

30 min

• Hour Hand • Match: Time • Problem Set

Land

• None

Students • Match: Time cards (1 set per student pair)

• Read the Math Past resource to support your delivery of Launch. • Prepare the digital interactive clock for the lesson.

10 min

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Fluency

10 10

Ready, Set, Add

30 and say an addition equation or related subtraction Students find the total equation to build addition and subtraction fluency within 20. 10

Let’s play Ready, Set, Add. Today, we will use both hands. Have students form pairs and stand facing each other. Model the action: Make two fists, and shake them on each word as you say, “Ready, set, add.” At “add,” open one or both fists, and hold up any number of fingers. Tell students that they will make the same motion. At “add” they will show their partner any number of fingers. Consider doing a practice round with students. Clarify the following directions:

Partners A and B: “10” Partner A: “6 + 4 = 10” Partner B: “10 – 4 = 6”

• To show zero, show closed fists at “add.” • Try to use different numbers each time to surprise your partner. Each time partners show fingers, have them both say the total number of fingers. Then have partner A say an addition equation to represent the fingers shown, followed by partner B saying a related subtraction equation. See the sample dialogue under the photograph. Switch roles after each round. Circulate as students play the game to ensure that each student is trying a variety of numbers.

Counting on the Clock Materials—T: Demonstration clock

Students count by hours or half hours to build fluency with telling time from module 5 and to develop fluency with the term half past from lesson 14. 218

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 15

Show students the demonstration clock with the hands set to 12:00. What time is shown on the clock? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 12:00 Use the clock to say the time as I move the minute hand to count half hours. The first time you say is 12:00. Ready? Move the minute hand on the clock in 30-minute intervals to 5:00, pause, and then move back to 12:00. 12:00, 12:30, 1:00, … , 5:00 5:00, 4:30, 4:00, … , 12:00 Let’s practice again, but this time say half past when you get to the half hour. The first time you say is 12:00. Ready? Move the minute hand on the clock in 30-minute intervals to 5:00, pause, and then move back to 12:00. 12:00, half past 12, 1:00, half past 1, … , 5:00 5:00, half past 4, 4:00, half past 3, … , 12:00

Choral Response: Tell Time Students tell time to the nearest half hour to build fluency with telling time from module 5. Display the picture of the clock that shows 2:00. What time does the clock show? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 2:00

2:00 219

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1 ▸ M6 ▸ TC ▸ Lesson 15

Display the answer. Repeat the process with the following sequence:

4:00

6:00

8:00

Teacher Note

8:30

1:30

3:30

Consider asking students to use the term half past to say the time another way. • What time does the clock show? 1:30 • Say it another way.

7:30

11:00

6:30

12:00

7:30

Half past 1

Launch

10 30

Students compare the features of a sundial and a clock and then use the sundial to tell time. 10

Gather students. What tools do we use to tell time? Clocks, watches, cell phones, microwaves, etc. In today’s world, we usually use mechanical or electronic tools. But before those tools were invented, people had other ways to tell time. Display the time-telling tools. What do you notice? What do you wonder?

220

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 15

Accept all responses. Support student-to-student dialogue by inviting the class to agree or disagree, ask a question, give a compliment, add to a statement, or restate an idea in their own words. Refer to the Talking Tool as needed. Advance students’ thinking during the discussion by asking questions like these: • How are these tools alike? How are they different? • How could these tools be used to tell time? • What shapes do you see in the tools? Students may notice that the obelisk looks like a rectangular prism with a pyramid on top, the sundial has a half-circle, and there are cones within the hourglass. Display only the sundial. What you notice and wonder about this tool?

Math Past Devices used to tell time were constructed as early as 3500 BCE. Egyptians developed several ways to keep time. An obelisk is shown in the first image. These tall columns were built into the ground so that ancient Egyptians could see the shadow they cast. The sundial was later used to tell time by using the sun’s shadow. This tool can be divided into 12 segments or 24 segments (two sets of 12). The Math Past resource contains more information about time-telling tools that may be of interest to your students.

It’s a big circle with numbers, like a clock. It looks partitioned into lots of parts. Why is there a shadow on it where the man is pointing? This is a sundial. A sundial uses shadows made by the sun to tell time. What about the sundial might help tell the time? The numbers going around the sundial might help. The shadow looks like the hand on a clock. The shadow is after 3 and before 4. It is halfway between the two numbers. What time do you think the sundial shows? Turn and talk to make a good guess.

Teacher Note Consider extending this lesson by reading aloud Ticktock Banneker’s Clock by Shana Keller. Benjamin Banneker (b. 1731) made drawings for and built the first American clock from wood. It worked for more than 50 years. The grade 2 curriculum directly features his work.

I think it shows half past 3. The sundial shows 3:30. I heard some very good guesses. The sundial shows 3:30 because the shadow is halfway between 3 and 4. We know that 3:30 is the same as half past 3. Transition to the next segment by framing the work. The shadow on the sundial is like the hour hand on a clock. Today, we will look carefully at the hour hand on a clock and see how it moves to tell time. Copyright © Great Minds PBC

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10 1 ▸ M6 ▸ TC ▸ Lesson 15 10

Learn Hour Hand

EUREKA MATH2

30 10

Students analyze the movement of the hour hand as time elapses. Show 3:30 on the analog clock only with the digital interactive clock. What time is it? 3:30 or half past 3 Point to the hour hand. What do you notice about the hour hand? It is halfway between the 3 and the 4, just like the shadow on the sundial. Yes, when the minute hand points straight down, it is 30 minutes, or half past, the hour. The hour hand is showing it is half past 3 too as it is half-way between the 3 and the 4. Where do you think the hour hand will be at 4 o’clock? Maybe it will point right to the 4. Show 4:00.

Promoting Mathematical Practice Students look for and make use of structure when they work to determine the time shown on the clock by using only the hour hand. Because it may be harder to remember that when the minute hand points to 6 it is half past, students must use their understanding of the structure of halves. Students now have a technical understanding of a half as 1 of 2 equal shares, as well as their intuitive ideas about “the middle.” Some students may benefit from connecting these ideas to their understandings of clocks. Consider using this image to show them how the hour hand partitions the part of the clock between 3 and 4 into halves.

At 4:00 the hour hand points directly at 4 and the minute hand points to 12. Let’s try to tell time with just the hour hand, like the sundial. Watch the hour hand carefully, and say “Stop!” when it shows 4:30, or half past 4. Turn off the minute hand. Move the hour hand to show 4:30. Listen for students to say “Stop!” halfway between 4 and 5.

222

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 15

How do you know the time is half past 4, or 4:30? The hour hand is halfway between the 4 and the 5. The hour hand is half past the 4. Turn the minute hand back on. Just like the minute hand travels halfway around the clock, the hour hand travels halfway between two numbers. Show the following times and ask students to chorally state them: 5:00, 5:30, 9:00, 9:30. For each time, show it twice—without the minute hand and with the minute hand. Show 11:30 with the hour and minute hand to explore a common misconception. One person thinks this clock shows 11:30. Another person thinks it shows 12:30. Who is correct? How do you know? The hour hand is past the 11 but not at the 12, so it can’t be 12:30. The hour hand is halfway between 11 and 12. That means it’s half past 11. The hour hand has not gotten to 12, the next hour, yet. This clock shows 11:30.

Match: Time

EUREKA MATH2

Write the times your matches show.

Students read and match times in various formats to the hour and half hour. Help students recall the directions for the Match game they played in lesson 14.

4:30

half past 4

4:30

Name

Materials—S: Match: Time cards

4:30

1 ▸ M6 ▸ TC ▸ Lesson 15

: 145

223

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 15

Place six cards faceup. Place the rest of the cards in a pile and set them aside. Find two cards that match because they show the same time. Record the time on a digital clock on the recording sheet in the student book. Set aside the matching cards and replace them with two new cards faceup. Keep playing until you have found all the matches.

UDL: Action & Expression Support students in monitoring their own progress as they play. Provide questions to guide students’ self-monitoring and reflection:

Partner students and distribute materials. Have students turn to the recording sheet with the digital clocks in their book. Allow 6–7 minutes for play. As students play, circulate and help them notice the placement of the hour hand by asking:

• Which times or forms of time are still confusing to me? What can I do to help myself?

• What do you notice about the hour hand? How does it show o’clock? How does it show half past ?

• In what ways is it still hard for me to tell time?

224

10 EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 15 30

Land Debrief

5 min

Objective: Reason about the location of the hour hand to tell time. Show only the analog clock set to 8:30 with both hands. What time is it? 8:30 What is another way to say 8:30? Half past 8 Sam and Mel have different ways of seeing that the clock shows half past 8. Display Sam’s thinking, and then Mel’s thinking.

The minute hand is halfway around the circle.

The hour hand is halfway between the numbers.

Sam

Mel

225

1 ▸ M6 ▸ TC ▸ Lesson 15

EUREKA MATH2

Who do you agree with, Sam or Mel? Why? I agree with both of them. You can use either way to tell when it is half past. I agree with Sam. The minute hand shows half past 8 because it is halfway around the clock. I agree with Mel. The hour hand is halfway between 8 and 9. What are two ways to know the time is half past 8? The minute hand is halfway around the clock. The hour hand is halfway between the numbers 8 and 9. Discuss times in students’ daily schedule that begin or end at half past an hour. When those times occur, invite the class to notice where the minute and hour hands are on the clock.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

226

EUREKA MATH2 1 ▸ M6 ▸ TC ▸ Lesson 15

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 15

Name

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 15

3. Draw or write to show 8 o’clock.

1. Circle all clocks that show 11 o’clock.

11:00

11:30

4. Draw or write to show half past 8. 2. Circle all clocks that show half past 4.

4:00

4:30

147

148

PROBLEM SET

227

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 15

EUREKA MATH2

1 ▸ M6 ▸ TC ▸ Lesson 15

5. Draw lines to match the times.

3 o’clock

1 o’clock

1:00

half past 10

half past 1

228

2:30

PROBLEM SET

149

This page may be reproduced for classroom use only.

229

Name

Why?

1 half of the cake

Which piece is larger? Circle.

Write

Color 1 fourth.

Color 1 half.

Draw

Cut 1 cake into fourths.

Cut 1 cake into halves.

There are 2 small cakes.

Read

Module Assessment

1 fourth of the cake

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

This page may be reproduced for classroom use only.

230

5:30

Draw a line to match the 2 clocks that show 5:00.

5:00

2. Circle the 2 clocks that show half past 5.

5:50

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

This page may be reproduced for classroom use only.

231

sphere

• Has 2 triangle faces

• Does not roll and

4. Circle the shape that:

The shape is a

cube

triangular prism

• 4 sides the same length

• All square corners and

3. Draw a shape with:

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

This page may be reproduced for classroom use only.

232

Circle the shapes that made the composed shape.

How many blocks are in your composed shape?

Write the name of the composed shape.

5. Trace a composed shape.

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

Achievement Descriptors: Proficiency Indicators 1.Mod6.AD1 Tell time to the half hour, including using the term half past. Partially Proficient

Proficient

Highly Proficient

Tell time to the half hour, including using the term half past. Circle the clocks that show half past 4.

4:30

234

2:30

EUREKA MATH2 1 ▸ M6

Highly Proficient Identify equal side lengths for two-dimensional shapes. Circle the shape with 4 equal sides.

Circle the shape with all square faces.

235

EUREKA MATH2

1 ▸ M6

1.Mod6.AD3 Draw two-dimensional shapes that have certain defining attributes. Partially Proficient

Proficient

Sketch two-dimensional shapes based on a mental image.

Draw two-dimensional shapes with given defining attributes by using dot paper and/or a straightedge.

Draw a triangle.

Draw a shape with:

Highly Proficient

• 3 sides • 1 square corner

236

EUREKA MATH2 1 ▸ M6

1.Mod6.AD4 Compose two-dimensional and three-dimensional shapes to create a composite shape. Partially Proficient Identify the shapes that make a composite shape.

Proficient

Highly Proficient

Compose two-dimensional and three-dimensional shapes to create a composite shape, including creating new shapes from composite shapes. Draw another shape to compose a trapezoid. Draw a trapezoid to compose a hexagon.

Circle the shapes that make the composed shape.

237

EUREKA MATH2

1 ▸ M6

1.Mod6.AD5 Partition circles and rectangles into 2 or 4 equal shares and describe the shares by using the words halves,

fourths, or quarters.

Partially Proficient Identify when shapes have been partitioned into equal shares. Circle the shapes that show equal parts.

Proficient

Highly Proficient

Partition circles and rectangles into 2 or 4 equal shares, describe the shares by using the words halves, fourths, or quarters, and describe the whole as 2 or 4 of the equal shares. Draw to show fourths. Color 1 fourth.

238

EUREKA MATH2 1 ▸ M6

1.Mod6.AD6 Draw or write to show that decomposing the same whole into more equal shares creates smaller shares. Partially Proficient

Proficient

Compare the size of the shares when decomposing the same object into halves and fourths.

Draw or write to show that decomposing the same whole into more equal shares creates smaller shares.

Which circle shows bigger shares?

Draw to show halves.

Highly Proficient

If we drew fourths, would they be bigger or smaller? How do you know?

239

Observational Assessment Recording Sheet Grade 1 Module 6

Student Name

Part 1: Attributes of Shapes Achievement Descriptors 1.Mod6.AD1

Tell time to the half hour, including using the term half past.

1.Mod6.AD2

Identify the defining attributes of two-dimensional shapes and three-dimensional shapes.

1.Mod6.AD3

Draw two-dimensional shapes that have certain defining attributes.

1.Mod6.AD4

Compose two-dimensional and three-dimensional shapes to create a composite shape.

1.Mod6.AD5

Partition circles and rectangles into 2 or 4 equal shares and describe the shares by using the words halves, fourths, or quarters.

1.Mod6.AD6

Draw or write to show that decomposing the same whole into more equal shares creates smaller shares. PP Partially Proficient

Notes

240

Dates and Details of Observations

This page may be reproduced for classroom use only.

P Proficient

HP Highly Proficient

EUREKA MATH2 1 ▸ M6 ▸ Observational Assessment Recording Sheet

Module Achievement Descriptors by Lesson ● Focus content ○ Supplemental content Lesson Achievement Descriptor

Topic A 1

Topic B 5

Topic C 9

1.Mod6.AD1

● ●

1.Mod6.AD2

● ● ● ● ●

1.Mod6.AD3

●

1.Mod6.AD4 1.Mod6.AD5 1.Mod6.AD6

○

● ● ● ●

○ ● ● ●

○ ○ ●

This page may be reproduced for classroom use only.

241

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

Module Assessment 1.

EUREKA MATH2

1 ▸ M6 ▸ Module Assessment

Name

1 ▸ M6 ▸ Module Assessment

2. Circle the 2 clocks that show half past 5.

Read There are 2 small cakes. Cut 1 cake into halves. Cut 1 cake into fourths. Draw

5:00

Color 1 fourth. Write

1 half of the cake Why?

1 fourth of the cake

Because it is shared with only 2 people.

5:50

Draw a line to match the 2 clocks that show 5:00.

Which piece is larger? Circle.

Sample:

242

This page may be reproduced for classroom use only.

229

Color 1 half.

5:30

230

EUREKA MATH2 1 ▸ M6

EUREKA MATH2

1 ▸ M6 ▸ Module Assessment

3. Draw a shape with:

1 ▸ M6 ▸ Module Assessment

5. Trace a composed shape. Sample:

• All square corners and • 4 sides the same length Sample:

The shape is a

Write the name of the composed shape.

square

Trapezoid

. How many blocks are in your composed shape? This page may be reproduced for classroom use only.

This page may be reproduced for classroom use only.

4. Circle the shape that:

• Has 2 triangle faces sphere

231

cube

triangular prism

Circle the shapes that made the composed shape.

• Does not roll and

232

243

Terminology The following terms are critical to the work of grade 1 module 6 part 1. This resource groups terms into categories called New, Familiar, and Academic Verbs. The lessons in this module incorporate terminology with the expectation that students work toward applying it during discussions and in writing. Items in the New category are discipline-specific words that are introduced to students in this module. These items include the definition, description, or illustration as it is presented to students. At times, this resource also includes italicized language for teachers that expands on the wording used with students. Items in the Familiar category are discipline-specific words introduced in prior modules or in previous grade levels. Items in the Academic Verbs category are high-utility terms that are used across disciplines. These terms come from a list of academic verbs that the curriculum strategically introduces at this grade level.

New composed shape A composed shape is a shape that is made up of other shapes. For example, a rhombus made with two green triangle blocks is a composed shape. (Lesson 6) These are usually known as composite shapes. Since students have already been introduced to the word compose, they are called composed shapes in this lesson for ease of language.

244

fourth/fourths/fourth of A fourth is one of 4 equal parts. A shape that is partitioned into 4 equal parts is partitioned into fourths. One of 4 equal parts of a shape is 1 fourth of that shape. (Lesson 11) half/halves/half of A half is one of 2 equal parts. A shape that is partitioned into 2 equal parts is partitioned into halves. One of 2 equal parts of a shape is 1 half of that shape. (Lesson 11) half past The phrase half past is used to tell the time when the minute hand is halfway around the clock. Half past two is the same time as 2:30. (Lesson 14) parallel Two sides that are across from each other and never touch, even when we imagine them going far out past the shape, are parallel. (Lesson 2) partition When we cut or break something into parts, we partition it. For example, we can partition a shape into halves. (Lesson 10) Note that partitioning a shape does not mean the shape is in equal parts. A shape can be partitioned into equal parts or unequal parts.

EUREKA MATH2 1 ▸ M6

quarter/quarter of Quarter is another word for fourth. Quarter of and fourth of mean the same thing. (Lesson 12) rhombus A rhombus is a closed shape with 4 straight sides that are all the same length. (Lesson 2) square corner If a square fits perfectly in a shape’s corner, then that corner is called a square corner. (Lesson 2) trapezoid A trapezoid is a closed shape with 4 straight sides. At least 2 of the sides are parallel. (Lesson 2) In grade 3, students learn that a trapezoid has at least 1 pair of parallel sides, but it can also have 2 pairs of parallel sides. For example, students learn to recognize that a parallelogram is a kind of trapezoid. Grade 1 students are not expected to recognize this, and the examples of trapezoids they are given all have exactly 1 pair of parallel sides.

Familiar circle compose cone

cylinder equal flat shape hexagon hour hand length minute hand part pyramid rectangle rectangular prism solid shape sphere square triangle whole

Academic Verb sketch

cube

245

Math Past Telling Time Why do clocks show the numbers 1 through 12? When did people start telling time? How did original time-telling devices work? Show your students an analog clock or the demonstration clock. Ask them to think about ways the clock can be split into equal shares, such as halves or fourths. Share with students that the numbers on the clock can also be used to separate it into 12 equal parts. Why do we use the numbers 1 through 12 to tell time? Why don’t we use another range of numbers, such as the numbers 1 through 10? To answer that question, we need to go back to ancient Egypt. Ancient Egyptians constructed devices that could be used to divide the day into parts as early as around 3500 BCE. These devices, called obelisks, were tall columns built into the ground. Ancient Egyptians used the shadows cast by the obelisks to tell time. Obelisks did not have numbers or divisions of time. Instead, ancient Egyptians used the point when the shadow’s length was at its shortest to divide the day into morning and afternoon.

246

By around 1500 BCE, Egyptians developed more precise ways to keep time. Devices such as this one—the oldest known example of a sundial—were divided into segments. Ask students how many parts they see. What shape do they see as the whole? Explain that a rod was placed in the hole. Its shadow moved through the segments, indicating the hour. Consider making your own sundials! Why did ancient Egyptians use the numbers 1 through 12 to tell time? Nobody knows for sure, but there are many theories. Twelve may have been an important number for ancient Egyptians. Here are two theories to share with your class. 4

1 2 3

5 6

7 8 9

10 11 12

One theory is based on the way ancient Egyptians counted on their fingers. They used the joints on their fingers, touching their thumb to each joint as they counted, allowing them to count to 12 on one hand. Consider counting as a class on your fingers like the ancient Egyptians did.

Another theory is based on Egyptian knowledge of the moon. Ancient Egyptian astronomers kept track of years long before the sundial was invented. Ancient Egyptians would have known that there are 12 lunar cycles in a year.

EUREKA MATH2 1 ▸ M6

While a sundial divided the hours between sunrise and sunset into 12 parts, the length of an hour on a sundial varied as days got longer and shorter with the changing seasons. Most people told time this way until the thirteenth century.

For centuries, people divided a 24-hour day into a 12-hour day and a 12-hour night, as we do today. Other units of measurement have changed, but we still use hours. It turns out that 12 is an important number in human history in more ways than one!

247

Materials The following materials are needed to implement this module. The suggested quantities are based on a class of 24 students and one teacher. 1

100-bead demonstration rekenrek

Glue

Balls

Learn books

Centimeter cubes, set of 500

Pencils

Chart paper, tablet

Personal whiteboards

Computer with internet access

Personal whiteboard erasers

Craft sticks, 6 color, package of 1,000

Plastic pattern blocks sets, 0.5 cm

Crayons

Projection device

Demonstration clock

Scissors

Dry-erase markers

207

Sticky notes

Eureka Math2™ Numeral Cards decks

Teach book

Geometric solids with nets, set of 12

Visit http://eurmath.link/materials to learn more.

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Before This Module

Overview

Grade K Module 6

Part 2: Advancing Place Value, Addition, and Subtraction

Students count by ones and tens to tell how many within 100. They also write numbers from 0 to 20.

Grade 1 Modules 2, 3, 4 Students solve word problems by using the Read–Draw–Write process. They primarily use 5-group drawings. Their number sentences reflect how they solved the problem by using the drawing.

Grade 1 Module 5 Students use base-ten place value structure to read, write, and represent two-digit numbers. Students learn to think of 10 ones as 1 ten. Students use Level 3 strategies (make easier problems) to add tens, one-digit and two-digit numbers, and 2 two-digit numbers within 50.

Topic D Count and Represent Numbers Beyond 100 Students work with three-digit numbers from 100 to 120 in the following ways: counting, reading numerals, writing totals, and representing numbers. Students count 100 or more objects by making groups of tens and ones. They represent the same total by using different combinations of tens and ones and reason about why it is possible to compose numbers in different ways. To write the number that represents the total, students relate the way they say the number to its written form. For example, one hundred seventeen is written as 117. Students recognize that the representation showing a group of 100, a group of 10, and 7 ones matches the numeral. They also read and write numbers greater than 100 by using patterns when numbers are presented in horizontal 17 and vertical sequences. EUREKA MATH2

Name

Write the missing numbers.

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1 ▸ M6 ▸ TD ▸ Lesson 17

101

111

102

112

103

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Topic E

After This Module

Deepening Problem Solving In topic E, students represent and solve all of the K–2 problem types. They make sense of word problems by drawing and labeling a tape diagram. Drawing and analyzing the resulting tape diagram clarifies the relationships in the problem. This helps students identify the meaning of the unknown and write an addition or subtraction equation to solve. Topic E also includes nonroutine problems with many different solution paths.

Grade 2 Module 1 Part 2 Students use a variety of tools to count by ones, tens, and hundreds within 1,000. Students use place value to make use of benchmark numbers, such as 20 or 200, to add, subtract, and compare.

Grade 2 Module 2

Topic F

Students use Level 3 strategies to add numbers up to three digits within 200 and relate them to a written recording.

Extending Addition to 100 Students add 2 two-digit numbers that have sums within 100. They use models such as ten-sticks and cubes, drawings, and number bonds. They make easier problems by decomposing one or both addends and combining the remaining parts. Students recognize that when composing the parts, it is sometimes necessary to compose a ten. They also recognize that when they have 10 tens, the total is 100. Students show how they made an easier problem by using a written method and through explaining their work.

Students use the Read–Draw–Write process and tape diagrams to solve two-step word problems.

Making Easier Two-Digit Addition Problems

36 + 49 30 6

36 + 49

40 9

35 1

30 + 40 = 70 6 + 9 = 15

36 + 40 = 76

49 + 1 = 50

70 + 15 = 85

76 + 9 = 85

50 + 35 = 85

• Add like units (tens with tens and ones with ones). • Add tens first. • Make the next ten.

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Why Part 2: Advancing Place Value, Addition, and Subtraction Which new word problem types, or addition and subtraction situations, are used in this module? Students work with all the problem types in this module. Listed below are the problem types students are introduced to for the first time in grade 1. • Add to with start unknown: The part that represents the add to action and the total are given. The unknown is the starting part. Kit has some dollars. She gets 7 more dollars for helping her mom. Now she has 15 dollars. How many dollars did Kit have to start? (Lesson 22) • Take from with start unknown: The part that represents the take from action and the part remaining are given. The unknown is the total at the start. Baz has some dollars. He spends 10 dollars. He still has 2 dollars left. How many dollars did Baz have to start? (Lesson 22) • Compare with longer length unknown (shorter suggests wrong operation): The shorter length and the difference are known, but the longer length is unknown. The word shorter incorrectly suggests subtracting the difference from the smaller length. Imani’s shoe is 11 paper clips long. Imani’s shoe is 6 paper clips shorter than Kioko’s shoe. How many paper clips long is Kioko’s shoe? (Lesson 24) • Compare with shorter length unknown (longer suggests wrong operation): The longer length and the difference are known, but the shorter length is unknown. The word longer incorrectly suggests adding the difference to the longer quantity. Kioko’s book is 13 paper clips long. Kioko’s book is 4 paper clips longer than Imani’s book. How many paper clips long is Imani’s book? (Lesson 24)

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How are the grade 1 problem types represented by using tape diagrams?

Add to

Result Unknown Val gets 8 points. Then she gets 7 points. How many points does she have?

Change Unknown Jade has 12 tickets. She gets some more tickets. Now she has 20 tickets. How many tickets did she get?

? 8

Take From

8+7=? 20 ?

19 + ? = 20 or 20 - 19 = ?

Put Together/ Take Apart

? 12

12 + 8 = ?

Tam plays for 12 minutes. Max plays for 4 minutes. How many more minutes does Tam play than Max plays?

4 + ? = 12 or 12 - ? = 4

Val hit 3 balloons. She got 19 points. What points were on the balloons?

4 ?

Tam has 9 points. Baz has some points. They have 15 points in all. How many points does Baz have?

4 ?

15 9

9 + ? = 15 or 15 - 9 = ?

Smaller/Shorter Unknown 2

Kit plays for 10 minutes. Ben plays for 4 fewer minutes than Kit plays. How long does Ben play?

10 ?

8+2=?

Vals’s hand is 6 cubes long. Val’s hand is 2 cubes shorter than Mom’s hand. How long is Mom’s hand?

6+2=?

10 - 4 = ? or ? + 4 = 10 2

(shorter suggests wrong operation)

Addend Unknown 19

Jon plays for 8 minutes. Deb plays for 2 more minutes than Jon plays. How long does Deb play?

? - 10 = 2 or 10 + 2 = ?

Bigger/Longer Unknown 12

Baz has some dollars. He spends 10 dollars. He has 2 dollars left. How many dollars did he have at first?

19 = ? + ? + ?

4 + ? = 12 or 12 - ? = 4 Math takes 12 minutes. Art takes 4 minutes. How many fewer minutes does art take than math takes?

Zan has 15 points. He uses some points. Now he has 8 points left. How many points did he use?

? + 7 = 15 or 15 - 7 = ?

Addends Unknown

Difference Unknown

Compare

? + 8 = 15 or 15 - 8 = ?

Total Unknown

Kit has some dollars. She gets 7 more dollars. Now she has 15 dollars. How many dollars did she start with?

12 + ? = 20 or 20 - 12 = ?

Baz has 20 points. He uses 19 points. How many points does he have left?

Max has 12 tickets. Kat has 8 tickets. How many tickets do they have in all?

Start Unknown

6 ?

(longer suggests wrong operation)

Val’s hand is 6 cubes long. Val’s hand is 2 cubes longer than her friend’s hand. How long is her friend’s hand?

6-2=?

6 ? 2

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Achievement Descriptors: Overview Part 2: Advancing Place Value, Addition, and Subtraction Achievement Descriptors (ADs) are standards-aligned descriptions that detail what students should know and be able to do based on the instruction. ADs are written by using portions of various standards to form a clear, concise description of the work covered in each module. Each module has its own set of ADs, and the number of ADs varies by module. Taken together, the sets of module-level ADs describe what students should accomplish by the end of the year.

Observational Assessment Recording Sheet Student Name

Grade 1 Module 6

Part 2: Advancing Place Value, Addition, and Subtraction Achievement Descriptors

Dates and Details of Observations

1.Mod6.AD7

Represent and solve word problems within 20 involving all addition and subtraction problem types by using drawings and an equation with a symbol for the unknown.

1.Mod6.AD8

Represent a set of up to 120 objects with a written numeral by composing tens.

1.Mod6.AD9

Represent three-digit numbers within 120 as tens and ones.

1.Mod6.AD10

Write missing numbers in a sequence within 120.

1.Mod6.AD11

Add a two-digit number and a one-digit number that have a sum within 100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

1.Mod6.AD12

Add 2 two-digit numbers that have a sum within 100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations. PP Partially Proficient

Notes

P Proficient

HP Highly Proficient

ADs and their proficiency indicators support teachers with interpreting student work on • informal classroom observations (recording sheet provided in the module resources), • data from other lesson-embedded formative assessments,

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This page may be reproduced for classroom use only.

• Exit Tickets, • Topic Tickets, and • Module Assessments. This module contains the six ADs listed. 1.Mod6.AD7

1.Mod6.AD8

1.Mod6.AD9

Represent and solve word problems within 20 involving all addition and subtraction problem types by using drawings and an equation with a symbol for the unknown.

Represent a set of up to 120 objects with a written numeral by composing tens.

Represent three-digit numbers within 120 as tens and ones.

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1.Mod6.AD10

1.Mod6.AD11

1.Mod6.AD12

Write missing numbers in a sequence within 120.

Add a two-digit number and a onedigit number that have a sum within 100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations.

The first page of each lesson identifies the ADs aligned with that lesson. Each AD may have up to three indicators, each aligned to a proficiency category (i.e., Partially Proficient, Proficient, Highly Proficient). While every AD has an indicator to describe Proficient performance, only select ADs have an indicator for Partially Proficient and/or Highly Proficient performance. An example of one of these ADs, along with its proficiency indicators, is shown here for reference. The complete set of this module’s ADs with proficiency indicators can be found in the Achievement Descriptors: Proficiency Indicators resource. ADs have the following parts: • AD Code: The code indicates the grade level and the module number and then lists the ADs in no particular order. For example, the first AD for grade 1 module 6 part 2 is coded as 1.Mod6.AD7. • AD Language: The language is crafted from standards and concisely describes what will be assessed. • AD Indicators: The indicators describe the precise expectations of the AD for the given proficiency category.

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2 AD Code EUREKA MATHGrade.Module.AD#

AD Language

1 ▸ M6

1.Mod6.AD11 Add a two-digit number and a one-digit number that have a sum within 100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations. Partially Proficient

Proficient

Add a two-digit number and a one-digit number that have a sum within 100 when composing a ten is not required and relate the strategy used to a written method.

Add a two-digit number and a one-digit number that have a sum within 100 when composing a ten is required, relate the strategy used to a written method, and explain the reasoning used.

Add. Show how you know.

72 + 6 = 70 2 70 + 2 + 6 = 78

I broke up 5 to make the next ten with 7 8. 8 0 and 3 is 83.

AD Indicators

Explain multiple strategies for adding a two-digit number and a one-digit number. Add. Show how you know.

27 + 5 =

78 + 5 = 80

Highly Proficient

3 2

I broke up 5 to make the next ten with 2 7. 3 0 and 2 is 32. Show another way to add.

27 + 5 =

20 7 7 + 5 = 12 20 + 1 2 = 32 I added the ones first. 7 and 5 is 1 2. 20 and 1 2 is 32.

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Topic D Count and Represent Numbers Beyond 100 Topic D launches work with three-digit numbers from 100 to 120. Students work with three-digit numbers in the following ways:

10 20 30 40 50 60 70 80 90 100

• Count on from any number. • Count a set and write a numeral to represent the total.

111

• Read and represent numerals.

110

112 113 114

• Write the number that comes 1 or 10 before and after a sequence of numbers. Students count a collection of more than 100 objects. They group the objects by tens and ones and record their work. This solidifies the idea that 10 tens is the same as 100. To write the number that represents the total, students relate the way they say the number to its written form (e.g., one hundred fourteen). Hide Zero cards provide a way for students to analyze and understand the relationship between how we say numbers and how we write them. This relationship is shown in the following examples: Our collection recording shows 10 tens, or 1 hundred, 1 more ten, and 4 ones. We nest our cards to show that there are 11 tens in 114.

Total

1 1 1 1

0 01 01 0

114

0 1 0 4 0 4 04 0 1 4

We nest our cards to show 11 tens and 4 ones together. This is how we write 114 (rather than 10014). We can pull our cards apart to show how the number sounds when we say it, one hundred fourteen. As students represent numbers, they show the same total by using different combinations of tens and ones. They reason about why there are different ways to compose the same total and discuss the idea that the representation showing a group of 100, a group of 10, and 7 ones matches the given numeral and is easily read as one hundred seventeen.

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Ways to Represent 117 1 hundred 1 ten 7 ones

11 tens 7 ones

10 tens 17 ones

9 tens 27 ones

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

Name

Students use their understanding of numbers greater than 100 to extend the counting sequence. They read and count numbers presented in horizontal and vertical sequences. They use patterns they notice or the number path to determine unknown numbers.

Write the missing numbers.

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101

111

102

112

103

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114

105

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Progression of Lessons Lesson 16 Count and record totals for collections greater than 100. 16 EUREKA

MATH2

1 ▸ M6 ▸ TD ▸ Lesson 16

Name

Lesson 17

Lesson 18

Read, write, and represent numbers greater than 100.

Count up and down across 100.

107, 108, 109, 110

How many do you think there are?

100

117 117 is composed of 100 and 17. 100 is 10 tens. 17 is 1 ten 7 ones.

70, 80, 90, 100, 110 I counted up by ones or by tens to find what number comes next. I counted down by ones or by tens to find what number comes before.

157

I counted by tens and then by ones. There are 103 pencils.

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Lesson 19 Write totals for collections larger than 100 shown in various groups of tens and ones.

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

tens

ones is the same as

111 .

I can compose tens by using ones. 11 tens 1 one makes 111 crayons. 190

LESSON

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13/04/21 1:44 AM

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LESSON 16

Count and record totals for collections greater than 100. Lesson at a Glance The class works together to notice, count, write, and read numbers greater than 100. Then partners organize, count, and record their collections of objects with totals greater than 100. The class shares and discusses student work. They model the totals greater than 100 with Hide Zero cards and read them. There is no Fluency component, Problem Set, or Exit Ticket for this lesson. Instead, use classroom observations and students’ written representations to analyze student thinking after the lesson.

Key Question • Where can we see the tens and ones when we write numbers that are greater than 100?

Achievement Descriptor 1.Mod6.AD8 Represent a set of up to 120 objects with a written numeral

by composing tens.

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 16

Agenda

Materials

Lesson Preparation

Launch

Teacher

• Copy or print the counting collection recording sheet to use for demonstration.

Learn

15 min

30 min

• Hide Zero® cards, demonstration set

• Organize, Count, and Record

• Chart paper

• Share, Compare, and Connect

• Marker

Land

15 min

• Class Totals chart • String • Paper clips (12)

Students • Counting collection (1 per student pair) • Organizing tools • Hide Zero® cards (1 set per student pair) • Index card (1 per student pair) • Marker (1 per student pair)

• Use small everyday objects to assemble at least one counting collection per student pair. Place each collection in a bag or box. Each collection should contain 100 to 120 objects. Assemble collections that have different digits in the tens place of the total (e.g., 1 hundred, 0 tens, some ones; 1 hundred, 1 ten, some ones; 1 hundred, 2 tens, 0 ones). Vary the number of objects in each collection based on the needs of your students. • Place tools students can choose from in a central location to organize their counting collections. Tools may include cups, plates, number paths, or 10-frames. • Consider providing large pieces of construction paper or trays for students to use as work mats. Work mats help students keep track of and organize the objects in their collections. They can also make students’ work portable. • In the lesson, the class makes a chart to write totals in different ways. Consider drawing a table and labeling columns on chart paper in advance. (See an example of a chart in Launch.) • Cut a string to hang horizontally that is long enough for students to attach their index cards. It is possible to substitute sticky notes for the string, index cards, and paper clips used in the lesson. If you choose to use sticky notes, have students place them on the board or on the wall.

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Launch

15 30

Materials—T: Hide Zero cards, chart paper, marker

Students count a collection with a total greater than 100 and learn how to write 15 the number. Display the quilt. Invite students to notice and wonder. Students may notice the quilt is composed of cubes with square faces. Explain that a 17-year-old named Adeline Harris collected signatures of famous people and used them to make this quilt. How might you count this collection of cubes efficiently? We can group them by tens and then count by tens. Let’s look at some ways to count larger collections. Display the four collections.

Teacher Note When Adeline Harris Sears was 17 in 1856, she made this quilt called Tumbling Blocks with Signatures. She sent small diamondshaped pieces of white silk worldwide to the most important people of her day, asking each person to sign one. The collection of autographs was then stitched together to compose cubes that make the quilt. Her quilt features the signatures of eight American presidents; scientists; religious and education leaders; Civil War heroes; authors and artists. Consider having students bring in and show things they like to collect, or share about these collections.

Invite students to think–pair–share about how the different collections are grouped. Three of them are in groups of tens and extra ones. The first collection is different because it is not grouped at all. Would you rather count a collection that is grouped or ungrouped? Why? It’s better to count a collection that is grouped. Then you can count by tens and ones. That’s faster, and you don’t make so many mistakes. Focus student attention on the pencil collection. Show the recording sheet. Write the title of the collection on the recording sheet and demonstrate estimating how many pencils are in the collection. 264

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 16

Display the collection.

Language Support

They grouped 10 pencils in each cup. Let’s count by tens and then by ones to find the total. (Gesture to the cups and then to the pencils, respectively.)

Consider using strategic, flexible grouping throughout the module.

10, … , 100, 101, 102, 103

• Pair students who have different levels of mathematical proficiency.

Show the recording sheet and write the total. Help students read the total aloud as one hundred three.

• Pair students who have different levels of English language proficiency.

Invite students to share how they could draw to represent the collection. Demonstrate making a math drawing to record the collection. EUREKA MATH2

How many groups of ten did we count and draw?

1 ▸ M6 ▸ TD ▸ Lesson 16

Name

10 tens How many do you think there are?

What is 10 tens?

• Join pairs of students to form small groups of four. As applicable, complement any of these groupings by pairing students who speak the same native language.

100 If students are unsure, then have them count by tens the math way to 100.

Teacher Note

Show the Hide Zero card for 100. How many ones did we count and draw? 3 ones

Total 157

Show the Hide Zero card for 3 next to the card for 100. 100 plus 3 equals 103. (Push the cards together.)

1 0 0

When reading a number such as 103 in standard form, be sure to say one hundred three instead of one hundred and three. In later grades, students read decimals and say the word and for the decimal point.

1 0 03

What happened when we pushed the cards together? A zero got covered up with a 3. Now, the 100 looks like 10. The 0 in the ones place is hidden by the 3 ones. But we can see that there are 10 tens, or 100, and 3 ones. Slide apart the Hide Zero cards to show 100 and 3. When we write 103, we write 10 tens and 3 ones. 10 tens is the same as 100. 3 more is 103. Copyright © Great Minds PBC

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Begin an anchor chart that shows numbers written in standard, expanded, and unit form. Use 103 to interactively complete the first row of the chart.

Promoting Mathematical Practice Students attend to precision when they write and say three-digit numbers. Students formally extend their understanding of place value to include the unit of hundreds in grade 2. However, they can still use place value concepts to precisely describe how to read and write three-digit numbers. For example, they can see that writing one hundred three as 130 or 1003 does not make sense because those numbers show 13 and 100 tens, respectively. Neither 13 tens nor 100 tens matches the collection. In contrast, writing the number as 103 matches the collection because it shows 10 tens.

Transition to the next segment by framing the work. Today, we will organize, count, and record the total of large collections. 15

Learn

30 15

Organize, Count, and Record Materials—S: Counting collection, organizing tools, Hide Zero cards

Students organize and count objects and then record the collection and the total. Briefly review the procedure for counting a collection and ask students to use Hide Zero cards to represent their totals for this collection. Partner students. Give each pair a set of Hide Zero cards and invite them to choose a collection, organizing tools, a work mat, and a workspace. Have partners open their student books to the counting collection recording page. 266

We will ... 1

Choose a collection.

Make a good guess.

Make a plan and count.

Record the collection.

1, 2, 3, 4, …

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 16

Circulate and notice how students organize, count, and record their collections. Expect to see a variety of ways to represent and label collections. Use any combination of the following questions to assess and advance student thinking: • What is the total of your collection? How do you know? • What does your drawing show? How can you label it? • How can you use numbers to show how you found the total? Find the Total When There Are 10 Tens EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 16

Name

circles circles How many do you think there are? How many do you think there are?

Find the Total When There Are 11 Tens EUREKA MATH2

16 94 94

If students finish early, consider having pairs do the following:

10 20 30 40 50 60 70 80 90 100

100 1

111

112

• Group their collection in another way, such as by 2s, 5s, or 20s.

110

113 114

• Write a number sentence to compare the total of two collections.

108

Total

Differentiation: Challenge

cubes cubes How many do you think there are? How many do you think there are?

10 10 10

Students may initially write numbers that are in the hundreds such as 103 as 1003. This signals that they are writing the number as they hear it. Hide Zero cards help students see that the number is composed of 100 plus 3 more ones and that it is written as 103.

1 ▸ M6 ▸ TD ▸ Lesson 16

Name

10 10 10 10 10 10 10

Teacher Note

108

Total 157

114

• Figure out how many more are needed to get to the next ten or hundred. Total

114 157

• Represent their collection in another way.

Select two work samples to share in the next segment. Choose samples from collections that have different digits in the tens place of the total (0, 1, or 2). The samples may show the same strategy, such as counting by tens and ones, but use different ways to record it.

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Share, Compare, and Connect Materials—T: Class Totals chart, Hide Zero cards

Students discuss ways to find the total of a collection with a total greater than 100. Gather the class to view and discuss the selected work samples. Invite partners to share their recordings and Hide Zero cards alongside their collection or a photograph of their collection. The following sample dialogue uses work that represents collections that have a 0 and 1, respectively, in the tens place of the total. The work uses the same strategy of counting by tens and ones but shows different ways of recording the thinking.

Teacher Note Some students may be able to say that 10 tens is 100 or that 11 tens is 110, but many will need repeated practice counting by tens and ones to establish that understanding. Although the sample dialogue incorporates place value understanding, counting to find the total is expected and valid, and it should be a significant part of the discussion.

Find the Total When There Are 10 Tens (Imani and Lucia’s Way) Tell us how you counted your collection. Our collection is a bag of counters. We made a guess that there are 79 of them. To check, we put them into groups of ten. We found the total is actually 108. How does your recording show your thinking? On our paper, we drew circles to show all the tens and ones. Then we counted by tens as much as we could and got to 100, so that’s labeled in the picture. We made a label to show that there are 8 ones.

EUREKA MATH2

Have the class chorally count by tens and ones to confirm the total.

1 ▸ M6 ▸ TD ▸ Lesson 16

Name

circles circles

This collection has 10 tens. What is 10 tens? 100 Have the pair show their Hide Zero card for 100. The collection also has 8 ones. Have the pair show their Hide Zero card for 8.

How many do you think there are? How many do you think there are?

1 0 0

10 10 10 10 10 10 10 10 10 10

1 0 08

100 1

268

108

Total

108 157

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 16

If the class is unsure, chorally count on by ones from 100 to 108. Slide the cards together to show 108. The total of this collection is one hundred eight. Use the total to interactively complete the next row of the anchor chart.

Find the Total When There Are 11 Tens (Edwin and Felipe’s Way) Tell us how you counted your collection. Our collection is cubes. We made a guess that there are 94 cubes. EUREKA MATH2

We put the cubes in sticks of 10 and had some extra ones. We counted the sticks by tens until we got to 100. Then we counted 10 and 4 more ones to get 14. 100 and 14 makes 114. How does your recording show your thinking? We drew lines to show the sticks of 10 and dots to show the extra ones. We wrote down how we counted. 10, 20, 30, … , 114.

1 ▸ M6 ▸ TD ▸ Lesson 16

Name

cubes cubes How many do you think there are? How many do you think there are?

Teacher Note

94 94

10 20 30 40 50 60 70 80 90 100

111

112

The numbers in this sample recording represent how the students counted their collection, rather than the value of each stick or dot. In contrast, the previous pair’s recording shows circles that are labeled with their actual value as well as boxes and brackets that show the total of each part. Both are acceptable recordings.

110

113 114

How is Edwin and Felipe’s work the same as Imani and Lucia’s? They both drew tens and ones. They counted by tens and then by ones.

114

Total

114 157

If you use work that shows the running count or total, help avoid confusion by pointing out that feature of the work.

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How is Edwin and Felipe’s work different from Imani and Lucia’s? Edwin and Felipe drew sticks and dots instead of circles. Edwin and Felipe’s total is different. It has a 1 in the middle. Imani and Lucia labeled their circles with 10 and 1 to show the value of each one. Edwin and Felipe labeled their drawing differently. They labeled their sticks and dots with the numbers they said as they counted. Point to the tens and ones as the class counts chorally to confirm the total. Have the pair show their Hide Zero cards for 100, 10, and 4. 100 is 10 tens. One more ten is 11 tens. Place the 10 card on top of the zeros in 100. Now, we see 11 tens. 11 tens and 4 ones is 114. Place the 4 card on top of the zero so the cards show 114. How do we read this number? One hundred fourteen Slide apart the cards so students see 100 and 14 side by side.

1 1 1 1

0 01 01 0

0 1 0 4 0 4 04 0 1 4

We can also think of 114 as 100 and 14 more. Use the total to interactively complete the next row of the anchor chart.

Allow a couple of minutes for cleanup.

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15 EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 16 30

Land Debrief

15 min

UDL: Representation

Materials—T: String, paper clips; S: Index card, marker

Objective: Count and record totals for collections greater than 100. Hang a string in the room where students can reach it. They will hang their totals from it in numerical order. Have partners continue to work together. Distribute an index card and a marker to each pair. Ask partner A to use the marker to write the total of their collection. Tell partner A to write the number large enough so that it takes up the whole card. Have partner B practice reading the total aloud. Make sure students have written their totals correctly.

119

We are going to hang our totals in order on the string. This is the beginning. (Point to the left side of the string.) One at a time, invite pairs to bring their number to the string. Ask partner B to read the total aloud to the class. Then the pair can use a paperclip to hang the number where they think it should go on the string. Have them explain their placement and ask the class to agree or disagree. (Help students adjust the cards to make room for new cards.)

Consider emphasizing that the first two digits in each student number show how many tens there are by drawing a box around the digits.

Teacher Note Instead of string, index cards, and paper clips, students may write their numbers on sticky notes and place them on the board or bulletin board paper. Consider repeating this activity throughout the module. Write numbers on index cards for pairs or small groups. Consider placing some number cards on the string in advance to serve as benchmarks (e.g., 90, 100). Have students read each number aloud, place the number on the string, and explain their reasoning. Invite the class to agree or disagree and to justify their thinking.

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Once all the cards have been placed, have students think–pair–share about what they notice. Some numbers are missing. All the numbers start with 1 (or one hundred). Some numbers have zeros. Some numbers have 11 tens, but one number has 12 tens. Where can we see the tens and ones when we write numbers that are greater than 100? The first two digits show how many tens. The last digit shows how many ones.

272

LESSON 17

Read, write, and represent numbers greater than 100.

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

Name

Count. Write the total.

Lesson at a Glance Students make math drawings and use number bonds to represent numbers that are greater than 100. They show that the numbers have two parts: 100 and some more. Their drawing matches the way they hear the numbers being said, which helps them read the numbers accurately. Students also practice writing numbers to 120 by using the patterns in a number chart.

Key Question • What helps us read and write numbers that are greater than 100?

Achievement Descriptors 1.Mod6.AD8 Represent a set of up to 120 objects with a written

100 + 10 Total

numeral by composing tens. 1.Mod6.AD10 Write missing numbers in a sequence within 120.

110

163

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 17

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The 100 and Some More removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Read Numbers to 120 • Write Numbers to 120 • Problem Set

Land

10 min

• 100 and Some More removable (digital download)

Students • 100 and Some More removable (in the student book)

• Copy or print the 100 and Some More removable and the number chart from 91 to 120 to use for demonstration.

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Fluency

10 10

Whiteboard Exchange: Add Within 100 30 Students add a two-digit number to a one-digit number to build addition within 100. 10

Display the equation 25 + 2 = ____. Write the equation and find the total. Show how you know.

Teacher Note

25 + 2 = 27

Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the answer.

Students may choose to use a variety of strategies to solve and to show their work, including counting on, adding the ones first, or making the next ten. Models and representations could include equations, number bonds, or the arrow way. 25 + 5 = 20 + 5 + 5 = 30

45 + 6 =

65 + 8 =

45 + 6

5 1 50 + 1 = 51

Repeat the process with the following sequence:

45 + 2 = 47 35 + 3 = 38 55 + 3 = 58 25 + 5 = 30 45 + 5 = 50 45 + 6 = 51 65 + 8 = 73

Green Light, Red Light Students count by ones from a given number to build fluency counting within 120.

Teacher Note

Display the green and red dots with the numbers 97 and 100. On my signal, start counting by ones with the green light number. Stop at the red light number. Look at the numbers.

276

100

If more movement is desired, consider having students run in place, hop, or engage in another physical exercise while counting.

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 17

Think. Ready? Green light! 97, 98, 99, 100 Repeat the process with the following sequence:

100

103

110

113

117

120

119

116

109

106

Whiteboard Exchange: Model Numbers with Quick Tens and Ones Students model a multiple of 10 or a number less than 20, and then say the number using unit form to prepare for reading and writing numbers greater than 100. Display the number 20.

Teacher Note Although drawing 1 ten and 10 ones to represent the number 20 is mathematically correct, invite students to group the extra ones into another ten whenever possible.

Draw tens to show the number 20. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

2 tens

Display the answer. On my signal, say how many tens and how many ones. Ready? 2 tens

Teacher Note

Display the number in unit form. Repeat the process with the following sequence:

100

For the numbers 3, 5, and 9, ask students to draw ones to show the number. Likewise, for the teen numbers in the sequence, ask students to draw tens and ones.

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1 ▸ M6 ▸ TD ▸ Lesson 17 10

Launch

10 30

Students count a collection and reason about how the corresponding numeral represents the total. 10

Display the 109 stickers. Invite students to notice and wonder about the picture. These are Sakon’s stickers. Each strip has 10 stickers. Sakon gave 1 sticker to a friend. Invite students to think–pair–share about the number of stickers Sakon has. How many stickers does Sakon have? How do you know? 109; I counted by tens and then by ones. 10 tens is 100. 100 and 9 more is 109. Point to each strip and guide students to chorally count by tens to 100 and then by ones to 109. Record the total below the stickers. Continue to display the stickers and share the following math story. Sakon has 109 stickers. He has 9 more than he needs to fill his sticker book. How many stickers does Sakon need to fill his book?

Differentiation: Support

Partner students. Ask them to use their personal whiteboards to represent the problem and to solve it. When students finish, facilitate a class discussion. How many stickers does Sakon need to fill his book? How do you know? 100 stickers fill up the book. To figure it out, I drew 109 with 10 tens and 9 ones. I circled the 9 stickers he does not need.

278

100

Show 109 using the 100 and 9 Hide Zero cards. Show them apart, then slide them together to demonstrate that one hundred nine is written as 109, not 1009. Consider using Hide Zero cards to show other numbers in the lesson as well.

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 17

Retell the story by using the sticker image and a number bond to record the referents. Write 100. Sakon needs 100 stickers to fill his book. Write 9 to the right of 100. He has 9 extra stickers. How many stickers does Sakon have in total? 109 Make a number bond by drawing arms from 100 and 9 to the total, 109. Point to the 100 and then to the 9. 100 plus 9 equals one hundred nine. (Point to 109.) Transition to the next segment by framing the work. Today, we will show, read, and write numbers that are greater than 100. 10 10

Learn

30 10

Read Numbers to 120

Teacher Note

Materials—T/S: 100 and Some More removable

Students model and read numbers between 100 and 120. Make sure students have the 100 and Some More removable in their whiteboards. Display the number 117.

Baz

117

There are many ways to compose 117. For example, it can be composed of 100, 10, and 7; 110 and 7; or 50, 50, and 17. In this segment, showing 117 composed as 100 and 17 supports reading the number as 100 and some more ones.

279

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1 ▸ M6 ▸ TD ▸ Lesson 17

Baz has this many stickers. (Point to 117.)

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17 ▸ 100 and Some More

Draw the number as 100 and some more.

Let’s draw to show this number.

Fill in the number bond.

Use the 100 and Some More removable. Have students follow along as you guide them to show 117 by drawing 10 tens and 1 ten 7 ones. Count aloud by tens and then ones as you draw.

100

What is 10 tens? (Point to the drawing.) 100 Point to the 100 as a part in the number bond. What is 1 ten 7 ones? (Point to the drawing.) 17

161

Write 17 as a part of the number bond under the drawing of 1 ten 7 ones. Write 117 as the total in the number bond. Reinforce the idea that 117 is composed of 100 and some more ones by pointing to each part in the number bond as you say it. Promoting Mathematical Practice

One hundred seventeen Point to the total and ask students to read the number. How many stickers does Baz have?

115

110

101

120

106

111

117 How many tens are in 117? How many extra ones are there? (Refer to the drawing.) 11 tens 7 ones Display all six additional sticker collection totals. Partner students and invite them to choose one total to represent with a drawing and a number bond. Give students 3 or 4 minutes to work. Then invite pairs to share.

280

Students look for and make use of structure when they read and write three-digit numbers by applying the idea that these numbers can be decomposed into 100 and some more. This is similar to students’ kindergarten experience with recognizing that the numbers 11 through 19 are composed of 10 ones and some extra ones. In both cases, although the new place value unit is not formally introduced (tens in kindergarten and hundreds in grade 1), students are exposed to the concept to help set a foundation for the year ahead.

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 17

Write Numbers to 120 Students read numbers and write the missing numbers in a sequence. Show the number chart from 91 to 120 in the student book. Have the class read the numbers chorally from 91 to 97. Point to each number as students read it.

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

Name

What number comes next?

Write the missing numbers.

101

111

102

112

How do you know that 98 comes next?

103

113

I know because 98 comes after 97 when you count.

104

114

I know because 98 comes before 99. I know because I can see a pattern. All of the numbers in the first line have 9 in the tens place. The number in the ones place goes up by one. 8 is missing. Write 98. Have students continue to read the numbers chorally, stopping after 103. What number comes next? How do you know? 104 comes next. It comes after 103. 104 comes next because it comes before 105. 104 is next because it is 10 more than 94. How do we write 104? How do you know? 1, 0, 4; it is 10 tens and 4 ones. There is a pattern. The numbers in this line have 1, 0, and then the ones go up by 1. Write 104. Have students continue to count, stopping after 109.

105

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117

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109

119

100

110

120 163

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Differentiation: Challenge

Consider having students use the blank chart to write numbers in order starting at any number (100+) and going up as far as they can. They may choose to write the numbers vertically or horizontally. Encourage students to notice patterns. EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

Write numbers.

What number comes next? How do you know?

109

110

111

112

109

119

113

114

115

116

110

120

110 comes next. I know because 10 is after 9 when you count by ones.

117

118

119

120

121

122

123

I know because 110 is 10 more than 100.

111

121

112

122

113

123

114 115

How do we write 110? How do you know?

116 117

1, 1, 0. Write 1 for one hundred, then write 10 for ten.

118 164

LESSON

EM2_0106TE_D_L17_classwork_page_2_studentwork.indd 164

EM2_0106TE_D_L17_classwork_page_2_studentwork.indd 165

LESSON

165

18/02/21 10:10 PM

281

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1 ▸ M6 ▸ TD ▸ Lesson 17

100 has 10 tens. When we add 1 more to 109, we make a ten. Now we have 11 tens and no extra ones. Write 110. Continue the process, stopping to ask the same questions for 114 and 120. Point out that 120 has 12 tens.

UDL: Representation

Ask students to turn to the number chart in the student book. Have them count in a whisper starting at 91 and write in the missing numbers as they go.

Support students to help them understand the vertical organization of the chart. If students read the numbers horizontally, encourage them to think about whether that count sequence is correct. For example, after 91 comes 92, not 101.

Lead a class discussion about patterns students see in the chart. Consider emphasizing these relationships by highlighting the chart. Students may make the following observations: • Numbers 91–99 have 9 tens, 100–109 have 10 tens, 110–119 have 11 tens, and 120 has 12 tens. (Consider pointing out this pattern if students do not notice it.) • As you move down the columns, the numbers increase by 1. • As you move across the rows, the numbers increase by 10.

Provide visual support by drawing a heart at the bottom of the first column and a star at the top of the second column. Tell students to follow their heart and reach for the star. EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

Name

Write the missing numbers.

Problem Set Differentiate the set by selecting problems for students to finish independently within the shorter timeframe. Problems are organized from simple to complex. Directions may be read aloud.

EM2_0106TE_D_L17_classwork_studentwork_CE.indd 163

282

101

111

102

112

103

113

104

114

105

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106

116

107

117

108

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100

110

120 163

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10 EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 17 30

Land Debrief

5 min

Objective: Read, write, and represent numbers greater than 100. Display the numbers 102, 112, and 120, one at a time. Ask the class to read them aloud. Have students ready their whiteboards. Say the numbers 103 and 113, one at a time. Tell students to write the number on the white side of their whiteboard and to show red when they are ready. Hold up your whiteboard to show me your number. Provide quick feedback, such as “Yes,” or “Check the digit in the ones place.” What helps us read and write numbers that are greater than 100? It helps to think about the number as 100 and some more. Like 113 is 100 and 13 more. It can help you write if you make a number bond or a math drawing that shows the number. Then you know how many tens and ones the number has. You can write the number of tens and the number of ones together. Like 11 tens 3 ones makes 113. When we think about numbers as tens and ones, we can see how the parts come together to make the number. This can help us read, write, and understand numbers greater than 100.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

Math Past The numerals we use today were created and developed by mathematicians and astronomers in India and were later passed on to Europeans through translations of texts that were written during the Islamic Golden Age. Because of these two sources, they are called the Hindu-Arabic numerals today.

Students may find it interesting to consider ways in which our numbers are similar to and different from the other number systems they have studied, such as the Ancient Chinese and Mayan systems. Consider creating an extension to this lesson by referring to the Math Past Resource for a more in-depth discussion of number systems.

283

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

Name

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

2. Write the part or the total.

1. Write the missing numbers.

101

111

102

112

103

113

104

114

105

115

106

116

107

117

108

118

109

119

100

110

120

284

Total

102

100

Total

113 100

9 107

109

112

100 115

100

159

160

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 17

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 17

3. Draw or write to show 120. Sample:

100

4. Draw or write to show 120 in a new way.

120 100

PROBLEM SET

161

285

LESSON 18

Count up and down across 100.

EUREKA MATH2

1 ▸ M6 ▸ TD

Name

EUREKA MATH2

1 ▸ M6 ▸ TD

3. Count. Write the total.

1. Fill in the blanks.

97, 98, 99, 100 , 101 , 102, 103,

104, 105, 106 , 107, 108, 109, 110

2. Count.

Write the total.

Total

108

apples

4. Draw to show 112. Sample:

112 Total

110

100

fish

10 10 10 10 10

100

175

176

TO P I C T I C K E T

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 18

Lesson at a Glance Student pairs play a game to practice counting up and down the number path, starting at 100. Then they work with number sequences and count up and down by ones and tens. They read numbers, notice patterns, and determine which numbers come just before and just after a given number.

Key Question • How can we tell what number comes before or after a number in the count sequence?

Achievement Descriptor 1.Mod6.AD10 Write missing numbers in a sequence within 120.

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Number Path 80–120 has two sections that must be torn out of the student book, and then cut and taped together. Consider whether to assemble these materials in advance or to have students tear them out during the lesson.

Launch Learn

10 min 15 min

25 min

• Count by Ones • Compare Counts • Problem Set

Land

10 min

• None

Students • Spinner removable (1 per student pair, in the student book) • Paper clip (1 per student pair) • Centimeter cube • Number Path 80–120 (in the student book)

• The Spinner removables must be torn out of student books. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. • Gather 1 centimeter cube of one color and 1 centimeter cube of a second color for each student pair.

287

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18

Fluency

10 15

Whiteboard Exchange: Add Within 100 25 Students add a two-digit number to a one-digit number to build addition within 100. 10

Display the equation 32 + 6 = . Write the equation and find the total. Show how you know. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display the answer.

32 + 6 = 38

Repeat the process with the following sequence:

52 + 6 = 58 41 + 7 = 48 61 + 7 = 68 64 + 6 = 70 84 + 6 = 90 84 + 8 = 92 73 + 9 = 82

Green Light, Red Light Students count by ones from a given number to build fluency counting within 120. Display the green and red dots with the numbers 98 and 101. On my signal, start counting by ones with the green light number. Stop at the red light number. Look at the numbers. Think. Ready? Green light! 98, 99, 100, 101 288

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 18

Repeat the process with the following sequence:

103

106

108

111

113

116

112

109

102

Whiteboard Exchange: Take Out 100 Students decompose a number into 100 and another part to develop fluency with reading numbers greater than 100. After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

101 100

Display the number 101. Write this number on your whiteboard.

101

Draw a number bond and take out 100. Display the number bond with 100 as a part. Write the unknown part.

100 1

Display the completed number bond. Repeat the process with the following sequence:

102

104

109

110

111

112

100 2

100 4

100 9

100 10

100 11

100 12

289

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18 10

Launch

Materials—S: Spinner25 removable, paper clip, centimeter cubes, Number Path 80–120

Students count up10and down on the number path and reason about their distance from 100. Partner students to play Closest to 100. Assign each partner as partner A or partner B. Give each pair a Number Path 80–120, two different-color centimeter cubes, and a paper clip. Make sure each pair has one Spinner removable. Give the following directions:

Support students as they engage in playing the game. After giving the directions, have partners retell the steps to each other to confirm their understanding of them.

• Both partners place their cubes at 100 on the number path.

96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18 ▸ Spinner

• Partner A uses a pencil and the paper clip to make a spinner on the dot at the center of the removable and spins.

As they begin to play, consider guiding students’ first turn to help them remember the steps.

Closest to 100

• Partner A moves their cube up or down on the number path by the number of spaces shown on the spinner. A white spin counts down the number of spaces shown, and a green spin counts up the number of spaces shown.

-3

-1

-2 -4

Teacher Note

• Partner A reads the number they landed on out loud. • Partner B takes a turn. Have students play for 6 to 8 minutes. When time is up, the player whose cube is the closest to 100 wins.

UDL: Action & Expression

167

Display the number path with cubes.

96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

290

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 18

Look at the cubes on this number path. Which cube is closest to 100? How do you know? The red cube is closest. It’s only 3 hops away from 100. The blue cube is more hops away. Point to the red cube at 97 and use your finger to hop 3 spaces to 100. We hop up 3 from 97 to 100. Point to the blue cube at 109 and use your finger to hop 9 spaces to 100. We hop down 9 from 109 to get to 100. 3 hops is less than 9 hops, so the red cube is closer to 100. Tell students to set aside their number paths for use in the next segment. Then transition to the next segment by framing the work. Today, we will practice counting numbers by counting up and down around 100. 10 15

Learn

25 10

Differentiation: Support

Count by Ones Students count up and down by ones and discuss patterns in the count. Display the first counting sequence.

Consider having students follow along on their number path.

104, 105, 106, 107, 108, 109 Guide students to chorally count up by pointing to each number.

Differentiation: Challenge

Depending on the needs of your class, consider adjusting the sequences to include counting by twos or fives.

291

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18

Revoice student thinking and record the pattern with labeled hops, as shown.

104, 105, 106, 107, 108, 109 In this count, the numbers go up by 1. We are counting up by ones. (Point to 109.) What number comes next? 110 How do we write 110? 1, 1, 0 Record 110 as the next number in the sequence. Display the second counting sequence.

100, 101, 102, 103, 104 Start at 104 and guide students to chorally count down by pointing to each number. We counted down. What patterns do you notice? The numbers still go in order, but they go down by 1 each time. All of the numbers but 100 have 100 and some more. That one doesn’t have more. They all have 10 tens. The ones place counts down by ones. Revoice student thinking and record the pattern with labeled hops, as shown. In this count, the numbers go down by 1. We are counting down by ones. (Point to 100.) What number comes just before 100? 99 Record 99 as the next number in the sequence.

100, 101, 102, 103, 104 292

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 18

Display the third counting sequence.

109, 101, 111, 112, 113 Look carefully at these numbers. There is a mistake in the sequence. Invite students to think–pair–share about the mistake in the counting sequence. EUREKA MATH2

Name

After 109 comes 110, and 110 comes before 111.

The number 101 is after 109 in this count. But that’s not right. It should be 110 instead.

EM2_0106TE_D_L18_classwork_student_work 3_CE.indd 173

What is the mistake? Why is it wrong?

99, 100 , 101, 102, 103, 104 , 105, 106, 107, 108, 109

110 , 111, 112, 113, 114, 115 , 116 , 117, 118, 119, 120

Cross off 101 and write 110.

109, 101, 111, 112, 113 , 12, 22,

, 120

1 ▸ M6 ▸ TD ▸ Lesson 18

, 70, 80, 90,

Promoting Mathematical Practice

Compare Counts Students compare and discuss sequences that count by ones and by tens. Display two counting sequences.

107, 108, 109, 110 70, 80, 90, 100, 110 These are two ways to count to 110. How are they different? They start with different numbers.

173

Direct students’ attention to the counting by ones sequences in the student book (green shaded portion only). Invite partners to count and fill in the missing numbers. Students may use number paths if they need to. As time allows, have some students share their solutions and reasoning.

, 04/03/21 1:22 AM

Counting up or down can help us find a missing number or a mistake.

, 42, 52,

Students look for and make use of structure when they analyze the number sequences and determine a pattern and the numbers that belong at either end of the sequence. Showing these two sequences at once helps students pinpoint the structural differences between a sequence that shows counting by ones and a sequence that shows counting by tens.

293

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18

Not all of the numbers in the blue count have 10 tens, but all of the numbers in the green count do. The green numbers are counting by ones. The blue numbers count by tens. (Point to the green sequence.) What number comes after 110 in this count? How do you know? 111 comes next. I know it’s 111 because that’s 1 more than 110. If students are unsure, have them count to determine which numbers belong in the sequence. Draw an arrow from 110 and label it + 1. Then write 111. (Point to the green sequence.) What number comes just before 107 in this count? How do you know? 106 is next. It is 1 less than 107. We know by counting back by ones. Draw an arrow from 107 and label it – 1. Then write 106.

107, 108, 109, 110 70, 80, 90, 100, 110

Direct students’ attention to the blue sequence. Guide them to chorally count up by pointing to each number. (Point to the blue sequence.) What number comes after 110 in this count? How do you know? 120 comes next. This count goes by tens. 120 is 10 more than 110. Draw an arrow from 110 and label it + 10. Then write 120. (Point to the blue sequence.) What number comes just before 70 in this count? How do you know? 60 is next. It is 10 less than 70. We know by counting back by tens.

294

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 18

Draw an arrow from 70 and label it – 10. Then write 60.

99, 100 , 101, 102, 103, 104 , 105, 106, 107, 108, 109

EUREKA MATH2

Name

Direct students’ attention to the counting by tens sequences in the student book. Invite partners to count and fill in the missing numbers. Students may use number paths if they need to. As time allows, have some students share their solutions and reasoning.

110 , 111, 112, 113, 114, 115 , 116 , 117, 118, 119, 120

Problem Set Differentiate the10 set by selecting problems for students to finish independently within the shorter timeframe. Problems are organized from simple to complex.

2 , 12, 22, 32 , 42, 52, 62 , 72 50 , 60 , 70, 80, 90, 100 , 110 , 120

173

1 ▸ M6 ▸ TD ▸ Lesson 18

15 read aloud. Directions may be 25

Land Debrief

5 min

Objective: Count up and down across 100. Display the four students with their classroom numbers.

120

Share the following scenario.

110

100

These students are in the Kindness Club at school. This month they decide to do an act of kindness for the teacher in the classroom next to their own classroom. One student is in room 100, another is in room 120, and two students are in room 110. Teacher Note

Display the student in classroom 100. This student goes 1 classroom up to deliver a flower. What classroom number does the student deliver the flower to? 101 Write 101 on the door tag. Then display the student in classroom 120.

100 At another time of day, consider connecting to the scenario in Land by using the book Kindness Makes Us Strong by Sophie Beer as a read-aloud. It is a colorful and joyful story that honors friendship and kindness.

295

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18

This student goes 1 classroom down to deliver cookies. What classroom number does the student deliver the cookies to?

120

121

119 Write 119 on the door tag. Then display the children in classroom 110. (Point to the student on the right.) This student goes up 1 classroom to deliver a picture. What classroom number does the student deliver the picture to? 111 Write 111 on the door tag. (Point to the student on the left.) This student goes down 1 classroom to offer some help. What is the classroom number this student goes to? 109 Write 109 on the door tag. How can we tell what number comes before or after a number?

110

We can just count up or down to figure it out. We can look at our number path. We can use a pattern. If the digit in the ones place counts up by ones, then we know what comes next.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

296

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 18

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18

Name

1 ▸ M6 ▸ TD ▸ Lesson 18

EUREKA MATH2

3. Count by ones.

1. Count up.

Write the numbers.

108 , 109 , 110, 111 , 112 116 , 117 , 118, 119 , 120

Write the numbers.

87, 88, 89, 90 , 91 , 92 , 93 , 94 43, 53, 63, 73 , 83 , 93 , 103 , 113 107, 108, 109, 110 ,

111 , 112 , 113 , 114 50, 60, 70, 80 , 90 , 100 , 110 , 120

4. Count by tens.

2. Count down. Write the numbers. Write the numbers.

70 , 80 , 90, 100 , 110 75 , 85 , 95, 105 , 115

96 , 97 , 98 , 99 , 100 , 101, 102, 103 30 , 40 , 50 , 60 , 70 , 80, 90, 100

171

172

PROBLEM SET

297

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 18

5. Cross out the number that does not fit.

86, 87, 88, 89, 80

111, 112, 103, 113, 114, 115

6. How close is the number to 100? Show how you know.

99 +1

100

106 100

80, 90, 100 2 tens Sample: 102

6 100, 101, 102 2 ones

298

PROBLEM SET

173

LESSON 19

Write totals for collections larger than 100 shown in various groups of tens and ones. Lesson at a Glance Students look at different ways the same total is represented. They reason about how they know the total is the same even though the representations are different. The lesson leads students through exploratory discussion, guided practice, and a game that students play with a partner. There is no Exit Ticket for this lesson. Instead, use students’ recordings to analyze their work after the lesson.

Key Question • How can we tell if different representations show the same number?

Achievement Descriptors 1.Mod6.AD8 Represent a set of up to 120 objects with a written numeral

by composing tens. 1.Mod6.AD9 Represent three-digit numbers within 120 as tens and ones.

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 19

Agenda

Materials

Lesson Preparation

Fluency

Teacher

The set of Match: Collection cards must be torn out of student books and cut apart. Decide whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Write the Total • Match: Collections

• None

Students • Match: Collection cards (1 set per student pair, in the student book)

• Problem Set

Land

10 min

301

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

Fluency

10 10

Green Light, Red Light 30 Students count by ones from a given number to build fluency counting within 120. 10

Display the green and red dots with the numbers 99 and 102. On my signal, start counting by ones with the green light number. Stop at the red light number. Look at the numbers. Think. Ready? Green light!

99, 100, 101, 102 Repeat the process with the following sequence:

109

112

117

120

117

113

109

102 103

302

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 19

Write this number on your whiteboard.

103

Draw a number bond and take out 100. Display the number bond with 100 as a part. Write the unknown part.

100 3

Display the completed number bond. Repeat the process with the following sequence:

108

110

113

115

118

120

100 8

100 10

100 13

100 15

100 18

100 20

Whiteboard Exchange: Model Numbers with Quick Tens and Ones Students model then say a number using unit form to develop place value fluency with numbers greater than 100. Display the number 80.

Draw tens to show the number 80. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

8 tens

Display the answer. On my signal, say how many tens and how many ones. Ready? 8 tens Display the number in unit form.

Teacher Note

Repeat the process with the following sequence:

101

103

105

110

111

113

115

120

For the numbers that have a digit in the ones place, ask students to draw tens and ones.

303

1 ▸ M6 ▸ TD ▸ Lesson 19 10

Launch

EUREKA MATH2

10 30

Students self-select ways to find the total of a collection and share their thinking. 10

Display the 120 paper clips. Use the Math Chat routine to engage students in mathematical discourse. Point to a row of paper clips. This part of the collection is organized in lines of 10 paper clips. What are some ways we could count this collection? We could count by tens and then by ones. We might be able to make more tens. Or we can count on the group that’s not in a line by ones. Invite students to think–pair–share to find the total. Have students signal when they are ready. Invite three or four students with different ways of counting the paper clips to share their ideas. Ask questions to probe their strategies. Record their thinking under the total, as shown. There are 120 paper clips. I counted all of the paper clips. There are 120. I counted by tens and then I counted on by ones. I made 2 more tens from the loose ones. Then I counted by tens. The total is 120. I know that 10 tens is 100. These rows over here have 20. 100 and 20 more is 120. Transition to the next segment by framing the work. There are many ways to count and show a total. Today, we will count and write the total for more collections like this.

304

10 EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 19 10

Learn

30 10

Write the Total Students count a collection in which not all the tens are composed and write the total.

Differentiation: Support EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

Name

If students need support finding the total, ask them if they can compose any more tens. Consider having them use Hide Zero cards to represent the composed image. Then have them slide the cards together to show the total.

Tell students to turn to the pictures of bowling pins in their student book. How many groups of ten bowling pins do you see? 8

UDL: Representation

Guide students to write 8 tens in the sentence frame. How many extra pins, or ones, do you see? 25

tens

ones is the same as

189

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

Guide students to write 25 ones in the sentence frame. Then have students think–pair–share about the following question.

105 .

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13/04/21 1:44 AM

105; 10 tens is 100 and there are 5 ones.

190

tens

ones is the same as

EUREKA MATH2

LESSON

111 .

EM2_0106TE_D_L19_classwork_studentwork_CE.indd 190

The number of bowling pins did not change. We just grouped and counted them differently. Repeat the process with the crayons problem in the student book. Release responsibility to the students as appropriate. Copyright © Great Minds PBC

100

1 ▸ M6 ▸ TD ▸ Lesson 19

I thought about 25 as 2 tens 5 ones. 8 tens and 2 tens make 10 tens, or 100. Then I counted by ones to 105.

Why is this statement true?

111

11 tens 1 one

How many total bowling pins are there? How do you know?

Guide students to complete the sentence frame by writing the total. Read the completed statement aloud. Then have students think–pair–share about the following question.

Tear out the page with the crayons from the student book and post it on chart paper. Have groups of two to four students draw or write other ways to represent the total on the chart paper. Consider sharing the posters during a Gallery Walk.

13/04/21 1:44 AM

190

tens

LESSON

100 + 10 + 1 EM2_0106TE_D_L19_classwork_studentwork_CE.indd 190

ones is the same as

111 .

111 ones 13/04/21 1:44 AM

305

1 ▸ M6 ▸ TD ▸ Lesson 19

EUREKA MATH2

Match: Collections Materials—S: Match: Collection cards

Students count and match collections that have the same total. Invite students to play a variation on the Match card game. Give students the following directions: • Partners set out all eight cards with the pictures facing up. • Partners find two cards with the same total. They may write or draw on the cards. • Partners write the total they matched on a whiteboard and read it out loud. • When they find all four matches, the game is over. Partner students and distribute a set of Match: Collection cards to each pair. Circulate as students play and ask them to explain how they know that two cards match. Consider having students use the cards to play these games at other times of the day: • Choose any two cards, find the total of each, and write a comparison number sentence. • Find the total of one card, and then draw or write other ways to show the same total.

Problem Set

Promoting Mathematical Practice As students play the Match game, they have the opportunity to construct viable arguments and critique the reasoning of others. Listen for students to explain to their partners why they think two cards show the same total. If partners disagree about a pair of cards, encourage them to ask each other questions and explain their thinking until they reach a consensus.

Differentiate the set by selecting problems for students to finish independently within the shorter timeframe. Problems are organized from simple to complex. Directions may be read aloud.

306

10 EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 19 30

Land Debrief

10 min

Objective: Write totals for collections larger than 100 shown in various groups of tens and ones. Display the different representations of 110. Ask students to find the total of one or more of the representations. They may self-select which representation they want to use. Have a few students who chose different representations share their totals and thinking. Record 110 below the image. The pictures are different. How can we be sure they all show the same number, 110?

9 tens 20 ones

If you count the tens and ones in all the pictures, you always get 110. If I make as many groups of ten as I can, they all have 11 tens. That’s the same as 110. Engage students in the Which One Doesn’t Belong routine. Each picture shows a different way to represent 110. Your job is to find a reason one picture does not belong with the others. Allow quiet think time, and then have partners turn and talk. Invite students to explain their thinking. It is not necessary for the class to generate all of the possibilities. Ask questions that model precise language and help students to make connections. Encourage students to ask one another questions of their own.

307

1 ▸ M6 ▸ TD ▸ Lesson 19

EUREKA MATH2

Here are examples of possible student thinking: The 10-sticks don’t belong because that picture only shows tens. The others all have some ones. The dimes and pennies don’t belong because they’re money. 9 tens 20 ones doesn’t belong because it’s the only one with words. The counters don’t belong because that picture shows only the ones.

308

EUREKA MATH2 1 ▸ M6 ▸ TD ▸ Lesson 19

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

Name

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

2. Write the total. Samples: Show how you know.

1. Draw lines to match the totals.

5 tens 20 ones is the same

9 tens 14 ones

70 10

10 10 10 10 10 10 10 10 10

9 tens 29 ones is the same

8 tens 7 ones

119

10 10 10 10 10 10 10

7 tens 33 ones is the same

103

and

100 110 119 70

80 90 100 103

8 tens 10 ones 107 is the same as

187

188

ones.

PROBLEM SET

tens

309

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

EUREKA MATH2

1 ▸ M6 ▸ TD ▸ Lesson 19

3. Write a number greater than 99. Show it in more than one way.

100

Sample:

9 tens 10 ones

310

70 80 90 100

PROBLEM SET

189

Topic E Deepening Problem Solving In topic E, students represent and solve all grade 1 problem types, including add to and take from with start unknown problems. The class works together to read and reread word problems, making sense of them one “chunk” at a time by drawing and labeling a tape diagram. Like number bonds, tape diagrams can be used to show part–whole relationships. However, unlike number bonds, tape diagrams are proportional, and there is more variety in how they can be drawn and labeled. Their flexibility makes tape diagrams a versatile tool that students continue to use beyond the elementary years.

Solving a word problem relies on students’ ability to decontextualize and recontextualize information. At first, they decontextualize to reason about the relationships in a problem. Students engage in this reasoning through the process of drawing a tape diagram. Both the process of drawing it and the resulting tape diagram clarify how quantities are related and help students identify the meaning of the unknown. The unknown often represents a part or a total. However, in comparison situations, the unknown represents a quantity or the difference between quantities. Using their understanding of relationships and what the tape diagram shows, students select the appropriate operation. They write an addition or subtraction equation and use it to solve the problem. Shortcuts such as finding key words discourage students from making sense of the problem. Key words may trigger students to add or subtract (often incorrectly), rather than to strategically apply an operation. Consider the following compare with smaller unknown problem: Kioko’s book is 13 paper clips long. Kioko’s book is 4 paper clips longer than Imani’s book.

7 ? + 7 = 15 15 - 7 = ?

K I

13 ?

13 - 4 = ? ? + 4 = 13

How many paper clips long is Imani’s book?

312

EUREKA MATH2 1 ▸ M6 ▸ TE

The words long and longer may lead some students to incorrectly add 13 and 4. However, drawing a tape diagram to represent the problem clarifies that the longer length and the difference between the two quantities are known. The shorter length is unknown. Students may represent the problem by using addition or subtraction. Although using an addition equation with an unknown addend is a valid solution path, combining 13 and 4 does not answer the question. At the end of the problem-solving process, students recontextualize their solution by generating a statement that directly answers the question. Recontextualizing helps students confirm that their solution makes sense. Recontextualizing is particularly useful with problems, such as the compare with smaller unknown example, that use complex language structures. In addition to the grade 1 problem types, topic E also includes nonroutine problems. These problems have many different solution paths. Students self-select models to help them make sense of the problems and to persevere in solving them by using self-selected strategies. They use drawings, words, and numbers to explain and justify their thinking to peers.

313

EUREKA MATH2

1 ▸ M6 ▸ TE

Progression of Lessons 2 MATH20 1 ▸ M6 ▸EUREKA TE ▸ Lesson

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Lesson 20

Lesson 21

Lesson 22

Name

1 ▸ M6 ▸ TE ▸ Lesson 22

Represent and solve put together and take Readapart word problems.

Represent and solve add to and take Readfrom word problems.

Max has 12 tickets.

Jade has 12 tickets.

Represent and solve add to and take from with start unknown word problems. Read

Kit has 8 tickets.

She gets more tickets to go on a ride.

Kit has some dollars.

They need 20 tickets to go on the ride.

Now she has 20 tickets.

She gets 7 more dollars for helping her mom.

Can they ride?

How many tickets did she get?

Now she has 15 dollars.

Draw

Sample:

Draw

How many dollars did Kit have to start?

Sample:

? 12 8 I need to figure out how M many total K

12 + 8

Write

12 + 8 = 20 They have

tickets, so they

Draw

10 2 can

1012 +

Jade got ride.

= 20

Sample:

20 ?

I need to figure out a part. I need R T to find how many more tickets she gets. 20 – 12 = ?

tickets they have. 12 + 8 = ?

EM2_0106TE_E_L20_classwork_studentwork_V1.indd 195

314

12 + 8 = 20

Write tickets.

8 + 7 = 15 8

dollars to start.

203

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I need to figure out ? a part. 7 I need 7 10 to find how many dollars D Mshe started with. ? + 7 = 15

EUREKA MATH

214

L E S12/02/21 S O N9:08 PM

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EUREKA MATH2 1 ▸ M6 ▸ TE

Lesson 23

Lesson 24

EUREKA MATH2

Represent and solve comparison word problems. Read Kit plays for 10 minutes.

Reason with nonstandard measurement units. Time

EUREKA MATH2

Activity

1 ▸ M6 ▸ TE ▸ Lesson 24

Solve nonroutine problems.

1 ▸ M6 ▸ TE ▸ Lesson 24

I see 3 heads.

Read

4 minutes Val’s is66paper paper clips long.long. Val’shand hand is clips

Ben plays for 4 fewer minutes than Kit plays.

10 minutes Val’s hand is 2 paper clips longer than her

How long does Ben play? Draw

Lesson 25 (Optional)

1 ▸ M6 ▸ TE ▸ Lesson 23

Math

Val’s hand is 2 paper clips longer than her sister’s hand. sister’s hand.

12 minutes How long is her sister’s hand?

How long is her sister’s hand?

Sample:

I see 8 legs.

Draw 8 minutes

Draw

Horses and Chickens

6 minutes

I need to figure out the shorter 4 length of time, or how long Ben plays. 10 – 4 = ? Write

Val’s Writehand is longer. Her sister’s hand is 2 paper clips 6-2=? 6 – 2shorter. =4 Her sister’s hand is Write

6 + 4 = 10 Ben plays for

minutes.

PROBLEM SET

First, I drew what I knew. There are 3 heads. Then I drew 2 legs on 2 heads and 4 legs on 1 head to make 8 legs. That is 2 chickens and 1 horse.

paper clips long.

6–2=4

Her sister’s hand is

PROBLEM SET

229

paper clips long. PROBLEM SET

229

221

315

LESSON 20

Represent and solve put together and take apart word problems.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 20

Name

Read Mel catches two fish. How many points does she have?

30 4

Draw

Lesson at a Glance Students represent different problem types by drawing and labeling tape diagrams. They analyze the part–whole relationships the tapes show and write equations they use to solve the problems. There is no Problem Set in this lesson to give students sufficient time to work with the new model.

Key Question

• Why is a tape diagram helpful for solving problems?

Achievement Descriptor 1.Mod6.AD7 Represent and solve word problems within 20 involving

all addition and subtraction problem types by using drawings and an equation with a symbol for the unknown.

Sample:

Write

4+5=9 Mel has

points.

197

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 20

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Carnival Game removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 5 min

35 min

• Tape Diagrams • Total Unknown • Addend Unknown

Land

10 min

• Carnival Game removable (digital download)

Students • Carnival Game removable (in the student book)

• Copy or print the Carnival Game removable to use for demonstration. • Copy or print the word problem pages from the student book to use for demonstration.

317

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 20

Fluency

10 5

Choral Response: Subtract 10 35 Students say the difference to build fluency with mentally subtracting 10.

Display the equation 30 – 10 = . 10

What is 30 – 10? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

30 - 10 = 20

20 Display the answer. Repeat the process with the following sequence:

60 - 10 = 50

90 - 10 = 80

34 - 10 = 24

64 - 10 = 54

94 - 10 = 84

81 - 10 = 71

41 - 10 = 31

44 - 10 = 34

24 - 10 = 14

25 - 10 = 15

Whiteboard Exchange: Unknown Addend Students find the unknown addend in an equation to prepare for unknown parts in tape diagrams. Display the equation 8 + = 11. Write the equation and find the unknown addend. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. 318

8 + 3 = 11

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 20

Display the unknown addend. Repeat the process with the following sequence:

6 + 5 = 11

9 + 4 = 13

7 + 6 = 13

8 + 7 = 15

6 + 9 = 15

9 + 8 = 17

7 + 10 = 17

Whiteboard Exchange: Three Addends Students find the total of an expression to prepare for situations with two or more parts. Display the equation 6 + 5 + 2 = .

6 + 5 + 2 = 13

Write the equation and find the total. Show how you know. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Teacher Note Students may self-select ways to solve the problems and show their work. Validate all correct responses.

Display the total. Repeat the process with the following sequence:

8 + 5 + 4 = 17

2 + 9 + 3 = 14

3 + 8 + 4 = 15

5 + 4 + 7 = 16

6 + 3 + 6 = 15

319

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 20 10

Launch

35 Game removable Materials—T/S: Carnival

EUREKA MATH2

1 ▸ M6▸ TE ▸ Carnival Game

Students combine various addends to make given totals.

PRIZES

Make sure all students have the Carnival Game removable inside their personal whiteboards.

Show the game. Engage students by providing context. Tell students that this is a carnival game. Point to the fish. Players try to catch the fish. They get a different number of points for each fish they catch. The number of points they get is the number shown on the fish. Players add up the points to get a prize. Invite students to circle their favorite prize on their whiteboard. Provide time for students to add the points on different fish to figure out which fish they could catch to get their prize. Encourage students to erase their whiteboards and try new combinations if they need to. The chart shows possible combinations.

10 + 5 + 4 15 + 4 = 19

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Ask one or two students to show their work and to explain their thinking. Transition to the next segment by framing the work.

Teddy Bear

Doll

Robot

Soccer Ball

10 + 5 + 4 = 19

20 + 5 = 25

20 + 10 + 4 = 34 30 + 4 = 34

30 + 20 + 5 = 55

Today, we will represent and solve different kinds of problems.

320

10 EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 20 5

Learn

35 10

Tape Diagrams

Differentiation: Support

Students draw and label a tape diagram. Continue to show the game and have students erase their whiteboards. Cross off the fish that are worth 10, 4, and 5 points and have students do the same. Pretend we got these points. Let’s draw a new kind of picture to show our points.

Model drawing a tape diagram.

Support students with drawing their tape diagram by having them make it with cubes first. They should use different colors of cubes to represent each part. They can lay the cube stick on their whiteboard and label it as shown.

Watch how I draw to show the different points, or parts. Show each part by drawing a rectangle, or unit. Draw the parts one at a time, thinking aloud about how to make them proportional and labeling them with the points they represent. Draw the units end-to-end so they form a tape. Invite students to replicate the drawing on their whiteboard. This kind of drawing is called a tape diagram. Ask students to turn and talk about where they see each fish’s points represented in the tape diagram. The parts on the tape diagram are labeled. We also need to label the total. Watch how I add to my drawing to label the total. Starting from the edges of the tape diagram, draw arms that are angled toward each other. Have we found the total yet? No. We haven’t found the total yet. It is unknown. Watch how I add to my drawing to label the unknown.

UDL: Action & Expression At this point in their learning, students may not draw proportional parts in their diagrams. That is okay. Model proportionality to make students aware that it is a feature of tape diagrams. While drawing, use a think-aloud process about how to determine the size of each part. For example, say, 10 is more than 5, so I’ll make the part for 10 longer than the part for 5. Five and 4 are close, so I’ll make those parts almost the same length. Emphasize that erasing and redrawing are common, and model those practices too.

321

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 20

Write a question mark where the arms nearly meet. Then invite students to add arms and a question mark to their drawings. The question mark tells us what we don’t know yet. It helps us see the unknown in our drawing. Have students hold up their boards to show you their work. Provide feedback. Look for the presence of three connected units, the presence and accuracy of labels, and arms starting at the edges of the tape instead of coming up from the middle. At this point, do not comment on the proportionality of students’ drawings. Invite students to think–pair–share about how a tape diagram and a number bond are similar to each other. How are a tape diagram and a number bond the same? They both show the parts and the total. They both have arms that go from the parts to the total. They both use numbers to label things. Ask students to work on their own to find the total and to write a number sentence below the tape diagram (10 + 5 + 4 = 19). Invite them to share what prize they can get. Why did we add to find the total?

Teacher Note As students get comfortable with tape diagrams, there will be variety in how students draw them. For example, students may label the parts inside or outside of the tape, draw arms or brackets in different ways, or label the total below the tape (or even on the side of it, in the case of a comparison diagram) instead of above it. These variations are valid. The primary goal for drawing and labeling is to represent the problem accurately, clearly, and completely.

We combined the points to get a prize.

8 ?

Yes, we add the parts to find the total. What prize can we get with 19 points? A bear

Total Unknown Students represent and solve a put together with total unknown word problem. Tell students to turn to the tickets word problem in their student book. Invite students to imagine the action as you read the problem aloud. Ask students to retell the story to a partner. Let’s draw a tape diagram to represent this problem. Have the class chorally reread the first sentence. 322

Teacher Note Using the tape diagram to retell the problem helps students determine whether their picture represents the problem accurately and completely. They can use this strategy to check their own work or to check a partner’s work. Validate with students the practice of revising their drawings as they need to.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 20

What can we draw to show the 12 tickets?

EUREKA MATH2

We can make a rectangle and write 12 in it.

1 ▸ M6 ▸ TE ▸ Lesson 20

Name

Read

Draw a rectangle and label it 12 as students do the same. Chorally reread the second sentence.

Max has 12 tickets. Kit has 8 tickets. They need 20 tickets to go on the ride. Can they ride?

What can we add to our drawing to show Kit’s 8 tickets?

Draw

Sample:

We can draw another rectangle and write 8 in it.

12 + 8

Draw a shorter rectangle that is connected to the first and label it 8. Have students follow along. Chorally reread the question.

Write

12 + 8 = 20 They have

What do we need to figure out? We have to find how many total tickets they have.

Teacher Note

? 12

tickets, so they

10 2 can

ride.

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13/04/21 1:49 AM

The total number of tickets they have is unknown. How can we add to our drawing to show the unknown? We can draw arms from the tape diagram and write a question mark to label the total.

Drawing and analyzing a tape diagram helps students make sense of mathematical relationships. For example, the tape diagram clarifies that the parts are known, and the total is unknown. Understanding the part–whole relationship supports students in developing an equation that leads to a solution. For example, students see that the unknown total can be found by adding the two parts.

Model adding arms and a question mark as students follow along. Listen as I use our tape diagram to retell the problem. Think about whether the tape diagram shows the whole problem. This part shows Max’s 12 tickets. (Point to the unit of 12.)

Differentiation: Support

This part shows Kit’s 8 tickets. (Point to the unit of 8.) Putting the parts together shows us how many total tickets they have. (Gesture to the whole tape.) We need to find out how many tickets they have altogether. We don’t know the total yet. We wrote a question mark to label the unknown total. Does our tape diagram show everything in the problem clearly? Yes. Ask students to write an equation with a box for the unknown and to find the total.

As a rule of thumb when drawing tape diagrams, label only as much as you need to let the diagram clearly and completely represent the word problem. If students require support to relate the parts of the tape diagram to the referents in the problem, then they may need to use more labels. Have them use the initials M for Max and K for Kit to label the parts. They can write the initials below the corresponding parts.

323

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 20

Ask a student to share their work and then bring the class to consensus. Tell students to complete the statement to answer the question.

Addend Unknown Students represent and solve a take apart with addend unknown word problem. Have students turn to the ice cream word problem in their student book. Invite students to imagine the action as you read the problem aloud. Ask students to retell the story to a partner.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 20

Name

Read Max and Kit are in line for ice cream. They have 19 tickets in all. Max has 8 tickets. How many tickets does Kit have? Draw

Let’s draw a tape diagram to represent this problem.

Sample:

Have the class chorally reread the first sentence. Can we draw something? No, it is just telling us what they are doing. Maybe we can draw Max and Kit. Suggest reading on and have the class chorally reread the second sentence.

Write

19 – 8 = 11 or 8 + 11 = 19 Kit has

tickets.

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195

01/04/21 8:07 PM

What can we draw? We can make a rectangle and write 19 to label it. Draw a tape diagram. Invite students to think–pair–share about where the label should go on the diagram.

Teacher Note

Where should we put the label? Does it go inside the tape, or should we draw arms and label 19 above the tape? Why?

If students are ready for more independence, reduce the guidance in this lesson segment. After students read and reread the problem, use the following basic prompts:

In the problem, 19 is how many tickets there are total. I think we draw arms and write 19 above the whole tape.

• Can you draw something? What can you draw?

Draw the arms and label the total 19 as students do the same. Chorally reread the third sentence.

• What does your drawing show? • What do you need to figure out? • What equation can you write? • What sentence answers the question?

324

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 20

Have students think–pair–share about the following question. Think about how to show what we know about Max’s tickets in our drawing. Should we draw a new part on our tape diagram or draw a line to partition the tape diagram we already made? Why? I think we should draw a line to split the tape diagram we already have. Max has part of the total tickets, not extra tickets. I think we should partition the tape diagram. We know that 19 is the total. 8 is a part. Draw a line to partition the tape into two parts. Label one part 8 as students follow along. Chorally reread the question. What do we need to figure out, or what is unknown? We need to figure out how many tickets Kit has. What can we add to our drawing to show the unknown?

Promoting Mathematical Practice Students model with mathematics when they learn to use the tape diagram to represent word problems. Tape diagrams are similar to number bonds in that they can help students determine if the unknown is a part or the total. However, unlike number bonds, tape diagrams are proportional, which can help students make sense of the quantities in the problem and evaluate whether their answer makes sense.

We can make a question mark in the other part. We need to find what part of the total is Kit’s. Let’s draw a question mark in Kit’s part to show it’s unknown. Have students turn and talk to use the tape diagram to retell the word problem. What equation could we write to find the total? Why? 8 + = 19. We need to figure out what to add to 8 to get 19. 19 – 8 = . We need to subtract the part we know from the total. Validate both equations, and have students write the equation of their choice in their book. Ask them to find the unknown part. Ask a student to share their work and then bring the class to consensus. Tell students to complete the statement to answer the question.

325

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 20

Problem Set The student book includes one more word problem of each type from the lesson. Use these problems as time allows or save them for another time of day. Have students represent 10 and solve the problems in pairs or independently. They may or may not choose to draw a tape diagram. 5

Land Debrief

5 min

Objective: Represent and solve put together and take apart word problems.

PRIZES Language Support

Gather students and display the carnival game. Corey wants the robot as a prize. Corey already has 30 points. Display the tape diagram. What does the tape diagram show us?

It shows the total points Corey needs to get the robot. It shows that Corey already has 30 points. It shows that we need to figure out a part.

It may help students to remember the name of the model to think about why this type of picture is called a tape diagram. Consider relating the shape of the diagram to a piece of tape. You might use the imagery of putting smaller parts together to make a longer piece of tape (or cutting a piece of tape into parts) to help students understand different ways to draw and interpret tape diagrams.

Which fish should Corey catch? Why? The fish with 4 on it because 30 and 4 make 34. Corey could catch any fish and get enough points. It’s just that some fish will give him more than enough points.

326

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 20

Why is the tape diagram helpful for solving the problem? It shows us that the unknown is a part, not the total. It makes it easy to see that we can take 30 from 34 and find the small part left. It makes it easy to see that we need 30 and a little more to make 34.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

327

LESSON 21

Represent and solve add to and take from word problems.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Name

Read

PRIZES

Baz has 16 points. He gets the top. How many points does he have left? Draw

6 20

Lesson at a Glance Students represent different problem types by drawing and labeling tape diagrams. They analyze the part—whole relationships shown by the tapes and write equations they use to solve the problems. This lesson uses different types of word problems than those used in lesson 20.

Key Question 4

• How does drawing a tape diagram help us to tell whether we need to find a part or the total?

Achievement Descriptor 1.Mod6.AD7 Represent and solve word problems within 20 involving

all addition and subtraction problem types by using drawings and an equation with a symbol for the unknown.

Write

16 – 7 = 9 Baz has

points left. 209

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 21

Agenda

Materials

Lesson Preparation

Fluency

5 min

Teacher

Launch

15 min

• The Match: Word Problem cards must be torn out of student books and cut apart. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. Shuffle each set before distributing them.

Learn

30 min

• Add To with Change Unknown • Take From with Change Unknown • Problem Set

Land

10 min

• None

Students • Match: Word Problem cards (1 set per student pair, in the student book)

• Copy or print the word problems from the student book to use for demonstration.

329

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Fluency

5 15

Choral Response: Subtract 10 30 Students say the difference to build fluency with mentally subtracting 10.

Display the equation 40 – 10 = . 10

What is 40 – 10? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

40 - 10 = 30

30 Display the answer. Repeat the process with the following sequence:

70 - 10 = 60

65 - 10 = 55

85 - 10 = 75

57 - 10 = 47

22 - 10 = 12

17 - 10 = 7

12 - 10 = 2

21 - 10 = 11

27 - 10 = 17

Teacher Note

Whiteboard Exchange: Unknown Addend Students find the unknown addend in an equation to build addition and subtraction fluency within 20. Display the equation + 6 = 12.

6 + 6 = 12

Point out that we can add the addends in any order, so the unknown is the same in the equations + 6 = 12 and 6 + = 12.

Write the equation and find the unknown addend. 330

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 21

8 + 4 = 12

7 + 7 = 14

9 + 5 = 14

8 + 8 = 16

9 + 9 = 18

8 + 5 = 13

9 + 7 = 16

Launch

Materials—S: Match:30 Word Problem cards

Students match tape diagrams to result unknown word problems and write 10 an equation to solve them. Display the game. This carnival game is called Balloon Pop. When you pop a balloon, you get the points that are shown on that balloon. The prizes for the game are shown above the balloons. Under each prize is the number of points you need to win that prize.

PRIZES

Turn and talk: Which prize would you want? Which balloon or balloons would you pop to get it? Leave the game displayed as you introduce the matching activity.

Promoting Mathematical Practice

Students reason abstractly and quantitatively when they match each word problem to a tape diagram. Students need to correctly decontextualize the information in the problem to determine if the given numbers and the unknown are parts or the total. Consider asking the following questions: • What is unknown? Which tape diagram shows that? • How does the tape diagram you matched with this problem help you to retell the story?

331

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Pair students. Make sure each pair has a set of Match: Word Problem cards. Tell students to place the two word problem cards and the two tape diagram cards faceup in front of them.

Teacher Note Students may write an equation that reflects the situation, such as 15 – 8 = . Or, they may write a solution equation that reflects how they will solve the problem, such as 8 + = 15.

Work together to read the word problems. Match each word problem with a tape diagram. You will need to look at the Balloon Pop game to make the matches. For each match, write an equation that represents the problem. Then solve it. Zan has 15 points.

Val pops the red balloon.

He gets the penguin. How many points does he still have?

• How does the tape diagram match the word problem?

Then she pops the blue balloon. How many points does she have?

15 8

EUREKA MATH2

EM2_0106TE_E_L21_removable_match_cards_studentwork.indd 201

Display the matching word problems and tape diagrams one at a time. Invite students to share their work. Facilitate a class discussion by using the following questions:

201

• What sentence answers the question? How do you know?

24/03/21 3:04 PM

• What equation did you write? Why?

1 ▸ M6 ▸ TE ▸ Match Cards

• Is the unknown a part or the total? How do you know?

Language Support

Transition to the next segment by framing the work. Today, we will draw tape diagrams to help us solve more word problems. 5

Learn

30 10

Add To with Change Unknown Students use a tape diagram to write an equation and to find an unknown part. Have students turn to the roller coaster word problem in their student book. Invite students to imagine the action as you read the problem aloud. Ask students to retell the story to a partner. 332

Avoid having students underline or discuss “key words” such as more. Teaching students to look for key words discourages them from making sense of problems by representing what they know one segment of the problem at a time. Teaching students to look for key words creates the misconception that certain words require certain operations. It tends to result in students applying operations without reasoning about the relationships between the quantities. Instead, support students to make sense of the language and relationships in word problems by helping them to read, reread, draw, and revise.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 21

Let’s draw a tape diagram to represent this problem. Have the class chorally reread the first sentence. Can we draw something? What can we draw? We can draw a rectangle for Jade’s tickets. How should we label Jade’s tickets? We can write 12 inside the rectangle. Draw a part and label it as students follow along. Chorally reread the second sentence. Turn and talk: How can we add to our drawing to show that Jade gets some more tickets? Instead of drawing another tape diagram to show more tickets, we can add to the tape diagram we started. Draw another part connected to the first part. Point to the new part. How should we label this section that represents more tickets? We don’t know a number yet, so I think we can write a question mark.

EUREKA MATH2

Teacher Note

1 ▸ M6 ▸ TE ▸ Lesson 21

Name

Read Jade has 12 tickets. She gets more tickets to go on a ride. Now she has 20 tickets. How many tickets did she get? Draw

• Can you draw something? What can you draw?

Sample:

20 12 T

? R

• What does your drawing show? • What do you need to figure out?

Write

12 + Jade got

= 20

12 + 8 = 20

EM2_0106TE_E_L21_classwork_studentwork.indd 203

What can we add to our drawing to show that Jade has 20 tickets now? We can draw arms from the tape diagram and write 20. Model adding arms and labeling the total as students follow along. Chorally reread the question. Let’s look at what our tape diagram shows. Do we need to find a part or the total? We need to find a part. We have to figure out how many tickets Jade got.

• What equation can you write?

tickets.

Label the unknown part with a question mark as students do the same. Chorally reread the third sentence.

If students are ready for more independence, reduce the guidance in this lesson segment. After students read and reread the problem, use the following basic prompts:

• What sentence answers the question? 203

22/03/21 5:36 PM

Teacher Note The add to action in this problem implies the equation 12 + = 20. However, students may think flexibly about the part—whole relationship and choose to write an equation such as 20 – 12 = .

333

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

What equation could we write to solve the problem? How do you know? 12 + = 20. We have 12, and we’re adding some more to get 20. 20 – 12 = . We can take away the part we know from 20. That tells us the other part. Validate both equations, and have students write the equation of their choice in their book. Ask them to find the unknown part. Ask a student to share their work and then bring the class to consensus. Tell students to complete the statement to answer the question.

Take From with Change Unknown Students use a tape diagram to write an equation and to find an unknown part. Have students turn to the pirate ship word problem in their student book. Invite students to imagine the action as you read the problem aloud. Ask students to retell the story to a partner. Let’s draw a tape diagram to represent this problem.

Read

He uses some tickets to go on a ride. He has 8 tickets left. How many tickets did he use? Draw

Sample:

Can we draw something? What can we draw? Invite students to think–pair–share about how they should label Nate’s tickets. How should we label Nate’s tickets?

After rereading the first line of the problem, students may not realize that 16 represents the total. The process of drawing the tape diagram helps students make sense of the part—whole relationships. Based just on the first line, the class may suggest writing 16 inside the tape, thinking that it represents a part and not the whole.

Nate has 16 tickets.

Have the class chorally reread the first sentence. We can draw a rectangle and label it 16.

UDL: Action & Expression

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

? R

16 - 8 = 8

8 T

10 6

10 - 8 = 2 6+2=8

Write

16 Nate used 204

LESSON

=8 tickets.

I think 16 is how many there are altogether because later Nate uses some tickets. That means we can draw arms and label the total 16. EM2_0106TE_E_L21_classwork_studentwork.indd 204

Use students’ thinking to draw and label the diagram as they follow along. Chorally reread the second sentence.

22/03/21 5:36 PM

If this happens, start by drawing and labeling according to their suggestion. As students reread the next lines and the part—whole relationships become clear, think aloud to model using the new information to revise the diagram. Revision is an important skill to develop. Say, Nate uses some tickets. He has 8 tickets left. So, 16 must be the total tickets he starts with. I will move the 16 to the top of the diagram.

Have students turn and talk about how to add to the drawing to show that Nate uses some tickets. 334

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 21

Let’s partition the tape into two parts. One of the parts can represent the tickets Nate uses. Draw a line to partition the tape into two parts. Point to one part. Do we know how many tickets Nate uses? No. How should we label this part? We can label it by writing a question mark. Label one part with a question mark. Chorally reread the third sentence. How can we add to our drawing to show that Nate has 8 tickets left? We can label that other part 8. Label the other part 8. Chorally reread the question. Let’s look at what our tape diagram shows. Do we need to find a part or the total? We need to find a part. We need to figure out how many tickets Nate uses. What equation could we write to solve the problem? How do you know? 16 – = 8. We know he has 16, then he uses part of them. The part left is 8. 8 + = 16. We know that 8 tickets and some more make 16. Validate both equations, and have students write the equation of their choice in their book. Ask them to find the unknown part. Ask a student to share their work and then bring the class to consensus. Tell students to complete the statement to answer the question.

Teacher Note The take from action in this problem implies the equation 16 – 8 = , which matches the situation. However, students may think flexibly about the part—whole relationship and choose to write an equation such as 8 + = 16 that matches the way they will solve the problem.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions and word problems may be read aloud. Students may choose to draw tape diagrams or another representation to help them solve the problems. Copyright © Great Minds PBC

335

15 EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21 30

Land Debrief

5 min

Objective: Represent and solve add to and take from word problems. Gather students and display the game from Launch.

PRIZES

Pretend you popped the balloons worth 10 and 5 points. How many points do you have? 15 points Which prizes could you get?

I could get the dog, penguin, or tiger. They are all less than 15 points. Let’s pretend we want the horse. Display two tape diagrams. Invite students to think–pair–share about which diagram will help them to find how many more points they need to get the horse.

15 20

Which tape diagram helps us figure out how many more points we need to get the horse?

The one with 20 as the total and the question mark as the part will help us. Display the tape diagram that correctly represents the situation. How many more points do we need to get the horse? How do you know? We need 5 points. 15 and 5 more make 20. How does drawing a tape diagram help us to tell whether we need to find a part or the total? We can see that we are missing a part. It’s easy to see that 15 needs 5 more to get 20. 336

20 15 20

Teacher Note Variety in how students draw and label their tape diagrams is acceptable as long as their diagrams accurately, clearly, and completely represent the problem. Some samples within lessons, such as the samples in this segment, intentionally show variations to validate this flexibility. Consider occasionally using variations as you model with tape diagrams as well.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 21

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

337

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Name

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Read

PRIZES

Baz has 20 points. Read

PRIZES

He gets the skateboard.

Ben gets 9 points. Then he gets 3 points.

How many points does he have?

Sample:

Draw

6 20

Draw

Sample:

6 20

4 9

? 9

How many points does he have left?

20 3

Write

9 + 3 = 12 Ben has

Write

20 – 19 = 1

points. Baz has

338

203

204

PROBLEM SET

point left.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 21

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Read

PRIZES

Read

PRIZES

Wes has 20 points.

Tam has 9 points. She got some more points.

Now she has 15 points. How many more points did she get?

He uses some points for a prize.

6 20

Sample:

Draw

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

He has 5 points left.

Which prize did he get?

Sample:

Draw

20 ?

15 9

Write

9 + 6 = 15 Tam got

20 – 5 = 15

more points.

Wes used PROBLEM SET

205

206

PROBLEM SET

points to get the

339

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 21

Read

PRIZES

Val wins the skateboard. How did she get 19 points? Draw

Sample:

19 ?

Write

9 + 6 + 4 = 19 She hit

340

, and

. PROBLEM SET

207

LESSON 22

Represent and solve add to and take from with start unknown word problems.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Name

Read Peg got some points. Then she got 6 more points.

Lesson at a Glance Students are introduced to start unknown problem types. The quantity at the start, which is either a part or the total, is unknown. Students will first be guided through a concrete experience, and then they will work through representing word problems with tape diagrams and equations.

Now she has 11 points.

Key Question

How many points did she get at first?

• Why is a tape diagram helpful for solving problems?

Draw

Achievement Descriptor 1.Mod6.AD7 Represent and solve word problems within 20 involving

all addition and subtraction problem types by using drawings and an equation with a symbol for the unknown.

Write

5 + 6 = 11 Peg got

points at first.

217

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 22

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Count out 10 blue and 10 red teddy bear counters for use in the lesson.

Launch Learn

10 min 10 min

30 min

• Teddy bear counters (10 blue, 10 red) • Paper bag (or opaque box)

• Take From with Start Unknown

Students

• Add To with Start Unknown

• None

• Problem Set

Land

• Put the 10 blue teddy bear counters inside a paper bag or box. • Copy or print the word problems from the student book to use for demonstration.

10 min

343

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Fluency

10 10

Happy Counting by Ones from 100–120 Students visualize a30number line while counting aloud to build fluency counting within 120. 10

Invite students to participate in Happy Counting. Let’s count by ones. The first number you say is 100. Ready? Signal up or down accordingly for each count.

100 101 102 103 102 103 104 105 104 105 106 107 108 109 110 109 Continue counting by ones to 120. Change directions occasionally, emphasizing crossing over 110 and where students hesitate or count inaccurately.

Choral Response: Subtract in Unit and Standard Form Students subtract multiples of 10 in unit form and say the equation in standard form to build subtraction fluency within 80. Display 4 tens – 1 ten = . What is 4 tens – 1 ten? Raise your hand when you know.

4 tens - 1 ten =

3 tens

40 - 10 = 30

Wait until most students raise their hands, and then signal for students to respond. 3 tens Display the answer.

344

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 22

When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.) 4 tens – 1 ten = 3 tens Display the equation with the numbers in standard form. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.) 40 – 10 = 30 Repeat the process with the following sequence:

4 tens - 2 tens

5 tens - 2 tens

7 tens - 2 tens

7 tens - 5 tens

8 tens - 4 tens

9 tens - 6 tens

7 tens - 3 tens

Teacher Note Students may choose to use a variety of strategies to solve and show their work, including but not limited to making the next ten or adding tens and ones. Representations could include equations, number bonds, or place value drawings with quick tens and ones.

Whiteboard Exchange: Add Within 100 Students add 2 two-digit numbers to build addition within 100. Display the equation 25 + 12 = . Write the equation and find the total. Show how you know.

25 + 12 = 37

25 + 12 = 5 7

25 + 5 = 30 30 + 7 = 37

25 + 12 = 20 5 10 2

25 + 12 =

20 + 10 = 30 5 + 2 = 7 30 + 7 = 37

3 tens 7 ones

345

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

45 + 12 = 57 35 + 23 = 58 55 + 23 = 78 25 + 35 = 60 45 + 35 = 80

Launch

30 counters, paper bag Materials—T: Teddy bear

Students solve start unknown problems. 10 Get out the paper bag with 10 blue teddy bear counters inside. Present an add to with start unknown situation. Show the bag and tell students that there are teddy bear counters inside. Shake the bag to confirm this, but do not tell or show students how many counters there are. Show 4 red bears. Put the red bears in the bag.

Teacher Note Grade 1 introduces the start unknown problem type but students are not expected to become proficient with it. Students continue to work with start unknown problems in grade 2.

Now there are 14 bears in the bag. Before I added 4 bears, how many bears were in the bag? Have students think–pair–share to find the starting amount. Invite them to self-select strategies and tools such as a tape diagram, fingers, number sentences, or a number path. We know that 4 + _____ = 14. 14 is 10 and 4, so there were 10 bears to start. The total is 14 and one part is 4. 14 – 4 = 10. 346

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 22

Take all the bears out of the bag. Sort them by color and have the class count the 10 bears that were in the bag at the start. Out of students’ view, place 10 blue bears and 6 red bears in the paper bag. Present a take from with start unknown situation. Show the bag and shake to confirm that there are bears inside, but do not tell students or show them how many. As students watch, take the 6 red bears out of the bag and show them to students. Now there are 10 bears in the bag. Before I took out 6 bears, how many bears were in the bag? Repeat the process of having students think–pair–share to find the starting amount. We can see that one part of the bears is 6. You told us that the other part is 10. 6 + 10 = 16, so there were 16 bears to start. Take the 10 blue bears out of the bag. Place them with the 6 red bears and have students count the total to confirm their thinking. Transition to the next segment by framing the work. Today, we will solve more problems like these, where we don’t know how many there are at the start.

347

10 EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22 10

Learn

30 10

Take From with Start Unknown Students use a tape diagram to write an equation and find a total. Display the three items with price tags. Explain to students that the number on each tag is the cost, in dollars, of that item. Pretend you have 7 dollars. Invite students to think–pair–share about which items they could buy. Could you buy all three items? Why? No. 2 + 3 + 5 = 10. 10 dollars is more than 7 dollars.

Promoting Mathematical Practice

Confirm that the total is 10 dollars for all three items. Have students turn to the word problem about Baz in their student book. Invite students to imagine the action as you read the problem aloud. Ask students to retell the story to a partner. Have the class chorally reread the first sentence. Let’s draw a tape diagram to show Baz’s dollars.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Name

Read Baz has some dollars. He spends 10 dollars. He still has 2 dollars left. How many dollars did Baz have to start? Draw

We can’t label it yet. We need more information. Let’s read on. Chorally reread the second sentence.

? 10

Write

10 + 2 = 12 Baz had

We know that Baz spends some dollars. How can we show that on our drawing?

For example, on first read, students may try to use subtraction to solve this problem because Baz spends his dollars. The tape diagram highlights the fact that both parts are known and the total is unknown.

Sample:

Draw an unlabeled tape as students follow along.

EM2_0106TE_E_L22_classwork_studentwork.indd 213

Consider using the following prompt and asking the following questions:

dollars to start.

213

02/03/21 11:48 PM

We can draw a line to make a part and label the part 10. Draw a line to partition the tape into two parts. Label one part 10 as students follow along. Chorally reread the third sentence. 348

Students model with mathematics when they draw tape diagrams and write equations to represent and solve word problems. Tape diagrams help students make sense of the problem and decide on an equation or solution path by helping them see the part–total relationship in the problem.

• Use the tape diagram to retell the word problem. • What is unknown, a part or the total? • What equation could you write to find the total?

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 22

What can we add to our drawing? We can label the other part 2. Label the other part as students do the same. If the tape diagram is partitioned into equal parts, consider thinking aloud about proportionality. Model erasing the original partition and redrawing the line to make the part labeled 10 visually bigger. Chorally reread the question.

UDL: Action & Expression

What do we need to figure out, or what is unknown?

To show that Kit gets 7 more dollars, students may suggest drawing a line to partition the rectangle based on their work with Baz’s problem.

The total amount of money Baz had at first. What can we add to our drawing to show the unknown? We can draw arms from the tape diagram and label the whole thing with a question mark.

Although the language in the first line of each problem is the same, in Baz’s problem, the first rectangle students draw represents the whole. In Kit’s problem, the first rectangle students draw represents a part. Students may not yet realize that the unit they drew to show Kit’s dollars represents a part. Continuing to read and draw the problem will eventually help them uncover that.

Draw arms and label the total with a question mark as students do the same. Have students turn and talk to use the tape diagram to retell the word problem. Look at the tape diagram. What is unknown, a part or the total? The total is unknown. What equation could we write to find the total? Why?

If students suggest partitioning, compare the second line in each problem. Elaborate on the difference in the action to help students visualize it and reason about the relationships. Use a think-aloud process like the one below to help them understand how to draw the diagram.

10 + 2 = _____. We have to add the parts to get the total. Have students write an equation and find the total. Ask a student to share their work and then bring the class to consensus. Tell students to complete the statement to answer the question.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Read Kit has some dollars. She gets 7 more dollars for helping her mom.

In the first problem, Baz has some dollars. He spends some of the dollars he already has. We partitioned the dollars he already has to show that action.

Now she has 15 dollars.

Add To with Start Unknown

How many dollars did Kit have to start? Draw

Students use a tape diagram to write an equation and find an unknown part. Have students turn to the word problem about Kit in their student book. Invite students to imagine the action as you read the problem aloud. Ask students to retell the story to a partner. Copyright © Great Minds PBC

Sample:

In the second problem, Kit has some dollars. She gets some more dollars to go with the ones she has. We draw another rectangle, or unit, to show the action of getting new dollars.

Write

8 + 7 = 15 Kit had 214

LESSON

EM2_0106TE_E_L22_classwork_studentwork.indd 214

dollars to start.

02/03/21 11:48 PM

349

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Let’s draw a tape diagram to represent this problem. Have the class chorally reread the first sentence. What can we draw to show that Kit has some dollars? We can draw a rectangle for her dollars, but we can’t label it yet. Draw a rectangle as students follow along. Chorally reread the second sentence. Kit gets more dollars. What can we add to our drawing to show that? We can draw another part with 7. Draw a new part connected to the first part and label it 7. Have students follow along. Chorally reread the third sentence. Invite students to think about what the 15 represents. Is 15 all of the dollars or part of the dollars? It’s all of the dollars. There were some dollars and then 7 more. Now there are 15. What can we add to our drawing to show there are 15 dollars? We can draw arms and label the total 15. Model adding arms and labeling the total as students follow along. Chorally reread the question. What do we need to figure out? We need to figure out how many dollars Kit started with. Point to the part of the tape diagram that shows the dollars she started with. Students should point to the unlabeled part. How can we label the unknown on our drawing? We can write a question mark in the first part. Model labeling the unknown with a question mark as students follow along. Have students turn and talk to use the tape diagram to retell the word problem. What equation could we write to solve the problem? Why? _____ + 7 = 15. We have to find a part. We know that some dollars plus 7 dollars makes 15 dollars. 15 – 7 = _____. We can find a part by taking away the part we know from the total. 350

Differentiation: Support Students may overgeneralize the word more and the action of getting more dollars as they think about how to solve the problem. If students suggest adding the total and the known part, redirect them to the tape diagram. Ask students if they need to find a part or the total. Help students use the tape diagram to identify that the unknown is a part. Then ask them how they might find the unknown part. They may suggest a strategy such as counting on from the known part to the total and keeping track of how many. Encourage valid ideas and have them use those strategies to solve the problem. Model their thinking as an equation, such as 7 + 8 = 15.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 22

Have students write an equation and find the unknown part. Ask a student to share their work and then bring the class to consensus. Tell students to complete the statement to answer the question.

Students may choose to draw tape diagrams or another representation to help them solve the problems. 10

Land Debrief

5 min

Objective: Represent and solve add to and take from with start unknown word problems. Gather students and display the six items with tags.

351

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Pretend you have some dollars in your pocket. You buy a spinning top and a lollipop. How many dollars do you spend? 5 dollars After buying those items, you have 5 dollars left. Display the two tape diagrams. Invite students to think–pair–share about which tape diagram matches the story.

? 5

5 5

Which tape diagram matches the story? How can you tell? The one that has the total labeled with a question mark matches. The other one doesn’t match because if we spent 5 dollars and have 5 dollars left, then the total has to be more than 5 dollars. Display only the correct tape diagram. You spent 5 dollars and you still have 5 dollars left.

Invite students to think–pair–share about how much money they had at first. How much money was in your pocket at first? How do you know?

We had 10 dollars. We spent 5 dollars and we have 5 dollars left. Why is a tape diagram helpful for solving problems? We can see if we have to find a part or the total. That makes it easier to know how to write an equation and solve it.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

352

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 22

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Name

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Read Ren got some points.

Read Liv got some points.

Then she got 2 more points.

Draw

He got the robot.

How many points did he get at first?

Now she has 6 points. How many points did she get at first?

Then he got 4 more points.

Draw

Sample:

6 ?

Write

6 + 4 = 10

4+2=6 Liv got

Ren got

points at first. 213

214

PROBLEM SET

points at first.

353

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Read

Read Ned has some points.

Sam has some points. He uses 6 points to get the ball.

He has 9 points left.

He uses points to get the glasses. He has 10 points left.

How many points did he have to start? Draw

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 22

Draw

Write

? 10

Write

15 = 6 + 9

354

Sample:

How many points did he have to start?

Sample:

Sam had

12 = 2 + 10

points.

Ned had PROBLEM SET

215

216

PROBLEM SET

points.

LESSON 23

Represent and solve comparison word problems.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Name

Read

Lesson at a Glance Students work with two different types of comparison situations in this lesson. They learn to draw comparison tape diagrams to represent the problems. They analyze the relationships the diagrams show and write equations they use to solve the problems.

Dan plays for 8 minutes.

Key Question

Kit plays for 10 minutes. How many more minutes does Kit play than Dan plays?

• How can a tape diagram help us to compare?

Draw

Achievement Descriptor 1.Mod6.AD7 Represent and solve word problems within 20 involving

all addition and subtraction problem types by using drawings and an equation with a symbol for the unknown.

Write

8 + 2 = 10 Kit plays for

more minutes. 223

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 23

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Prepare sets of cubes with mixed colors.

Launch Learn

10 min 10 min

30 min

• Difference Unknown

• None

Students • Unifix® Cubes (20)

• Smaller Unknown • Problem Set

Land

10 min

357

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Fluency

10 10

Happy Counting by Ones from 100 to 120 Students visualize a30number line while counting aloud to build fluency counting within 120. 10

Invite students to participate in Happy Counting. Let’s count by ones. The first number you say is 107. Ready? Signal up or down accordingly for each count.

107 108 109 110 109 110

111

112

113

112

113

114

115

114

115

116

Continue counting by ones to 120. Change directions occasionally, emphasizing crossing over 110 and where students hesitate or count inaccurately.

Choral Response: Subtract in Unit and Standard Form Students subtract in unit form and say the equation in standard form to build subtraction fluency within 80. Display 5 ones – 3 ones = . What is 5 ones – 3 ones? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 2 ones

5 ones - 3 ones =

2 ones

5-3=2

Display the answer.

358

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 23

When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.) 5 ones – 3 ones = 2 ones Display the equation with the numbers in standard form. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.) 5–3=2 Repeat the process with the following sequence:

8 ones - 2 ones

7 ones - 4 ones

9 ones - 3 ones

9 ones - 4 ones

9 ones - 8 ones

9 ones - 9 ones

8 ones - 5 ones

Whiteboard Exchange: Add Within 100 Students add 2 two-digit numbers to build addition within 100. Display the equation 35 + 12 = . Write the equation and find the total. Show how you know. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Copyright © Great Minds PBC

35 + 12 = 47 359

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Display the answer. Repeat the process with the following sequence:

55 + 12 = 67 45 + 24 = 69 65 + 24 = 89 66 + 33 = 99 34 + 46 = 80

Launch

30 Materials—S: Unifix Cubes

Students compare10lengths of time of given activities. Display the chart of carnival activities. Explain that it is called a chart and that one side shows the activities at the carnival and the other side shows how many minutes each activity takes.

Activity

Time 6 minutes 3 minutes 5 minutes 4 minutes 1 minute 2 minutes

360

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 23

Invite students to share some activities on the chart they would like to do. Model drawing a tape diagram to show the total amount of time two to three activities would take (see samples). Consider having students follow along on their personal whiteboards.

Ferris Wheel and Fishing Game

Pirate Ship, Swings, and Roller Coaster

Swings and Slide

Distribute Unifix Cubes and partner students. Assign students as partner A or partner B. Partner A, make a stick of cubes to show how long it would take to go on the Ferris wheel, the swings, and the roller coaster. Partner B, make a stick of cubes to show how long it would take to go on the pirate ship and the slide. Have students give a silent signal when they are ready. Invite a partner A and a partner B to share the total minutes and their cubes. Make sure each partner A has a ten-stick and each partner B has a stick of 7 cubes. Who needs more time to finish their activities, partner A or partner B? How do you know? Partner A needs more time. 10 minutes is longer than 7 minutes. Display the sets of cubes organized in two ways. How should we organize our sticks to see how many more minutes partner A needs than partner B? Why? We should put one under the other so we can compare them. Let’s line them up to compare them. Put partner A’s cubes on top and partner B’s cubes below partner A’s. Display the cubes organized for comparison. Ask partners to organize their cubes the same way. Copyright © Great Minds PBC

361

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

How many more minutes does partner A need than partner B? How do you know? Partner A needs 3 more minutes. Partner A has 3 extra cubes. Transition to the next segment by framing the work. 10

Today, we will use a tape diagram to compare different totals. 10

Learn

30 10

Difference Unknown Students represent and solve a compare with difference unknown word problem. Display the word problem and read it aloud. Ask students to retell the story to a partner. Tell the class to ready their whiteboards. Let’s draw a tape diagram to represent this problem. Have the class chorally reread the first sentence.

Nate plays for 10 minutes. Max plays for 7 minutes. How many fewer minutes does Max play?

Can we draw something? What can we draw? We can draw a rectangle to show Nate’s 10 minutes. Draw a rectangle and label it 10 as students follow along. Chorally reread the second sentence. How can we add to our drawing to show Max’s minutes? We can draw another rectangle for Max’s minutes and label it 7. Nate plays for 10 minutes and Max plays for 7 minutes. Should Max’s rectangle be longer than Nate’s, shorter than Nate’s, or the same length as Nate’s? It should be shorter. Draw another rectangle connected to the first one and label it 7 as students follow along. Chorally reread the question. What do we need to figure out?

Teacher Note The sample dialogue in Learn includes a question about proportionality as students draw to represent each word problem. Proportional drawings are especially useful in comparison situations because they help students see two quantities in relation to each other. Model and expect students to draw reasonable approximations. Do not expect or require precision.

We have to figure out how much less time Max spends playing. 362

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 23

We have to compare Max’s minutes to Nate’s minutes. Invite students to think–pair–share about how to compare the numbers of minutes. How do we organize other things, like our cube sticks, to compare their length? We put one on top of the other or standing side by side. You have to line the things up on one end if you want to compare them. If we could see Nate’s minutes and Max’s minutes that way, it would help us to compare them. Let’s change our diagram to match how we compared the cubes before. Erase the unit that represents 7 and redraw it directly below the unit that represents 10. Think aloud about aligning the units on the left as you redraw.

Teacher Note

We can write N for Nate next to Nate’s rectangle. We can write M for Max next to Max’s rectangle.

Write initials to the left of each unit as students follow along. Chorally reread the problem.

Comparison situations tend to be challenging, so comparison tape diagrams usually use an initial to the left of each unit to support students with keeping track of the unit’s referent in the problem.

Does our tape diagram show the whole problem? No, it doesn’t show the unknown. Point to where you see the unknown in our tape diagram.

Promoting Mathematical Practice

Students should point to the space under 10 to the right of 7. Draw arms below the space that represents the unknown and label it with a question mark as students follow along. Tell students that we call this kind of picture a comparison tape diagram. What equation could we write to solve the problem?

Students look for and make use of structure when they rely on the tape diagram to determine how to solve comparison problems.

7 + _____ = 10 Students may also use 10 – _____ = 7 or 10 – 7 = _____. Have students think–pair–share about how each equation represents the problem. Tell students to write the equation of their choice and ask them to find the unknown.

Comparison problems can be difficult to analyze based on words alone. In fact, the language used in comparison problems can sometimes be misleading, causing students to add when they should subtract (and vice versa). By drawing the tape diagram, students can see how the quantities of the problem are related and determine a solution path to find the unknown quantity.

363

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Ask a student to share their work and then bring the class to consensus. Invite students to share a statement that answers the question.

Smaller Unknown Students represent and solve a compare with smaller unknown word problem. Display the word problem and read it aloud. Ask students to retell the story to a partner. Tell the class to ready their whiteboards. Let’s draw a tape diagram to represent this problem.

Kit plays for 10 minutes. Ben plays for 4 minutes fewer than Kit plays. How many minutes does Ben play?

Have the class chorally reread the first sentence. Can we draw something? What can we draw? We can draw a rectangle for the minutes Kit plays and label it 10. Draw a rectangle and label it 10 as students follow along. Chorally reread the second sentence. What do we know about Ben’s minutes? They aren’t as many as Kit’s minutes.

They are 4 fewer than Kit’s minutes. Notice that we can’t talk about Ben’s minutes without talking about Kit’s minutes too. Turn and talk: Why? The problem tells us about Ben’s minutes by comparing them to Kit’s minutes. Because the problem compares Ben’s minutes to Kit’s minutes, let’s make a comparison tape diagram. We will draw a rectangle to show Ben’s minutes below Kit’s. Begin to draw a new unit to show Ben’s minutes, aligned on the left with Kit’s, and then pause and ask the following question. Should Ben’s rectangle be longer than Kit’s, shorter than Kit’s, or the same length as Kit’s? Why? It should be shorter. He plays for fewer minutes. 364

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 23

Finish drawing the unit as students follow along. Then model writing K for Kit and B for Ben to the left of each unit as a way to keep track of the referents. Point to where you see Ben’s 4 fewer minutes in our tape diagram. Students should point to the space under the 10 to the right of Ben’s rectangle. Draw arms below the space that represents 4 minutes and label it 4 as students follow along. Chorally reread the question. What do we need to figure out? We need to figure out how many minutes Ben plays. Ask students to point to the part of the diagram that shows the unknown. Ask them how to label it. Write a question mark inside Ben’s unit. Have students turn and talk to use the tape diagram to retell the word problem. What equation could we write to solve the problem? Why? _____ + 4 = 10. Ben’s minutes and 4 more minutes are the same as 10 minutes. 10 – 4 = _____. 10 minutes take away 4 minutes tells us how many minutes Ben plays. Validate both equations. Tell students to write the equation of their choice and ask them to find the unknown. Ask a student to share their work and then bring the class to consensus. Invite students to share a statement that answers the question. As time allows, display the chart and invite students to find at least two ways that Ben could have used 6 minutes.

Activity

Time 6 minutes 3 minutes 5 minutes 4 minutes 1 minute 2 minutes

365

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions and word 10 problems may be read aloud. Students may choose to draw tape diagrams or drawings to help them solve the problems. 10

Land Debrief

UDL: Engagement Provide mastery-oriented feedback as students draw comparison tape diagrams on their own and encourage their efforts. At first, students may draw the units next to each other, or the units may be disproportionate. If this happens, consider offering feedback that emphasizes that making mistakes in the drawings is expected and the mistakes can be easily erased or adjusted when students recognize the error.

5 min

Objective: Represent and solve comparison word problems. Share a word problem. Malik has 5 tickets. Ming has 15 tickets. How many more tickets does Ming have than Malik has? Invite students to look at the first tape diagram. Look at this tape diagram. Does it help us to see how many more tickets Ming has than Malik has?

Not really. How could we redraw this tape diagram to make it easier to compare Malik’s tickets with Ming’s tickets? We could draw a rectangle for Malik’s tickets on top, and another rectangle for Ming’s tickets below the one for Malik.

366

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 23

Display the second tape diagram.

Now, we see a comparison tape diagram. Is it more helpful? Why? Yes, now you can see both of the tickets stacked one on top of the other to compare them.

Even though it’s a comparison tape diagram I don’t think it’s more helpful. It looks like 5 and 15 are the same size. But 15 is a lot more than 5.

If students do not mention proportionality, elicit this idea by asking them if there are ways to improve the drawing. Display the third tape diagram. Is this tape diagram helpful for comparing the tickets? Why? Yes, now we can see that one is longer and one is shorter. How does this tape diagram help us to think about a way to solve the problem?

5 15

It’s easy to see 5 needs 10 more to be the same as 15.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

367

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Name

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Read

Activity

Math takes 12 minutes. Read

How many more minutes does Tam play than Max plays?

Draw

Math

Sample:

6 minutes

12 4 ?

Write

6 + 4 = 10 Tam plays

12 minutes 8 minutes

Sample:

368

10 minutes

How many fewer minutes does art take than math takes?

Max plays for 6 minutes.

Draw

4 minutes

Art takes 4 minutes.

Tam plays for 10 minutes.

Time

4 + 8 = 12

more minutes.

Art takes 219

220

PROBLEM SET

fewer minutes.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 23

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

Read

Activity

Kit plays for 10 minutes.

Math

Sample:

Activity

10 minutes

How many minutes does Deb play?

12 minutes

Draw

8 minutes

Math

Sample:

6 minutes

? 4

Write

6 + 4 = 10 Ben plays for

12 minutes 8 minutes

6 minutes

Time 4 minutes

Deb plays for 2 more minutes than Jon plays.

10 minutes

How long does Ben play?

Read Jon plays ball.

4 minutes

Ben plays for 4 fewer minutes than Kit plays.

Draw

Time

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 23

8 + 2 = 10

minutes.

Deb plays for

minutes.

Circle what Deb plays. PROBLEM SET

221

222

PROBLEM SET

369

LESSON 24

Reason with nonstandard measurement units.

EUREKA MATH2

1 ▸ M6 ▸ TE

Name

EUREKA MATH2

1 ▸ M6 ▸ TE

Read Tam has a box of 5 pencils.

Read

He finds some more.

A pencil is 9 paper clips long.

He now has 13 pencils. How many did he find?

A book is 16 paper clips long.

Draw How much longer is the book than the pencil? Draw

Write

5 + 8 = 13

9 + 7 = 16 The book is

paper clips longer than the pencil.

Tam finds 231

232

TO P I C T I C K E T

pencils.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 24

Lesson at a Glance Students measure the length of an object twice by using a different nonstandard unit each time. They discover that they need more shorter units than longer units to measure the same object. Students also solve comparison word problems involving nonstandard units when the language of the problem suggests the opposite operation.

Key Question • Why does it take more of a smaller tool than it does of a larger tool to measure the length of an object?

Achievement Descriptor 1.Mod6.AD7 Represent and solve word problems within 20 involving all addition

and subtraction problem types by using drawings and an equation with a symbol for the unknown.

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Rectangle removables must be torn out of student books. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 5 min

35 min

• Nonstandard Measurement Units

• String (18 cm) • Unifix Cubes® (10) • Crayons (2)

• Length Unknown

Students

• Problem Set

• Rectangle removable (in the student book)

Land

10 min

• Paper clips (10) • Craft sticks (2)

• Consider creating a set of 2 craft sticks and 10 paper clips per student for easy distribution during the lesson. • Cut a piece of string that is 18 cm long that will be measured by using Unifix Cubes® and then by using crayons.

371

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 24

Fluency

10 5

Happy Counting by Ones from 100–120 Students visualize a35number line while counting aloud to build fluency counting within 120. 10

Invite students to participate in Happy Counting. Let’s count by ones. The first number you say is 111. Ready? Signal up or down accordingly for each count.

111

112

113

114

115

114

115

116

117

118

119

120

119

118

119

120

Continue counting by ones within 120. Change directions occasionally, emphasizing crossing over 110 and where students hesitate or count inaccurately.

Choral Response: Subtract in Unit and Standard Form Students subtract multiples of 10 in unit form and say the equation in standard form to build subtraction fluency within 80. Display 5 tens – 3 tens = . What is 5 tens – 3 tens? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 2 tens

5 tens - 3 tens =

2 tens

50 - 30 = 20

Display the answer: 2 tens.

372

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 24

When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.) 5 tens – 3 tens = 2 tens Display the equation with the numbers in standard form. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.) 50 – 30 = 20 Repeat the process with the following sequence:

8 tens - 2 tens

7 tens - 4 tens

9 tens - 3 tens

9 tens - 4 tens

9 tens - 8 tens

9 tens - 9 tens

8 tens - 5 tens

Whiteboard Exchange: Add Within 100 Students add 2 two-digit numbers to build addition within 100. Display the equation 35 + 21 = . Write the equation and find the total. Show how you know. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Copyright © Great Minds PBC

35 + 21 = 56 373

1 ▸ M6 ▸ TE ▸ Lesson 24

EUREKA MATH2

Display the answer. Repeat the process with the following sequence:

46 + 33 = 79 55 + 25 = 80 55 + 27 = 82 49 + 34 = 83 54 + 46 = 100

Launch

5 35

Students reason about a length measured with different nonstandard units of measure. 10

Display the lizard that is being measured in two ways.

My neighbors have a pet lizard called a bearded dragon. Their children, a brother and a sister, each measured its length. What do you notice? One person used paper clips. There are a lot of them. The other person used craft sticks. They only used 5 sticks. Validate students’ observations. The brother says the lizard is 20 long. The sister says it is 5 long. Invite students to think–pair–share about whether the brother or the sister is correct. 374

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 24

Who is correct? Why? I think they can both be right. They used different tools, so the numbers don’t match. They both measured the same lizard. The lizard’s length didn’t change, but the units they used to measure it changed. The lizard is 20 paper clips long and 5 craft sticks long. It is important to say what tool or unit we use to measure. Display the lizard being measured once, this time with more than one tool. Invite students to notice and wonder.

Can we say how long the lizard is if we measure it this way? Why? No, there are two different tools. We can’t say just how many craft sticks it is or how many paper clips it is. We use just one tool to measure a length. For example, we can use all centimeter cubes, all paper clips, all craft sticks, or all of any other tool that is the same size. Transition to the next segment by framing the work. Today, we will measure and solve problems that use lengths.

375

10 EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 24 5

Learn

35 10

Nonstandard Measurement Units Materials—S: Rectangle removable, paper clips, craft sticks

Students compare the number of nonstandard units required to measure a length.

UDL: Representation

Make sure students have a Rectangle removable to measure.

Activate students’ prior knowledge from grade 1 module 4 by having them talk about their experiences with measuring. Consider revisiting the measurement chart.

Touch the long sides of the rectangle. Show a craft stick and a paper clip. Tell students they will measure each long side twice, once with the craft sticks and once with the paper clips.

I Can Measure EUREKA MATH2

Are the long sides the same length? How do you know?

EM2_0106TE_E_L24_shape_removable_studentwork.indd 227

Distribute the materials and invite students to measure the long sides of the rectangle.

Yes. Both sides needed the same number of paper clips or the same number of craft sticks. 8

2 craft sticks

craft sticks long

227

18/02/21 11:29 PM

How many paper clips long is the rectangle?

paper clips long

1 ▸ M6 ▸ TE ▸ Rectangle

How many craft sticks long is the rectangle?

8 paper clips Have students record the numbers at the bottom of the Rectangle removable. Display the tape diagrams. Each of these tape diagrams represents one way to measure the length of the rectangle. What do you notice? The diagrams are the same length. One diagram has 2 parts and one diagram has 8 parts. 376

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 24

Point to the tape with 2 units. This tape shows that the rectangle is 2 units long. We used 2 of which unit to measure the length of the rectangle? Craft sticks Point to the tape with 8 units. This tape shows that the rectangle is 8 units long. We used 8 of which unit to measure the length of the rectangle?

Teacher Note

Paper clips The tape diagrams are the same length because the rectangle’s length doesn’t change. Why does it take more paper clips than it does craft sticks to measure the same length? The paper clips are shorter than the craft sticks. When we use a unit that is a smaller length, we need more of them to measure an object.

As students worked with shapes in module 6 part 1, they saw that decomposing a whole into more equal shares results in smaller shares. Understanding the idea that different sets of same-size units can compose the same whole is foundational to multiplication and work with fractions students will do in later grades.

If time allows, repeat the process with other objects such as student books or desks.

Length Unknown Students represent and solve a compare with smaller unknown word problem. Display the word problem and read it aloud. Kioko’s book is 13 paper clips long. Kioko’s book is 4 paper clips longer than Imani’s book. How many paper clips long is Imani’s book? Ask students to retell the story to a partner. Tell the class to ready their whiteboards. Let’s draw a tape diagram to represent this problem. Have the class chorally reread the first sentence.

377

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 24

Can we draw something? What can we draw? We can draw a rectangle for Kioko’s book and label it 13. We can draw a rectangle for Kioko’s book and make 13 spaces in it. Draw a rectangle and label it 13 as students follow along. Chorally reread the second sentence. What do we know about the length of Imani’s book? Imani’s book must be shorter than Kioko’s. We know that Kioko’s book is 4 paper clips longer.

Notice that we can’t talk about the length of Imani’s book without talking about the length of Kioko’s book too. Turn and talk: Why not? The problem tells us about the length of Imani’s book by comparing it to the length of Kioko’s book. How should we show Imani’s book so we can see the comparison?

Teacher Note It may feel natural for students to label Imani’s unit with a question mark after drawing it, rather than waiting to reread the question and then label the unknown. Such variations in drawing and labeling the diagrams are acceptable and should be expected. The order of how to draw and label the diagram can shift depending on how students recognize and make sense of the information in the problem.

We should draw Imani’s book under Kioko’s book. Should Imani’s rectangle be longer than Kioko’s, shorter than Kioko’s, or the same length as Kioko’s? Why? It should be shorter. The problem says Kioko’s book is longer than Imani’s book. That means Imani’s book is shorter than Kioko’s. Draw a new unit to show the length of Imani’s book, aligned on the left with Kioko’s, as students follow along. Model writing K for Kioko and I for Imani to the left of each unit as a way to keep track of the referents. Chorally reread the second sentence. We know that Kioko’s book is 4 paper clips longer than Imani’s. Let’s label that on our tape diagram. Point to where you can see that Kioko’s book is 4 paper clips longer.

Teacher Note Grade 1 introduces the comparison problem types where the words shorter and longer suggest the wrong operation but students are not expected to become proficient with it. Students continue to work with these problems in grade 2.

Students should point to the space under 13 and to the right of Imani’s unit. Draw arms below the space that represents 4 paper clips and label it 4 as students follow along. Chorally reread the question. What do we need to figure out? We need to figure out how long Imani’s book is.

378

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 24

Ask students to point to the part of the diagram that shows the unknown and ask them how to label it. Write a question mark inside Imani’s unit. Have students turn and talk about how to use the tape diagram to retell the word problem. What equation could we write to solve the problem? Why? + 4 = 13. Imani’s book and 4 more paper clips is as long as Kioko’s book. 13 – 4 = . The length of Kioko’s book is 4 paper clips more than Imani’s.

4 + 9 = 13 +6 +3 4

13 - 4 = 9 10 3 - 4 6

Validate both equations. Tell students to write the equation of their choice and ask them to find the unknown. Ask a student to share their work and then bring the class to consensus. Invite students to share a statement that answers the question. Display another word problem and repeat the process. Release responsibility to the students as appropriate. Imani’s shoe is 11 paper clips long. Imani’s shoe is 6 paper clips shorter than Kioko’s shoe. How many paper clips long is Kioko’s shoe?

6 I

? 11 + 6 = 17

Problem Set Differentiate the set by selecting problems for students to finish independently within the shorter timeframe. Problems are organized from simple to complex.

10 1

Promoting Mathematical Practice Students must attend to precision when they solve comparison problems in which words such as more, longer, fewer, or shorter imply the incorrect solution path. For example, a student who is still learning to attend to precision may see the word longer in this problem and think they should add 13 + 4. Encourage students to use their tape diagram to explain how the quantities relate to each other and how those relationships are reflected in their equation.

UDL: Action & Expression Consider providing an opportunity for students to monitor and reflect on their learning by asking them the following questions: • What have I learned about tape diagrams? • What am I getting better at? • What is still a challenge for me?

Directions and word problems may be read aloud. Students may choose to draw tape diagrams or another representation to help them solve the problems.

379

5 1 ▸ M6 ▸ TE ▸ Lesson 24 35

Land Debrief

EUREKA MATH2

5 min

Materials—T: String, Unifix Cubes, crayons

Objective: Reason with nonstandard measurement units. Lay the string on a flat surface and gather the class around it. Hold up a Unifix Cube and a crayon and align their endpoints. I will measure this string with cubes and then with crayons. Invite students to think–pair–share about the different sizes of the two tools. Which tool or unit will I need more of? How do you know? You will need more cubes because they are smaller. Measure the string twice. Place cubes above it and crayons below it. Invite students to validate the prediction that it takes more cubes and fewer crayons to measure the same length. Invite students to suggest other tools or units they could use to measure the string. As students make suggestions, use the following questions to evaluate and briefly discuss their ideas: • Does the size of the tool make sense in relation to the length of the string? For example, blocks or glue sticks make more sense for this measurement than rugs or desks. • Is the size of the suggested tool somewhat standard so that several can be placed end to end for a reliable measurement? For example, cubes are all the same length, and so are new crayons from the same box. Pencils or crayons may be very different sizes depending on whether they are new or used. • To measure the string, would you need more of or fewer of this item than the cubes?

380

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 24

Why does it take more of a smaller tool than it does a larger tool to measure the length of an object? They are shorter, so you need more than with a longer tool.

Topic Ticket

5 min

Provide up to 5 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem.

381

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 24

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 24

Name

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 24

Read Val’s hand is 6 paper clips long.

1. Write the total length.

Val’s hand is 2 paper clips shorter than her mom’s hand. How long is her mom’s hand? Draw

cubes

paper clips

cars

2. Draw or write. Why do we need more cubes than paper clips to measure the marker? Sample:

They are shorter.

Write

6+2=8

Why do we need fewer cars than paper clips to measure the marker? Sample:

They are longer.

Her mom’s hand is

382

227

228

PROBLEM SET

paper clips long.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 24

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 24

Read Val’s hand is 6 paper clips long. Val’s hand is 2 paper clips longer than her sister’s hand. How long is her sister’s hand? Draw

Write

6–2=4 Her sister’s hand is

paper clips long. PROBLEM SET

229

383

LESSON 25

Solve nonroutine problems. (Optional) Lesson at a Glance Students act like mathematicians to solve nonroutine problems that have many solution pathways. They use information they know and self-select strategies and tools to solve a problem. Students share their solution and discuss their thinking. They relate the problem-solving process to the work that mathematicians do.

Key Question • How do mathematicians solve problems?

Achievement Descriptor 1.Mod6.AD7 Represent and solve word problems within 20 involving all addition

and subtraction problem types by using drawings and an equation with a symbol for the unknown.

Exit Ticket There is no Exit Ticket in this lesson. Use students’ work to informally assess their understanding of the concepts presented.

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 25

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Subtract in Unit and Standard Form Sprints must be torn out of student books. Consider whether to tear out the pages in advance of the lesson or have students tear them out during the lesson.

Launch Learn

10 min 10 min

30 min

• How Many? • Share, Compare, Connect • Problem Set

Land

10 min

• None

Students • Subtract in Unit and Standard Form Sprint (in the student book) • Assorted math tools • Map of Mathematicians removable (in the student book)

• Have assorted math tools, such as centimeter cubes and number paths, available for students to self-select during the lesson.

385

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25

Fluency

10 10

Sprint: Subtract in Unit and Standard Form Materials—S: Subtract30 in Unit and Standard Form Sprint

Students subtract tens in unit or standard form to build subtraction fluency 10 EUREKA MATH 1 ▸ M6 ▸ TE ▸ Lesson 25 ▸ Sprint ▸ Subtract in Unit and Standard Form within 80. 2

Have students read the instructions Sprintand complete the sample problems. Subtract. 1.

9 tens - 2 tens 7 tens 90 - 20

2. 3.

8 tens - 4 tens 4 tens

80 - 40

386

Teacher Note Today’s Sprint goes from 20 problems to 24 problems in preparation for Sprints with 30 problems beginning in grade 2. The goal continues to be improvement.

233

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 25

Teacher Note Consider asking the following questions to discuss the patterns in Sprint A: • What patterns do you notice about problems 1–6? 1–12? • How can you use problem 12 to solve problem 13?

Take your mark. Get set. Improve! Time students for 1 minute on Sprint B. Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct.

Teacher Note

Read the answers to Sprint B quickly and energetically. Count the number you got correct and write the number at the top of the page. Stand if you got more correct on Sprint B. Celebrate students’ improvement.

Count forward by tens from 0 to 90 for the fast-paced counting activity. Count backward by tens from 90 to 0 for the slow-paced counting activity.

387

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25 10

Launch

10 30

Students count or add units (dice or dots). Display the picture of10dice. Invite students to notice and wonder. Tell students to turn to the same picture in their student book. Read the title, How Many? Have students work on their own or with a partner to find the total. They may find the total of different units, such as the following: • There are 25 dice. • There are 50 dots. Encourage students to self-select a strategy (e.g., count all, count on, skip-count, count groups and add) and show their thinking on the page. Allow about 5 minutes of work time.

Differentiation: Challenge Invite students to answer the question of how many in more than one way. Also consider providing students with dice to make their own configurations. They can share them with a partner or group to find how many.

Invite two or three students to show their total and share their strategy. Ask students to verbally label their total with a unit, either as dots or as dice. Support student-to-student dialogue by inviting the class to agree or disagree, ask questions, give compliments, make suggestions, or to restate ideas in their own words. Transition to the next segment by framing the work. Some students counted dice, and some counted the dots on the dice. Today, we will try another problem where we need to count different units.

388

10 EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 25 10

Learn How Many?

30 10

Materials—S: Assorted math tools

Students reason about the relationship between units to solve a problem. Display the farm fence. Invite students to notice and wonder. Then share a scenario.

I see 3 heads.

Two friends visit a farm. One friend looks over the fence and sees the tops of animals’ heads. (Point to and read the speech bubble.) The other friend looks under the fence and sees animals’ legs. (Point to and read the speech bubble.)

I see 8 legs.

Differentiation: Challenge Provide a more challenging number combination, such as 14 legs and 5 heads.

Horses and Chickens

(Point to and read the sign.) How many horses and chickens do they see? Before we solve the problem, let’s make a list of what we already know. What does the picture tell us? If there are 3 heads, there are 3 animals. There are horses and chickens. There are 8 legs. Horses have 4 legs and chickens have 2 legs. Copyright © Great Minds PBC

389

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25

Record students’ thinking. Have students turn and talk about tools they might use to help them solve the problem. Then have them turn to the problem in their book and solve it on their own or with a partner. Encourage students to show their thinking. Circulate and provide support, referring to the class’s list as needed. Select two or three students or pairs to share in the next segment. Ideally each work sample should show a different way to think about the problem.

Share, Compare, Connect Students share their strategies and solutions for the farm animal problem. Invite the students or student pairs whose work was selected in the previous segment to share their work and explain their thinking. Have students refer to the Talking Tool as needed. C

heads

Promoting Mathematical Practice As students reason about the nonroutine problem, they make sense of problems and persevere in solving them. Routine problem types in grade 1 can be solved by adding or subtracting the given numbers. The farm problem is different. Students will persevere through trial and error as they consider different combinations, counting and revising their models as needed. With nonroutine problems such as this one, finding an entry point can be challenging. Encourage students to start by thinking about how many animals there are. Encourage them to try different combinations of 3 animals, both chickens and horses, and count the legs. Ask the following questions: • Are there too many legs or too few legs?

1, 2, 3, 4, 5, 6, 7, 8

2 + 2 + 4 + 8 legs

How many chickens and horses do the friends see? How do you know?

• How would trading one animal for a different animal help? If needed, invite students to act out the problem with horses and chickens from the farm animal counters set.

I made 3 stacks of cubes for the 3 animals. The cubes are their legs. 2 and 2 is 4, and 4 and 4 is 8. There are 2 chickens and 1 horse. First, we drew 3 circles to show the 3 heads. Then, on the first 2 heads, we drew 2 legs and 2 legs to make 4 legs. We drew 4 legs on the last head. That makes 8 legs. There are 2 chickens and 1 horse. Confirm that there are 2 chickens and 1 horse. Then help students compare the work samples and make connections about them. What is the same about this work? What is different? 390

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 25

They both used the clues from the picture to help them solve the problem. Everyone counted legs, heads, and animals. One way shows cubes and the other way shows drawings. One way counts on and the other way makes groups and adds them.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions and word problems may be read aloud. 10

Land Debrief

UDL: Engagement 5 min

Objective: Solve nonroutine problems. Tell students to turn to the Map of Mathematicians in their student book.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25 ▸ Map of Mathematicians

These are some well-known mathematicians from around the world. Mathematicians have an important job. What do you think they do? Ada Lovelace

They work with numbers. They solve math problems. They teach math.

Alan Turing

Katherine Johnson Srinivasa Ramanujan

They help the world.

Mariel Vázquez

Consider allowing students to work in small groups to learn more about a mathematician of their choice. Have students create presentations or posters to share with the school community.

Alberto Pedro Calderón

The Math Past resource contains more information about each mathematician shown on the map. As time allows, share this information about the contributions this diverse group of mathematicians made to mathematics. As students make connections between the problems they solved in this lesson and the work of these mathematicians, encourage students to give personal examples of how they could apply this kind of thinking and problem solving in their own lives.

237

391

1 ▸ M6 ▸ TE ▸ Lesson 25

EUREKA MATH2

Listen in as students discuss their ideas. How did we solve problems today the way mathematicians do? We asked questions. We used clues to help us understand the problems. We used strategies and tools to solve the problems. We showed our thinking with drawings, numbers, and words. We talked to each other about our ideas. Sometimes mathematicians work on problems for a very long time and never solve them! Mathematicians often make mistakes but keep trying. We persevere when we work on challenging problems too. Persevere means we keep working to solve a problem even when it is hard to solve. Today, we used clues, strategies, and tools to work on problems, just like mathematicians do.

392

EUREKA MATH2 1 ▸ M6 ▸ TE ▸ Lesson 25

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25 ▸ Sprint ▸ Subtract in Unit and Standard Form

Number Correct:

Subtract. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25 ▸ Sprint ▸ Subtract in Unit and Standard Form

Number Correct:

Subtract.

4 tens – 2 tens 2 tens 40 – 20

6 tens – 2 tens 4 tens 60 – 20

8 tens – 2 tens 6 tens 80 – 20

5 tens – 3 tens 2 tens 50 – 30

7 tens – 3 tens 4 tens 70 – 30

9 tens – 3 tens 6 tens 90 – 30

234

13.

90 – 40

14.

70 – 40

15.

70 – 50

16.

90 – 50

17.

70 – 60

18.

90 – 60

19.

80 – 70

20.

90 – 70

21.

90 – 80

22.

80 – 80

10.

23.

80 – 10

11.

24.

70 – 30

12.

236

3 tens – 2 tens 1 ten 30 – 20

5 tens – 2 tens 3 tens 50 – 20

7 tens – 2 tens 5 tens 70 – 20

4 tens – 3 tens 1 ten 40 – 30

6 tens – 3 tens 3 tens 60 – 30

8 tens – 3 tens 5 tens 80 – 30

13.

80 – 40

14.

60 – 40

15.

60 – 50

16.

80 – 50

17.

60 – 60

18.

80 – 60

19.

80 – 70

20.

90 – 70

21.

90 – 80

22.

80 – 80

23.

80 – 10

24.

70 – 20

393

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25

Name

Read

Read Mel takes care of 6 bats.

I see 7 heads.

How many zebras do they see?

Val cares for 3 fewer animals than Mel does.

Jon cares for 10 more animals than Mel does.

Val’s animals cannot fly.

How many flamingos do they see? Draw

EUREKA MATH2

1 ▸ M6 ▸ TE ▸ Lesson 25

Zebras and Flamingos

I see 20 legs.

Draw

J M

16 6 10

V 3 3 Write

Name

Write

2+2+2+2+4+4+4 They see

394

zebras and

flamingos. 241

242

PROBLEM SET

Animal

How many?

Jon

Mel

Val

Topic F Extending Addition to 100 The final topic of the year provides more practice with adding 2 two-digit numbers, this time with larger totals. Students apply their place value understanding and knowledge of Level 3 strategies to add pairs of two-digit numbers that have sums within 100. Like in module 5, students explore three primary ways to solve problems. They add like units (tens with tens and ones with ones), add tens first, and make the next ten. Based on their prior experience with these ways of decomposing and composing, students are now more likely to examine the structure of the addends in a problem and strategically select a way to solve it. In this topic, students continue to • solve problems in more than one way and compare the solution pathways, • reason about common errors in written methods, and • determine the equality of various expressions that are used to make easier problems. Students come to this topic understanding that when they add, it is sometimes useful to compose a ten. In preparation for working with larger numbers in grade 2, these lessons present the idea that it is possible to compose 1 hundred when there are 10 tens. Students relate their knowledge of partners to 10 to working with multiples of 10 to make 100, and they apply the different ways they know to add 2 two-digit numbers. Students end the grade 1 year well equipped to approach addition problems in grade 2 with a variety of flexible and efficient strategies.

395

EUREKA MATH2

1 ▸ M6 ▸ TF

Progression of Lessons Lesson 26

Lesson 27

Make a total in more than one way.

Add two-digit numbers in various ways, part 1.

Lesson 28

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

Add two-digit numbers in various ways, part 2. Name

54 + 28 I know this number sentence is true because there are 6 tens and 5 ones on both sides. I can break apart addends and add the parts to make a problem easier.

50 + 20 + 4 + 8 70

12 = 82

70 + 12 = 82

28 + 2 + 52 30 + 52 = 82

30 + 52 = 82

I can break apart addends and add the parts in different ways.

396

273

EUREKA MATH2 1 ▸ M6 ▸ TF

Lesson 29

Lesson 30

Lesson 31

Add tens to make 100.

Make the next ten and add tens to make 100.

Add to make 100.

I can make the next ten and then add tens to get to 100.

I can use what I know about partners to 10 to think about ways to make 100.

I can add different kinds of numbers to make 100.

397

LESSON 26

Make a total in more than one way.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

Name

Draw tens and ones to add.

10 + 35 =

Lesson at a Glance Students study pictures of numbers represented in terms of tens and ones. They try to figure out which two numbers can be combined to make a given total. Then students systematically move tens from one addend to the other. They find patterns in the resulting expressions and see that the total stays the same.

Key Question

• Why do we get the same total even when we combine addends in different ways?

Achievement Descriptor 1.Mod6.AD12 Add 2 two-digit numbers that have a sum within

20 + 25 =

30 + 15 =

100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of equations.

257

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 26

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Rectangles removables and the Match: Make 65 Recording Sheets must both be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Match: Make 65

• Chart paper • Centimeter cubes (5) • Base 10 rods (6)

• Equal Expressions

Students

• Problem Set

• Rectangles removable (in the student book)

Land

10 min

• Match: Make 65 Recording Sheet (in the student book) • Match: Make 65 cards (1 set of 14 cards per student pair, in the student book) • Centimeter cubes (5) • Base 10 rods (6)

• The Match: Make 65 cards need to be torn out of student books and cut apart. Prepare this material before the lesson. • Consider creating resealable plastic bags with 6 base 10 rods and 5 centimeter cubes for easy distribution during the lesson. Save these for use in the next lesson. Note: Base 10 rods are referred to as ten-sticks throughout the lesson.

399

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

Fluency

10 10

Whiteboard Exchange: Equal Shares 30 removable Materials—S: Rectangles

Students partition rectangles into halves or fourths and name the equal shares 10 to build reasoning with shapes from topic C. Make sure students have a personal whiteboard with a Rectangles removable inside. After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections. Display two rectangles. Draw a line on the first rectangle to show 2 equal shares, or parts. Display a sample answer. Does the shape show halves or fourths? Raise your hand when you know. Halves

Halves

Display the answer. Color half of the shape. Display a sample answer. Draw a line on the other rectangle to show 2 equal shares a different way. Display a sample answer. Does the shape show halves or fourths? Raise your hand when you know. Halves 400

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 26

Display the answer.

Teacher Note

Color half of the shape. Display a sample answer. Repeat the process, partitioning the rectangles two different ways into 4 equal shares.

For the rectangles partitioned into fourths, consider asking students to color a fourth of the shape or a quarter of the shape.

Choral Response: Add in Unit and Standard Form Students add ones or tens in unit form and say the equation in standard form to prepare for adding and subtracting tens. Display 4 ones + 1 one = _____. What is 4 ones + 1 one? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 5 ones Display the answer: 5 ones. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.)

4 ones + 1 one = 5 ones 4+1= 5

4 ones + 1 one = 5 ones Display the equation with the numbers in standard form. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.)

4 tens + 1 ten = 5 tens 40 + 10 = 50

4+1=5 Continue with 4 tens + 1 ten = _____.

401

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

Repeat the process with the following sequence:

5 ones + 2 ones

6 ones + 3 ones

8 ones + 1 one

3 ones + 5 ones

5 tens + 2 tens

6 tens + 3 tens

8 tens + 1 ten

3 tens + 5 tens

I Say, You Say: Partners to 10 Students say the partner to 10 for a given number to prepare for composing 100 with groups of ten. Invite students to participate in I Say, You Say. When I say a number, you say its partner to 10. Ready?

Teacher Note

When I say 8, you say? 2

The repetition of the vignette is intentional. Consider adding energy to the routine in one or more of the following ways:

8 2

• Use the call-and-response like an upbeat chant heard at sporting events.

8 2

• Build to a quick pace.

Repeat the process with the following sequence:

402

• Use gestures such as leaning in, pointing, or cupping your ear to signal students to respond.

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 26 10

Launch

Materials—S: Match:30 Make 65 Recording Sheet

EUREKA MATH2

Students find two addends 10 that make 65.

1 ▸ M6 ▸ TF ▸ Lesson 26 ▸ Make 65

20 + 45 = 65

+ 10

45 + 20 = 65

Display the five Match: Make 65 cards shown. These cards show five different numbers. Turn and talk: Which two numbers do you think have a total of 65?

Tell students to self-select strategies and tools to find two cards that total 65. Make sure students have the Match: Make 65 Recording Sheet in their personal whiteboard and have them use it to record their thinking. Have students discuss their thinking. Facilitate discussion by asking two or three students to show and explain their work. Focus the discussion on strategies, such as composing or decomposing addends, rather than on models or recordings. Refer students to the Talking Tool as needed. Which two cards make 65? How do you know? 20 and 45; 20 and 40 is 60. 60 and 5 is 65.

= 65

EM2_0106SE_F_L26_removable_make_65.indd 1

Teacher Note

= 65 1

04/03/21 2:44 AM

Students are likely to need more than one attempt to make 65 as a total of two cards. Encourage them to erase and try again if their combination does not total 65. Share that trying more than once is expected and provides an opportunity for learning.

45 and 20; I counted on by tens: 45, 55, 65. Transition to the next segment by framing the work. Today, we will make the same total in different ways.

403

10 EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26 10

Learn

30 10

Match: Make 65

Promoting Mathematical Practice

Materials—S: Match: Make 65 cards, Match: Make 65 Recording Sheet

Students combine two sets of tens and ones to make a given total. Pair students. Assign students as partner A or partner B. Demonstrate how to play Match: Make 65 by using the following procedure: • Arrange the 14 Match: Make 65 cards with the ten-sticks and cubes facing up (or the numbers facing up). • Partner A studies the cards and tries to choose two cards that make 65. • Partner A self-selects strategies and tools to confirm the total. • If the total is exactly 65, then partner A records their thinking on their recording sheet. They keep the cards. If the total is not 65, they put the cards back.

• Partner B takes a turn. Distribute the Match: Make 65 cards to each student pair. Have students play for 6 or 7 minutes. Circulate and ask the following assessing and advancing questions: • Why did you choose those cards?

When students try to determine a total by studying the composition of numbers, they look for and make use of structure. Students must rely on the structure of the numbers as they complete this segment. For example, some students might notice that by using this set, only one card can have ones if the total is 65. Students also rely on the structure of numbers when they notice that even though the tens and ones are arranged differently among the various representations of 65, the total is the same each time.

Differentiation: Support Provide ten-sticks and cubes for students to use to represent the numbers with concrete tools as needed.

• How did you find the total? • How did you use tens and ones to make finding the total easier? Have students clean up. Invite two or three students to show their recording sheets and share the ways they made 65.

Differentiation: Challenge Have sticky notes available so students can record other number pairs with a total of 65.

404

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 26

Equal Expressions Materials—T: Chart paper, base 10 rods, centimeter cubes; S: Base 10 rods, centimeter cubes

Students manipulate tens to systematically represent ways to make 65 in two parts. Hang a piece of chart paper in a central location. Have students take a removable out of their whiteboard so that one side of their whiteboard is blank. Distribute ten-sticks and cubes. Show a blank whiteboard in landscape orientation. Demonstrate drawing a line down the middle to make two parts and have students do the same thing. On the right side of the whiteboard, guide students to use tensticks and cubes to represent 65 as 6 tens and 5 ones. Let’s represent all the ways we made 65 with two addends. The first way is 0 + 65. On the chart paper, write 0 + 65. On the whiteboard, move 1 ten-stick to the left side of the whiteboard as students do the same. Do we still have 65 on the whiteboard? How do you know? Yes, we did not take anything away. We just moved a ten across the line. 1 ten, 5 tens, and 5 ones is 65. On the chart paper below 0 + 65, write 10 + 55. On the whiteboard, move another ten-stick from right to left as students do the same.

405

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

Do we still have 65? How do you know? Yes, we did not take anything away. We just moved another ten to the other side. 20 and 45 is 65. We still have 6 tens and 5 ones. On the chart paper below 10 + 55, write 20 + 45. Repeat the process until there are no more tens on the right side of the whiteboard.

UDL: Representation

Direct students’ attention to the chart. Ask them to think– pair–share about patterns they see.

Consider color coding and annotating the patterns students notice on the chart to help the class access and engage in the mathematics.

The first addend goes up by 1 ten each time. The second addend goes down by ten each time. We used different addends every time. Why did we always get the same total? We just moved tens around. We didn’t add any or take any away, so the total stayed the same. You can move around tens and ones in lots of different ways. Write 15 + 50 = 25 + 40 and invite students to reason about the equality of the expressions. Record student thinking as shown. Is this a true number sentence? How do you know? Yes, both sides total 65. They both have 6 tens and 5 ones. A ten moved from one addend to the other.

406

Teacher Note Writing a new number sentence to equate expressions students already know the totals for encourages them to use relational thinking. Students can look on both sides of the equal sign and notice that the tens and ones are balanced, and therefore the expressions are equal.

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 26

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

5 min

Objective: Make a total in more than one way. Display the Match: Make 65 cards that show 35 and 45. Show thumbs-up if you think these cards make 65. Show thumbs-down if you think they do not make 65. Invite students to brainstorm ways the cubes could be combined to find the total. Guide them as needed. Share any of the following three strategies that students do not mention and record them as shown by using quick ten drawings:

• Add like units: 30 and 40 is 70. Five and 5 is 10. 70 and 10 is 80. • Add tens first: 35 and 4 more tens, 40, is 75. Five more is 80. • Add ones first to make the next ten: 35 and 5 is 40. 40 and 40 is 80. Did we make 65? No.

407

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

Why did we get the same total even though we combined the addends in different ways? You can move around tens and ones in lots of different ways. We just moved tens and ones around. We didn’t add any or take any away, so the total stayed the same.

Exit Ticket

10 70

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

40 40

408

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 26

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

Name

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

2. Make 75 with two cards. Show how you know.

1. Draw tens and ones to add.

0 + 55 =

10 + 45 =

+ 10 + 5

75 20 + 35 = 30 + 25 =

70 + 5 = 75

60 70

60 + 15 = 75

50 + 25 40 + 15 =

70 20 5

50 + 5 =

50 + 25 = 75

253

254

PROBLEM SET

409

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 26

3. Write any two-digit number. Make that number with two parts in different ways. Show how you know. Sample:

49 40 + 9 30 + 19 20 + 29 10 + 39

410

PROBLEM SET

255

LESSON 27

Add two-digit numbers in various ways, part 1.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

Name

Add. Show how you know.

29 + 32 =

Lesson at a Glance Students use concrete materials to decompose addends and compose parts to solve addition problems with 2 two-digit addends. Through class discussion they share and compare various ways to solve the problems. They relate their work to number sentences. Students critique a flawed response that shows a common error.

Key Question

• What are ways to make an easier problem?

29 + 32

Achievement Descriptors

1 31 29 + 1 = 30 30 + 31 = 61

1.Mod6.AD11 Add a two-digit number and a one-digit number that

have a sum within 100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of equations. 1.Mod6.AD12 Add 2 two-digit numbers that have a sum within

100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of equations.

265

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 27

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Circles removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Share, Compare, Connect

• Chart paper • Base 10 rods (10) • Centimeter cubes (20)

• Make an Easier Problem

Students

• Problem Set

• Circles removable (in the student book)

Land

10 min

• Base 10 rods (9 per student pair) • Centimeter cubes (20 per student pair)

• Consider adding the additional base 10 rods and centimeter cubes to the resealable plastic bags previously created for easy distribution. Save these materials for use in the rest of the topic. Note: Base 10 rods are referred to as ten-sticks throughout the lesson.

413

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

Fluency

10 10

Whiteboard Exchange: Equal Shares 30 Materials—S: Circles removable

Students partition circles into halves or fourths and name the equal shares 10 to build reasoning with shapes from topic C. Make sure students have a personal whiteboard with a Circles removable inside. After each prompt for a written response, give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

Halves

Display two circles. Draw a line on the first circle to show 2 equal shares, or parts. Display a sample answer. Does the shape show halves or fourths? Raise your hand when you know. Halves Display the answer. Color half of the shape. Display a sample answer. Draw a line on the other circle to show 2 equal shares a different way. Display a sample answer.

Halves 414

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 27

Does the shape show halves or fourths? Raise your hand when you know. Halves Display the answer. Color half of the shape. Display a sample answer. Repeat the process, this time partitioning the circles into 4 equal shares.

Choral Response: Add in Unit and Standard Form Students add ones and tens in unit form and say the equation in standard form to build addition fluency within 100. Display 2 tens + 1 ten = _____ tens. What is 2 tens + 1 ten? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond. 3 tens

2 tens + 1 ten = 3 tens 20 + 10 = 30

Display the answer: 3 tens. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in unit form.) 2 tens + 1 ten = 3 tens Display the equation with the numbers in standard form. When I give the signal, read the number sentence. Ready? (Point to each addend and the total as students say the equation with the numbers in standard form.) 20 + 10 = 30

415

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

Repeat the process with the following sequence:

2 tens + 1 ten 5 ones

3 tens + 1 ten 5 ones

3 tens + 2 tens 5 ones

4 tens + 5 ones

1 ten 5 ones + 4 tens

2 tens 5 ones + 4 tens

I Say, You Say: Partners to 10 Students say the partner to 10 for a given number to build addition and subtraction fluency within 10. Invite students to participate in I Say, You Say. When I say a number, you say its partner to 10. Ready? When I say 7, you say? 3 7 3 7 3

416

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 27

Repeat the process with the following sequence:

Launch

10 30

Materials—S: Base 10 rods, cubes

Students use concrete materials to find the total of 2 two-digit numbers. 10 Play part 1 of the counting steps video about a boy walking to school and counting his steps as he walks. Invite students to notice and wonder about the video. He took 36 steps to the corner. Then he took 49 steps to the school. He wants to know how many steps he took in all. How many steps did he take in all? Guide students to use their whiteboards to draw a tape diagram and write an equation to represent the situation. Distribute the ten-sticks and cubes and have partners represent the problem.

49 ?

36 + 49 = ?

Teacher Note This lesson activates prior knowledge about the three ways to decompose and combine two-digit addends that students learned in module 5. However, students can decompose the addends and combine the resulting parts in any way that makes sense to them. Help students articulate their ideas by asking the following questions:

Before you add, take time to make sense of the ten-sticks and cubes. Think about how you can make this problem easier. What could you combine first?

• How did you break up the addends? • How did you combine the parts?

417

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

Have students solve the equation. Listen for the following ways of decomposing addends and combining parts: • Add like units (tens with tens, ones with ones). • Add tens first (decompose the second addend into tens and ones and add the tens to the first addend). • Add the ones first to make the next ten (with either addend). Identify student work that uses different ways to solve the problem and ask those students to share their solutions in the following segment. Transition to the next segment by framing the work. Today, we will look at different ways to add and find a total. 10 10

Learn

30 10

Share, Compare, Connect Materials—T: Chart paper, base 10 rods, cubes

UDL: Representation

Students explain, analyze, and compare solutions. Facilitate a class discussion by inviting the students you identified in the previous segment to share their way of solving the problem. Use drawings and number sentences to record their strategies on chart paper.

418

Consider representing student thinking in another format by using more abstract number bonds.

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 27

Student thinking may include the following methods for solving the problem: • (Add like units.) 3 tens and 4 tens is 7 tens. 6 ones and 9 ones is 15. 70 + 15 = 85. • (Add tens first.) 36 and 40 is 76. Nine more is 85. • (Make the next ten.) 49 needs 1 to make 50. 50 and 35 is 85. If students did not share any example from the sample chart, demonstrate it with tensticks and cubes. Have students show thumbs-up if they did something similar. As time allows, consider having students use their materials to try different ways of solving the same problem. How many steps did the boy take in all? He took 85 steps in all. Invite students to compare the ways of solving the problem on the chart. What is the same about these ways to find the total? They break apart numbers and put them back together in different ways.

419

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

What is different about these ways to find the total? One breaks apart numbers into tens and ones, then puts together just the tens and just the ones, and then puts those totals together. They use different number sentences. All of these ways make the problem easier. How do they do that? If the numbers are really big, you can break them up into smaller numbers that are easier to add.

Make an Easier Problem Materials—S: Base 10 rods, cubes

Students add 2 two-digit numbers by decomposing and composing parts. Play part 2 of the counting steps video about the boy walking to the park and counting his steps. How many steps did the boy take in all? Guide students to write 36 + 57 = _____ on their whiteboard to represent the situation. Have them find the total. They may use ten-sticks and cubes, drawings, or number bonds to help them solve the problem. Circulate and ask the following questions to assess and advance thinking: • How did you break apart the addends? • How did you combine the parts to find the total?

UDL: Action & Expression Before students solve the problem, encourage them to take time to make sense of the addends. Consider providing the following questions that can guide their planning: • How can I break apart the addends and combine the parts to make this problem easier? • What ways did my classmates try with the last problem that I can use?

• How did your way make the problem easier for you? • What number sentence(s) can you write to show how you found the total? • How did using those number sentences make the problem easier for you? • Try another way to solve this problem. Do you get the same answer? Why? When students finish, invite partners to turn and talk about their work. If students disagree about a total, facilitate a class discussion to bring the class to consensus.

420

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 27

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

5 min

Objective: Add two-digit numbers in various ways. Display an incorrect solution to 63 + 27, which students solved in the Problem Set.

Promoting Mathematical Practice

63 + 27 = 83 Students construct viable arguments and critique the reasoning of others when they examine, critique, and correct a flawed response.

Use the Critique a Flawed Response routine to engage students in discussion. This student makes the problem easier by adding the tens first. But there is a mistake in the work. Invite students to think–pair–share about the mistake in the student’s work.

Help students make sense of the flawed work by asking the following questions:

63 + 20 = 83

What is the mistake? They forgot to add the 7 ones.

• What do you not understand about this work? • What questions could you ask this student about their work?

They need to finish solving by adding 83 + 7. Let’s learn from this mistake. Ask students to think–pair–share about how to correct the flawed response. You just have to add the 7. Three and 7 make ten. The next ten after 83 is 90, so 83 and 7 make 90. We can count on 7 more from 83. Copyright © Great Minds PBC

421

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

Record student thinking by adding to the displayed work.

63 + 27 = 83

What are the ways we made easier problems today? We broke up addends into tens and ones to make easier number sentences. We added the parts in chunks instead of all at once. When we add 2 two-digit numbers, we can break up one or both addends into smaller parts. That helps us combine them more easily.

Exit Ticket

63 + 20 = 83

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

422

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 27

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

Name

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

2. Add. Show how you know.

1. Add. Show how you know.

13 + 17 =

10 3 10 7 10 + 10 = 20 3 + 7 = 10 20 + 10 = 30 63 + 27 =

63 + 17 =

65 + 33 =

79 + 15 =

60 3 10 7 60 + 10 = 70 3 + 7 = 10 70 + 10 = 80 90

60 3 20 7 60 + 20 + 3 + 7 = 90

261

262

PROBLEM SET

423

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 27

3. Write a problem with two-digit numbers. Show two ways to add. Sample:

28 + 42 = 70 28 + 42 20

8 40

+ 40

60 + 10 = 70

424

PROBLEM SET

263

LESSON 28

Add two-digit numbers in various ways, part 2.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

Name

Add. Show how you know.

59 + 33 =

Lesson at a Glance This lesson parallels lesson 27. The difference is that students use pictorial models rather than concrete ones to decompose addends and compose parts to solve problems that use 2 two-digit addends. Through class discussion they share and compare various ways to solve the problems. They relate their work to number sentences. Students critique a flawed response that shows a common error.

Key Question • What are ways to make an easier problem?

Achievement Descriptors

59 + 1 = 60 60 + 32 = 92

1.Mod6.AD11 Add a two-digit number and a one-digit number that

100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of equations.

275

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 28

Agenda

Materials

Lesson Preparation

Fluency

Teacher

The Carnival Game must be torn out of student books. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Share, Compare, Connect • Add Two-Digit Numbers • Problem Set

Land

10 min

• Chart paper

Students • Carnival Game (1 per student pair, in the student book) • 6-sided dot die (1 per student pair) • Two-color counter

427

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

Fluency

10 10

Whiteboard Exchange: Tell and Write Time Students write the 30 time to the nearest half hour to build fluency with time from module 5. 10

Display the clock that shows 5:00. Write the time shown on the clock. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

5:00

Display the answer. Repeat the process with the following sequence:

Teacher Note 6:00

9:00

9:30

2:30

4:30

1:00

11:30

Choral Response: Add Within 100 Students add a multiple of 10 to a number less than 20 to build addition fluency within 100. Display the equation 10 + 4 = _____. What is 10 + 4? Raise your hand when you know. Wait until most students raise their hands, and then signal for students to respond.

When students make an easier problem by using the make ten or make the next ten strategy, they make problems like those in this sequence (i.e., equations that include a multiple of 10 and a one- or two-digit number). For example, an easier problem than 27 + 15 is 30 + 12 or 22 + 20.

27 + 15 =

10 + 4 = 14

14 Display the answer. 428

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 28

Repeat the process with the following sequence:

20 + 3 = 23

20 + 6 = 26

30 + 4 = 34

30 + 8 = 38

40 + 7 = 47

40 + 14 = 54

50 + 9 = 59

50 + 17 = 67

30 + 12 = 42

Whiteboard Exchange: Make Ten to Add Students make ten to prepare for making an easier problem to add within 100. Teacher Note

Display the equation 9 + 2 =_____. Write the equation.

9 + 2 = 11

Break apart one addend to make ten and find the total. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

1 1

Students may choose to decompose either addend to make ten. The following sample solution demonstrates another way to add 9 and 2:

9 + 1 = 10 10 + 1 = 11

Display the number bond, the equations, and the total.

9 + 2 = 11 1

Repeat the process with the following sequence:

3 + 9 = 12 8 + 3 = 11 4 + 8 = 12

11 = 7 + 4

11 = 6 + 5 14 = 5 + 9 12 = 5 + 7

Encourage students to be more efficient by using only the number bond to show the decomposition instead of writing both the number bond and the equations.

429

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28 10

Launch

10 30

Students use pictorial models to find the total of 2 two-digit numbers.

Differentiation: Support

Have students turn to10the drawings of 54 and 28 in the student book. Both drawings represent the same addition problem. What equation can we write? How do you know? 54 + 28 = _____. The first number is 54 and the second number is 28 in both drawings. Ask students to write the equation at the top of the page.

Provide ten-sticks and cubes that students can use to model the problem if needed. Have students relate their concrete model to the pictorial representation. They should record their work on the pictorial model.

Before we add, let’s take time to make sense of the problem. Turn and talk: What parts would you combine first to make this problem easier? Have students use one of the drawings to find the total. Ask them to show their thinking by circling parts and writing number sentences. As time allows, have them use the other drawing to try to solve the problem in a different way.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

Name

54 + 28

Students look for and make use of structure when before they add, they make sense of the problem by looking for ways to combine the parts and make an easier problem.

Circulate and listen for the following ways of decomposing the addends and combining parts: • Add like units (tens with tens, ones with ones). • Add tens first (decompose the second addend into tens and ones and add the tens to the first addend). • Add the ones first to make the next ten (with either addend).

50 + 20 + 4 + 8 70

12 = 82

70 + 12 = 82

28 + 2 + 52 30 + 52 = 82

30 + 52 = 82

273

Identify student work that uses different ways to solve the problem and ask those students to share their solutions in the following segment. Consider selecting student work that shows ways of solving the problem that are less common in your classroom.

430

Promoting Mathematical Practice

Students are asked more than they were in earlier modules to examine the structure of the given addends and to think critically about how they can make an easier problem. Students should continue to solve problems in ways that make sense to them. However, encourage them to solve a problem in more than one way to give them opportunities to notice when one approach is more helpful than another one.

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 28

Transition to the next segment by framing the work. Today, we will look at different ways we can break apart one or both addends to make an easier problem. 10 10

Learn

Teacher Note If students add the tens first, they will end up with 74 + 8. Students will need to count on or make the next ten to find the final total.

74 + 8 = 82

80 6 2

Share, Compare, Connect Materials—T: Chart paper

Students explain, analyze, and compare solutions. Facilitate a class discussion by inviting the students you identified in the previous segment to share their solutions. Use drawings and number sentences to record their strategies on chart paper.

UDL: Representation Consider representing student thinking in another format by using more abstract number bonds.

431

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

Student thinking may include the following ways of solving the problem: • (Add like units.) 5 tens and 2 tens is 7 tens. 4 ones and 8 ones is 12. 70 + 12 = 82. • (Make the next ten.) 54 needs 6 to make 60. 60 and 22 is 82. • (Make the next ten.) 28 needs 2 to make 30. 30 and 52 is 82. • (Add tens first.) 54 and 20 is 74. 8 more is 82. All four examples from the sample chart do not need to be shared and discussed. What is 54 + 28? 82 Invite students to compare the ways of solving the problem that are shown on the chart. All of these ways make the problem easier. How do they do that? They all break up addends into smaller numbers that are easier to add. They all add parts to find the total.

Add Two-Digit Numbers Materials—S: Carnival Game, 6-sided dot die, two-color counter

Students practice making easier problems by playing a game.

46 + 28 =

52 + 29 =

• Partner A uses the red side of a counter and partner B uses the yellow side. Partners place their counters on the Ferris wheel, which is the start of the game.

29 + 35 =

57 + 37 =

72 + 19 =

45 + 16 =

31 + 19 =

12 + 66 =

29 + 55 =

38 + 39 =

432

21 + 48 = 267

• The popcorn, ice cream cone, and frozen pop are free spaces. If a student lands on a free space, they do not need to solve a problem on that turn.

67 + 31 =

11 + 59 =

27 + 29 =

24 + 36 =

1 ▸ M6 ▸ TF ▸ Lesson 28 ▸ Carnival Game

• Partner A rolls the die and moves their counter that number of spaces to the right. • If partner A lands on a problem, they solve it by making an easier problem on their personal whiteboard. They explain their thinking to partner B.

EUREKA MATH2

Explain the following directions for the activity:

Pair students. Assign one student in each pair as partner A and the other student as partner B. Make sure partners have a Carnival Game, a die, and 2 two-color counters.

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 28

• Partner B takes a turn. • The first student to land on or pass the roller coaster wins. The other student may then roll to get to the roller coaster as well or partners may start the game again as time allows. As students play, assess and advance their thinking by asking the following questions: • How did you break apart the addends? How did you combine the parts to find the total? • How did your way make the problem easier for you? • What number sentence or sentences can you write to show how you found the total? • Try another way to solve this problem. Do you get the same answer? Why? Have students clean up their materials. Consider using the game again at another time of day.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. Directions may be read aloud.

433

10 EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28 30

Land Debrief

5 min

Objective: Add two-digit numbers in various ways.

48 + 25 = 70

Display an incorrect solution to 48 + 25, which students solved in the Problem Set. Use the Critique a Flawed Response routine to engage students in discussion. Invite students to think–pair–share to identify the error. This student tried to make the problem easier by making the next ten with 48. But there is a mistake in the work. What is the mistake?

50 + 20 = 70

They forgot to add the 3 leftover ones. Let’s learn from this mistake.

48 + 25 = 70

Ask students to think–pair–share about how to correct the flawed response. You have to add in 3 more. We can find 50 + 20 + 3. Record student thinking by adding to the displayed work. What are ways we made easier problems today? We broke up addends into tens and ones to make easier number sentences.

50 + 20 = 70

We added the parts in chunks instead of all at once. When we add 2 two-digit numbers, we can break up one or both addends into smaller parts. That helps us to combine them more easily.

434

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 28

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

435

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

Name

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

2. Add two ways.

48 + 25 =

1. Add two ways.

66 + 33 =

48 + 25 = 20

66 + 33 = 99

90 + 9 = 99 44 + 36 =

60 + 13 = 73 53 + 39 =

52 1 40 52 + 40 = 92

30 80 + 12 = 92

70 + 10 = 80

436

70 2

53 + 39 =

44 + 36 = 80

48 + 20 = 68 68 + 5 = 73

30 3 66 + 30 = 96 96 + 3 = 99

50 6

271

272

PROBLEM SET

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 28

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 28

3. Write a problem with 2 two-digit numbers. Show two ways to add. Sample:

16 + 43 = 59 16 + 43 9

7 43 + 7 = 50 50 + 9 = 59

PROBLEM SET

273

437

LESSON 29

Add tens to make 100.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 29

Name

Add. Show how you know.

Lesson at a Glance Students watch a video and reason about tens to find the value of a set of dimes. Students use their knowledge of partners to 10 to find all the ways to make 100 with two addends that are both multiples of 10. Students apply this thinking to solve word problems.

Key Question

50 + 50 =

100

• How are partners to 10 helpful when finding ways to make 100?

Achievement Descriptor 1.Mod6.AD12 Add 2 two-digit numbers that have a sum within

100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of equations.

60 +

= 100

283

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 29

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Add Tens removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

30 min

• Add Tens removable (digital download)

Students

• Use Tens to Make 100

• Dimes (10 per student pair)

• 100 Pencils Problem

• Add Tens removable (in the student book)

• Problem Set

Land

10 min

• Copy or print the Add Tens removable to use for demonstration. • Assemble sets of 10 dimes.

439

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 29

Fluency

10 10

Whiteboard Exchange: Tell and Write Time Students write the 30 time to the nearest half hour to build fluency with time from module 5. 10

Display the clock that shows 2:00. Write the time shown on the clock. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

2:00

Display the answer. Repeat the process with the following sequence:

8:00

8:30

1:30

Teacher Note

7:30

11:00

6:30

Consider asking students to use the term half past to say the time another way by using the following question and prompt (on the clocks that are set to the half hour): • What time does the clock show? • Say it another way.

12:00

Choral Response: Add Within 100 Students add a multiple of 10 to a number less than 20 to build addition fluency within 100.

20 + 5 =

Display the equation 20 + 5 = _____. What is 20 + 5? Raise your hand when you know. 440

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 29

Wait until most students raise their hands, and then signal for students to respond. 25 Display the answer. Repeat the process with the following sequence:

20 + 15 = 35 30 + 6 = 36 30 + 16 = 46 40 + 9 = 49

50 + 18 = 68 60 + 13 = 73 70 + 19 = 89

40 + 19 = 59

80 + 11 = 91

Whiteboard Exchange: Make Ten to Add Students make ten to build addition fluency within 20. Display the equation 9 + 4 = _____. Write the equation. Break apart one addend to make ten and find the total. Give students time to work. When most students are ready, signal for students to show their whiteboards. Provide immediate and specific feedback. If students need to revise, briefly return to validate their corrections.

9 + 4 = 13

1 3 9 + 1 = 10 10 + 3 = 13

Display the number bond, the equations, and the total. Repeat the process with the following sequence:

6 + 9 = 15 8 + 5 = 13 7 + 8 = 15 13 = 7 + 6 16 = 7 + 9 14 = 8 + 6 17 = 8 + 9

441

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 29 10

Launch

10 30

Students add tens to make a total of 100. Gather students and 10 play the video about Ko and a friend, who combine coins and donate the money. Invite students to retell the events in the video to a partner. How many dimes did they give to the food bank? How much money is that? Ask students to solve the problem. Have them draw on their whiteboards to represent their thinking. Circulate and look for a variety of thinking. Invite two or three students to share their work with the class. Support discussion by referring students to the Talking Tool.

10 tens = 100

+ 10

Differentiation: Support Consider having students act out the problem with dimes.

100 100

7 dimes, or tens, is 70. I counted on: 70, 80, 90, 100. I drew 7 dimes and 3 dimes. That is 10 dimes. 10 dimes is like 10 tens. That is 100. I drew a picture to show the two parts. I know 3 tens and 7 tens makes 10 tens. So, 30 and 70 make 100. We can think of a dime as 1 ten because 10 pennies make a dime. Write 3 tens + 7 tens = _____ tens. What is 3 tens + 7 tens? 10 tens Write 10 tens to complete the equation in unit form. Then ask each of the following questions and record students’ responses to make a number sentence. How many is 3 tens? 30 442

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 29

How many is 7 tens? 70 How many is 10 tens? 100 Highlight each number of tens in the number sentence in unit form. Point to the number sentence. What do you notice about the highlighted numbers? I see partners to 10. 3 + 7 = 10 Using the number of tens can help us to add. If there are 10 tens, then the total is 100. Transition to the next segment by framing the work. Today, we will find all the ways to combine tens to make 100. 10 10

Learn

Differentiation: Support 10

Use Tens to Make 100 Materials—S: Dimes

Students add multiples of 10 to compose 100 with two parts.

If students need to see the 10 ones that compose 1 ten, have them use ten-sticks rather than dimes.

Pair students and give each student pair 10 dimes. You have 10 dimes, or 10 tens. 10 tens make 100. How many ways can you organize your dimes into two groups that make 100? Work with your partner to write down all the combinations you find on your whiteboard.

443

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 29

After a few minutes, invite students to share their thinking. As students share, support student-to-student dialogue by inviting the class to agree or disagree, ask a question, give a compliment, make a suggestion, or restate an idea in their own words.

Differentiation: Challenge Provide a challenge by asking students to show and record ways of composing 100 by making three or four groups of tens.

Make sure students have the Add Tens removable in their whiteboards. Guide them to systematically find all the ways to group tens in two parts to make 100 and record them. Draw 1 ten by making a quick ten or by drawing labeled circles as students follow along. This part is 1 ten. How many more tens do we need to make 100? 9 tens Draw another part with 9 tens as students do the same. Guide students to fill in the unit form. As you ask each of the following questions, record students’ responses to make a number sentence. Have them follow along. How many is 1 ten? 10 How many is 9 tens? 90

EUREKA MATH2

ten +

1 ▸ M6 ▸ TF ▸ Lesson 29 ▸ Add Tens

9 tens = 10 tens

Promoting Mathematical Practice

10 + 90 = 100 2 tens + 8 tens = 10 tens

Students look for and express regularity in repeated reasoning when they repeatedly use equations in unit form to find all the ways to make 100 by using two multiples of 10.

20 + 80 = 100 3 tens + 7 tens = 10 tens 30 + 70 = 100

By comparing the unit form and the standard form equations, students can see when they have used all the partners to 10. This helps them to confirm that they have found all the ways to make 100 in two parts.

277

How many is 10 tens? 100

In grade 2, students rely more heavily on the place value structure of numbers. This repeated reasoning lays the groundwork for that understanding.

Repeat the process for 2 tens + 8 tens, and continue in order through 4 tens + 6 tens. Release responsibility to the students as appropriate. Before completing 5 tens + 5 tens, ask the following questions. What is the next way to make 100 with tens in two parts? How do you know? 5 tens + 5 tens, or 50 and 50 I see a pattern. First, we did 1 ten, then 2 tens, then 3 tens, and then 4 tens as the first part. Next comes 5 tens. Have students complete the drawing, unit form, and number sentence for 5 tens + 5 tens. Invite students to think–pair–share about how to continue. 444

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 29

Should we continue with 6 tens + 4 tens? Is 6 tens + 4 tens a new way to make 10 tens? Explain your thinking. We could, but we don’t have to because it’s not a new way. It’s the same as 4 tens + 6 tens. It just switches the order. Confirm that we can add numbers in any order. If needed, talk through the remaining combinations (7 tens + 3 tens, 8 tens + 2 tens, and 9 tens + 1 ten) and compare them to the number sentences that students already recorded.

100 Pencils Problem Students solve an add to with start unknown problem. Have students turn to the word problem in their student book. Chorally read the problem. Have students turn and talk to retell the problem. Encourage students to reread the problem. Tell them to represent the problem by drawing on their whiteboards and then have them solve it. As needed, students may model with ten-sticks and then represent their thinking with a drawing. Students may or may not write an equation. Invite two or three students to share their thinking. I drew 6 tens to show the boxes he buys. Then I counted on by tens to 100. I added 4 tens. That is 40. He had 40 pencils at first. I drew a tape diagram. I made one part with a question mark and one part with 6 tens. I labeled the whole thing 10 tens. I know 6 and 4 make 10, so the first part must be 4 tens. 4 tens is 40.

Teacher Note Consider avoiding teaching students that they can simply add a zero to each number in a partners to 10 fact to find partners to 100. Working through the process in this segment builds conceptual understanding about why that shortcut works. Having that understanding serves students as they explore place value more deeply in grade 2. If students notice the shortcut as they study the relationships between equations in this segment, validate the observation and move on. Land provides an opportunity for brief discussion about the shortcut.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 29

Name

Read Mr. West has some boxes of 10 pencils. He buys 6 more boxes of 10 pencils. Now he has 100 pencils total. How many pencils does he have at first? Draw

What number sentences can we write to show our thinking?

100

40 + 60 = 100

10 10 10 10 10 10 60

60 + 40 = 100 100 – 60 = 40 Tell students to complete the statement that answers the question if they have not done so already.

40 10 10 10 10

Write

40 + 60 = 100 Mr. West has

pencils at first. 279

445

1 ▸ M6 ▸ TF ▸ Lesson 29

EUREKA MATH2

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Word problems may be read aloud. 10

Land Debrief

5 min

Objective: Add tens to make 100. Display the charts of partners to 10 and partners to 100. Look at the two charts. How are they the same? How are they different? I see partners to 10 in both charts. In the first chart all the totals are 10. In the second chart the totals are 10 tens, or 100. Display 35 + 70. How can knowing partners to 10 help us find the total of this problem? 3 + 7 = 10, so 3 tens and 7 tens is 10 tens, or 100. 100 + 5 = 105.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem. 446

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 29

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 29

Name

Read

Val has 4 dimes.

Ren has 10 bags of apples.

She finds 6 more dimes.

There are 10 apples in each bag.

How much money does Val have?

Ren sells 2 bags of apples.

Read

Sample:

Nate puts some books on the shelf.

There are 100 flowers in packs of 10.

He puts 10 books in his desk.

Some packs are yellow.

There are 100 books total.

Some packs are blue.

How many books did Nate put on the shelf?

How many apples does Ren still have?

Draw

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 29

Draw

packs are yellow.

packs are blue.

Draw

Write

40 + 60 = 100 Val has

Write

100

cents.

100 – 10 = 90

100 – 20 = 80 Ren has

Write

Nate put

apples.

books on the

50 + 50 = 100 There are

100

flowers.

shelf. 281

282

PROBLEM SET

447

LESSON 30

Make the next ten and add tens to make 100.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

Name

Find the unknown number. Show how you know.

68 +

32 70

Students start from different two-digit numbers and add tens and ones to make or get to 100. They either add ones to make the next ten and then add tens to make 100, or they add tens first and then add the ones. They use the arrow way and number sentences to record their thinking.

Key Question

= 100

+ 30

Lesson at a Glance

• What are some strategies we can use to get to 100 from any number?

100

Achievement Descriptors 1.Mod6.AD11 Add a two-digit number and a one-digit number that

100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of equations.

291

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 30

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Number Path to 100 removables must be torn out of student books, cut, and put together to form a number path from 1 to 100.

Launch Learn

10 min 10 min

30 min

• Make 100 • Hop to 100 Game • Problem Set

Land

10 min

• 100-bead rekenrek

Students • Eureka Math2 Numeral Cards (1 set per student group) • Number Path to 100 removable (1 per student pair, in the student book) • 10-sided dice (2 per student pair) • Counters (2 per student pair) • Make 100 removable

• The Make 100 removables must be torn out of student books and placed in personal whiteboards. Consider whether to prepare these materials in advance or to have students prepare them during the lesson. • Counters are used as game pieces in the lesson. Use any counters that are available in different colors so partners can distinguish between each other’s pieces. Bear counters, Unifix® Cubes, and two-color counters are good options.

449

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

Fluency

10 10

I Say, You Say: Partners to 20 30 Students say the partner to 20 for a given number to build addition fluency within 20. 10

Invite students to participate in I Say, You Say. When I say a number, you say its partner to 20. Ready? When I say 19, you say? 1 19 1 19 1 Repeat the process with the following sequence:

Numbers Up! Materials—S: Numeral Cards

Students find an unknown total or part to build addition and subtraction fluency within 20. Have students form groups of three. Assign roles: Player A is one part, player B is one part, and player C is the total. Distribute sets of Numeral Cards to each group and have them play according to the following rules. Consider doing a practice round with students. • Players A and B each take a card and hold it to their own foreheads so they can’t see the number. 450

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 30

• Player C looks at both cards and says the total. • Players A and B find the number on their own card, based on the total and the other part. • Player C confirms the two parts. Circulate as students play the game and provide support as needed. Have students switch roles after a few rounds.

Launch

If the total is 8, and my partner has 3, I must have 5.

The total is 8.

Player C

If the total is 8, and my partner has 5, I must have 3.

Player A

Player B

10 30

Materials—T: 100-bead rekenrek

Students add to a two-digit number to make 100. 10 Show 72 on the rekenrek. How many? How do you know? 72; I see 7 tens 2 ones. What is the next ten? 80 How many do we need to make the next ten? 8 Slide the remaining 8 beads in the row to the left all at once to show 80. Record making the next ten by using the arrow way. We started at 72. Write 72. Copyright © Great Minds PBC

451

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

Plus 8 makes the next ten. Draw an arrow labeled + 8. The next ten is 80. Write 80. Look at the rekenrek. To go from 80 to 100, how many tens do we need? How do you know? We need 2 more tens. There are 2 more rows on the rekenrek. I know 8 + 2 = 10, so 80 + 20 = 100. Let’s check our thinking. Count on with me as I slide over the tens. 80, 90, 100 Add to the arrow way recording. Start at 80 and draw an arrow labeled + 20. Then write 100. 80 plus 2 tens, or 20 beads, is 100. How much did we add to 72 to get to 100? How do you know? 28; I see an arrow with + 8 and an arrow with + 20. 8 + 20 = 28.

Teacher Note

What number sentence can we write to show how we got from 72 to 100?

If students suggest a three-addend number sentence, help them think about it as a twoaddend number sentence by drawing the arms of a number bond from 8 and 20 to a total of 28.

72 + 8 + 20 = 100 72 + 28 = 100 Write 72 + 28 = 100 under the arrow way recording. Reset the rekenrek to show 56 and repeat the process, asking the following questions: • How many? • What is the next ten? How many to get to the next 10? • How many tens to get to 100? • How much did we add to 56 to get to 100? 452

Although the three-addend number sentence is valid, this lesson lays a foundation for grade 2 work that includes adding any 2 two-digit numbers and solving unknown addend problems such as 72 + _____ = 100. Recording the various steps of students’ thinking with a two-addend number sentence bridges this lesson with grade 2 objectives.

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 30

Transition to the next segment by framing the work. Today, we will add to different numbers to make 100. 10 10

Learn Make 100

30 10

Materials—S: Number Path to 100

Students hop on a number path to get to the next ten and then to 100. Pair students. Give partners a number path and make sure all students have their whiteboards ready. Guide students to use the number path to get to 100 from a starting number. Let’s get to 100 from 63. Put your finger on 63. What is the next ten? 70 +7 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Hop to 70. How many spaces did you hop? 7

453

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

Hop to 100. How many tens did you hop? How do you know?

Differentiation: Support

3 tens; the colors on the number path help me see the tens. 3 tens; I counted on. 70, 80, 90, 100. +7

Consider providing additional visual support in the following ways:

+ 30

63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

• Provide markers, such as cubes, to help students remember the starting number and the next ten.

Use the arrow way and a number sentence to record students’ answers to the following questions. Have them follow along on their whiteboard. Let’s show our thinking the arrow way. Where did we start? 63 How many spaces did we did we hop to get to the next ten? 7 Where did we land?

+ 30

• Use a highlighter to mark groups of ten on the number path.

100

• Make an arrow way drawing that shows each ten so students can use the recording to find how many tens they counted.

63 + 37 = 100 +7

+ 10

63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

70 How did we get to 100? We hopped 3 tens or 30 more.

Promoting Mathematical Practice

What number sentence can we write? 63 + 7 + 30 = 100 63 + 37 = 100 Write 63 + 37 = 100 as students follow along. How does this number sentence show our thinking? We started at 63. Then we added 7 and 30 and ended on 100.

454

As students record ways to get to 100 in two hops, they look for and make use of structure. Recording a two-addend number sentence helps students to think about the amount needed to get to 100 in terms of the place value structure of tens and ones. The twoaddend number sentence also makes use of the associative property, which makes it possible to add no matter how numbers are grouped: 52 + 8 + 40 = 52 + 48.

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 30

Ask partners to repeat the process, this time starting at 52. After they solve the problem by using their number paths, have them use the arrow way and a number sentence to record their thinking.

+ 40

100

52 + 48 = 100

Invite a student to share their work. If possible, consider sharing more than one solution. Display two different ways to get from 38 to 100. This is how two students got from 38 to 100.

+ 60

100

+ 60

100

Invite students to think–pair–share about what is different and what is the same about the two ways. What is the same about these ways? How are the ways different from each other? They both hopped 2 and 60 from 38. They both used two hops to get to 100. One got the next ten or 40. The other did not. They hopped in different orders, 2 then 60 or 60 then 2. What number sentence can we write? Why? 38 + 62 = 100. They started at 38, added 60 and 2, and ended on 100. Write the expressions for both representations and record a two-addend number sentence. We can get to 100 by making the next ten first or by adding tens first.

455

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

Hop to 100 Game Materials—S: Number Path to 100, 10-sided dice, counters, Make 100 removable

Students start at different numbers and add on a number path to make 100. Distribute two 10-sided dice and two different-color counters to each pair. Make sure each student pair has their number path ready. Also make sure each student has their whiteboard ready with the Make 100 removable in it. Give the following directions for the game:

UDL: Action & Expression Consider supporting students by posting recordings of earlier examples that students can use for reference.

• To start the game, partners take turns rolling the dice to determine their starting number. For example, if a student rolls a 2 and a 1, they can choose to start their counter on 12 or on 21.

Differentiation: Support

• Each partner uses their counter to hop to 100 on the number path.

Ask the following guiding questions:

• They use the arrow way and a number sentence to record their thinking on the Make 100 removable.

• What is the next ten?

• Partners check each other’s work.

• How many spaces do you need to hop to get to the next ten?

• Each partner rolls the dice again to get a new starting number and then repeat the process.

• How many tens are there to get to 100?

456

2 3 4 5 6 7 8 9 10 11 12 13 14

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 30

Use the following questions to advance and assess student understanding as they play: • How will you get to 100? Will you add tens or ones first? • How does your arrow way recording show how you got to 100? • How does your number sentence match your thinking?

Differentiation: Challenge Invite students to get to 100 with only 2 hops in as many ways as they can.

Problem Set Differentiate the set by selecting problems for students to finish independently within the timeframe. Problems are organized from simple to complex. 10 Directions may be read aloud. 10

Land Debrief

5 min

Materials—S: Number Path to 100

Objective: Make the next ten and add tens to make 100. Gather partners with their number paths. Max says he started at 12 and got to 100 in just two hops. Invite students to think–pair–share about how Max could have done this. What hops could Max have made? He could hop to 20 and then to 100. He could hop to 92 and then to 100.

457

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

Display two different ways to get from 12 to 100. Here are two ways to get from 12 to 100 in just two hops.

+ 80

100

+ 80

100

What number sentence can we write to represent both ways? 12 + 88 = 100 Write 12 + 88 = 100. How does this number sentence show both ways of thinking? Both ways show arrows with + 8 and + 80. 8 and 80 make 88. Both start at 12 and end at 100, so 12 is the first number and 100 is the total. What are some strategies we can use to get to 100 from any number? We can make the next ten. We can add tens first and then add ones.

Exit Ticket

5 min

Provide up to 5 minutes for students to complete the Exit Ticket. It is possible to gather formative data even if some students do not complete every problem.

458

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 30

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

Name

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 30

1. Add.

Use your number path.

70 66 +

100

54 + 6 + 40 =

43 + 7 + 50 =

100 = 100

100 3. Find the unknown part.

100

14 + 6 + 80 =

23 + 7 + 70 =

Show how you know.

100

54 +

2. Make 100 with your number path.

+ 40

36 +

= 100

100 68

68 +

32 70

= 100

+ 30

100

60 77 +

100

= 100 289

290

23 80

PROBLEM SET

= 100

+ 20

100 89

89 +

11 90

= 100

+ 10

100

459

LESSON 31

Add to make 100.

EUREKA MATH2

1 ▸ M6 ▸ TF

Name

1. Add.

36 + 64 =

100

44 + 55 =

Lesson at a Glance Students study pictures of numbers represented in terms of tens and ones. They try to figure out which two numbers in the pictures can be combined to make 100. To culminate the year, students consider where they see math in the world around them and reflect on their learning during the year. There is no Problem Set in this lesson. This allows students to spend more time exploring ways to make 100.

Key Question • What addends make 100? How do you know? 2. Draw or write. What did you learn in math this year?

Achievement Descriptors

What are you good at in math?

1.Mod6.AD11 Add a two-digit number and a one-digit number that

1.Mod6.AD12 Add 2 two-digit numbers that have a sum within

What do you like about math?

100, relate the strategy used to a written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of equations.

305

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 31

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• The Add Within 100 Sprints must be torn out of student books. Consider whether to prepare these materials in advance or to have students prepare them during the lesson.

Launch Learn

10 min 10 min

25 min

• Match: Make 100 • Find the Total

Land

15 min

• None

Students • Add Within 100 Sprint (in the student book) • Match: Make 100 Recording Sheets (in the student book) • Match: Make 100 cards (1 set of 18 cards per student pair, in the student book)

• The Match: Make 100 Recording Sheets must be torn out of student books and placed in personal whiteboards. There are 2 pages. Students should place them so that both pages are visible. • The Match: Make 100 cards must be torn out of student books and cut apart. Consider whether to prepare the cards in advance or during the lesson.

461

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 31

Fluency

10 10

Sprint: Add Within 100 Materials—S: Add Within 25 100 Sprint MATH 1 ▸ M6 ▸ TF ▸ Lesson 31 ▸ Sprint ▸ Add Within 100 Students add tens and onesEUREKA to build addition fluency within 100. 2

Have students read the instructions and complete the sample problems. Sprint Add. 1.

3 tens + 2 tens 5 tens

30 + 20

20 + 5

20 + 15

462

293

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 31

Read the answers to Sprint A quickly and energetically. Count the number you got correct and write the number at the top of the page. This is your personal goal for Sprint B. Celebrate students’ effort and success. Provide about 2 minutes to allow students to analyze and discuss patterns in Sprint A. Lead students in one fast-paced and one slow-paced counting activity, each with a stretch or physical movement. Point to the number you got correct on Sprint A. Remember this is your personal goal for Sprint B. Direct students to Sprint B. Take your mark. Get set. Improve! Time students for 1 minute on Sprint B. Stop! Underline the last problem you did. I’m going to read the answers. As I read the answers, call out “Yes!” and mark your answer if you got it correct. Read the answers to Sprint B quickly and energetically.

Teacher Note Consider asking the following questions to discuss the patterns in Sprint A: • What patterns do you notice about problems 1–6? About problems 1–12? • How can you use problem 13 to solve problem 14? • How can you use problem 14 to solve problem 15?

Teacher Note Count on by tens from 5 to 105 for the fastpaced counting activity. Count backward by tens from 105 to 5 for the slow-paced counting activity.

Count the number you got correct and write the number at the top of the page. Stand if you got more correct on Sprint B. Celebrate students’ improvement.

463

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 31 10

Launch

10 25

Materials—S: Match: Make 100 Recording Sheet

Students find two 15 addends that make 100.

Teacher Note

Display four of the Make 100 cards. These cards show four different numbers. Turn and talk: Which two numbers do you think total 100?

Tell students to self-select strategies and tools to find two cards that total 100. Make sure students have the Make 100 Recording Sheet in their personal whiteboard, and have them use it to record their thinking. Facilitate a discussion about students’ reasoning. Which two cards make 100? How do you know? 93 and 7; 3 and 7 make ten. 90 and 10 make 100. No other pair of cards shown makes 100. Why?

Students are likely to need to make more than one attempt to make 100 as a total of two cards. Encourage them to erase and try again if their combination does not total 100. Share with students that they may have to try more than once and doing this provides an opportunity for learning.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 31 ▸ Match: Make 100

93 + 7 = 100 3

= 100

99 is only 1 away from 100 and there is no 1 card. 50 + 7 = 57. 93 and 99 are both very close to 100, so they would be more than 100 if we put them together.

= 100

Today, we will write number sentences to show different ways to make 100.

464

10 EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 31 10

Learn

25 15

Match: Make 100

Differentiation: Support

Materials—S: Match: Make 100 cards, Match: Make 100 Recording Sheet

Students combine two sets of tens and ones to make a given total. Pair students. Assign students as partner A or partner B. Demonstrate how to play Match: Make 100 by using the following procedure: • Arrange the 18 Match: Make 100 cards with numbers facing up.

Provide ten-sticks and cubes as concrete tools for students to use to represent the numbers, if needed.

Differentiation: Challenge

100

Have sticky notes available for students to use to record other number pairs that total 100.

• Partner A studies the cards and tries to choose two cards that make 100. • Partner A self-selects strategies and tools to confirm the total.

Promoting Mathematical Practice

• If the total is exactly 100, then partner A records their thinking on their Match: Make 100 Recording Sheet. They keep the cards. If the total is not 100, partner A puts the cards back. • Partner B takes a turn. Distribute the Match: Make 100 cards to each student pair. Have students play for 6 or 7 minutes. Circulate and ask the following assessing and advancing questions:

0 + 100 1 + 99 5 + 95

• Why did you choose those cards?

7 + 93

• How did you find the total?

10 + 90

Display all the ways students could have made 100.

30 + 70

Guide students to reflect on the problems they solved.

50 + 50

11 + 89

As students play Match: Make 100, they choose appropriate tools strategically. This year students worked with a variety of tools including physical tools like cubes and number paths, and mathematical tools like equations, number bonds, and tape diagrams. In this lesson segment, students self-select ways of combining cards to find a total, which gives them an opportunity to think about the tools they know and select the ones that work best for a given number pair. Encourage all students to record their thinking with a written method.

48 + 52 465

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 31

70 + 30 because it is easier to add addends that do not have ones. 50 + 50 because I know 5 + 5 = 10. 5 tens and 5 tens is 10 tens, or 100. Which problem was the hardest for you to solve? Why? 48 + 52 and 11 + 89 are both hard because you have to add the tens and the ones.

Find the Total Students find the number of objects in a collection that totals 100. Display the picture of 100 candies. Invite students to notice and wonder. How many candies do you think there are? Why? 100; I see a 1, 0, 0.

Teacher Note As an alternative activity, invite students to make 100 with manipulatives such as pattern blocks. Ask them to show the total using a number sentence.

100; there are a lot of them. Let’s find out! What are some ways we could count and add to find the total? We could count the candies in the three groups and add them. We could count the colors of the candies and add them. We could count the large candies and the small candies and add them. Let’s see how many ways we can count and add the candies to find the total. Ask students to turn to the picture of candies in their student book. Tell them to find the total number of candies and record their thinking. Encourage them to confirm their total by finding it a second way. Circulate and identify student work samples that show a variety of ways to make 100.

466

8 + 20 + 8 + 24 + 12 + 28 = 100

EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 31

Size (small, large): 89 + 11

89 + 80 9

11 10 1

90 + 10 = 100

Numbers (1, 0, 0): 34 + 33 + 33

34 + 33 + 33 = 100

Colors (red, yellow, green, blue, orange): 20 + 20 + 20 + 20 + 20

20, 40, 60, 80, 100

30 4 30 3 30 3 30 + 30 + 30 = 90 4 + 3 + 3 = 10 90 + 10 = 100

Invite two or three students to share their work. Encourage the class to engage in the mathematics by asking one another questions and making observations about one another’s work.

Differentiation: Challenge Invite students to use the candies picture to collect, represent, and analyze data in the following ways: • Identify two to four categories, such as color or size. • Use the categories to make a graph or chart. • Find the total of all the categories. • Figure out how many more one category has than another.

I counted the candies in the three groups and added them. I counted the colors of the candies and added them. I counted the large candies and the small candies and added them.

467

10 EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 31 25

Land Debrief

5 min

Objective: Add to make 100. Display the picture of the city street. Allow a moment for students to notice and wonder. Then invite them to consider the mathematics in the picture. There are many ways to see math in the world around us.

Teacher Note

What math do you see in this picture?

If time allows, invite students to use the image to do the following activities:

What math could we use to find out more about this picture?

• Write a number sentence.

The picture has shapes. I see a cone, a sphere, and rectangles.

• Write and solve a word problem.

There is a clock telling time.

• Make a graph.

There are lots of people. We could count them or add the number of people in the picture.

Consider having students show or share their work using a gallery walk.

We could measure things in the picture to see how long they are. Invite students to reflect on their grade 1 learning. Prompt student thinking with questions if needed. Invite students to think–pair–share about what they learned in math this year.

Language Support

What did you learn about math this year? Invite students to summarize the work they’ve completed this year. Support them in doing this by pairing a student who speaks one native language with another student who speaks the same native language. Encourage students to share in their native language first and then to share in English.

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EUREKA MATH2 1 ▸ M6 ▸ TF ▸ Lesson 31

Topic Ticket

10 min

Provide up to 10 minutes for students to complete the Topic Ticket. It is possible to gather formative data even if some students do not complete every problem. More time is included to allow students to answer end-of-year reflective questions on the Topic Ticket.

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1 ▸ M6 ▸ TF ▸ Lesson 31

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 31 ▸ Sprint ▸ Add Within 100

Number Correct:

2. 3. 4. 5.

4 tens + 1 ten 5 tens 40 + 10

5 tens + 2 tens 7 tens 50 + 20

6 tens + 3 tens 9 tens

13.

40 + 5

14.

40 + 15

15.

50 + 15

16.

50 + 25

17.

60 + 25

3 tens + 1 ten 4 tens 30 + 10

4 tens + 2 tens 6 tens 40 + 20

5 tens + 3 tens 8 tens

13.

30 + 5

14.

30 + 15

15.

40 + 15

16.

40 + 25

17.

50 + 25

60 + 30

18.

60 + 35

50 + 30

18.

50 + 35

30 + 60

19.

35 + 60

30 + 50

19.

35 + 50

20 + 50

20.

25 + 60

20 + 40

20.

25 + 50

10 + 40

21.

15 + 70

10 + 30

21.

15 + 60

10.

20 + 40

22.

25 + 70

10.

20 + 30

22.

25 + 60

11.

30 + 50

23.

35 + 50

11.

30 + 40

23.

35 + 40

12.

40 + 60

100

24.

45 + 50

12.

40 + 50

24.

45 + 40

294

470

Number Correct:

Add.

Add. 1.

EUREKA MATH2

1 ▸ M6 ▸ TF ▸ Lesson 31 ▸ Sprint ▸ Add Within 100

296

This page may be reproduced for classroom use only.

471

Name

10 10

3. Draw tens and ones to show 115.

, 105, 106,

, 101, 102, 103,

2. Count. Write the total.

108, 109,

1. Count by ones. Write the missing numbers.

Module Assessment

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

This page may be reproduced for classroom use only.

472

The toy puppy is

Write

Draw

How many more points is the toy puppy than the ball?

The ball is 9 points.

The toy puppy is 18 points.

Read

ball

giant lollipop

more points than the ball.

binoculars

toy puppy

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

This page may be reproduced for classroom use only.

473

Baz needs

Write

Draw

How many more points does he need?

He has 8 points.

Baz wants to win the toy puppy.

Read

more points.

ball

binoculars

giant lollipop

toy puppy

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

This page may be reproduced for classroom use only.

474

62 + 9 =

43 + 53 =

Show how you know.

6. Add.

54 + 27 =

38 + 32 =

EUREKA MATH2 1 ▸ M6 ▸ Module Assessment

Achievement Descriptors: Proficiency Indicators 1.Mod6.AD7 Represent and solve word problems within 20 involving all addition and subtraction problem types by using

drawings and an equation with a symbol for the unknown. Partially Proficient

Proficient

Highly Proficient

Represent word problems by using drawings and an equation with a symbol for the unknown and solve word problems within 20 involving add to with result unknown, take from with result unknown, and put together and take apart with total unknown problem types.

Represent word problems by using drawings and an equation with a symbol for the unknown and solve word problems within 20 involving add to with change unknown, take from with change unknown, put together and take apart with addend unknown, and comparison problem types.

Represent word problems by using drawings and an equation with a symbol for the unknown and solve word problems within 20 involving add to with start unknown, take from with start unknown, and comparison problem types where more and fewer suggest the incorrect operation.

Read

Read Jade has 9 tickets.

Math takes 10 minutes.

She gets 3 more tickets.

She gets some more tickets.

Math takes 4 more minutes than art.

How many tickets does she have?

Now she has 15 tickets.

How many minutes does art take?

How many more tickets did she get?

Draw

? 9

9 + 3 = ?

She has

She got

Write

10 - 4 = 6

9 + ? = 15 tickets.

10 – 4 = ?

Write

9 + 3 = 12

Draw

9 + ? = 15

Write

476

Read

Jade has 9 tickets.

more tickets.

Art takes

minutes.

EUREKA MATH2 1 ▸ M6

1.Mod6.AD8 Represent a set of up to 120 objects with a written numeral by composing tens. Partially Proficient

Proficient

Represent a set of up to 99 objects with a two-digit number by composing tens.

Represent a set of 100–120 objects with a written numeral by composing tens.

Circle all the groups of 10.

tens

Highly Proficient

ones

Total

tens

ones

Total

477

EUREKA MATH2

1 ▸ M6

1.Mod6.AD9 Represent three-digit numbers within 120 as tens and ones. Partially Proficient

Proficient

Highly Proficient

Represent two-digit numbers within 99 as tens and ones.

Represent three-digit numbers within 120 as tens and ones.

Draw tens and ones to show 78.

Draw tens and ones to show 118.

1.Mod6.AD10 Write missing numbers in a sequence within 120. Partially Proficient

Highly Proficient

Write missing numbers in a sequence within 99.

Write missing numbers in a sequence within 120.

Count by ones. Write the missing numbers.

, 76, 77, 78, 79,

478

Proficient

, 81, 82,

, 98, 99,

, 101, 102, 103,

, 105, 106, 107

Write a missing number in a sequence within 120, counting by tens. Count by tens. Write the missing numbers.

10, 20,

, 40,

, 60, 70,

, 90,

, 110,

EUREKA MATH2 1 ▸ M6

1.Mod6.AD11 Add a two-digit number and a one-digit number that have a sum within 100, relate the strategy used to a

written method, and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations. Partially Proficient

Proficient

Add a two-digit number and a one-digit number that have a sum within 100 when composing a ten is not required and relate the strategy used to a written method.

Add a two-digit number and a one-digit number that have a sum within 100 when composing a ten is required, relate the strategy used to a written method, and explain the reasoning used.

Add. Show how you know.

72 + 6 = 70 2 70 + 2 + 6 = 78

Explain multiple strategies for adding a two-digit number and a one-digit number. Add. Show how you know.

27 + 5 =

78 + 5 = 80

Highly Proficient

I broke up 5 to make the next ten with 78. 80 and 3 is 83.

3 2

I broke up 5 to make the next ten with 27. 30 and 2 is 32. Show another way to add.

27 + 5 =

20 7 7 + 5 = 12 20 + 12 = 32 I added the ones first. 7 and 5 is 12. 20 and 12 is 32.

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EUREKA MATH2

1 ▸ M6

1.Mod6.AD12 Add 2 two-digit numbers that have a sum within 100, relate the strategy used to a written method,

and explain the reasoning used. Use concrete models, drawings, strategies based on place value, and/or properties of operations. Partially Proficient Add 2 two-digit numbers that have a sum within 100 when composing a ten is not required and relate the strategy used to a written method. Add. Show how you know.

45 + 21 = 20 1 45 + 20 = 65 65 + 1 = 66

Proficient Add 2 two-digit numbers that have a sum within 100 when composing a ten is required, relate the strategy used to a written method, and explain the reasoning used. Add. Show how you know.

77 + 14 =

Highly Proficient Explain multiple strategies for adding 2 two-digit numbers that have a sum within 100. Add. Show how you know.

77 + 14 = 91

10 4 77 + 10 = 87 87 + 4 = 91 I broke apart 14 into 10 and 4. I know 77 and 10 is 87. Then I counted on four more from 87: 88, 89, 90, 91.

10 4 77 + 10 = 87 87 + 4 = 91 I broke apart 14 into 10 and 4. I know 77 and 10 is 87. Then I counted on four more from 87: 88, 89, 90, 91. Show another way to add.

77 + 14 = 80

3 11

I broke apart 14 to make the next 10 with 77. 80 and 11 is 91.

480

Observational Assessment Recording Sheet Grade 1 Module 6

Student Name

Part 2: Advancing Place Value, Addition, and Subtraction Achievement Descriptors 1.Mod6.AD7

Represent and solve word problems within 20 involving all addition and subtraction problem types by using drawings and an equation with a symbol for the unknown.

1.Mod6.AD8

Represent a set of up to 120 objects with a written numeral by composing tens.

1.Mod6.AD9

Represent three-digit numbers within 120 as tens and ones.

1.Mod6.AD10

Write missing numbers in a sequence within 120.

1.Mod6.AD11

1.Mod6.AD12

Notes

482

Dates and Details of Observations

This page may be reproduced for classroom use only.

P Proficient

HP Highly Proficient

EUREKA MATH2 1 ▸ M6 ▸ Observational Assessment Recording Sheet

Module Achievement Descriptors by Lesson ● Focus content ○ Supplemental content Lesson Achievement Descriptor

Topic D 16

Topic E 19 20 21

1.Mod6.AD7

Topic F

22 23 24 25 26 27 28 29 30 31

● ● ● ● ● ●

1.Mod6.AD8

● ●

●

1.Mod6.AD9

○

●

1.Mod6.AD10 1.Mod6.AD11 1.Mod6.AD12

○

● ● ● ●

● ●

● ● ● ● ● ●

This page may be reproduced for classroom use only.

483

Sample Solutions Expect to see varied solution paths. Accept accurate responses, reasonable explanations, and equivalent answers for all student work.

EUREKA MATH2

1 ▸ M6 ▸ Module Assessment

Module Assessment

1 ▸ M6 ▸ Module Assessment

Read The toy puppy is 18 points.

Name

The ball is 9 points. 1. Count by ones. Write the missing numbers.

How many more points is the toy puppy than the ball?

99 , 100 , 101, 102, 103, 104 , 105, 106, 107 , 108, 109, 110

binoculars

ball

giant lollipop

toy puppy

Draw

2. Count. Write the total. 10

104

101

3. Draw tens and ones to show 115.

100 15

484

This page may be reproduced for classroom use only.

471

Write

18 - 9 = 9 The toy puppy is

more points than the ball.

472

EUREKA MATH2 1 ▸ M6

EUREKA MATH2

1 ▸ M6 ▸ Module Assessment

6. Add.

Read Baz wants to win the toy puppy. He has 8 points.

binoculars

ball

giant lollipop

Show how you know. 5

How many more points does he need?

toy puppy

43 + 53 =

Draw

38 + 32 =

40 3 50 3

2 30

40 + 50 = 90 3+3=6

This page may be reproduced for classroom use only.

18 = 8 + 10 Baz needs

more points.

54 + 27 =

473

Write

62 + 9 =

474

485

Terminology The following terms are critical to the work of grade 1 module 6 part 2. This resource groups terms into categories called New, Familiar, and Academic Verbs. The lessons in this module incorporate terminology with the expectation that students work toward applying it during discussions and in writing.

Familiar addend

one(s)

compare

part

efficient

partners

equal

represent

equation

subtract

expression

take away

Items in the Familiar category are discipline-specific words introduced in prior modules or in previous grade levels.

false

ten(s)

fewer

total

Items in the Academic Verbs category are high-utility terms that are used across disciplines. These terms come from a list of academic verbs that the curriculum strategically introduces at this grade level.

greater

true

less

unit

minus

unknown

New

Academic Verbs

Module 6 part 2 does not introduce any new terminology.

Module 6 part 2 does not introduce any academic verbs from the grade 1 list.

Items in the New category are discipline-specific words that are introduced to students in this module. These items include the definition, description, or illustration as it is presented to students. At times, this resource also includes italicized language for teachers that expands on the wording used with students.

486

Math Past 0, 9, 8, 7, 6, 5, 4, 3, 2, 1 Where did the numerals we use today come from? What’s the same and what’s different about the numeral systems we’ve studied? We have learned a lot about how people throughout the world, both in the past and today, write and talk about numbers! We learned about Chinese number rods.

We learned about the Yoruba people and how they describe 15 as 5 before 20. We even learned about why the number 12 was important to ancient Egyptians, which is why we see it on our clocks! All of this leads us to wonder: Where did the numbers we use come from? It turns out to be a complicated story that’s missing a few pieces! The numerals we use today were created and developed by mathematicians and astronomers in India. They were later 1 2 3

A key person in the development of the Hindu-Arabic numerals in India was the mathematician Brahmagupta (c. 598–670). His book Brahma Sphuta Siddhanta (The Opening of the Universe) appears to be the original text that brought Indian mathematics and their numerals to the Islamic world.1 Another important person in the story is Abu Ja’far Muhammad ibn Mūsā al Khwārizmī, usually shortened to al Khwārizmī. His book On Indian Numbers, which was later translated into Latin, became one of the main sources Europeans used to learn the Indian numerals.2

We also learned about Maya numerals, which use the shell symbol for 0.

passed on to Europeans through translations of texts that were written during the Islamic Golden Age. Because of these two sources, they are called the Hindu-Arabic numerals.

In fact, according to some scholars, the word algorithm also comes from the work of al Khwārizmī, but only because of a mistake. Some of the translations of his work were not very good ones, and one even identified the author as Algor, a former king of India. Because On Indian Numbers taught people throughout Europe how to do arithmetic and algebra with Hindu-Arabic numerals, the word algorithm came to be named after Algor, since Europeans thought he had written the book!3 Guide students to compare the Hindu-Arabic numerals with some of the other systems they have studied. Show students the following table of the numerals 9, 10, and 11. Explain that the first row shows the Hindu-Arabic numerals, the second row shows the same numbers represented by Chinese number rods, and the bottom row shows the Maya numerals for 9, 10, and 11.

Jeff Suzuki, Mathematics in Historical Context, 78–79. Suzuki, Mathematics in Historical Context, 86. Suzuki, Mathematics in Historical Context, 86.

488

EUREKA MATH2 1 ▸ M6

You can also ask students these questions to prompt discussion: Why do you think the systems have so much in common even though they look different? Why did we end up using Hindu-Arabic numerals instead of another system, like Maya numerals?

Ask students what they notice about the three different ways to write 9, 10, and 11. What’s the same about each system? What is different? Remind students that the boxes used with Chinese number rods are not part of the number but are used to show place value. Students might notice when looking at the column for 10 that the Chinese number rods do not have a symbol for 0. Instead, the box is empty. They might also notice that Hindu-Arabic numerals and Chinese number rods both use a new place once they get to 10, while the Maya numerals keep going without a new place. Next, show students the different ways of writing 19, 20, and 21. Again, ask students what is the same about the numerals and what is different about them.

The relationship between the Hindu-Arabic numerals and the Chinese numeration system is less clear, however. There is evidence that these groups of people shared ideas, mostly due to the spread of Buddhism from India to China in the first century CE. However, the historical record isn’t clear on who contributed what to the numeral systems and when.4 The Bakhshali manuscript, shown here, is one of the earliest known examples of Hindu-Arabic numerals. As you can see, they look very different from the numerals we’re used to!

Students might notice that the Maya numerals use a symbol for 0, a shell. They might also notice that starting with 20 Maya numbers show the larger place value vertically. The dot in the Maya number 20 has a value of 20. Similarly, with the Maya number 21, the dot on top has a value of 20, and the dot on the bottom has a value of 1. Our system uses place values based on the number 10, but Mayan place values are based on 20. Ask students what they think is useful about the different numeral systems. 4

The Hindu-Arabic numerals and the Maya numerals developed independently. Because the Maya people are located in Central and South America, as far as we know, there was no contact between the people there and the people of India until centuries after the development of both numeral systems.

None of these systems is better or worse than any of the others. We use Hindu-Arabic numerals in America because they spread

Suzuki, Mathematics in Historical Context, 78–79.

489

1 ▸ M6

throughout Europe in the period of time just before various European countries colonized other parts of the world. During that time, Europeans replaced the indigenous numeral systems with Hindu-Arabic numerals because they were used to them. This is similar to how Europeans forced the replacement of indigenous languages with their own languages, such as English, Spanish, and French.

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EUREKA MATH2

The Hindu-Arabic numerals weren’t created all at once. Instead, they developed in a similar way as language, over time, and with different people contributing to their development. New ideas were added as they were needed. As we’ve seen throughout the year, incorporating different perspectives of mathematical thinking makes us stronger mathematicians!

Mathematician Sketches Who Are Mathematicians? Alberto Pedro Calderón

Katherine Johnson

Alberto Pedro Calderón (1920–1998) was an Argentinian mathematician. He founded the Chicago school of mathematical analysis along with his mentor, Antoni Zygmund. Dr. Calderón studied a special kind of equation called a partial differential equation. This equation can be used to describe many things, like the way water moves when you drop a stone into a pond or how the heat moves through a room after a heater is turned on.

Katherine Johnson (1918–2020) was an American mathematician. She worked with NASA to calculate how to launch rockets so they would reach space! Her calculations were critical in ensuring that the first Americans to travel to space did so safely and successfully. She also worked on flights to the Moon and on plans for a mission to Mars.

Alan Turing

Srinivasa Ramanujan Alan Turing (1912–1954) was an English mathematician, computer scientist, and philosopher. His work on code-breaking was important to the success of the Allies (Great Britain, France, the Soviet Union, United States, and China) in World War II. Because of his work, the Allies were able to build a machine that decoded German military communications. He also wrote about the idea of artificial intelligence and proposed an experiment now known as the Turing Test to help people determine if a computer is intelligent.

492

Srinivasa Ramanujan (1887–1920) was an Indian mathematician. He was largely self-taught, having almost no formal mathematical training. Even so, he made substantial contributions to what we know about mathematics–because of his lack of training, not in spite of it. He was able to see mathematics in his own way and approach problems with new and novel ideas, allowing him to solve many problems that had stumped the great mathematicians of his time.

EUREKA MATH2 1 ▸ M6

Mariel Vázquez

Ada Lovelace

Mariel Vázquez is a Mexican mathematical biologist. This means she uses her mathematical knowledge to study problems in biology, the science of living things. She specializes in a field called the topology of DNA. Topology is a special kind of math that studies shapes. DNA is a chemical that can be thought of as the recipe for how to make a living creature. Dr. Vázquez uses mathematics to study the shape of DNA so we can better understand how different creatures are made.

Ada Lovelace (1815–1852) was an English mathematician and writer. She is thought to have been the first person to recognize how useful computers could be! She realized that computers could be used for more than calculations, like adding and subtracting, and she wrote the first computer program (on paper!). However, the actual machines that could run such a program wouldn’t be invented until years after her death.

493

Materials The following materials are needed to implement this module. The suggested quantities are based on a class of 24 students and one teacher. 1

100-bead demonstration rekenrek

Index cards

10-sided dice, set of 24

Learn books

Base 10 rods, plastic, sets of 50

Markers

Centimeter cubes, sets of 500

Paper bag or opaque box

Chart paper, tablet

Paper clips, boxes of 100

Computer with internet access

Pencils

Craft sticks, 6 color, package of 1,000

Personal whiteboards

120

Dimes

Personal whiteboard erasers

Dot dice, set of 12

Projection device

Dry-erase markers

String, spool

Eureka Math2™ Hide Zero® cards, demonstration set

Teach book

Eureka Math2™ Hide Zero® cards, basic student set of 12

Teddy bear counters, set of 96

Eureka Math2™ Hide Zero® cards, student extension set of 12

Two-color counters, set of 200 pieces

Eureka Math2™ Numeral Cards decks

Unifix® Cubes, set of 1,000

Visit http://eurmath.link/materials to learn more. Please see lesson 16 for a list of organizational tools (cups, plates, number paths, etc.) suggested for the counting collections.

494

Works Cited Andrewes, William J. H. “A Chronicle of Timekeeping.” Scientific American, February 1, 2006. Retrieved from https://www.scientificamerican.com/article/a-chronicle -of-timekeeping-2006-02, July 29, 2020.

Fosnot, Catherine Twomey, and Maarten Dolk. Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann, 2001.

Carpenter, Thomas P., Megan L. Franke, and Linda Levi. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann, 2003.

Franke, Megan L., Elham Kazemi, and Angela Chan Turrou. Choral Counting and Counting Collections: Transforming the PreK-5 Math Classroom. Portsmouth, NH: Stenhouse, 2018.

Carpenter, Thomas P., Megan L. Franke, Nicholas C. Johnson, Angela C. Turrou, and Anita A. Wager. Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education. Portsmouth, NH: Heinemann, 2017.

Hattie, John, Douglas Fisher, and Nancy Frey. Visible Learning for Mathematics: What Works Best to Optimize Student Learning. Thousand Oaks, CA: Corwin Mathematics, 2017.

CAST. Universal Design for Learning Guidelines version 2.2. Retrieved from http://udlguidelines.cast.org, 2018. Clements, Douglas H. and Julie Sarama. Learning and Teaching Early Math: The Learning Trajectories Approach. New York: Routledge, 2014. Danielson, Christopher. How Many?: A Counting Book: Teacher’s Guide. Portland, ME: Stenhouse, 2018. Danielson, Christopher. Which One Doesn’t Belong?: A Teacher’s Guide. Portland, ME: Stenhouse, 2016. Empson, Susan B. and Linda Levi. Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH: Heinemann, 2011. Flynn, Mike. Beyond Answers: Exploring Mathematical Practices with Young Children. Portsmouth, NH: Stenhouse, 2017.

Huinker, DeAnn and Victoria Bill. Taking Action: Implementing Effective Mathematics Teaching Practices. Kindergarten–Grade 5, edited by Margaret Smith. Reston, VA: National Council of Teachers of Mathematics, 2017. Kelemanik, Grace, Amy Lucenta, Susan Janssen Creighton, and Magdalene Lampert. Routines for Reasoning: Fostering the Mathematical Practices in All Students. Portsmouth, NH: Heinemann, 2016. Keller, Shana. Ticktock Banneker’s Clock. Ann Arbor, MI: Sleeping Bear Press, 2016. Lombardi, Michael A. “Why is a minute divided into 60 seconds, an hour into 60 minutes, yet there are only 24 hours in a day?” Scientific American, March 5, 2007. Retrieved from https://www.scientificamerican.com/article/experts-time -division-days-hours-minutes, July 29, 2020.

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Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. New York: Routledge, 2010. National Institute of Standards and Technology. “A Walk Through Time – Early Clocks.” Retrieved from https://nist.gov/pml /time-and-frequency-division/popular-links/walk-through -time/walk-through-time-early-clocks, July 29, 2020. Parker, Thomas and Scott Baldridge. Elementary Mathematics for Teachers. Okemos, MI: Sefton-Ash, 2004. Shumway, Jessica F. Number Sense Routines: Building Mathematical Understanding Every Day in Grades 3–5. Portland, ME: Stenhouse Publishing, 2018. Smith, Margaret S. and Mary K. Stein. 5 Practices for Orchestrating Productive Mathematics Discussions, 2nd ed. Reston, VA: National Council of Teachers of Mathematics, 2018. Smith, Margaret S., Victoria Bill, and Miriam Gamoran Sherin. The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom,

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2nd ed. Thousand Oaks, CA: Corwin Mathematics; Reston, VA: National Council of Teachers of Mathematics, 2020. Suzuki, Jeff. Mathematics in Historical Context. Providence, RI: American Mathematical Society, 2009. Van de Walle, John A. Elementary and Middle School Mathematics: Teaching Developmentally. New York: Pearson, 2004. Van de Walle, John A., Karen S. Karp, LouAnn H. Lovin, and Jennifer M. Bay-Williams. Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction for Grades 3–5, 3rd ed. New York: Pearson, 2018. Zwiers, Jeff, Jack Dieckmann, Sara Rutherford-Quach, Vinci Daro, Renae Skarin, Steven Weiss, and James Malamut. Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Retrieved from Stanford University, UL/SCALE website: http://ell .stanford.edu/content/mathematics-resources-additional -resources, 2017.

Credits Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module. All United States currency images Courtesy the United States Mint and the National Numismatic Collection, National Museum of American History. For a complete list of credits, visit http://eurmath.link/ media-credits. Cover, Edward Hopper (1882–1967), Tables for Ladies, 1930. Oil on canvas, H. 48-1/4, W. 60-1/4 in. (122.6 x 153 cm.). George A. Hearn Fund, 1931 (31.62). The Metropolitan Museum of Art. © 2020 Heirs of Josephine N. Hopper/Licensed by Artists Rights Society (ARS), NY. Photo Credit: Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY; pages 8, 153, 189, 198, 203, Krakenimages.com/Shutterstock. com; pages 15, 60, 62, 64, robuart/Shutterstock.com; pages 17, 71, 88, Sashkin/Shutterstock.com;page 40, petekarici/ DigitalVision Vectors/Getty Images; page 70, (left, from top) Frank Rocco/Alamy Stock Photo, ixpert/Shutterstock.com, Pawel Horazy/ Shutterstock.com, Pineapple studio/Shutterstock.com, domnitsky/ Shutterstock.com, Yulia Glam/Shutterstock.com, O.Bellini/ Shutterstock.com, Sashkin/Shutterstock.com, (right) “Unisphere, 1960” by Khan.saqib01, courtesy Wikimedia Commons, is licensed under the Attribution-Share Alike 4.0 International (CC BY-SA 4.0) https://creativecommons.org/licenses/by-sa/4.0/deed.en; page 73, Bogdan Dreava/Alamy Stock Photo; page 75, robuart/ Shutterstock.com, design56/Shutterstock.com, tomeqs/ Shutterstock, BlueRingMedia/Shutterstock.com; pages 104 Copyright © Great Minds PBC

(left), 105, Theo van Doesburg, Card Players, 1916–1917, Gemeentemuseum den Haag/HIP/Art Resource, NY.; page 104 (right), Public domain via Wikimedia Commons; page 133, Created by: Stephen Blumrich. Black Uncle Sam pieced miniature quilt, 1986. cotton, 30 × 21 7/8 × 1/4 in. (76.2 × 55.6 × 0.6 cm). Collection of the Smithsonian National Museum of African American History and Culture, Gift of the Collection of James M. Caselli and Jonathan Mark Scharer; pages 152, 186, Ejichka/ Shutterstock.com; page 172, (left) Diego Rivera, Watermelons, 1957, Museo Dolores Olmedo Patiño, Mexico City, D.F., Mexico. Licensed by Art Resource, NY. © 2020 Banco de México Diego Rivera Frida Kahlo Museums Trust, Mexico, D.F. / Artists Rights Society (ARS), New York, (right) Albert Kahn (1869-1942) American industrial architect and Arts Commissioner; Architect of Detroit; Frida Kahlo (1907-54) Mexican painter; Diego Rivera (1886-1957) Mexican painter; possibly taken by a DIA staff photographer; American Photographer, (20th century) / American; Credit: Detroit Institute of Arts, USA ©Detroit Institute of Arts / Bridgeman Images; page 178, Jar, c. 1895–1910, Acoma, New Mexico, ceramic, natural pigment, H: 8.5 x Dia 10.5 in., Fenimore Art Museum, Cooperstown, New York, Gift of Eugene V. and Claire E. Thaw, Thaw Collection T0423. Photograph by Richard Walker; pages 187, 188, (composite image) AlexeiLogvinovich/ Shutterstock.com, asiandelight/Shutterstock.com, bergamont/ Shutterstock.com, kosam/Shutterstock.com; pages 195, 196, 197, Krakenimages.com/Shutterstock.com, vectorpouch/Shutterstock. com; page 201, venski/Shutterstock.com; page 220, (left) TVR/Shutterstock.com, (right) Denver Post/Getty Images; page 221, (from top left) Pixel-Shot/Shutterstock.com, The Picture Art Collection/Alamy Stock Photo, Denver Post/Getty Images, MPVHistory/Alamy Stock Photo; page 248 (left) TVR/

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Shutterstock.com, (right) The Picture Art Collection/Alamy Stock Photo; page 249, Denver Post/Getty Images; page 266, Adeline Harris Sears (1839-1931), Signature Quilt. ca. 1857-62. Rhode Island, USA. Silk with inked signatures, 77 x 80 in. (195.6 x 203.2 cm). Purchase, William Cullen Bryant Fellows Gifts, 1996 (1996.4). Image copyright © The Metropolitan Museum of Art. Image source: Art Resource, NY; pages 280, 281, lattesmile/Shutterstock. com; page 306, (composite image) Jay Venkat/Shutterstock. com, sirtravelalot/Shutterstock.com; page 307, (composite image) doomu/Shutterstock.com, NiglayNik/Shutterstock.com; pages 376, 377, Nynke van Holten/Shutterstock.com; page 393, (composite image) Public domain via Wikimedia Commons, Archive PL/Alamy Stock Photo, Photo credit: University of California Davis.

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Photo by Gregory Urquiaga, Photograph Courtesy of the University of Chicago, Courtesy NASA/Bob Nye, Intellson/Shutterstock. com; page 396 (top) BlueRingMedia/Shutterstock.com, (bottom), subarashii21/Shutterstock.com; page 470, Eva Daneva/ Shutterstock.com; page 493, Public domain via Wikimedia Commons; page 496, (from top left) Photograph Courtesy of the University of Chicago, Courtesy NASA/Bob Nye, famouspeople/ Alamy Stock Photo, Photograph of Srinivasa Ramanujan. Public domain via Wikimedia Commons; page 497, (left) Photo credit: University of California Davis. Photo by Gregory Urquiaga.; (right) Margaret Sarah Carpenter, Portrait of Ada Lovelace, 1836. Public domain via Wikimedia Commons; All other images are the property of Great Minds.

Acknowledgments Kelly Alsup, Dawn Burns, Jasmine Calin, Mary Christensen-Cooper, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Brittany duPont, Melissa Elias, Lacy Endo-Peery, Scott Farrar, Krysta Gibbs, Melanie Gutierrez, Eddie Hampton, Tiffany Hill, Robert Hollister, Christine Hopkinson, Rachel Hylton, Travis Jones, Kelly Kagamas Tomkies, Liz Krisher, Ben McCarty, Maureen McNamara Jones, Cristina Metcalf, Ashley Meyer, Melissa Mink, Richard Monke, Bruce Myers, Marya Myers, Andrea Neophytou Hart, Kelley Padilla, Kim L. Pettig, Marlene Pineda, Elizabeth Re, John Reynolds, Meri Robie-Craven, Robyn Sorenson, Marianne Strayton, James Tanton, Julia Tessler, Philippa Walker, Lisa Watts Lawton, MaryJo Wieland Trevor Barnes, Brianna Bemel, Adam Cardais, Christina Cooper, Natasha Curtis, Jessica Dahl, Brandon Dawley, Delsena Draper,

Sandy Engelman, Tamara Estrada, Soudea Forbes, Jen Forbus, Reba Frederics, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Nathan Hall, Cassie Hart, Marcela Hernandez, Rachel Hirsh, Abbi Hoerst, Libby Howard, Amy Kanjuka, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Crystal Love, Maya Márquez, Siena Mazero, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Max Oosterbaan, Tamara Otto, Christine Palmtag, Andy Peterson, Lizette Porras, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Samuel Weyand, Dave White, Charmaine Whitman, Nicole Williams, Glenda Wisenburn-Burke, Howard Yaffe

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EM2 Teach Grade 1 Module 6 UTE

Articles inside

Mathematician Sketches

Works Cited

Credits

Terminology

Math Past

Topic F

Acknowledgments