EM2 TEACH Level 2 Module 1 Lesson 1 Thin Slice

2 A Story of Units® Ten Tens

TEACH ▸ Module 1 ▸ Place Value Concepts Through Metric Measurement and Data · Place Value, Counting, and Comparing Within 1,000

What does this painting have to do with math?

The bold brushstrokes and vivid colors in Maurice Prendergast’s painting invite us to step inside this lively street scene in Venice, Italy. A group of ladies with parasols is crossing a bridge. Getting lost in a crowd can be intimidating, but as we learn about base ten, counting large numbers—of people, parasols, or anything— will be a breeze.

On the cover

Ponte della Paglia, 1898–1899; completed 1922

Maurice Prendergast, American, 1858–1924

Oil on canvas

The Phillips Collection, Washington, DC, USA

Maurice Prendergast (1858–1924), Ponte della Paglia, ca. 1898/ reworked 1922. Oil on canvas. The Phillips Collection, Washington, DC, USA. Acquired 1922.

Great Minds® is the creator of Eureka Math® , Wit & Wisdom® , Alexandria Plan™, and PhD Science®

Published by Great Minds PBC. greatminds.org

© 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

ISBN 978-1-64497-161-1

Ten Tens

Module 1 Place Value Concepts Through Metric Measurement and Data · Place Value, Counting, and Comparing Within 1,000

2 Addition and Subtraction Within 200

3 Shapes and Time with Fraction Concepts

4 Addition and Subtraction Within 1,000

5 Money, Data, and Customary Measurement

6 Multiplication and Division Foundations

Use information presented in a bar graph to solve put together and take apart problems.

Metric Measurement and Concepts About the Ruler

to physical units by iterating a centimeter cube.

Part 2: Place Value, Counting, and Comparing Within 1,000

Count and bundle

tens, and hundreds to 1,000.

Count efficiently within 1,000 by using ones, tens, and hundreds.

Use counting strategies to solve add to with change unknown word problems.

Organize, count, and record a collection of objects.

Express Three-Digit Numbers In Different Forms

Count up to 1,000 by using place value units.

Write three-digit numbers in unit form and show the value that each digit represents.

Write base-ten numbers in expanded form.

Read, write, and relate base-ten numbers in all forms.

Count the total value of ones, tens, and hundreds with place value disks.

Exchange 10 ones for 1 ten, 10 tens for 1 hundred, and 10 hundreds for 1 thousand.

Model numbers with more than 9 ones or 9 tens.

Problem solve in situations with more than 9 ones or 9 tens.

Compare Two Three-Digit Numbers in Different Forms

Compare three-digit numbers by using >, =, and <.

Apply place value understanding to compare by using >, =, and <.

Organize, count, represent, and compare a collection of objects.

numbers in different forms.

Before This Module

Overview

Grade 1 Module 1

Students collect data by answering questions, sorting sets, and making observations. They create bar graphs, picture graphs, and tally charts to visually represent the data. As students count to find totals and visually compare quantities, they recognize that linear organizations are useful.

Grade 1 Module 4

Students explore indirect comparison, whereby the length of one object is used to compare two other objects, and they order objects by length. Students begin measuring with same-size standard units, centimeter cubes. They express the length of an object as the total number of centimeter cubes laid end to end. As students measure objects longer than 10 cm, they use 10 cm sticks and additional centimeter cubes and practice counting by tens and some ones. Students use measurement as a context for solving comparison problems.

Part 1: Place Value Concepts Through Metric Measurement and Data Topic A Represent Data to Solve Problems

In topic A, students mathematize their world by organizing categorical data on bar graphs. Students use a scale to help them track data without counting all. Then they use bar graphs to solve put together, take apart, and compare problems. Students may use counting, one-to-one matching, or addition and subtraction strategies to solve problems.

Topic B

Metric Measurement and Concepts About the Ruler

Metric measurement lays the groundwork for place value understanding in topic B as students work with units of ones, tens, and hundreds. Students begin by using centimeter cubes to create a 10 cm ruler. Students come to understand that the numerals on a ruler represent the number of length units, or the distance, from zero. As the need arises to measure longer objects, students use ten 10 cm rulers to build a 100 cm tool, a meter stick. With a growing toolbox, students self-select appropriate measuring tools based on the size and shape of various objects. Students use the relationship between metric units to express measurements with different units, such as 105 cm and 1 m 5 cm.

Topic C Estimate, Measure, and Compare Lengths

In topic C, students use measurement benchmarks to estimate the length of objects. They compare estimates with the actual measurements and model the difference in length by using a tape diagram. Students see that comparison problems can be solved with both addition and subtraction strategies—by adding or subtracting a part to make the tapes the same or by subtracting the matching part. They then apply this understanding to solving comparison problems in the context of height.

Topic D

Solve Compare Problems by Using the Ruler as a Number Line

In Topic D, students draw on their understanding of length as they explore problem solving through linear models and measurement contexts. Students model adding and subtracting efficiently by getting to a benchmark number when they use a measuring tape as a number line. Students engage in the Read–Draw–Write routine and use a tape diagram to represent and solve compare with difference unknown word problems. Students share and compare solution strategies and notice that the same problem can be solved by using different operations and equations.

After This Module

Grade 3 Module 2

Students estimate and measure weight and liquid volume. They explore the relationship between place value units by reasoning that there are 1,000 grams in 1 kilogram and 1,000 milliliters in 1 liter. Students apply their understanding of metric measurement as they represent word problems with a tape diagram and solve flexibly. In addition, students use their understanding of the number line to read vertical measurement scales. Finally, students represent data in scaled bar graphs and solve problems related to graphs.

Grade 3 Module 5

Students use the interval from 0 to 1 on the number line as the whole. They iterate fraction tiles to partition a number line into fractional units. Students count unit fractions and relate the placement of a fraction on the number line to its distance from 0. Then students apply their understanding of fractions on the number line to rulers and to the creation of line plots.

Why Part 1: Place Value Concepts Through Metric Measurement and Data

Why does the year start with categorical data?

During the first week of school, teachers and students spend time establishing a classroom community. By launching with categorical data, teachers can leverage getting-to-knowyou activities to generate student data, create graphs, and answer questions.

Bar graphs provide students with a concrete and visual experience of comparison. Comparing categories on a bar graph sets up students for solving compare word problems by using a more abstract model, the tape diagram. Labeling the categories on a bar graph supports the practice of labeling tape diagrams, where students must visualize the amount or length.

Students revisit strategies for answering questions by using bar graphs to solve word problems. When students count on, take away, or use matching to answer how many more or how many fewer questions, they may use simple addition or subtraction to solve, which is a precursor to work in topic D. Moreover, when students find the total number of data points, they combine up to four addends, which prepares them for solving put together problems with four 2-digit addends in module 2.

The linear nature of bar graphs also supports students in understanding measurement, and it helps them transition from work on the number path in kindergarten and grade 1 to work on the number line in grade 2. The count scale on a bar graph primes students for using the ruler as a number line to solve problems.

Why does the first module of the year emphasize measurement?

After much consideration of our students’ learning, teachers’ input, and research on how students learn and how mathematical concepts progress, we decided it makes the most sense to include measurement in module 1. Why?

1. One of the major areas of emphasis of grade 2 math standards, as noted by the content standards, is measurement. By focusing on the relationship between metric units, students begin to develop key place value understanding that is inherent in the base-ten number system; more specifically, that 10 smaller units make 1 of the next larger unit.

2. When students begin the year with a concrete measurement experience that highlights the relationship between 100 cm, 10 cm, and 1 cm, they are able to work more flexibly and make explicit connections to place value units in module 1 part 2.

3. Once students have an understanding of the meaning of the spaces and tick marks on a ruler, they are ready to use the number line as a tool for solving addition and subtraction problems in topic D. After its introduction in this module, the number line becomes a reliable tool for students to use when solving problems throughout the year.

Why are so many different measuring tools used in topics B and C?

Through the concrete experience of creating a ruler, rather than using a standard tool, students come to see that length is the number of same-size units from zero, as opposed to the number of tick marks. Students iterate a centimeter cube to create a 10 cm ruler. Then they iterate ten 10 cm rulers to create a meter stick. In doing so, students internalize the proportionality of units. This early experience of building measuring tools, rather than working with standard ones, lays the groundwork for deeper place value understanding when students compose and decompose units in module 1 part 2.

In addition, the double-sided meter stick, an innovative, new measuring tool in Eureka Math2, reinforces Say Ten counting and the base-ten structure of the number system. When students use this tool, they focus on units of ten, as opposed to each number. Students also notice relationships between units. For example, a student may correctly claim to be 120 cm tall, twelve 10 cm rulers tall, or 1 m two 10 cm rulers tall.

Beth and Kate measure the same desk. Beth says the desk is 1 m 2 cm. Kate says it is 102 cm. Who is correct?

Which word problem types, or addition and subtraction situations, are used in this module?

The table shows examples of addition and subtraction situations.1 Darker shading in the table indicates the four kindergarten problem types. Students in grades 1 and 2 work with all problem types. Grade 2 students reach proficiency with the unshaded problem types.

Grade 2 students are expected to master all addition and subtraction problem types by the end of the year. They revisit types that were introduced and mastered in kindergarten and grade 1. However, in grade 2, the problems are one- and two-step, and use numbers within 100 (not just within 20).

Students use graphs to solve take from and put together/take apart problems in topic A.

• Take from with result unknown:

6 red balloons pop. How many red balloons are there now? (Lesson 3)

• Put together/take apart with total unknown: Up to four parts are given. No action joins or separates the parts. Instead, the parts may be distinguished by an attribute such as type, color, size, or location.

How many balloons are there in all? (Lesson 3)

• Compare with difference unknown: Two quantities are given and compared to find how many more or how many fewer.

Ling’s plant is 64 cm tall. Alex’s plant is 39 cm tall. How much taller is Ling’s plant than Alex’s plant? (Lesson 18)

1 Common Core Standards Writing Team, Progressions for the Common Core (draft), Grades K–5, Counting and Cardinality & Operations and Algebraic Thinking, 9.

Achievement Descriptors: Overview

Part 1: Place Value Concepts Through Metric Measurement and Data

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

• informal classroom observations (recording sheet provided in the module resources),

• data from other lesson-embedded formative assessments,

• Exit Tickets,

• Topic Tickets, and

• Module Assessments.

This module contains the nine ADs listed.

2.Mod1.AD1

Measure lengths of objects by using metric units (centimeters and meters).

Estimate lengths of objects by using metric units (centimeters and meters).

2.Mod1.AD3

Measure and find a difference in length by using metric units (centimeters and meters).

2.Mod1.AD4

Add or subtract within 100 to solve word problems involving length by using drawings and equations.

2.MD.B.5

2.Mod1.AD5

Represent whole numbers within 100 on a number line.

2.Mod1.AD6

Represent sums within 100 by using a number line.

2.MD.A.1

2.Mod1.AD2

2.MD.A.3

2.MD.A.4

2.MD.B.6

2.MD.B.6

2.Mod1.AD7

Represent differences within 100 by using a number line.

2.MD.B.6

2.Mod1.AD8

Draw and label picture and bar graphs to represent a data set with up to four categories.

2.Mod1.AD9

Solve addition, subtraction, and comparison problems by using information from a bar graph.

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.

• 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 2 module 1 part 1 is coded as 2.Mod1.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.

• Related Standard: This identifies the standard or parts of standards from the Common Core State Standards that the AD addresses.

Achievement Descriptors: Proficiency Indicators

AD Code Grade.Module.AD#

AD Language

2.Mod1.AD1 Measure lengths of objects by using metric units (centimeters and meters).

RELATED CCSSM

2.MD.A.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

Partially Proficient Proficient

Measure lengths of objects by using metric units (centimeters and meters) for objects that are easily measured with a ruler (e.g., flat and straight).

Measure the pencil with a 10 cm ruler.

The pencil is cm long.

Related Standard

Measure lengths of objects by using metric units (centimeters and meters) for objects that require choosing an appropriate tool before measuring.

Circle the best tool to measure the length around a ball.

10 cm ruler meter stick measuring tape

Use the tool to measure the length around a ball.

2.Mod1.AD2 Estimate lengths of objects by using metric units (centimeters and meters).

RELATED CCSSM

2.MD.A.3 Estimate lengths using units of inches, feet, centimeters, and meters.

Highly Proficient

AD Indicators

2.MD.D.10

2.MD.D.10

Topic A Represent Data to Solve Problems

Topic A channels the excitement of students as they enter grade 2 by mathematizing getting-to-know-you activities, which often include student interest surveys. Lesson 1 uses these activities to show students that math is a part of the world around them. As students express personal preferences and organize responses on a graph, they come to see how a graph can be used to organize data that would otherwise be difficult to visualize.

As students transition to working with bar graphs, they represent data more abstractly by coloring spaces on a grid. Students use a scale to help them track data without always counting all. The scale is a bridge between the number path in kindergarten and grade 1 and the number line in grade 2. The scale also previews concepts about the ruler. For example, students learn that, on a bar graph, the space from the beginning of the bar to the first line represents a count of 1, just as they will learn that the space from 0 to 1 on the ruler is one length unit.

In the last two lessons of this topic, students apply their knowledge of bar graphs to solve put together, take apart, and compare problems. Students may solve by counting all, by counting on, or by using simple addition or subtraction. Students answer questions such as, How many more worms than bees are at the park? When solving comparison problems, students determine how many more or fewer by comparing number or length. Students may use one-to-one matching to solve. Alternatively, they may add or subtract to make the bars equal in length. The visual nature of a bar graph sets the stage for using tape diagrams as a representational tool to solve word problems later in the module.

Intentionally launching grade 2 with categorical data provides the opportunity throughout the year to use data contexts to give meaning to and support problem solving with addition and subtraction—the major work of grade 2.

Progression of Lessons

Lesson

Draw and label a picture graph to represent data.

Favorite Subject

Draw and label a bar graph to represent data.

Lesson

Use information presented in a bar graph to solve put together and take apart problems.

Each symbol stands for 1 vote.

Lesson 4

Use information presented in a bar graph to solve compare problems.

The bars help me see the difference and compare: There are 3 more pigs than cows.

Draw and label a picture graph to represent data.

Lesson at a Glance

Students vote on a personal favorite to generate data and make a class picture graph. They create a graph by using symbols to represent votes. Then students read and interpret picture graphs to answer questions. This lesson introduces the terms table, data, category, and key.

Key Question

• Why are graphs useful?

Achievement Descriptor

2.Mod1.AD8 Draw and label picture and bar graphs to represent a data set with up to four categories. (2.MD.D.10)

Agenda Materials

Fluency 10 min

Launch 10 min

Learn 30 min

• Make a Picture Graph

• Use a Picture Graph to Answer Questions

• Problem Set

Land 10 min

Teacher

• Chart paper (3)

• Marker

• Projection device*

• Teach book*

• Teacher computer or device* Students

• Sticky note

• Dry-erase marker*

• Personal whiteboard*

• Personal whiteboard eraser*

• Learn book*

• Pencil*

* These materials are only listed in lesson 1. Ready these materials for every lesson in this module.

Lesson Preparation

• Create a blank table on chart paper with the title Favorite Subject. Label the four categories Reading, Writing, Math, and Science. (Favorite Subject is a suggested topic. Consider choosing a topic relevant to your students and adjusting materials accordingly.)

• Create a blank graph on chart paper. Include lines for a title and categories to be filled in later with the class. The graph should match the graph from the classwork page.

• Create a terminology chart to record new mathematical terms introduced throughout the lesson. This chart will be used in subsequent lessons.

Fluency

Happy Counting by Ones Within 50

Students visualize a number line while counting aloud to build fluency counting within 1,000.

Invite students to participate in Happy Counting.

When I give this signal, count up. (Demonstrate.) When I give this signal, count down. (Demonstrate.)

Let’s count by ones. The first number you say is 28. Ready?

Signal up or down accordingly for each count.

28293029303132333233343536353637

Continue counting by ones to 50, changing directions occasionally. Emphasize crossing over multiples of 10 and where students hesitate or count inaccurately.

Ready, Set, Add

Students find the total and say an addition equation to maintain addition fluency within 10 from grade 1.

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.

Teacher Note

Choose signals that you are comfortable with, such as thumbs-up and thumbs-down or two fingers pointing up and down. Show your signal and gesture up or down with each count. The goal is to be clear and crisp so that students count in unison. Avoid saying the numbers with the class; instead, listen for errors and hesitations.

Differentiation: Challenge

Challenge students who demonstrate fluency adding within 10 to add within 20. Encourage each partner to use both hands to show a number.

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.”

• 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 each student say the addition equation, starting with the number of fingers on their own hand. See the sample dialogue under the photograph.

Circulate as students play the game to ensure that each student is trying a variety of numbers.

Choral Response: Related Facts Within 20

Partner A: “4 + 2 = 6”

Partner B: “2 + 4 = 6”

Students say a related addition equation to prepare for work with put together, take apart, and compare problems beginning in lesson 3.

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 number bond.

A subtraction equation that matches this number bond is 10 – 8 = 2. (Gesture to the total and parts while saying the equation.)

Display the equation: 10 – 8 = 2.

What is a related addition equation, starting with 8? 8 + 2 = 10

Display the equation: 8 + 2 = 10.

Teacher Note

Use hand signals to introduce a procedure for answering choral response questions. For example, cup your hand around your ear for listen, lift your finger to your temple for think, and raise your own hand to remind students to raise theirs.

Teach the procedure by using general knowledge questions, such as the following:

• What grade are you in?

• What is the name of our school?

• What is your teacher’s name?

10 – 2 = 8 is another subtraction equation that matches this number bond. (Gesture to the total and parts while saying the equation.)

Display the equation: 10 – 2 = 8.

What is a related addition equation, starting with 2?

2 + 8 = 10

Display the equation: 2 + 8 = 10.

Repeat the process with the following sequence:

Launch

Materials—T: Favorite Subject table, terminology chart, marker Students generate data by voting on a personal favorite.

Gather students and invite them to participate in a fun getting-to-know-you activity.

One way we can get to know each other is to ask questions and record the answers. For example, I could ask you to tell me your favorite subject—reading, writing, math, or science.

Language Support

Consider using strategic, flexible grouping throughout the module based on students’ mathematical and English language proficiency.

• Pair students who have different levels of mathematical proficiency.

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

• Join two 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.

Teacher Note

This lesson introduces four mathematical terms. Students will be expected to gesture to identify the terms by the end of the lesson. For example, students identify the meaning of the word key by pointing to the key on a picture graph. They will continue to hear and use these terms throughout the year. The term picture graph should be familiar from grade 1.

Display the Favorite Subject table. Introduce the terms table and category.

This is a table. It lists the four subjects you can choose. Each subject is a category, or type of group.

Vote by raising your hand when I call out your favorite subject. I’ll record the number of votes for each category on the table.

Add the new terms table and category to the terminology chart you prepared in advance. Conduct the survey and record the counts for each category. Then introduce the new term data.

The information we just recorded about our favorite subjects is called data.

I wonder how many more students like math than writing.

Add the term data to the terminology chart. Transition to the next segment by framing the work.

Today, we will look at a way to show this data, or information, that makes it easier to answer that question.

Learn

Make a Picture Graph

Materials—T: Blank graph, Favorite Subject table; S: Sticky note Students make picture graphs to represent data.

Display the blank graph next to the Favorite Subject table. Guide the class to make a graph by using the data from the table. Leave space at the bottom to write in a key.

Teacher Note

The lesson uses the example Favorite Subject for the table and graph. Consider selecting another topic to align with student interest.

Language Support

Support students’ language development by pointing out that table has multiple meanings.

Point to a tabletop and say, “This is one kind of table. We can sit at a table when we eat lunch.” Then point to the chart and say, “This is another kind of table. We use it to show information.”

The term key is introduced later in the lesson. Consider using a similar support as you introduce that term.

Teacher Note

The data generated in the classroom will differ from the data displayed on the example. Use the data generated from students.

Let’s use the data from our table to make a graph.

What title can we give our graph?

Favorite Subject

Let’s write the four categories from the table—Reading, Writing, Math, and Science— toward the bottom of the paper.

Now let’s use a sticky note to represent your vote.

Give each student a sticky note. Have students write their name or initials on the note and record their vote by placing the note directly above their favorite subject. Ensure that students arrange sticky notes in columns without gaps or overlaps.

Once all votes are recorded, have students think–pair–share to compare the table with the graph.

What is the same and different about the table and the graph?

The title is the same.

They both show reading, writing, math, and science.

The table shows numbers, but the graph shows sticky notes.

Students may notice that the category counts are the same on both charts. If the category counts are different, encourage them to reason about why. Ask, “Did some people change their vote?”

We made a graph. A graph is another way to show data. You will see different kinds of graphs this year.

On this graph, your sticky note represents, or stands for, your vote.

Let’s make a key on the graph that shows what these sticky notes represent.

What does each sticky note represent?

1 vote

Add the key to the bottom of the graph. Add the new term key to the terminology chart.

Now that our graph is complete, what math questions can we ask about it?

Which subject got the most votes?

Which subject got the fewest votes?

How many people like math the most?

Can we tell how many more students like math better than they like writing? How?

Yes, I can count the extra sticky notes in the math category.

Help students understand why the graph cannot answer a question such as: Why don’t people like writing as much as math?

Tell students you want to save this data about their favorite subjects, but the sticky notes might fall off. Therefore, they will re-create this graph in their student book.

When we copy the data into a new graph, the graph will have the same information, even if it doesn’t look exactly the same.

UDL: Representation

Consider providing additional clarification for terms by showing students a map with a key. Explain how a map key is used in the same way a graph key is used.

Discuss how symbols make it easier for people to understand information. Graphs also use symbols to help people understand information.

Guide students to complete the graph. Begin by filling in the title, key, and categories.

Review the terms symbol and picture graph that were introduced in grade 1.

On our class graph, we used 1 sticky note to show 1 vote. A picture graph shows data by using symbols, or pictures.

We can draw a symbol to stand for 1 vote. Let’s show 1 vote by making 1 symbol in 1 box on the graph.

Invite students to generate ideas about a symbol to draw in each box of the graph (e.g., circle, star, check mark, smiley face). The example uses check marks but consider allowing students to choose their own symbol.

Let’s use a check mark to show 1 vote on the graph. How many people voted for reading?

Find the reading category. Draw 5 check marks, 1 in each box, as symbols for each of our 5 votes.

Model recording the total above the category as students do the same.

Have students work in pairs to graph the other three categories.

Use a Picture Graph to Answer Questions

Students interpret data presented in a picture graph to answer questions.

Direct students’ attention to the completed picture graph in their student book that shows how another class voted.

Teacher Note

Students may use words or an initial to label categories. For example, they may write the word Reading or the letter R.

Labeling with initials prepares students to use initials when labeling tape diagrams in the next topic.

Promoting the Standards for Mathematical Practice

Students attend to precision (MP6) when they make and interpret a picture graph. In making the graph, students display precision by being careful to only draw one symbol in each box without skipping any boxes. In interpreting the graph, students are precise in determining what kinds of questions they can and cannot use the graph to answer.

Ask the following questions to promote MP6:

• What kinds of questions can we answer with this graph?

• What kinds of questions can’t we answer with this graph?

Have students use the graph to answer the questions. If time permits, invite students to think of other questions they could answer by using this graph.

Problem Set

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

Help students recognize the words picture, graph, and title in print. Invite students to underline them as you read them aloud. Land

Debrief 5 min

Materials—T: Class-created picture graph, terminology chart

Objective: Draw and label a picture graph to represent data.

Gather students near the class-created picture graph and have them think–pair–share about what they learned.

What did we learn about our class from this graph? How did the graph help us learn it?

We learned that a lot of us like math because math has the most votes.

More people like science than like reading or writing. Science has more check marks than reading or writing.

We learned that only a few people like writing. That category has the fewest sticky notes.

Display the terminology chart beside the class-created table and graph. Invite students to gesture to identify each new term. For example, have students identify the meaning of the word key by pointing to the key on the picture graph.

Close this segment with the following question:

Why are graphs useful?

They make it easy to see information.

They make it easy to see which category has more or less.

We can see how many more of something.

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.

Language Support

Consider providing visual support directly on the terminology chart by including images of a table and a picture graph that are labeled with the applicable terms to aid students in expressing their ideas.

Sample Solutions

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

Pets We Like

2. What is the title of this graph?

3. How many people are there?

4. Who has the most books?

Each

stands for 1 vote.

5. Who has the fewest