Supplemental Materials: Grade 1 Module 5 Lesson 2 by General

Supplemental Materials

Adapt

Optimizing Instruction, K–2

A Story of Units®

Supplemental Materials

Adapt: Optimizing Instruction, K–2

Contents Analyze Student Work ............................................................................................................................. 3 Grade 1 Module 5 Topic A Overview .................................................................................................... 3 Grade 1 Module 5 Topic A Progression of Lessons ............................................................................... 5 Grade 1 Module 5 Lesson 2 Overview .................................................................................................. 6 Achievement Descriptor – 1.Mod5.AD1 ............................................................................................... 8 Achievement Descriptor – 1.Mod5.AD3 ............................................................................................... 9 Grade 1 Module 5 Lesson 2 ................................................................................................................... 10 Credits................................................................................................................................................... 11 Works Cited........................................................................................................................................... 11

Topic A Grouping Units in Tens and Ones Topic A builds on work with tens and ones that students completed in modules 3 and 4. At first students reason about units in the context of time. They learn through experience that smaller units can compose larger units. For example, they discover that 1 hour is made of 60 minutes and 1 half hour is made of 30 minutes. Lessons build on the idea that smaller units can be used to compose larger units by considering the place value units of tens and ones. Students work with sets of objects to compose groups of 10 and represent two-digit totals in different ways. For example, 26 ones can also be represented as 1 ten 16 ones or 2 tens 6 ones. Working with numbers that have more than 9 ones prepares students for adding and subtracting with larger numbers in later grades. However, students come to understand that the digits we use to write a number, such as the 2 and the 6 in 26, show how many tens and ones there are when the number is expressed in its “most composed” form. This leads to recognition that the value of digits can be determined based on their place in the number. The value of the digit 2 can be expressed as 2 tens or 20. The value of the digit 6 can be expressed as 6 ones or simply 6. Students compose (or decompose) a total such as 26 by place value units: 20 and 6 or 2 tens 6 ones. Using different representations of the same total invites students to consider equivalence and deepens their number sense.

50 pennies 50 ones

5 dimes 5 tens

Several place value models that increase in complexity help students internalize the basic understanding that 10 ones are equivalent to 1 ten.

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EUREKA MATH2

Groupable Students group 10 ones to compose a new unit of ten. They may put 10 bears into 1 cup, link 10 cubes into a stick, or circle 10 donuts to represent a box of 10. Students can see and manipulate the individual units within the new larger unit. The size of the new unit is proportionally larger than the base unit.

Pregrouped Students group 10 ones and trade them for a new item that represents 1 ten. For example, given 23 centimeter cubes, students trade 10 cubes for 1 ten-centimeter stick. The new item is proportionally larger than the base unit.

In this topic, students also add 10 and take 10 all at once from numbers. They add to and subtract from numbers in sequence: 54 + 10 = 64, 64 + 10 = 74, and so on. From this a pattern becomes visible: the digit in the tens place changes by 1, but the digit in the ones place remains the same.

Nonproportional Students trade 10 ones for a new item that represents 1 ten, but the ten looks different from the 10 ones. An example is trading 10 pennies for 1 dime. These models are nonproportional because the new unit, in this case a dime, is not visually 10 times larger than the base unit, or penny. Nonproportional models prepare students to work with place value disks in grades 2–5.

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EUREKA MATH2

Progression of Lessons

Lesson 1

Lesson 2

Lesson 3

Tell time to the hour and half hour by using digital and analog clocks.

Count a collection and record the total in units of tens and ones.

Recognize the place value of digits in a two-digit number.

4:30 The minute hand is pointing at the 6, and the hour hand is not at 5 yet, so it is 4:30. bears How many do you think there are?

5 03

10 10

After we composed all of the tens, there were 5 tens and 3 ones. The digits 5 and 3 make 53. The value of the digit 5 is 50 and the value of the digit 3 is 3.

10 5

tens

Total

ones

We composed tens by making groups of 10. We had 5 groups of ten and 2 extras. That is 52 bears. EM2_0105TE_A_L02_classwork_1_studentwork_CE.indd 2

07/04/21 3:45 PM

LESSON 2

Count a collection and record the total in units of tens and ones. Lesson at a Glance Students analyze a counting collection organized into groups of tens and ones and discuss the values of the digits in the total. Partners organize, count, and record their own collections. The class discusses student work and considers how groups of 10 and extra ones combine to make a total. The term digit is introduced in this lesson. There is no Fluency component, Exit Ticket, or Problem Set in this lesson. This allows students to spend more time completing the counting collection activity. Use student recordings to analyze their work.

Key Question • What do the digits in a number tell us?

Achievement Descriptors 1.Mod5.AD1 Represent a set of up to 99 objects with a two-digit number by composing tens. (1.NBT.A.1, 1.NBT.B.2.a) 1.Mod5.AD3 Determine the values represented by the digits of a two-digit number. (1.NBT.B.2)

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EUREKA MATH2

Agenda

Materials

Lesson Preparation

Launch

Teacher

• Copy or print the counting collection recording page to use for demonstration.

Learn

15 min

40 min

• Chart paper

• Organize, Count, and Record

• Hide Zero® cards, demonstration set

• Share, Compare, Connect

Students

Land

• Counting collection (1 per student pair)

5 min

• Work mat (1 per student pair) • Organizing tools • Hide Zero® cards (1 set per student pair)

• Use small, everyday objects to assemble at least one counting collection per pair of students. Place each collection in a bag or box. Each collection should contain 50–100 objects. Differ the number of objects in the collections based on the needs of your students. Provide a challenge by creating collections with 101–120 objects. Save collections for future use. • Provide tools students can choose from to organize their counting. Place them in a central location. Tools may include cups, plates, number paths, or 10-frames. • Gather 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 collection. They can also make students’ work portable. • Prepare an anchor chart that will be used to keep track of tens, ones, and totals in the lesson (see image in Launch).

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EUREKA MATH2

1.Mod5.AD1 Represent a set of up to 99 objects with a two-digit number by composing tens. RELATED CCSSM

1.NBT.A.1 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1.NBT.B.2.a 10 can be thought of as a bundle of ten ones — called a “ten.”

Partially Proficient

Proficient

Represent a set of up to 50 objects with a two-digit number by composing tens.

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

tens

Total

ones

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EUREKA MATH2

1.Mod5.AD2 Represent two-digit numbers within 99 as tens and ones. RELATED CCSSM

1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases: 1.NBT.B.2.b The numbers from 11 to 19 are composed of a ten and one, two, three, four, ﬁve, six, seven, eight, or nine ones. 1.NBT.B.2.c The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, ﬁve, six, seven, eight, or nine tens (and 0 ones).

Partially Proficient

Proficient

Highly Proficient

Represent two-digit numbers within 50 as tens and ones.

Represent two-digit numbers within 99 as tens and ones.

Represent numbers through 100–120 as tens and ones.

Draw the number with tens and ones.

Show the total with a number bond or number sentence.

Draw the number with tens and ones.

114

1.Mod5.AD3 Determine the values represented by the digits of a two-digit number. RELATED CCSSM

1.NBT.B.2 Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:

Partially Proficient

Proficient

Highly Proficient

Determine the number represented by given amounts of tens and ones.

Determine the values represented by the digits of a two-digit number.

Write the total.

Fill in the number bond.

6 tens and 3 ones is

LESSON 2

Key Question • What do the digits in a number tell us?

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EUREKA MATH2

Agenda

Materials

Lesson Preparation

Launch

Teacher

• Copy or print the counting collection recording page to use for demonstration.

Learn

15 min

40 min

• Chart paper

• Organize, Count, and Record

• Hide Zero® cards, demonstration set

• Share, Compare, Connect

Students

Land

• Counting collection (1 per student pair)

5 min

• Work mat (1 per student pair) • Organizing tools • Hide Zero® cards (1 set per student pair)

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Launch

EUREKA MATH2

Materials—T: Chart paper, Hide Zero cards

We will ...

Students analyze the way a counting collection is organized and describe it in terms of tens and ones.

Choose a collection.

If needed, briefly review the procedure of counting a collection by using the chart from module 3 lesson 15.

Make a good guess.

Display a picture of a counting collection. Give students a quiet moment to study the image.

Make a plan and count.

How is the counting collection organized?

Record the collection.

The cubes are in sticks of 10. There are 5 extra cubes next to the sticks. Why do you think the collection is organized this way?

1, 2, 3, 4, …

our 5 Share work. Language Note

It is fast to count by tens. There are a lot of cubes. It’s helpful to put them into groups of 10 to make them easier to count.

Support students in reading two-digit numbers by using the rekenrek and the Say Ten way.

Organizing larger collections into tens and ones can help make counting efficient.

For example, show 75 on the rekenrek. Help students read the number the Say Ten way: 7 tens 5. Connect the Say Ten way to the standard form: 7 tens is 70, so we say seventy-five.

Have students turn and talk to estimate or make a good guess about the total. Then guide the class to chorally count by tens and ones to find the total, 75. Show 75 by using Hide Zero cards. Then separate the cards to show 70 and 5. 70 and 5 make 75. (Point to the 70 card.) Where do you see 70 in the collection? The ten-sticks equal 70.

7 05

7 0 5 12

Saying 75 as 7 ten 5, or as 7 tens 5 ones, helps students relate the number name to its place value structure, helping them connect the idea that -ty means tens.

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EUREKA MATH2

If needed, count the ten-sticks by tens to 70. (Point to 5.) Where do you see 5 in the collection? There are 5 extra cubes to the side of the tens. 70 and 5 is … 75 Put the cards back together to show 75. Numbers such as 7 and 5 are called digits. When we write digits next to each other, we make another number. For example, we write the digits 7 and 5 next to each other to make 75. In 75, the digit 7 tells us that there are 7 tens. We know that 7 tens is 70. (Separate the cards again to show 70 and 5.) The digit 5 in 75 tells us that there are 5 ones, or 5. Put the cards back together to show 75.

Name

What are the digits in 75? How many do you think there are?

7 and 5 Show the counting collection recording page from the student book. Use a combination of the following questions to interactively demonstrate how to record a collection: • What are we counting in this collection? • What was one of our good guesses about the total number of objects?

tens

• What can we draw to show how the counting collection is organized?

ones

Total

• How many groups of 10 are there? How many extra ones are there? • What is the total number of objects in the collection? EM2_0105TE_A_L02_classwork_1_studentwork_CE V2.indd 1

Post a chart for keeping track of counting collection totals in terms of tens and ones. Record the sample on the chart.

07/04/21 3:42 PM

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EUREKA MATH2

Let’s keep track of all the counting collections we talk about today. In this collection there are 7 groups of 10 and 5 extra ones. What is the total? 75 Transition to the next segment by framing the work. Today, we will organize, count, and record a collection.

Learn

Promoting the Standards for Mathematical Practice

Organize, Count, and Record Materials—S: Counting collection, organizing tools, Hide Zero cards, work mat

Students organize, count, and record a collection of objects. Partner students and invite them to choose a collection, organizing tools, a work mat, and a workspace. Have them open their student book to the counting collection recording page. After you count your collection and record your work, use Hide Zero cards to represent the total. Look for the digits that show how many tens and how many ones. Circulate as students work. Use any combination of the following questions or statements to assess and advance student thinking: • Show me how many tens and ones are in your collection. • What is the total? How do you know?

Students model with mathematics (MP4) when they record their collection. Using a symbol such as a line or a box to record a group of 10 shows that students are thinking abstractly and understand that you can represent 10 without drawing 10 distinct items. Ask the following questions to promote MP4: • How is what you wrote or drew the same as your collection? How is it different from your collection? • Why is it helpful to draw groups of 10 instead of drawing every item in your collection?

• What does your drawing show? How can you label it? • How can you show the total with Hide Zero cards? 14

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• What are the digits that make your total? Teacher Note

• What could be a more efficient way to organize the collection? Select student work that makes use of tens and ones to share in the next segment. The following chart shows samples. If some pairs finish early, invite them to draw number bonds or write number sentences to represent their total. Corey and Kioko

Name

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90 + 3 = 93

80 10

How many do you think there are?

tens

Total

EM2_0105TE_A_L02_classwork_1_studentwork_CE.indd 1

10 10

1 1 1

Consider providing distributed practice with groupable models during the remainder of the year. Invite students to group and count various collections. Have them label their collections with Hide Zero cards and represent them by using number bonds, unit form, and number sentences.

bears

10 5

ones

tens

Total

07/04/21 3:45 PM

Grouping also allows students to see that the size of the new unit is proportionally larger than the base unit. For example, 10 disks in a 10-frame are visually about 10 times larger than a single disk.

Name

circles How many do you think there are?

By grouping, students see the individual units that compose the new, larger unit. For instance, one cup of 10 bears contains 10 individual bears.

Sakon and Violet

EUREKA MATH

To fully grasp place value concepts, students need ample experience with grouping, or putting together items to make a new unit.

EM2_0105TE_A_L02_classwork_1_studentwork_CE V1.indd 1

ones

12/03/21 8:29 PM

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Share, Compare, Connect Materials—T: Chart, Hide Zero cards; S: Hide Zero cards Teacher Note

Students share and discuss recordings of counting collections. Invite two pairs to share their work. Encourage the class to use the Talking Tool to engage in discussion by asking questions, making observations, and sharing compliments.

Corey and Kioko

The sample student work shows common responses. Look for similar work from your students and encourage authentic classroom conversations about the key concepts. If your students do not produce similar work, choose a student’s work to share and highlight how it shows movement toward the goal of this lesson.

How did you organize and count your collection? We put 10 disks in each line, 5 red and 5 yellow. Tell us about your recording.

Then select a provided sample that advances your class’s thinking. Consider presenting the work by saying, “This is how another student counted the collection. What do you think this student did?”

We drew rectangles to show a group of 10. We drew 3 circles to show our extra disks. Draw attention to the unit form at the bottom of the recording page. Class, where do you see 9 tens in the drawing? Where do you see 3 ones? The 9 rectangles are 9 tens.

Name

The 3 circles labeled with a 1 are 3 ones.

circles

Invite students to turn and talk to their partner.

How many do you think there are?

Do you agree this recording shows a total of 93? Why? Using the recording, guide students to count chorally by tens and ones. Show 93 by using Hide Zero cards.

10 10

1 1 1

What digits do you see?

90 + 3 = 93

9 and 3

EM2_0105TE_A_L02_classwork_1_studentwork_CE.indd 1

tens

Total

Refer back to the recording of the collection as needed to support students with answering the following questions.

ones

07/04/21 3:45 PM

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EUREKA MATH2

What does the digit 9 tell us in the number 93? It tells there are 9 tens.

Differentiation: Challenge

How many is 9 tens? 90 Slide apart the cards to confirm. Then put them back together. Repeat the process for the digit 3. 9 tens is 90 and 3 ones is 3. 90 and 3 make 93. Record the pair’s work under 75 on the class chart.

10 20 30 40 50 60 70 80 90 100 101 102 103 103

This collection has 9 groups of 10 and 3 more ones.

100

tens

What is the total? Total

Sakon and Violet Invite a different pair to share their work. Then direct the class’s attention to the unit form.

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EUREKA MATH

Name

bears How many do you think there are?

At another time, invite pairs who count collections with more than 100 objects to share their work. Facilitate discussion by using the following questions:

10 5

tens

Total

EM2_0105TE_A_L02_classwork_1_studentwork_CE V1.indd 1

05/04/21 4:35 PM

• Do you all agree this recording shows a total of 103 cubes? Why? • How many tens and ones do you see?

Invite students to think–pair–share about the second recording.

103

• How many is 10 tens 3 ones? 10

They have 5 tens. Corey and Kioko had 9 tens. They have 2 ones, not 3 ones.

ones

EM2_0105TE_A_L02_classwork_2_studentwork_CE.indd 1

Class, how is this recording different from the other group’s recording? This one has circles instead of rectangles for the groups of 10.

ones

12/03/21 8:29 PM

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EUREKA MATH2

Do you agree that this recording shows a total of 52? Why? Yes. 10, … , 50, 51, 52. 50 plus 2 equals 52. 5 tens and 2 ones is 52. Ask partners to show 52 by using their set of Hide Zero cards. What digits do you see? 5 and 2 In 52, what does the digit 5 tell us? 5 tens How many is 5 tens? 50 Have students slide apart the cards to confirm and then put them back together. Repeat the process for the digit 2. Record the pair’s work on the class chart. In this collection there are 5 groups of 10 and 2 ones. What is the total? 52 Allow a few minutes for cleanup. Collect students’ recordings to review as an informal assessment.

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EUREKA MATH2

Land Debrief

5 min

Materials—T: Chart, Hide Zero cards

Objective: Count a collection and record the total in units of tens and ones. Gather students and display the class chart. (Point to the first row.) What was the total of this collection? 75 The digits of these numbers tell us how many tens or ones there are. In the number 75, what does the digit 7 tell us? (Point to the 7 in the tens column.) There are 7 groups of 10. How many is 7 tens? 70 As needed, use Hide Zero cards to support students. In the number 75, what does the digit 5 tell us? (Point to the digit in the ones column.)

7 0 5

There are 5 ones. How many is 5 ones? 5 70 and 5 is 75.

Ask a pair to share a new total and add it to the chart. Repeat the process.

7 05

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EUREKA MATH2

Name

How many do you think there are?

tens

Total

ones

Supplemental Materials

Adapt: Optimizing Instruction, K–2

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 acknowledgement in all future editions and reprints of this handout.

Works Cited Great Minds. Eureka Math2TM. Washington, DC: Great Minds, 2021. https://greatminds.org/math.

Supplemental Materials: Grade 1 Module 5 Lesson 2

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Achievement Descriptor – 1.Mod5.AD3

Achievement Descriptor – 1.Mod5.AD1

Grade 1 Module 5 Lesson 2