Supplemental Materials: Grade 3 Module 3 Lesson 5 by Great Minds

Supplemental Materials

Adapt

Optimizing Instruction, 3–5

A Story of Units®

Supplemental Materials

Adapt: Optimizing Instruction, 3–5

Contents Analyze Student Work ............................................................................................................................. 3 Grade 3 Module 3 Topic A Overview .................................................................................................... 3 Grade 3 Module 3 Topic A Progression of Lessons ............................................................................... 4 Grade 3 Module 3 Lesson 5 Overview .................................................................................................. 6 Achievement Descriptor – 3.Mod3.AD5 ............................................................................................... 8 Grade 3 Module 3 Lesson 5 ..................................................................................................................... 9 Credits................................................................................................................................................... 26 Works Cited........................................................................................................................................... 26

Topic A Multiplication and Division Concepts with an Emphasis on Units of 6 and 8 Students apply multiplication and division concepts from module 1 to the units of 6 and 8. They see how threes and fours facts are related to sixes and eights, respectively, and they use that relationship as a strategy to help them multiply and divide. Students use equal groups, skip-counting, arrays, tape diagrams, and the commutative, associative, and distributive properties to represent relationships and to find products, quotients, and unknown factors. As in module 1, topic A opens with students counting a collection of objects. Each collection consists of images of packaged objects. This facilitates efficient counting through the application of multiplication concepts from module 1. The lesson serves as a formative assessment of the strategies students use to count. The counting is revisited at the end of the module, when students count another collection. Beginning in lesson 2, students use a letter to represent an unknown quantity instead of a question mark or blank. This transition away from the question mark or blank provides more flexibility in representing unknowns and in solving two-step word problems with more than one unknown. Students use letters that make sense to the contexts of the problems. Throughout the topic, students continue to develop their ability to apply properties of operations as strategies for multiplying and dividing. They identify equal groups within arrays, and they write expressions to represent the equal groups by using three factors and parentheses. This prepares students for the formal introduction of the associative property in topic B. Students use the break apart and distribute strategy to multiply with units of 6 and 8. They use arrays, tape diagrams, and written notation to show how to break apart the first factor. Arrays and number bonds are used to represent the break apart and distribute strategy for division. In topic B, students continue to formalize multiplication and division concepts and strategies with units of 7.

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EUREKA MATH2

Progression of Lessons

Lesson 1

Lesson 2

Lesson 3

Organize, count, and represent a collection of objects.

Count by units of 6 to multiply and divide by using arrays.

Count by units of 8 to multiply and divide by using arrays.

CRAYONS

6 12 18 24 30 36 42 48 54 60

CRAYONS

When I make equal groups, I can multiply to count efficiently. Sometimes the number of items in the package represents the size of the group. Other times I combine the number of items in smaller packages to make a larger group.

Knowing that 2 groups of 3 is 6 helps me multiply and divide by 6. Skip-counting by threes helps me skip-count by sixes. I can double my threes facts to find sixes facts. Identifying equal groups in an array or thinking about division as an unknown factor problem helps me divide by 6.

Thinking about fours helps me multiply and divide by 8 just like thinking about threes helps me with sixes. I can use an array or I can think of two groups of a number of fours to find an eights fact. Finding unknown factors helps me divide.

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EUREKA MATH2

Lesson 4

Lesson 5

Lesson 6

Decompose pictorial arrays to create expressions with three factors.

Use the break apart and distribute strategy to multiply with units of 6 and 8.

Use the break apart and distribute strategy to divide with units of 6 and 8.

48 ÷ 8 = 3 + 3 = 6

9 5×9

3×9

8 × 9 = (5 + 3) × 9 = (5 × 9) + (3 × 9)

groups of (

×(

× ×

)

The break apart and distribute strategy helps me multiply with units of 6 or 8 by breaking apart the number of groups into an addition fact that makes the multiplication simpler. I often use a fives fact or doubles because I know them really well.

)

× There are different ways to see equal groups within arrays. I can represent the equal groups with expressions that have three factors. This helps me simplify equations with large, unfamiliar factors. I can decompose one large factor to make smaller facts I know better. Copyright © Great Minds PBC

The break apart and distribute strategy helps me divide by breaking the total into numbers I know how to divide. There are different ways that I can break apart the total. I can use an array or a number bond to show my thinking.

LESSON 5

Use the break apart and distribute strategy to multiply with units of 6 and 8. Lesson at a Glance

Name

Use the break apart and distribute strategy to find 6 × 7.

Students demonstrate the break apart and distribute strategy by using arrays, tape diagrams, and known factors. They use expressions in the form of ( + )× to represent the strategy.

Key Questions • What helps you decide how to break apart a factor? • When does the break apart and distribute strategy help you multiply?

Sample:

6×7=(

)×

)+(

7 1

Achievement Descriptor

)

3.Mod3.AD5 Apply the distributive property to multiply. (3.OA.B.5)

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EUREKA MATH2

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Consider tearing out the Sprint pages in advance of the lesson.

Launch Learn

15 min 5 min

30 min

• Break Apart and Distribute 8 Groups • Break Apart and Distribute 6 Groups

• 100-bead rekenrek

Students • Round to the Nearest Ten Sprint (in the student book)

• Break Apart and Distribute with a Tape Diagram • Problem Set

Land

10 min

EUREKA MATH2

3 ▸ M3

3.Mod3.AD5 Apply the distributive property to multiply. RELATED CCSSM

3.OA.B.5 Apply properties of operations to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) 2

Students need not use formal terms for these properties.

Partially Proficient Apply the distributive property to generate equivalent expressions. Is each expression equal to 9 × 6? Circle Yes or No.

(5 + 4) × 6

Yes

(10 × 6) + (1 × 6)

Yes

(10 × 6) − (1 × 6)

Yes

(5 × 6) × (4 × 6)

Yes

Proficient Apply the distributive property to multiply.

Explain the distributive property for multiplication.

Break apart the 7 to find 7 × 8.

Carla says she can find 16 × 5 by using the expression (10 × 5) + (6 × 5). Is she correct? Explain.

7×8=( =

× 8) + (

× 8)

EM2_0303TE_AD_resource.indd 424

Highly Proficient

12/18/2020 12:36:26 PM

LESSON 5

Use the break apart and distribute strategy to multiply with units of 6 and 8. Lesson at a Glance

Name

Use the break apart and distribute strategy to find 6 × 7.

Students demonstrate the break apart and distribute strategy by using arrays, tape diagrams, and known factors. They use expressions in the form of ( + )× to represent the strategy.

Key Questions • What helps you decide how to break apart a factor? • When does the break apart and distribute strategy help you multiply?

Sample:

6×7=(

)×

)+(

7 1

Achievement Descriptor

)

3.Mod3.AD5 Apply the distributive property to multiply. (3.OA.B.5)

3 ▸ M3 ▸ TA ▸ Lesson 5

EUREKA MATH2

Agenda

Materials

Lesson Preparation

Fluency

Teacher

Consider tearing out the Sprint pages in advance of the lesson.

Launch Learn

15 min 5 min

30 min

• Break Apart and Distribute 8 Groups • Break Apart and Distribute 6 Groups

• 100-bead rekenrek

Students • Round to the Nearest Ten Sprint (in the student book)

• Break Apart and Distribute with a Tape Diagram • Problem Set

Land

10 min

3 ▸ M3 ▸ TA ▸ Lesson 5

Fluency

EUREKA MATH2

Sprint: Round to the Nearest Ten Materials—S: Round to the Nearest Ten Sprint

Students round two- and three-digit numbers to the nearest ten to build fluency with the skill from module 2. Have students read the instructions and complete the sample problems.

Round to the nearest ten.

54 ≈

138 ≈

140

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!” if you got it correct. If you made a mistake, circle the answer. 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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EUREKA MATH2

Celebrate students’ effort and success. Provide about 2 minutes to allow students to complete more problems or to analyze and discuss patterns in Sprint A. If students are provided time to complete more problems on Sprint A, reread the answers but do not have them alter their personal goals. 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.

Teacher Note

Consider asking the following questions to discuss the patterns in Sprint A: • How do problems 1–3 compare to problems 4–6? • Did your strategy change for problems 12–22? If so, how?

Direct students to Sprint B. Take your mark. Get set. Improve! Teacher Note 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!” if you got it correct. If you made a mistake, circle the answer.

Count forward by fours from 0 to 40 for the fast-paced counting activity. Count backward by fours from 40 to 0 for the slow-paced counting activity.

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. Determine your improvement score and write the number at the top of the page. Celebrate students’ improvement.

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EUREKA MATH2

Counting on the Rekenrek by Eights Materials—T: Rekenrek

Students count by eights in unit and standard form to build fluency with using arrays to multiply and divide. Show students the rekenrek. Start with all the beads to the right side. Say how many beads there are as I slide them over. Slide 8 beads in the top row all at once to the left side.

8 The unit is 8. In unit form, we say 1 eight. Say 8 in unit form.

1 eight Slide 8 beads in the next row all at once to the left side. How many beads are there now? Say it in unit form.

2 eights Continue sliding over 8 beads in each row all at once as students count.

3 eights, 4 eights, 5 eights, 6 eights, 7 eights, 8 eights, 9 eights, 10 eights

Teacher Note

Slide all the beads back to the right side. Now let’s practice counting by eights in standard form. Say how many beads there are as I slide them over. Let’s start at 0. Ready? Slide over 8 beads in each row all at once as students count.

Eights are introduced in lesson 3. Therefore, expect productive struggle and a slower pace when students are counting by eights. Listen to student responses and be mindful of errors, hesitation, and lack of full-class participation. If needed, limit the range of numbers.

0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 80

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EUREKA MATH2

Launch

Students determine the total in an array that is composed of smaller arrays. Display the picture of the soup cans.

Teacher Note

Liz sees a display of tomato soup and chicken soup cans at the grocery store. She wonders how many soup cans there are altogether. Work with a partner to find the total number of soup cans in the display.

A context video for this word problem is available. It may be used to remove language or cultural barriers and provide student engagement. Before providing the problem to students, consider showing the video and facilitating a discussion about what students notice and wonder. This supports students in visualizing the situation before being asked to interpret it mathematically.

After giving partners time to work, discuss the strategies that students used to determine the total number of soup cans. What is the total number of soup cans? What strategy did you use to find the total number of soup cans? There are 6 soup cans in each column, so we skip-counted by sixes. We saw the array as 2 groups of 3 × 7. We know that 3 × 7 = 21 and 21 + 21 = 42. Display the following expressions: 6 × 7 and (3 × 7) + (3 × 7). Invite students to turn and talk to a partner about how both expressions describe the array. What is the name of the strategy where we break apart one factor? It’s the break apart and distribute strategy.

Promoting the Standards for Mathematical Practice

Students attend to precision (MP6) as they communicate by using multiple operations— addition and multiplication—within the same context or equation. Ask the following questions to promote MP6:

Transition to the next segment by framing the work. Today, let’s represent the break apart and distribute strategy in different ways.

• What do the multiplication and addition symbols in your equation mean in terms of the soup cans? • How are you using addition and multiplication together when finding the total number of soup cans? • How are you using parentheses in your work?

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Learn

EUREKA MATH2

Break Apart and Distribute 8 Groups Students break apart 8 to find 8 × 7 by using the break apart and distribute strategy. Direct students to problem 1 in their books. Invite students to write an expression that represents the array by filling in the first two blanks. 1. Liz sees a display of cans of peas at the grocery store. How many cans of peas are in the display? Use the break apart and distribute strategy to find the total number of cans of peas.

)×

)+(

7 4

)

There are 56 cans of peas in the display. 15

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EUREKA MATH2

What expression did you write to represent the cans of peas? Write 8 × 7. To find 8 × 7, let’s break apart 8. What addition facts can we list with a sum of 8?

Teacher Note

As students name ways to break apart 8, record their thinking with number bonds. We are breaking apart 8 to make facts we know that we can use to multiply by 7. Let’s think about all the ways to make 8. Look at the number bonds and think about what factors we know well. Point to the number bond that shows 8 decomposed into 0 and 8.

Students may think about factors with a product of 8 instead of addends with a sum of 8 because of the work they did in lesson 4. Redirect them to thinking about addition facts, and support students in using number bonds to represent part–part–total relationships.

To use this combination, we need to multiply 7 by 8 and by 0. Would multiplying 7 by 8 and 0 simplify the problem? Which number bond has parts that are factors we know well? Circle the decompositions of 8 that the class identifies as well-known factors. Point to the number bond that shows 8 broken apart into 4 and 4. We’ve been thinking about 8 as 2 groups of 4. Let’s see whether that is helpful as we use the break apart and distribute strategy. Direct students to the array in problem 1.

Teacher Note

Students will have varying levels of fluency with different factors. Guide the discussion to select factor pairs for which students are comfortable working with both factors and that show how the break apart and distribute strategy can be most helpful.

We have 8 groups of 7. How can we break the 8 groups into two smaller groups? We can break the 8 groups into 2 groups of 4. Where can we draw a line in the array to show how to break apart 8 into 2 fours? Draw a line between the fourth and fifth rows in the array. Invite students to do the same. Let’s show that 8 × 7 = (4 + 4) × 7. We use parentheses to help us see that we are thinking about the 8 as 4 + 4. Complete the equation and invite students to do the same.

UDL: Representation Consider highlighting the 8, 4, and 4 to connect the parts of the equation.

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What do you notice about the array now? It’s broken apart into two smaller arrays.

What expressions represent the two smaller arrays? Write 4 × 7 next to each smaller array. How can these expressions help me find 8 × 7? You can add the products of the two smaller arrays to find the total number of cans.

Model how to write the expression (4 × 7) + (4 × 7) to represent the sum of the two smaller arrays. Invite students to write the expression in the second row of blanks in problem 1. Where do you see the original factors, 8 and 7, in this new expression? I see 8 broken apart into 4 and 4. Seven is in both expressions, because it is the unit. 4 sevens and 4 sevens make 8 sevens. Invite students to find the product of the two smaller arrays and add to find the total number of cans in the display. What is the total number of cans of peas in the display? Direct students to write a statement to answer the question. Point to the fours in the expression (4 + 4) × 7. We broke apart 8 into 4 and 4.

Language Support

Point to the sevens in the expression (4 × 7) + (4 × 7). Then we distributed the other factor, 7, to multiply it by both parts that we broke 8 into. Invite students to turn and talk to a partner about how the expressions (4 + 4) × 7 and

(4 × 7) + (4 × 7) show the break apart and distribute strategy.

As time allows, quickly guide students through using 8 × 7 = (5 + 3) × 7. Then briefly discuss which combination was more helpful for them when finding 8 × 7.

Consider supporting the term distribute by using the synonym pass out. Act out passing out, or distributing, papers or other supplies. As possible, use the terms interchangeably throughout the day in normal class procedures so that students become comfortable with the word.

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EUREKA MATH2

Break Apart and Distribute 6 Groups

Differentiation: Support

Students work with a partner to apply the break apart and distribute strategy to multiply by 6. Direct students to problem 2. Invite them to work with a partner to use the break apart and distribute strategy to find the total number of jars of sauce. Circulate as partners work and use the following questions to advance student thinking: • What are some ways you can break apart 6 groups? • What factors do you already know that will help you decide how to break apart 6? • How can you use the array to show how to break apart 6 groups? • What new expression can you write to show how you decided to break apart 6? • What expressions can you write to represent the smaller arrays? • How can you use the expressions that represent the smaller arrays to find 6 × 9? 2. Liz sees a display of sauce at the grocery store. How many jars of sauce are in the display? Use the break apart and distribute strategy to find the total number of jars of sauce.

)×

)+(

9 1

)

If students need support with the break apart and distribute strategy because they select factors that do not give them facts they know, consider guiding them with a think-aloud such as: “I can think about 6 nines another way. I can think of it as 3 nines + 3 nines, but that’s not helpful if I don’t know 3 × 9. I can think of it as 5 nines + 1 nine. That’s helpful because I know 5 × 9 and I can see that 1 nine is 9. I can add 45 and 9 by using a mental math strategy.”

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EUREKA MATH2

Facilitate a class discussion about using the break apart and distribute strategy to solve problem 2. How did you and your partner break apart 6? Explain why you broke apart 6 the way you did. We broke 6 apart into 5 and 1 because we are good at our fives facts. We decided to break apart 6 into 3 and 3 because we thought about 6 as 2 groups of 3.

Teacher Note

The sample solutions are examples of how the break apart and distribute strategy can be used for these problems. Accept all answers that correctly use the strategy.

What factor was distributed into both parts of the expression? How do you know? The 9 was distributed because we broke apart the 6, so the other factor gets distributed. Teacher Note

I know 9 was distributed because you can see it in our expression, (5 × 9) + (1 × 9). The 6 is broken apart into 5 and 1, and the 9 is distributed.

Instead of using the provided image from problem 2, consider displaying actual student work that mirrors the tape diagram work.

Break Apart and Distribute with a Tape Diagram Students analyze how the break apart and distribute strategy is represented in a tape diagram. Guide students to see how the break apart and distribute strategy can be represented with a tape diagram.

UDL: Representation

To support students in transitioning from the array to the tape diagram, consider using interlocking cubes. Model the array vertically as 6 nines by using 5 cubes of one color and

Display the picture of the jars of sauce and tape diagram.

1 cube of another color. Then rotate the array horizontally to show that it looks like the tape diagram.

5 × 9

9 1×9 5 × 9

1 × 9

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EUREKA MATH2

Invite students to think–pair–share about how the break apart and distribute strategy is represented in the tape diagram. Circulate as students share their thinking, and provide support as needed. Select a few partners to share their ideas with the class. Encourage students to point or gesture to where they see 6 broken into 5 and 1 on both the array and tape diagram. We can see that 6 is broken apart in the tape diagram just like it is in the array. There are 6 nines, and a line is drawn to show 5 nines and 1 nine. So the 6 is broken apart and the 9 is distributed to both parts of the expression. We noticed that the tape diagram is labeled with the same expressions as the array,

5 × 9 and 1 × 9. These expressions show how to break apart 6 into 5 and 1 and then distribute the 9 to both parts of the expression. As time allows, direct students to problem 3. Ask students to draw a tape diagram and use the break apart and distribute strategy to find the total number of tomatoes. 3. Liz sees a display of 8 rows of tomatoes at the grocery store. There are 9 tomatoes in each row. How many tomatoes are in the display? a. Draw a tape diagram to represent the tomatoes.

9 Teacher Note

5×9

3×9

b. Use the break apart and distribute strategy to find the total number of tomatoes.

)×

)+(

9 3

There are 72 tomatoes in the display.

)

Students have multiple opportunities to master the break apart and distribute strategy throughout the module. The strategy reappears in module 4 with the context of area.

3 ▸ M3 ▸ TA ▸ Lesson 5

EUREKA MATH2

Display the following expressions: 6 × 3, 3 × 4, 8 × 8, 6 × 8, 5 × 6, and 8 × 4. Invite students to turn and talk to a partner to determine whether break apart and distribute is an efficient strategy to use to find the product of each expression.

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

Land Debrief

5 min

Objective: Use the break apart and distribute strategy to multiply with units of 6 and 8. Use the following prompts to guide a discussion about the break apart and distribute strategy. When does the break apart and distribute strategy help you multiply? It helps when I don’t know the product, but I can break apart one of the factors into smaller factors that I know the product of. It helps when I can use break apart and distribute to rewrite the problem as facts I already know or that are easier for me to figure out by skip-counting. What helps you decide how to break apart a factor? I look at the factors, and I think about facts that I know. I think about how I can break apart the factor so that I can use familiar facts.

3 ▸ M3 ▸ TA ▸ Lesson 5

EUREKA MATH2

Display the picture of the tomato soup and chicken soup cans, the expression (3 × 7) + (3 × 7), and the frame ( + ) × 7. Earlier you discussed how this expression describes the display of soup cans. What other expression did you learn today that you can use to show the break apart and distribute strategy? Complete the frame for (3 + 3) × 7. How do both expressions show the same thinking?

(3 + 3) × 7 shows that I am breaking apart 6 into 3 + 3 and need to multiply 7 by each part and then find the sum. (3 × 7) + (3 × 7) also shows that I am breaking apart 6 into two parts and that I need to find the sum of 3 sevens and 3 sevens.

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.

3 ▸ M3 ▸ TA ▸ Lesson 5

EUREKA MATH2

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

Number Correct:

Round to the nearest ten.

Number Correct: Improvement:

Round to the nearest ten.

29 ≈

23.

337 ≈

340

19 ≈

23.

278 ≈

280

49 ≈

24.

307 ≈

310

39 ≈

24.

208 ≈

210

89 ≈

25.

563 ≈

560

79 ≈

25.

464 ≈

460

34 ≈

26.

503 ≈

500

24 ≈

26.

404 ≈

400

64 ≈

27.

766 ≈

770

54 ≈

27.

657 ≈

660

94 ≈

28.

706 ≈

710

84 ≈

28.

607 ≈

610

36 ≈

29.

894 ≈

890

26 ≈

29.

792 ≈

790

63 ≈

30.

804 ≈

800

62 ≈

30.

702 ≈

700

58 ≈

31.

932 ≈

930

57 ≈

31.

843 ≈

840

10.

85 ≈

32.

902 ≈

900

10.

75 ≈

32.

803 ≈

800

11.

99 ≈

100

33.

361 ≈

360

11.

99 ≈

100

33.

261 ≈

260

12.

241 ≈

240

34.

555 ≈

560

12.

141 ≈

140

34.

555 ≈

560

13.

246 ≈

250

35.

505 ≈

510

13.

146 ≈

150

35.

505 ≈

510

14.

419 ≈

420

36.

497 ≈

500

14.

319 ≈

320

36.

398 ≈

400

15.

412 ≈

410

37.

507 ≈

510

15.

312 ≈

310

37.

408 ≈

410

16.

647 ≈

650

38.

698 ≈

700

16.

547 ≈

550

38.

599 ≈

600

17.

641 ≈

640

39.

708 ≈

710

17.

541 ≈

540

39.

609 ≈

610

18.

853 ≈

850

40.

996 ≈

1,000

18.

753 ≈

750

40.

997 ≈

1,000

19.

858 ≈

860

41.

1,654 ≈

1,650

19.

758 ≈

760

41.

1,653 ≈

1,650

20.

924 ≈

920

42.

1.057 ≈

1,060

20.

824 ≈

820

42.

1,058 ≈

1,060

21.

926 ≈

930

43.

1,606 ≈

1,610

21.

826 ≈

830

43.

1,607 ≈

1,610

22.

928 ≈

930

44.

1,008 ≈

1,010

22.

828 ≈

830

44.

1,009 ≈

1,010

3 ▸ M3 ▸ TA ▸ Lesson 5

EUREKA MATH2

Name

Use the arrays to help you fill in the blanks and find the totals. 2.

1. Draw part of the array to complete the number bond. Then use it to help you fill in the blanks and find the total.

8 sixes = 5 sixes +

8 sixes

3 3

× 6)

8×6=

)

8×6=

8 × 7 = (5 +

= (5 × 7) + ( = 35 +

5 sixes

sixes

8 × 6 = (5 × 6) + ( +(

5×7=

sixes

×7=

)×7 3

× 7)

5×8=

8 × 8 = (5 +

= (5 × 8) + (

PROBLEM SET

)×8 3

× 8)

3 ▸ M3 ▸ TA ▸ Lesson 5

EUREKA MATH2

6. Adam walks 9 laps around the track every day for 8 days. How many total laps does he walk?

Label the tape diagrams. Then complete the equations. 4. (5 × 6) =

(

× 6) =

a. To find the total, Jayla breaks 8 × 9 into 5 × 9 and 3 × 9. Then she adds 45 and 27 to get 72. Explain why her strategy works.

Jayla’s strategy works because she broke 8 apart into 5 and 3, and then she multiplied 9 by 5 and 9 by 3. I know 8 nines is the same amount as 5 nines + 3 nines.

7 × 6 = (5 + 2) × 6 = (5 × 6) + ( = 30 + =

× 6)

b. Show another way 8 × 9 can be broken apart into smaller facts to find the product. Sample:

8 × 9 = (4 + 4) × 9 5.

(

× 6) = 30

× 6) = 24

= (4 × 9) + (4 × 9) = 36 + 36 = 72

9 × 6 = (5 + =(

)×6

× 6) + ( +

× 6)

PROBLEM SET

Supplemental Materials

Adapt: Optimizing Instruction, 3–5

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.