Grade 3 Module 3 Lesson 6

6

LESSON 6

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

Lesson at a Glance

6

Name

Use the break apart and distribute strategy to find 48 ÷ 4.

Students apply the break apart and distribute strategy to division by using arrays and number bonds. Students make decisions about how to break apart the total by using known facts.

Shade the array to show how you broke apart 48.

Key Questions

Sample:

• How can facts you know help you divide?

• How is a number bond helpful when using the break apart and distribute strategy to divide?

48 ÷ 4 =

40

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10 +

2

=

12

Achievement Descriptor 3.Mod3.AD6 Apply the distributive property to divide. (3.OA.B.5)

8

65

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3 ▸ M3 ▸ TA ▸ Lesson 6

EUREKA MATH2

Agenda

Materials

Lesson Preparation

Fluency

Teacher

• Students need numbers 2–10 from a deck of Numeral Cards. Consider removing 0 and 1 cards from the deck.

Launch Learn

10 min 10 min

30 min

• Break Apart and Distribute to Divide by 6 • Break Apart and Distribute with Number Bonds • Problem Set

Land

• Number Bond Signs (in the teacher edition)

Students

• Copy Number Bond Signs and hang them in the classroom.

• Eureka Math2 Numeral Cards (1 deck per student pair) • Hidden Factor Mat (1 per student pair, in the student book)

10 min

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Fluency

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10

Choral Response: Round to the Nearest Hundred Students round a three- or four-digit number to the nearest hundred to build fluency with the skill from module 2.

Display 361 ≈

.

What is 361 when rounded to the nearest hundred? Raise your hand when you know.

Wait until most students raise their hands, and then signal for students to respond.

400

361 ≈ 400

Display the rounded value.

Repeat the process with the following sequence:

128

750

509

667

1,835

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

Students find a product and say an equation to build multiplication fluency within 100.

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 on the Hidden Factor Mat. Assign a factor for students to practice (e.g., 3), or allow them to choose one and have them write the factor in the empty box next to the deck.

102

Teacher Note

Students have only formally studied factors of 2, 3, 4, 5, 6, 8, and 10 at this point. Consider whether you prefer to limit this game to these factors or challenge students to use others as they are ready.

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• Partner A flips over the top card and places it back on the deck.

• Both students say the product. See the sample partner dialogue under the image.

6

×

3

• Partner A says the multiplication equation starting with the Numeral Card. Partner B says a related multiplication equation by switching the order of the factors.

Partner A: “6 × 3 = 18”

• Students discard the card into a separate pile.

Partner B: “3 × 6 = 18”

Partners A and B: “18”

Circulate during the activity to ensure that students are saying accurate multiplication equations.

If students run out of cards before the time ends, they can switch roles, place the discard pile facedown on their mat, and continue playing. They may use the same factor, be assigned a different factor, or choose a different factor.

Counting the Math Way by Eights Students construct a number line with their fingers while counting aloud to develop fluency with counting by eights and to maintain a strategy for multiplying.

For each skip-count, show the math way on your own fingers while students count, but do not count aloud.

Let’s count the math way by eights. Each finger represents 8.

Have students count the math way by eights from 0 to 80 and then back down to 0.

0

8

16

24

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32

40

48

56

64

72

80

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Launch

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10

Students determine how the total is broken apart in given arrays.

Direct students to the three arrays in their books.

The arrays show different ways to use the break apart and distribute strategy to find 32 ÷ 4.

Direct students to problem 1. Invite them to work with a partner to complete the number bonds to show how 32 is broken apart in each array. After giving partners time to work, display the picture of the completed number bonds to confirm their answers.

Array A

Array A

Array B

32 ÷ 4

20

12

Array C

32 ÷ 4

32 ÷ 4

24

16

8

Array B

16

Array C

1. Complete the number bonds.

Array A

Array B

32 ÷ 4

20

104

12

Array C

32 ÷ 4

24

8

32 ÷ 4

16

16

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3 ▸ M3 ▸ TA ▸ Lesson 6

EUREKA MATH2

Direct students to problem 2. Invite students to work with a partner to shade the array and complete the number bond to show a different way to break apart 32.

2. Shade the array and complete the number bond to show a different way to break apart 32.

Teacher Note

Sample:

32 ÷ 4

28

4

The digital interactive Break Apart Arrays supports students’ understanding of breaking apart a quantity visually.

Consider allowing students to experiment with the tool individually or demonstrating the activity for the whole class.

Invite students to turn and talk to a partner about which number bond from problems 1 or 2 they would use to help them break apart 32 to find 32 ÷ 4.

Transition to the next segment by framing the work.

Today, we will use facts we know and the break apart and distribute strategy to divide.

Learn

30

Break Apart and Distribute to Divide by 6 Materials—T: Signs

Language Support

To support students with defending the reasons for their choice to the class, see the Agree or Disagree section of the Talking Tool.

Students identify and justify how they would use the break apart and distribute strategy to find 48 ÷ 6.

Introduce the Take a Stand routine to the class. Draw students’ attention to the signs hanging in the classroom.

Direct students to problem 3. Have students read the problem and think about how they would break apart 48. Invite students to stand beside the sign that best describes their thinking.

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When all students are standing near a sign, allow 2 minutes for groups to discuss the reasons they chose that sign.

Then call on each group to share reasons for their selection. Encourage students who change their minds during the discussion to join a different group. Invite students to partner with a group member to complete problem 3.

3. Use the break apart and distribute strategy to find 48 ÷ 6. Shade the array to show how to break apart 48.

Promoting the Standards for Mathematical Practice

Students construct viable arguments and critique the reasoning of others (MP3) during and after the Take a Stand routine as they discuss and reflect on how they decided to break apart 48.

Ask the following questions to promote MP3:

48 ÷ 6 =

24

4

+

4

=

• Why is breaking 48 into 24 and 24 an

8

efficient strategy? Convince the class.

• What questions can you ask the other groups to make sure you understand their arguments?

24

Have students return to their seats. As a class, reflect on how students decided to break apart 48 and how the break apart and distribute strategy helped them find 48 ÷ 6.

Display a number bond with 48 decomposed into 40 and 8. Use the following prompts to facilitate a discussion to support students in recognizing the need to decompose 48 into multiples of 6.

48 ÷ 6

40

8

Would you choose to break 48 into 40 and 8 like this, to find 48 ÷ 6? Why? I wouldn’t choose to break apart 48 that way, because I don’t know how to divide 40 or 8 by 6.

Teacher Note

Specific language is essential during this discussion. A student may incorrectly state, for example, “We can’t divide 40 or 8 by 6.”

Guide the discussion to focus on breaking apart the numbers into smaller numbers that we know how to divide.

No, I wouldn’t, because I don’t know how to make 40 or 8 using sixes.

Even though 40 and 8 make 48, it’s not a helpful way to break apart 48. We’re dividing by 6, and I don’t know any facts with 6 that make 40 or 8.

What I hear you saying is that when you use the break apart and distribute strategy, it’s important to think about the unit you’re dividing by and facts you already know.

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Break Apart and Distribute with Number Bonds Students make decisions about how to break apart a total and how to use a number bond to model the break apart and distribute strategy.

Teacher Note

Write the expression 72 ÷ 8.

Let’s break apart 72. What are all the ways we can break apart 72 into the sum of two numbers, both of which we can divide by 8?

As students name ways to break apart 72, record their thinking with number bonds.

Listing pairs to break apart a total could present a challenge. Consider counting out 7 tens and 2 ones to model a total of 72 on the rekenrek. Cover the remaining beads.

Move 8 beads at a time to the right to show ways to break apart 72. Relate the rekenrek to parts in a number bond.

We’re breaking apart 72 into smaller parts to make facts we know we can divide by 8.

Look at the number bonds and think about facts that we know well.

Point to the number bond that shows 72 decomposed into 64 and 8.

To use this combination, we need to divide 64 by 8 and 8 by 8.

72

Are 64 ÷ 8 and 8 ÷ 8 both facts we know well?

Ask similar questions about the other combinations. Circle the decompositions of 72 that the class identifies as well-known facts.

Point to the number bond that shows 72 broken apart into 40 and 32. Ask what makes those facts simpler, and possibly easier, to work with than the other facts. Engage students in a discussion about how breaking a total into a fives fact and another fact can usually be done with mental math.

72 ÷ 8 = 5 + 4 = 9 Direct students to find 72 ÷ 8 by breaking apart 72 into 40 and 32, using a number bond to show their work. Provide only as much support as necessary while they work.

40 32

64

72 56

16

72 48

Direct students to complete problems 4–6 with a partner. Remind partners that they will need to make decisions about how they want to break apart the total.

24

72 40

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8

32

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Use the break apart and distribute strategy to divide. Show your work with a number bond.

UDL: Action & Expression

4. 28 ÷ 4

28 ÷ 4 = 5 + 2 = 7 20

8

5. 54 ÷ 6

Consider providing grid paper for students to model the break apart and distribute strategy by shading the array. The pictorial representation can help support the number bond work.

54 ÷ 6 = 5 + 4 = 9 Teacher Note

30

24

6. 48 ÷ 8

48 ÷ 8 = 3 + 3 = 6 24

The sample student work shows some possible ways to divide by using the break apart and distribute strategy. Accept all answers that demonstrate an understanding of how to apply the strategy to divide.

24

Facilitate a class discussion about using the break apart and distribute strategy to divide by using the following possible sequence.

How did you and your partner decide how to break apart the total?

We thought about facts that we already know that could help us. We broke apart 54 into 30 and 24, because 30 is a fives fact and we know our fives facts well.

Using fives facts helped us break apart 54 and 28, but we thought about threes facts to break apart 48. We broke apart 48 into 24 and 24.

How did you and your partner use a number bond to show your work?

We wrote 28 ÷ 4 and used a number bond to show how we broke apart 28 into 20 and 8.

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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

10

5 min

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

Gather the class with their books and consider the following questions to facilitate a discussion about the break apart and distribute strategy.

Direct students to problem 2 and display the picture that shows repeated subtraction as a strategy for finding 32 ÷ 4.

This student found 32 ÷ 4 a different way. How did this student get the answer of 8?

She subtracted 4 eight times.

Is this strategy more efficient than breaking apart the 32? Why? No. All this subtraction is more steps.

Would it be helpful to break apart 32 into 30 and 2? Why? No, it wouldn’t, because I don’t know how to make 30 or 2 using fours.

32 28 24 20 16 12 8 4

-

4 4 4 4 4 4 4 4

= = = = = = = =

28 24 20 16 12 8 4 0

32 ÷ 4 = 8

How can facts you know help you divide?

I can break apart the total into smaller parts that make facts that I know.

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How is a number bond helpful when using the break apart and distribute strategy to divide?

It helps me see how to break apart the total. Then I use mental math to find the quotients for the smaller facts.

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.

6

Name

Use the array to help you complete each equation.

3.

4.

Use the array to help you complete each number bond and equation. The first one is started for you.

1.

21 ÷ 3 36 ÷ 4 = 21 ÷ 3 = 5 + 15 ÷ 3

2

=

+

4

=

9

5

+

2

=

7

5

+

4

=

9

7 20

6÷3 15

5

6

36 ÷ 6 = 5 +

30

1

=

16

6

6

Use the break apart and distribute strategy to divide.

42 ÷ 6 = 5 +

5.

2.

2

=

7

56 ÷ 8 =

6.

32 ÷ 4 30

20 ÷ 4

12

32 ÷ 4 =

÷4

5

+

3

=

48 ÷ 8 =

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5

+

1

=

6

54 ÷ 6 =

8.

12 40

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16

8 7.

20

40

12

61

62

8

PROBLEM SET

30

24

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9. Use the break apart and distribute strategy to find 64 ÷ 8. Explain your thinking.

64 ÷ 8 = 5 + 3 = 8

40

24

I broke apart 64 into 40 and 24, because I know 40 ÷ 8 = 5. It’s a fives fact. Then I divided 24 by 8, which equals 3. I added 5 and 3 to get 8. So 64 ÷ 8 = 8.

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112

PROBLEM SET

63

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36

48 ÷ 6 =

18 30

48 ÷ 6 = Copyright © Great Minds PBC

12

3 ▸ M3 ▸ TA ▸ Lesson 6 ▸ Number Bond Signs

EUREKA MATH2

This page may be reproduced for classroom use only.

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114

This page may be reproduced for classroom use only.

24 24

48 ÷ 6 =

6

EUREKA MATH2

42

48 ÷ 6 =

3 ▸ M3 ▸ TA ▸ Lesson 6 ▸ Number Bond Signs

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