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Use the distributive property to break apart multiplication problems into known facts.

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Lesson 19

Key Questions

How is using a number bond to represent break apart and distribute similar to using an array? How is it different?�How do we use tens to help us multiply by nine?

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Fluency �Counting the Math Way by Threes and Fours

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Fluency �Whiteboard Exchange: Add Within 1,000 (1 of 3)

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Fluency �Whiteboard Exchange: Add Within 1,000 (2 of 3)

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Fluency �I Say, You Say: 5 or 2 of a Unit

2 twos

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Fluency �I Say, You Say: 5 or 2 of a Unit

5 fives

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Fluency �I Say, You Say: 5 or 2 of a Unit

5 threes

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Fluency �I Say, You Say: 5 or 2 of a Unit

5 fours

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Launch

Mrs. Smith bakes a tray of mini muffins.

The tray has 7 rows of 4 mini muffins.

What is the total number of mini muffins Mrs. Smith bakes?

9

[Direct students to problem 1 in their books. Use the Math Chat routine to engage students in mathematical discourse.]

[Give students 2 minutes of silent work time to solve. Have students give a silent signal to indicate they are finished.]

[Have students discuss their work with a partner. Circulate and listen as they talk. Identify a few students to share their thinking. Purposefully choose work that allows for rich discussion about the strategies students chose and their reasoning. Emphasize thinking that shows the break apart and distribute strategy.]

[Then facilitate a class discussion. Invite students to share their thinking with the whole group, and record their reasoning.]

[Ask questions that invite students to make connections, and encourage them to ask questions of their own.]

When we use the break apart and distribute strategy, we break apart the columns. We can also use the strategy by breaking apart the rows.

[Transition to the next segment by framing the work.]

Today, we will break apart the rows of an array to multiply

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Learn �Break Apart and Distribute 10 Units to Multiply by 9 Units ( 1 of 2)

3. Mrs. Smith bakes a tray of mini muffins.

The tray has 9 rows of 4 mini muffins.

What is the total number of mini muffins Mrs. Smith bakes?

10

[Direct students to problem 3]

[Guide students through the process of using the break apart and distribute strategy by breaking apart the rows. Consider the following possible sequence:]

Let’s find 9 × 4. One way to do this quickly in my head is to think about 10 × 4. We know how to multiply by 10 really well, and 9 is 1 less than 10. Let’s use this relationship to help us find 9 × 4.

Look at the array. How many fours are in the entire array?

[Label the array 10 fours.]

9 fours is 1 four less than 10 fours. So I can think about 9 fours as 10 fours minus 1 four.

[Label the shaded row as 1 four on the array.]

[Write 9 fours = 10 fours − 1 four.]

Let’s write that as a multiplication equation.

[Write 9 × 4 = (10 × 4) − (1 × 4).]

[Guide students to complete the equations to find 9 × 4.]

[Conclude by asking the following question.]

What is the product of 9 and 4?

[Invite students to think–pair–share about where they see the break apart and distribute strategy being used.]

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Learn �Break Apart and Distribute 10 Units to Multiply by 9 Units ( 2 of 2)

4. Mrs. Smith bakes a tray of mini muffins.

The tray has 9 rows of 3 mini muffins.

What is the total number of mini muffins Mrs. Smith bakes?

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Learn �Break Apart and Distribute 10 Units to Multiply by 9 Units

9 x 4

9 x 7

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Learn�Problem Set (1 of 4)

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Learn�Problem Set (2 of 4)

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Learn�Problem Set (3 of 4)

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Learn�Problem Set (4 of 4)

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Land �Debrief

How is using the break apart and distribute strategy to break apart the rows of an array similar to using it to break apart the columns of an array? How is it different?
How is using a number bond to represent break apart and distribute similar to using an array? How is it different?
How do we use 10 to help us multiply by 9?

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Land �Exit Ticket

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