1 of 18

Eureka Math

5th Grade

Module 2

Lesson 7

At the request of elementary teachers, a team of Bethel & Sumner educators met as a committee to create Eureka slideshow presentations. These presentations are not meant as a script, nor are they required to be used. Please customize as needed. Thank you to the many educators who contributed to this project!

Directions for customizing presentations are available on the next slide.

2 of 18

Customize this Slideshow

Reflecting your Teaching Style and Learning Needs of Your Students

When the Google Slides presentation is opened, it will look like Screen A.
Click on the “pop-out” button in the upper right hand corner to change the view.
The view now looks like Screen B.
Within Google Slides (not Chrome), choose FILE.
Choose MAKE A COPY and rename your presentation.
Google Slides will open your renamed presentation.
It is now editable & housed in MY DRIVE.

Screen A

“pop-out”

Screen B

3 of 18

Icons

Read, Draw, Write

Learning Target

Think Pair Share

Individual

Partner

Whole Class

Small Group Time

Small Group

Personal White Board

Problem Set

Manipulatives Needed

Fluency

4 of 18

5 of 18

I can connect area models and the distributive property to partial products of the standard algorithm with renaming.

6 of 18

Multiply Mentally

Sprint: Multiply by Multiples of 10 and 100 (8 minutes)

7 of 18

Multiply Using the Area Model (4 minutes)

Solve these problems using the area model:

24 x 15

824 x 15

8 of 18

Application Problem

The length of a school bus is 12.6 meters. If 9 school buses park end-to-end with 2 meters between each one, what’s the total length from the front of the first bus to the end of the last bus?

9 of 18

Application Problem

10 of 18

Concept Development Problem 1

524 x 136 Compare this problem with the problems in the previous lesson. What do you notice?

How will the area model for this problem be different than the previous models?

Partner A: area model /Partner B: use algorithm

When finished, compare products.

T: (Write 524 × 136.) Compare the problem on the board with the problems in the previous lesson. What do you notice?

S: In the previous lesson, we multiplied using only two-digit numbers as the number of units. The problems yesterday had a two-digit number in them.

T: So, which one of these factors should we designate as our unit? Turn and talk.

S: I think it’s easier to count 136 units of 524 than 524 units of 136. It seems like a lot less units to count that way. I’m not sure which one to use as the unit. It seems like it won’t really matter this time because they are both three-digit numbers. I think we should count 136 units of 524 because then we just have to multiply by 100 and 30 and 6. These seem easier to me than multiplying by 500, 20, and 4. I’m going to count 524 units of 136. I don’t think multiplying by 500 then 20 then 4 will be any harder than the other way.

T: Very thoughtful conversations. Let’s designate 524 as our unit. How will the area model for this problem be different than previous models?

S: There will be 3 columns and 3 rows. In the previous lesson, we only had 2 rows because we used the smaller number to tell the number of units. We used our larger numbers yesterday as our units.

T: Partner A, draw an area model to find the product. Partner B, solve using the standard algorithm. S: (Work.)

T: What’s the product of 524 × 136?

S: 71,264.

T: Compare your solutions by matching your partial products and final product.

NOTES ON MULTIPLE MEANS OF REPRESENTATION: Some students may find it difficult to align digits in the standard algorithm. Consider offering graph paper as a scaffold to support them.

11 of 18

Concept Development Problem 2

4519 x 326

What’s different about this problem?

Let’s estimate our product, round the factors and make an estimate.

Solve the problem: Partner B: area model / Partner A: algorithm

T: What is different about this problem?

S: We have a four-digit number this time.

T: Which factor will be our unit? Is one more efficient to use than the other? Turn and talk.

S: (Discuss as in Problem 1.)

T: Does the presence of the fourth digit change anything about how we multiply? Why or why not?

S: We will have an extra column in the area model, but we just multiply the same way.

T: Before we solve this problem, let’s estimate our product. Round the factors and make an estimate.

S: 5,000 × 300 = 1,500,000.

T: Now, solve this problem with your partner. Partner B should do the area model this time, and Partner A should use the algorithm. As you work, explain to your partner how you organized your thoughts to make this problem easier. (How did you decompose your factors?)

S: (Work and explain to partners.)

T: (Circulate and then review the answers. Return to the estimated product, and ask if the actual product is reasonable given the estimate.)

NOTES ON MULTIPLE MEANS OF ACTION AND EXPRESSION: When multiplying multi-digit numbers, (especially those with three-digit multipliers) encourage students to remember which partial product they are finding. This will help to remind students about the zeros in the partial products. Ask, “Are we multiplying by ones, tens, or hundreds? When multiplying by a ten, what will the digit in the ones place be? When multiplying by hundreds, what will the digits in the ones and tens places always be?”

12 of 18

Concept Development Problem 3

4509 x 326 (estimate the product)

We will count 326 units of 4,509.

Compare 4,519 and 4,509. How are they different?

What does 4,509 look like in expanded form?

What will the length of our rectangle look like? How many columns will we need to represent the total length?

This is a four-digit number. Why only three columns?

Solve the problem: Partner A: area model B: algorithm

T: We will count 326 units of 4,509.

T: Compare 4,519 and 4,509. How are they different?

S: There’s a zero in the tens place in 4,509.

T: What does 4,509 look like in expanded form?

S: 4,000 + 500 + 9.

T: Can you imagine what the length of our rectangle will look like? How many columns will we need to represent the total length?

S: We will need only three columns.

T: This is a four-digit number. Why only three columns?

S: The rectangle shows area. So, if we put a column in for the tens place, we would be drawing the rectangle bigger than it really is. We are chopping the length of the rectangle into three parts— 4,000, 500, and 9. That is the total length already. The width of the tens column would be zero, so it has no area.

T: Work with a partner to solve this problem. Partner A will use the area model, and Partner B will solve using the algorithm. Compare your work when you finish.

T: (Circulate and review answers. Have students assess the reasonableness of the product given the estimate.)

13 of 18

Concept Development Problem 4

4,509 x 306 (estimate the product)

How is counting 306 units of 4,509 different from problem 3?

How will the area model be different?

How will the length and width be decomposed?

How will it compare to Problem 3?

Solve the problem by drawing the model and writing the algorithm.

T: This time we are counting 306 units of 4,509. How is this different from Problem 3?

S: It’s going to be 20 units less of 4,509 than last time. There is a zero in both factors this time.

T: Thinking about the expanded forms of the factors, imagine the area model. How will the length and width be decomposed? How will it compare to Problem 3?

S: Like Problem 3, there are only three columns in the length again even though it’s a four-digit number. The model doesn’t need three rows because there’s nothing in the tens place. We only need to show rows for hundreds and ones.

T: (Allow students time to solve with the model.) What two partial products do these two rows represent?

S: 6 × 4,509 and 300 × 4,509.

T: Let’s record what we just drew with the algorithm. We’ll begin with the first partial product 6 × 4,509. Find that partial product.

S: (Record first partial product.) T: Now, let’s record 300 × 4,509. When we multiply a number by 100, what happens to the value and position of each digit?

S: Each becomes 100 times as large and shifts two places to the left.

T: In the case of 4,509, when we multiply it by 300, what would need to be recorded in the ones and tens place after the digits shift?

S: Zeros would go in those places.

14 of 18

Problem Set

15 of 18

Debrief

Explain why a multiplication problem with a three-digit multiplier will not always have three partial products. Use Problems 1(a) and (b) as examples.

How are the area models for Problems 2(a) and (b) alike, and how are they different?

What pattern did you notice in Problem 3?

You may choose any combination of the debrief questions to lead the discussion.

Take time to discuss with students that the choice of decomposition in the area model and the order in which the partial products are found can be highly variable. Use a context, such as a rug or garden, to make the thinking even more concrete.

Lesson Objective: Connect area models and the distributive property to partial products of the standard algorithm with renaming. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. Any combination of the questions below may be used to lead the discussion.

16 of 18

Debrief

What are some other area models we could use to decompose 52 x 35?
Share results:

17 of 18

Debrief

Does it matter which factor goes on the top of the model or the algorithm? Why or why not?
How many ways can you decompose the length? The width?
What are you thinking about as you make these decisions on how to split the area into parts? (Mental math considerations, easier basic facts, etc.)
Do any of these choices affect the size of the area (the product)? Why or why not? (The outer dimensions of the rectangle are unchanged regardless of the way in which it is partitioned.)
What new (or significant) math vocabulary did we use today to communicate precisely? How did the Application Problem connect to today’s lesson?

18 of 18

Exit Ticket