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### Lesson 7: I can connect area diagrams and the distributive property to partial products of the standard algorithm with renaming.

5th Grade Module 1 – Lesson 7

Time to Sprint! property to partial products of the standard algorithm with renaming.

Your teacher will give you today’s sprint.

5th Grade Module 1 – Lesson 7

Let’s Review Multiplying property to partial products of the standard algorithm with renaming.Using the Area Model & Algorithm(solve in your notebook)

24 x 15 = _____

Solve each using an area model

Solve each using the standard algorithm

824 x 15 = _____

Solutions on next slide.

5th Grade Module 1 – Lesson 7

2 property to partial products of the standard algorithm with renaming. 4

x 1 5

1 2 0

+ 2 4 0

3 6 0

20

40

8 24

x 1 5

4 1 2 0

+ 82 4 0

1 236 0

800 20 4

20 4

20

100

5

5

4,000

100

40

200

200

8,000

10

10

5th Grade Module 1 – Lesson 7

Application Problem property to partial products of the standard algorithm with renaming.

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?

5th Grade Module 1 – Lesson 7

Solution to Application Problem property to partial products of the standard algorithm with renaming.

5th Grade Module 1 – Lesson 7

524 x 136 property to partial products of the standard algorithm with renaming.

Let’s name

524

as our unit.

We will have

3 columns & 3 rows

What do you notice about this problem compared to the problems we did yesterday?

Turn & Talk

Which factor should we use as our unit?

524 or 136?

Think which way would be easier to count.

How will our area model be different than the ones we made in yesterday’s lesson?

Let’s work together to solve using the area model & standard algorithm

5th Grade Module 1 – Lesson 7

Problem 1 property to partial products of the standard algorithm with renaming.

524 x 136Let’s label the top unit (524)

Draw a rectangle with 3 columns & 3 rows

Let’s build the area model. Record in your notebook with me.

Let’s label the rows using the other factor

Work with your partner to to solve the partial products.

Then solve for the final product.

500 20 4

6

30

100

Solution on next slide…

5th Grade Module 1 – Lesson 7

Solution Using Area Model property to partial products of the standard algorithm with renaming.

500 20 4

6

30

100

3,144

+

15,720

+

52,400

= 71,264

Notice how the partial products match up to the partial products in the standard algorithm.

Now try to solve this problem using the standard algorithm. Remember that you are multiplying with 3 different place values so you will have 3 addends!

Compare the solutions

5th Grade Module 1 – Lesson 7

Problem 2 property to partial products of the standard algorithm with renaming.

4,519 x 326

5,000 x 300 = 1,500,000

What is different about this problem?

Before we solve,

let’s ESTIMATE our product.

Round the factors & make an estimate.

Which factor will be our unit?

Is one more efficient to use?

Turn & Talk

Will the fourth digit change anything about how we multiply?

Why or why not?

Let’s Solve the Actual Product

Partner A

Solve using the

Area Model

Partner B

Solve using the

Standard Algorithm

Volunteers will share their solutions!

Is your actual product reasonable given the estimate?

5th Grade Module 1 – Lesson 7

Problem 3 property to partial products of the standard algorithm with renaming.

5,000 x 300 = 1,500,000

4,509 x 326

Let’s estimate the product first. Round each factor to multiply.

The first factor has a zero in the tens place.

Let’s write 4,509 in expanded form.

4,000 + 500 + 9

How many columns will we need to represent the top length of our area model?

We need 3 columns!

Why only three columns if we have a 4-digit number?

Work with your partner to solve in your notebook.

Partner B solve using the area model. Partner A solve using the standard algorithm.

Compare your solutions!

5th Grade Module 1 – Lesson 7

Solution property to partial products of the standard algorithm with renaming.4,509 x 326

Is our product reasonable compared to our estimate of 1,500,000?

5th Grade Module 1 – Lesson 7

Problem 4 property to partial products of the standard algorithm with renaming.

4,509 x 306

5,000 x 300 = 1,500,000

Estimate the Product

How is the problem different from 4,509 x 326?

Thinking about the expanded forms of the factors, imagine the area model.

How will you decompose the

length & width?

Why don’t we need three rows this time?

5th Grade Module 1 – Lesson 7

Problem 4 property to partial products of the standard algorithm with renaming.

4,509 x 306

Solve the area model in your notebook.

Record the partial products for each row.

Let’s record what we drew with the algorithm.

4 5 0 9

x 3 0 6

24,000

3,000

54

2 7 0 5 4

+ 1 3 5 2 7 0 0

Now let’s record

300 x 4,509

When we multiply a number by 100, what happens to the value and position of each digit?

Begin with the first partial product 6 x 4,509

27,054

So, if we multiply 4,509 x 300 what needs to be recorded in the ones and tens place after the digit shift?

1,200,000

150,000

2,700

1, 3 7 9, 7 5 4

1,352,700

5th Grade Module 1 – Lesson 7

Get Ready to Complete the property to partial products of the standard algorithm with renaming.Problem Set on Your Own!

Complete Pages 2.B.63 - 2.B.65

You will have 10-15 minutes to work.

Try your Best!

5th Grade Module 1 – Lesson 7

LET’S Debrief property to partial products of the standard algorithm with renaming.

- Explain why a multiplication problem with a three-digit multiplier will not always have three partial products. Use Problem 1 (a) and (b) as examples.
- How are the area models for Problem 2 (a) and (b) alike and how are they different?
- What pattern did you notice in Problem 3?
- Does it matter which factor goes on the top of the model or the algorithm? Why or why not?
- What are you thinking about as you make these decisions on how to split the area into parts?

5th Grade Module 1 – Lesson 7

EXIT property to partial products of the standard algorithm with renaming.

TICKET

Page 2.B.66

5th Grade Module 1 – Lesson 7

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