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Lesson 1: I can multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties. 5th Grade Module 2 – Lesson 1 Associative Property Distributive Property

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Lesson 1: I can multiply multi-digit whole

numbers and multiples of 10 using

place value patterns and the

distributive and associative properties.

5th Grade Module 2 – Lesson 1

Associative Property

Distributive Property

5th Grade Module 2 – Lesson 1

We are going to learn how to multiply multi-digit whole numbers using the “Associative Property”

The Associative Property of Multiplication can help you to multiply quickly and correctly.

It means that we can re-group our factors but still get the same product.

(2 x 5) x 3 = 2 x (5 x 3)10 x 3 = 2 x 15

30 = 30

It is important to remember to multiply what is in the parentheses ( ) first!

Concept Development

5th Grade Module 2 – Lesson 1

Let’s Multiply 4 x 30 using units

To find the product of 4 x 30, we can start by multiplying using whole numbers. Renaming 30 as 3 tens.

Remember we need to state the unit in our product.

4 x 3 tens = __________________12 tens

Show 12 tens on your place value chart. What is 12 tens in standard form?

12 tens = 120

4 x 30 = 120So…

Let’s solve4 tens x 3 tens

How can the previous problem help us solve this problem?

5th Grade Module 2 – Lesson 1

We can also record this problem like this …

(4 x 3 ) x 100

10 x 10

12 x 100= 1200

Let’s multiply the whole numbers first then the units.

4 x 3 = 12

ten x ten = hundredSo,

4 tens x 3 tens = 12 hundreds

12 hundreds = 1,200

4 tens x 3 hundreds = ____How is this problem different than

4 tens x 3 tens?

5th Grade Module 2 – Lesson 1

We are multiplying tens and hundreds, not tens

& tens.Let’s record and solve:

4 tens is the same as

4 x 10

4 tens x 3 hundreds

3 hundreds =

3 x _____100

(4 x 10) x (3 x 100) We can express our problem this way.

(4 x 3) x (10 x 100) Is this equation equal to the one above?

12 1000x

12,000

OR

So, 4 tens x 3 hundreds =

12 thousandsOr

12,000

12,000

Let’s try this one…4 thousands x 3 tens = ____

5th Grade Module 2 – Lesson 1

Let’s record and solve:

4 thousands is the same as

_______ x ________

4 thousands x 3 tens

3 tens =

____ x _____3 10

(4 x 1000) x (3 x 10)4,000 x 30

120,000

We can express our problem this way.

(4 x 3) x (1000 x 10)Here is a different way we can set up

our problem.12 10,000x

120,000

OR

120,000

4 1,000

60 x 5

5th Grade Module 2 – Lesson 1

(6 x 10) x 5 (6 x 5) x 10Are both these

equations equal to 60 x 5

Turn & Talk

When we change the order of the factors we are using the commutative property.When we GROUP the factors differently we are using the associative property of multiplication

Let’s solve this using (6 x 5) x 10

30 x 10

300

60 x 50

5th Grade Module 2 – Lesson 1

Work with your partner to solve this problem and explain how you solved it.

Possible Solution:(6 x 5) x (10 x 10)

30 x 100

3,000

What would make the distributive property useful here?Why does it help here, but we didn’t really use it in our other problems?

5th Grade Module 2 – Lesson 1

Find the product of 451 x 8 (use any method you want)

Distributive Property = (400 x 8) + (50 x 8) + (1 x 8)

3,608

3200 + 400 + 8

3,608

5th Grade Module 2 – Lesson 1

1). 451 x 80 2). 4,510 x 80 3). 4,510 x 800

Evaluate these problems with your partner.

36,080 360,080 3,608,000

Complete Pages 2.A.9- 2.A.11