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
Get Your Place Value Charts Ready!
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
How can 451 x 8 help you solve these?
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
Get Ready to Complete the
Problem Set on Your Own!
Complete Pages 2.A.9- 2.A.11
Try your Best!
5th Grade Module 1 – Lesson 13
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