Multiplicationwith the Expanded Method

We are going to learn:

1.02c – Different multiplication strategies

Expanded Method– Break Apart Strategy

Review

• Commutative Property – Changing the order of the factors doesn’t change the product

• Examples?

Review

• Identity Property of Multiplication – Any number times one is that same number.

• Identity Property of Addition – Any number plus zero is that same number.

• Examples?

• Associative Property - Changing the grouping of the numbers, doesn’t change the answer.

• Remember:

8 + (9 +7) = (8 + 9) + 7

(3 x 4) x 5 = 3 x (4 x 5)

Let’s try something new!

• Use the expanded method to solve the expression 5 x 10 another way…– Distribute or share the 5 with the 6 and 4.

Check it out:

5 x 10…. Break up 10 into 6 and 4.

5 x (6 + 4) = (5 x 6) + (5 x 4)

- Solve the parentheses and then add them together! The answer is the same.

Example: 5 x (6 + 4)

It’s like the area model without the boxes!

Or

3 x 16

3 x (10 + 6)

(3 x 10) + (3 x 6)

It’s like the area model without the boxes!

Or

6 x 28

6 x (20 + 8)

(6 x 20) + (6 x 8)

You find the product using the area model –

we’ll use the expanded method together.

5 x 17 9 x 73

3 x 29 8 x 156

4 x 226 7 x 305

Let’s Try: 20 x 56

I don’t mind multiplying with 20 because it has a zero, but 56 is

more difficult! So…I am going to break up 56

into 50 and 6.

20 x 56 = (20 x 50) + (20 x 6)

Another example:

Let’s break up – 11 x 17

Which number should we break apart? Why?

(10 x 11) = 110

17 ( 7 x 11) = + 77

x 11 187

36 x 22

Expanded Method (Distributive Property)

24 x 551. Pick one of the numbers to break apart 242. Break it apart by:

the value of the tens place – 20 the value of the ones place – 4.

3. Multiply each piece x the second number – 55.(20 x 55) + (4 x 55)

4. Add the products together.

• Now – you try some examples in your journal.

• Solve the following problems by the breaking apart the underlined number.

47 x 30 63 x 41

12 x 52 23 x 29

23 x 29Player A – Area Model

Player B – Distributive Property

(20 x 29) + (3 x 29)

Player C – Calculator =

Player D – 20 x 30 = 600