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