1. Comparative Relational Thinking
Multiplication

2. How do you know the equation is true?
Let’s Review
Are these equations true or false? = =
How do you know?
Talk me through your thinking…
How do you know the equation is true?
TRUE
FALSE

3. Talk me through your thinking.
Let’s Review
Fill in the blank
= __ + 20
Talk me through your thinking.
How did you solve?
100

4. What strategies do you use to multiply?
Let’s Review
What strategies do you use to multiply?
Break Apart
Repeated Addition
Doubling and
Halving
Partial Products
Draw Pictures

5. Why does Doubling and Halving work?
8 x 6
Let’s think about an easy problem.
8 x 6 = 48
If I take half of the cubes, and put them at the bottom of the array, what happens to the amount of rows and columns?
I have 4 columns and 12 rows.
The rows DOUBLE and the columns are cut in HALF!
4 x 12 = 48
I will use the draw an array strategy first!
I have 8 columns and 6 rows.

6. 8 x 6 8 x 6 = 48 4 x 12 = 48 2 x 24 = 48 Let’s Double and Half again….
I have 2 columns and 24 rows.
I have 4 columns and 12 rows.

7. Think about using Doubling and Halving to multiply…
X 2= 10
÷ 2 = 7
14 x 5
Then I multiply 7 and 10 to find the product.
7 x 10= 70
If I divide 14 by 2, then I need multiply 5 by 2.
I look for the even factor first…
I can divide 14 by 2.
The answer is 70!

8. Think about using Doubling and Halving to multiply…
X 3 = 72
÷ 3 = 1
24 x 3
Then I multiply 1 and 72 to find the product.
1 x 72= 72
If I divide 3 by 3, then I need multiply 24 by 3.
No, I can look for a factor that I can divide easily…
I can divide 3 by 3.
Do I always have to use 2?
The answer is 72!

9. Using Doubling and Halving in Comparative Relational Thinking
x 2 = 256
÷ 2 = 2
Let’s determine if this equation is TRUE or FALSE.
128 x 4 = 256 x 2
128 x 4 = 256 x 2
x2 ÷2
256 x 2 = 256 x 2
If you divide 4 by 2, you need to multiply 2 and 128.
Change one factor on one side to match the other side.
It does not matter which factor is matched…
BOTH factors MATCH, so it is TRUE!!!
128 x 2 is
= 256.
So, I can divide 4 by 2 to get 2?
I don’t want to solve… I just want to COMPARE

10. True or False?
36 x 4 = 2 x 62
false

11. True or False?
86 x 6 = 258 x 2
true

12. Find the missing factor.
32 x 5 = ___ x 1
5 divided by 5 = 1
32 x 5 = 160