Comparative Relational Thinking Multiplication

How do you know the equation is true? Let’s Review Are these equations true or false? 432 + 234 = 440 + 240 567 + 129 = 566 + 130 How do you know? Talk me through your thinking… How do you know the equation is true? TRUE FALSE

Talk me through your thinking. Let’s Review Fill in the blank 93 + 27 = __ + 20 Talk me through your thinking. How did you solve? 100

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

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.

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.

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!

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!

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 200 + 40 + 16 = 256. So, I can divide 4 by 2 to get 2? I don’t want to solve… I just want to COMPARE

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

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

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