PBA2

Strategy

Example

Probing Questions

Direct Modeling

Equal groups

Array

· How does this represent the problem?

· Could you represent it in a different way?

· 18 groups of 5 instead of 5 groups of 18

Traditional Algorithm

· Why did you put a little 4 on top of the 1?

· Why didn’t you put the little 4 on top of the 8?

· What does the little 4 represent?

Partial Products

· How is the 40 represented in the traditional algorithm?

· Why is it 50 instead of 5?

· How did you know how to line up the 40 and the 50?

· Can you apply this method to 32 x 9?

Box Method

· How did you know where to put the numbers and what to write in the boxes?

· Why did you add 50 and 40?

Distributive Property

a(b+c) = ab + ac

5 x ( 10 + 8)

50 + 40

90

OR

5 x (5 + 5 + 8)

25 + 25 + 40

90

OR

5 x (11 + 7)

55 + 35

90

OR

5 x (20 - 2)

100 - 10

90

· Why did you decide to break 18 into 10 and 8?

· You broke the 18 into 10 and 8. If you broke it up differently, would your method still work?

· Does the distributive property work with subtraction?

Doubling/Halving

5 x 18

Double 5 → 10

Halve 18 → 9

10 x 9 = 90

· Why does this strategy work? What is happening here?

Repeated Addition

18 + 18 + 18 + 18 + 18 = 90

OR

5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = 18

· Is adding 18 five times the same as adding 5 eighteen times? Why?

Associative Property

5 x 18

5 x (6 x 3)

(5 x 6) x 3

30 x 3

90

· Why does this work?

· Why did you choose to factor 18 into 6 and 3?