Grades 3-5 Math Problem Solving in Action_ Getting Students to Love Word Problems

Figure 4.4 Strategies for Dividing

Partial Quotients (modeled with open

array)

589 ÷ 7

40 + 40 + 4 r1

280 280 28

Halving and Halving

144 ÷ 12

72 ÷ 6

36 ÷ 3

12

Paper and Pencil

(Grandma’s Way)

8 4

7 5 8 9

–5 6

2 9

–2 8

1

Friendly Dividends

589

7

40 + 40 + 4

280 + 280 + 29

7 r1

84 r1

Figure 4.3 Strategies for Multiplying

Distributive Property (modeled with

open array)

15 × 18

10 + 8

10

5

100 + 80 + 50 + 40 = 270

Doubling and Halving

15 × 18

30 × 9 = 270

Partial Products (modeled with carets)

15 × 18

10 5 10 8

10 × 10 = 100

10 × 8 = 80

5 × 10 = 50

5 × 8 = 40

270

Paper and Pencil

(Place value)

4

15

× 18

120

150

270

+

100 80

50 40