‘A Property of Division’

1. ‘A Property of Division’ • A lesson delivered by a Shanghai teacher to a year 7 class in a Devon comprehensive school, November 2015

2. Calculate fast 20×5= 40×5= 60×5= 80×5= 100×5= 10 100 • 2×5= • 4×5= • 6×5= • 8×5= • 10×5= 20 200 30 300 40 400 50 500

3. 2×25= 4×25= 6×25= 8×25= 10×25= 20 50 • 2×10= • 4×10= • 6×10= • 8×10= • 10×10= 40 100 60 150 200 80 250 100

4. 5 groups ofchildrenplanted trees. • Thereare2 children in a group. • They planted 30 trees in all. • Q: How many trees did they plant per person? 30 ÷ 5 ÷ 2 30 ÷ 5 ÷ 2 = 6 ÷ 2 = 30 ÷（5×2） = 30 ÷ 10 = 3 = 3 = 30 ÷ 5 ÷ 2 30 ÷（5×2）

5. Can all the division calculations use this method? Please try! 10 ÷ 2 ÷ 5 10 ÷ (2 × 5) 18 ÷ 3 ÷ 2 18 ÷ (3 × 2) 100 ÷ 25 ÷ 4 100 ÷ (25 × 4) What do you find?

6. Anumber is divided by two numbers successively.Orfind the product of the two numbers, and then divide thenumber.Theanswerremainsthesame. The property of division a ÷ b ÷ c = a ÷ (b × c) b ≠ 0,c ≠ 0

7. Fill the sign of operation in the circle ÷ × • 56 ÷ 7 ÷ 8 ＝ 56 （7 8） ÷ ÷ 15 3 5 ＝ 15 ÷ (3 × 5） × ÷ 24 4 ÷ 6 ＝ 24 ÷(4 6）

8. Fill the right number in the box 2 5 • 30 ÷ ÷ ＝30 ÷(2 × 5) 48 ÷ ( × 3)＝ ÷ 4 ÷ 3 4 48

9. Is it right? 14 ÷（2 × 7 ） ＝14 ÷ 2 × 7 ＝7 × 7 ＝49 What do you think? Can you correct it?

10. True or false? (1) 48 ÷ 4 ÷ 2 = 48 ÷（4×2 ） （ ） √ × （2）40 ÷（4 × 5）＝ 40 ÷ 4 × 5 （ ） (3) 54 ÷（3 × 3）= 54 ÷ 3÷ 3 （ ） √ × （4）100 ÷（25 × 4）＝100 ÷ 25 × 4（ ）

11. Which one is faster? • 140 ÷ 7 ÷ 4 140 ÷（7 × 4） What do you find? Do all division questions fit this rule?

12. Observe the numbers carefully! 10 100 ÷ 25 ÷ 4 ＝ 100 ÷ (25 × 4） 100 15 ÷ 3 ÷ 5＝15 ÷ (3 × 5） 15 24 ÷ 4 ÷ 6＝24 ÷ (4 × 6） 24

13. Who can do faster? • 1200 ÷ 25 ÷ 4 • 680 ÷ 17 ÷ 4 680 ÷ 68 ÷ 2