1. Commutative law
Associative law

2. Let’s play a game. （1）70、50、30 （2）32、40、68 （3）100、150、850
Find the sum of three numbers in 1 minute.
（1）70、50、30
（2）32、40、68
（3）100、150、850
Add up to the tens 、hundreds or thousands

3. Task 1 Q:How many tins of fruit juice sold in the last three days?
These days are School Open Day, the whole class sell fruit juice to collect money for the poor people.
Sales Situation
Date
Nov. 1st
Nov. 2nd
Nov. 3rd
Apple juice（tin） 63 55 45
Q:How many tins of fruit juice sold in the last three days?

4. Task 1 same or different? 63＋55＋45 63＋55＋45 =（63＋55）＋45 =63＋（55＋45）
= 118＋45
= 163
63＋55＋45
=63＋（55＋45）
=63＋100
=163
same or different?
（63＋55）＋45=63＋（55＋45）

5. Task 1 （27+36）+64=27+（36＋64） 27＋36＋64 27＋36＋64 =27＋（36＋64） =27＋100
=127
=（27＋36）＋64
= 63＋64
= 127
（27+36）+64=27+（36＋64）

6. Who can give some examples like this?
Task 1
（63＋55）＋45=63＋（55＋45）
（27+36）+64=27+（36＋64）
Who can give some examples like this?

7. associative law of addition
Task 1
Add three numbers.
Add the first two numbers and then add the third number.
Or add the last two numbers and then add the first number.
Their sum remains the same.
associative law of addition

8. Task 1
Algebraically:
(a + b)+c = a+(b + c)

9. follow-up exercises （33＋16）＋84= ＋（16＋ ） （168＋24）＋76= ＋（ ＋ ）
Fill in the blanks by using associative law of addition
（33＋16）＋84= ＋（16＋ ）
（168＋24）＋76= ＋（ ＋ ）
（25＋ ）＋72= ＋（28＋72）
（a＋ ）＋c=a＋（b＋ ） 33 84 24 76
168 28 25 c b

10. Task 2
Danny's father bought 3 boxes of juice, 25 cans per box, each can cost £4 ，how many did his father pay totally?
3×25 ×4

11. Task 2 3×25×4 3×25×4 =（3×25）×4 =3×（25×4） = 75×4 =3×100 = 300 =300
= 75×4
= 300
3×25×4
=3×（25×4）
=3×100
=300
What do you find?
（3×25）×4= 3×（25×4）

12. Task 2 26×8×125 =26×（8×125） 26×8×125 =（26×8）×125 = 208×125 =26×1000
26×8× =26×（8×125）
26×8×125
=（26×8）×125
= 208×125 =
=26×1000
=26000
（26×8）×125= 26×（8×125）
（□×□）×□= □×（□×□）

13. Who can give some examples like this?
Task 2
（3×25）×4= 3×（25×4）
（26×8）×125= 26×（8×125）
Who can give some examples like this?

14. associative law of multiplication
Task 2
Multiply three numbers.
Multiply the first two numbers and then multiply the third number.
Or multiply the last two numbers and then multiply the first number.
Their product remains the same.
associative law of multiplication

15. Task 2
Algebraically:
(a × b)×c = a×(b × c)

16. follow-up exercises 36×(71×26)=（ ____ × _____ ）×26
Fill in the blanks by using associative law of addition
36×(71×26)=（ ____ × _____ ）×26
(57×95)×83=57×（ ____ × ____ ）
●×▲×★=___ ×（▲× __ ）
=（ ___ × ▲）× ____ 36 71 95 83 ● ★ ● ★

17. (a ＋ b) ＋ c = a ＋ (b ＋ c)
(a × b) × c = a × (b × c)
Compare with the associative law of addition and multiplication，what do you find?
three numbers
calculate from left to right in turn
calculate the last two numbers first
the answer remain the same

18. Exercise

19. 1、Line the same number sentence
(1) a×（b×c） A. 24＋（42＋58）
(2) 76＋18＋ B. 76＋（18＋22）
(3) 24＋42＋ C. 67×（125×8）
(4)（67×125）× D. （a×b）×c

20. 2、Which number sentence conforms to the associative law?
(1) a×(b×c)=(a×b)×c  (2) 15＋(7＋3)=(15＋2)＋3
(3) (23+41)+72+28=23+41+(72+28) √ × √

21. 3、Fill in the blanks by using associative law
(1) 25＋34＋66=___＋（ ___＋____ ）
(2) 25×40×78=（ ____ × ____ ）×78
(3) 56＋72＋44=(___＋ ___)＋72
(4) 75×8×2×125=
（ ___ × ___ ）×（ ___ × ___ ） 25 34 66 25 40 56 44 8
125 75 2

22. 4、Solve in simpler way
92＋89＋11  ×5× ×17×8  
85＋41＋15＋ ×125
=92+（89+11）
=92+100
=192
=39×（5×2）
=39×10
=390
=125×8×17
=1000×17
=17000 =
=（85+15）+（41+59） =
= 200
=8×8×128
=8×（8×125）
=8×1000
=8000

23. Summary
What have you learned today？