Commutative law Associative law

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

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?

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）

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）

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?

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

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

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

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

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）

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

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?

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

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

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 ● ★ ● ★

(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

Exercise

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

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) √ × √

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

4、Solve in simpler way 92＋89＋11  39×5×2 125×17×8   85＋41＋15＋59 64×125 =92+（89+11） =92+100 =192 =39×（5×2） =39×10 =390 =125×8×17 =1000×17 =17000 = 85+15+41+59 =（85+15）+（41+59） = 100+100 = 200 =8×8×128 =8×（8×125） =8×1000 =8000

Summary What have you learned today？