Laws of operation

Monkey king and peaches Story: Monkey king and peaches 8000 10815 0.2961 How do you feel? Explain it in maths

Find similarities and differences 3+4=7 4+3=7 3+4=4+3

Task 1 8+18=26 18+8=26 8+18=18+8 How many cans of fruit juice in all?

Task 1 Can you give other examples like this?

commutative law of addition Task 1 Add two numbers, exchange the place of addends and their sum remains the same. commutative law of addition

Task 1 a + b = b + a

Game Time I say 1+2 you say 2+1

follow-up exercises 214 y ☆ △ 1 1 5 5 …… Fill in the blanks by using commutative law of addition 256＋214=           ＋256 X+Y=          ＋X △+☆=          ＋ 十 367=367 ＋       214 y ☆ △ 1 1 5 5 …… Add two numbers, exchange the place of addends and their sum remains the same.

Task 2 Does any other operation have commutative law?

commutative law of multiplication Task 2 Multiply two numbers. Exchange the places of factors and their product remains the same. commutative law of multiplication

Task 2 a × b = b × a

34×71= × 45× =55× ×▲= ×■ × =C×D 71 34 55 45 ■ ▲ D C Fill in the blanks by using commutative law of multiplication 34×71= × 45× =55× ×▲= ×■ × =C×D 71 34 55 45 ■ ▲ D C Multiply two numbers. Exchange the places of factors and their product remains the same.

EXERCISE

1、true or false： 56+38=83+56 is using the commutative law of addition.（ ） 2×3=1×6 is using commutative law of multiplication. （ ） (3) A×B=B+A。（ ） (4) □+△+○= □+○+△。（ ） × × × √

2、Fill in the blanks by using commutative law 52×（ ）=141 ×（ ） 55+87+45=55+（ ）+87 ☆+（ ）=●+（ ） 25×18×4=（ ）×（ ）×（ ） △×（ ）×★=（ ）×★×☺ 141 52 45 ● ☆ 25 4 18 ☺ △

3、 QUICK CACULATION (STEP BY STEP) 28＋45＋72      62＋38＋123  67+（151+33) 8×23×125 25×43×40 =67+151+33 =67+33+151 =100+151 =251 =28+72+45 =100+45 =145 =62+38+123 =100+38 =138 =25×40×43 =1000×43 =43000 =8×125×23 =1000×23 =23000

4、Solve the problem Miss White bought gifts for the class, the class has 25 students and each present need 12 pounds, how much does Miss White pay altogether? 25×12 =25×4×3 =100×3 =300

5. Alex is going to have a party at home 5. Alex is going to have a party at home. His Mum bought 2 dozens of coke, 32 apples, 24 bananas and 8 peaches. How many fruits did she buy?

Try your best: John and Lucy are calculating 98 ＋ 998 ＋ 98 ＋ 2 × 3, John find the correct answer right away. Can you?

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

Task 3 63＋55＋45 =（63＋55）＋45 = 118＋45 = 163 63＋55＋45 =63＋（55＋45） =63＋100 =163 What are the similarities and differences between two number sentences? （63＋55）＋45=63＋（55＋45）

Task 3 （27+36）+64=27+（36＋64） Which method is best? WHY? 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 3 （63＋55）＋45=63＋（55＋45） （27+36）+64=27+（36＋64） Who can give some examples like this?

associative law of addition Task 3 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 3 (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 4 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 4 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 can you find? （3×25）×4= 3×（25×4）

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

associative law of multiplication Task 4 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 4 (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、Quick Calculate step by step 92＋89＋11  5×39×2 125×17×8   85＋41＋15＋59 64×125 =39×5×2 =39×（5×2） =39×10 =390 =92+（89+11） =92+100 =192 =125×8×17 =1000×17 =17000 = 85+15+41+59 =（85+15）+（41+59） = 100+100 = 200 =8×8×125 =8×（8×125） =8×1000 =8000