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Commutative law

Commutative law. Associative law. Let’s play a game. 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 1.

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Commutative law

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  1. Commutative law Associative law

  2. Let’s play a game. 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

  3. Task 1 The dates below are school open days where the whole class sells fruit juice to raise money for charity. Q:How many tins of fruit juice were sold on these dates in total?

  4. Task 1 63＋55＋45 =（63＋55）＋45 = 118＋45 = 163 63＋55＋45 =63＋（55＋45） =63＋100 =163 What is the same and what is different between the two number sentences? （63＋55）＋45=63＋（55＋45）

  5. Task 1 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. Task 1 （63＋55）＋45=63＋（55＋45） Who can create a similar question? （27+36）+64=27+（36＋64）

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

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

  9. Follow-up exercises Fill in the blanks by using the 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. There are 25 cans per box and each can costs £4. How much did his father pay in total? 3×25 ×4

  11. Task 2 3×25×4 =（3×25）×4 = 75×4 = 300 3×25×4 =3×（25×4） =3×100 =300 Which method is better? （3×25）×4= 3×（25×4）

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

  13. Task 2 Who can create a similar question? （3×25）×4= 3×（25×4） （26×8）×125= 26×（8×125）

  14. Task 2 • To multiply three numbers • Multiply the first two numbers • Now multiply by the third number. • Or • Multiply the last two numbers • Now multiply by the first number. • Their product remains the same. associative law of multiplication

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

  16. Follow-up exercises Fill in the blanks by using the 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、Match the number sentences (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

  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 the associative law (1) 25＋34＋66=___＋（ ___＋____ ） (2) 25×40×78=（ ____ × ____ ）×78 (3) 56＋72＋44=(___＋ ___)＋72 (4) 75×8×2×125= （ ___ × ___ ）×（ ___ × ___ ） 66 25 34 25 40 44 56 125 8 2 75

  22. 4、 Solve by making the question simpler 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

  23. Summary What have you learned today？

  24. Using your brain: John and Lucy are calculating 98 ＋ 998 ＋ 9998 ＋ 2 × 3, John said the correct answer right away. Can you？

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