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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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