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Something to Think About

Something to Think About. What does a student need to know before they can understand how to multiply two decimals? e.g. What does 0.2 x 0.3 mean?. Secondary Numeracy Project. Multiplication, Division, and Algebra. Making Chocolate Bars.

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Something to Think About

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  1. Something to Think About • What does a student need to know before they can understand how to multiply two decimals? • e.g. What does 0.2 x 0.3 mean?

  2. Secondary Numeracy Project Multiplication, Division, and Algebra

  3. Making Chocolate Bars • Cadbury is making a variety of rectangular chocolate bars. They have different numbers of pieces in them, with different shapes. • For example, their 6-piece chocolate bar can have two shapes: • A 6 by 1 bar • and a 3 by 2 bar

  4. Task One Work out and draw the different shapes Cadbury can make for chocolate bars with a) 8 pieces b) 12 pieces c) 18 pieces

  5. 18 Piece Candy Bars

  6. Task Two Write down all the different shapes Cadbury can make for chocolate bars with:

  7. Task Three Copy and complete this table for the number of pieces in chocolate bars with these lengths and widths: Length of chocolate bar 1 2 3 4 5 6 7 8 9 1 Width of chocolate bar 2 3 4 5 6 7 8 9

  8. x 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 3 0 3 6 15 27 30 4 0 4 8 12 20 36 40 5 0 5 10 15 20 25 30 35 40 45 50 6 0 6 12 18 24 30 54 60 7 0 7 14 21 28 35 42 63 70 8 0 8 16 24 32 40 48 56 72 80 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90 Times Tables 9 12 18 21 24 16 24 28 32 36 42 48 49 56 64

  9. 9 12 18 21 24 24 28 32 36 42 48 49 56 64 Times Tables - Hot Spots x 0 1 2 3 4 5 6 7 8 9 10 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 2 0 2 4 6 8 10 12 14 16 18 20 3 0 3 6 15 27 30 4 0 4 8 12 16 20 36 40 5 0 5 10 15 20 25 30 35 40 45 50 6 0 6 12 18 24 30 54 60 7 0 7 14 21 28 35 42 63 70 8 0 8 16 24 32 40 48 56 72 80 9 0 9 18 27 36 45 54 63 72 81 90 10 0 10 20 30 40 50 60 70 80 90

  10. Algebra in Multiplication • Computing using the distributive law • Recognising structure in numbers • Exploring algebraic expressions

  11. What’s the answer? 7 x 98 How did you do it? 7 x 98 = 7 x 100 - 7 x 2

  12. What’s the answer? 597 x 5 How did you do it? 597 x 5 = 600 x 5 - 3 x 5

  13. What’s the answer? 407 x 8 How did you do it? 407 x 8 = 400 x 8 + 7 x 8

  14. True or False? 7 x 98 = 7 x 100 - 7 x 2 915 x 8 = 900 x 8 + 15 x 8 597 x 11 = 600 x 11 - 3 x 7 3 x (400 - 8) = 3 x 400 – 3 x 8

  15. True or False? 8 x 300 - 7 x 8 = 8 x 293 80 x 7 - 5 x 7 = 85 x 7 79 x 11 = 70 x 11 + 11 x 9 12 x 40 – 8 x 12 = 8 x (40 - 12)

  16. What’s missing? 6 x 600 + 7 x 6 = 6 x 607 80 x 6 - 6 x 6 = 74 x 6 58 x 13 = 50 x 13 + 8 x 13 5 x (70 - 2) = 5 x 70 – 5 x 2

  17. Fill in the Gaps 6(m + 7) = 6m + 42 8c - 48 = 8(c - 6) 7( m + 9 ) = 7m + 63 5(y - 2) = 5y - 10

  18. Expand 5( y + 6) = 5y + 30 7x - 70 =7( x – 10 ) 4( 2m + 3 ) = 8m + 12 18r - 54 =6( 3r – 9 )

  19. Factorise 3 ( n + 2 ) = 3n + 6 8( x – 4 ) = 8x - 32 20p + 15 =5 ( 4p + 3 ) 7( 6 - 5y ) = 42 - 35y

  20. Recognising Structure a(b ± c) = ab ± ac

  21. Algebra in Long Multiplication • Using arrays to illustrate multiplication • Exploring polynomial expansions • Touching factoring

  22. What’s the answer? 5 x 21 5 20 1

  23. What’s the answer? 14 x 21 10 4 20 1

  24. What’s the answer? 23 x 21 20 3 20 1

  25. Abstraction #1 23 x 21 20 3 20 1

  26. Abstraction #1 23 x 21 20 3 400 60 20 1 20 3 400 + 80 + 3 = 483

  27. Abstraction #2 23 x 21 20 3 400 60 20 1 20 3 400 + 80 + 3 = 483

  28. Link to the Algorithm 23 x 21 3 20 60 +400 483 20 3 400 60 20 1 20 3

  29. Expanding Expressions (x+3)(x+2) x +3 x2 3x x 2x 6 +2 x2 +5x +6

  30. Expanding Expressions (x-3)(x-2) x -3 x2 -3x x -2x 6 -2 x2 -5x +6

  31. Algorithm? x-3 xx-2 6 -2x -3x x2 x2-5x+6 x -3 x2 -3x x -2x 6 -2

  32. Leading to Factorising Notice that both diagonals have the same product: -2xx-3x = 6x2 x2 x6 = 6x2 x -3 x2 -3x x -2x 6 -2

  33. Factorising Expressions X2-5x+6 Sum: -5x x2 -3x -3x -2x 6 -2x Product: 6x2

  34. Factorising Expressions X2-5x+6 X2-5x+6 = (x-2)(x-3) Now factor each pair x -3 x2 -3x x -2x 6 -2

  35. Multiplying Decimals • When do we introduce students to 5.2 x 6.3? • Not until they know how to multiply fractions 5 0.2 1.2 30 6 0.3 1.5 ?

  36. Tips for Using T&T Books • Planning Guide (p 10 on) • Division (p 122 on) • Learning Intention • Linked knowledge/Numeracy books • Materials needed • Colour coded questions (p 3)

  37. Now YOU! Choose • Multiplication/Division • Algebra (year 9 or 10) Plan a unit for your students Use HIBS Planning Notes, T & T Books, purple books

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