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The Numeracy Professional Development Project in Secondary Schools

The Numeracy Professional Development Project in Secondary Schools. Addition and Subtraction Strategies. Kevin Hannah National Coordinator, Secondary Numeracy Project. Addition and Subtraction strategies. The Number Strategy Framework A Model for a Teaching Progression Some Questions

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The Numeracy Professional Development Project in Secondary Schools

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  1. The Numeracy Professional Development Project in Secondary Schools Addition and Subtraction Strategies Kevin Hannah National Coordinator, Secondary Numeracy Project

  2. Addition and Subtraction strategies • The Number Strategy Framework • A Model for a Teaching Progression • Some Questions • Using materials • Encouraging Imaging • Towards number properties • Subtraction strategies • Subtraction and addition problems • From Number to Algebra - solving equations

  3. Strategy Framework 0 Emergent 1 One-to-one counting 2 Counting from one with materials 3 Counting from one by imaging 4 Counting on 5 Early Part-Whole 6 Advanced Part-Whole 7 Advanced Multiplicative 8 Advanced Proportional

  4. Objective • To explore links between numeracy and algebra In particular: • To show that images used to help solve number problems also develop understanding for solving complicated linear equations.

  5. 46 + 19 61 – 27 14 + ? = 101 78 + 124 9000 – 8985 403 - 98 7. 47 + y = 83 8. 53 - m = 27 9. 2x + 1 = x + 7 10. 2x - 1 = 8 - x 11. 26 + 7 = ? + 12 12. 88 + x = 120 + ? Answers Only Please

  6. A Teaching Progression Start by: • Using materials, diagrams to illustrate and solve the problem Progress to: • Developing mental images to help solve the problem Extend to: • Working abstractly with the number property

  7. 46 + = 83 46 83 Using Materials 37 10 10 10 4 3

  8. 48 + = 81 29 + = 75 10 10 10 2 1 48 75 81 29 40 5 1 Using Materials 33 46

  9. 39 + = 63 10 10 3 1 30 40 50 60 70 39 63 Encouraging Imaging 24

  10. 28 + = 54 16 + = 73 10 10 3 4 2 73 28 16 54 20 20 30 40 50 70 60 50 4 Encouraging Imaging 26 57

  11. 18 + = 62 Using Number Properties 44 From 18: add 2 to get to 20 add 40 to get to 60 add 2 to get to 62 Total: add 44

  12. 39 + = 93 27 + = 52 46 + = 82 55 + = 72 17 + = 64 54 25 36 17 47 Using Number Properties

  13. Where to from here? • A subtraction strategy • Other strategies on number line • Link to Algebra - solving equations

  14. 47 81 Using Materials- subtraction 81 - 47 = 34 10 10 10 3 1

  15. 10 10 4 3 30 40 50 60 70 37 64 Imaging - subtraction 64 - 37 = 27

  16. 3 26 83 30 80 50 4 Imaging - subtraction 83 - 26 = 57

  17. Using Number Properties 82 - 17 = 65 From 17: add 3 to get to 20 add 60 to get to 80 add 2 to get to 82 Total: add 65

  18. Other strategies & problems • The number line is a versatile tool and image. • It can be used to support and explain a variety of strategies. • It can be used to solve a wide range of problems. • It can prepare students for algebra.

  19. 10 10 10 10 6 1 41 81 34 Other subtraction strategies 81 - 47 = 34

  20. 10 10 10 10 10 3 31 81 34 Other subtraction strategies 81 - 47 = 34

  21. 10 10 10 10 10 10 5 27 92 92 - 65 = Other subtraction problems 92 - = 65 27

  22. 10 10 5 2 65 92 65+ = 92 Other subtraction problems 92 - = 65 27

  23. 10 8 43 61 = 43 + 18 61 Other subtraction problems - 18 = 43 61

  24. 10 10 10 10 3 18 61 18 + 43 = 61 Other subtraction problems - 18 = 43 61

  25. 5 10 10 10 10 27 72 + 27 = 27 + Other addition problems + 27 = 72 45

  26. 7 10 10 45 72 = 72 - 27 45 Other addition problems + 27 = 72 45

  27. 10 10 6 57 83 Other addition problems 57 + 26 = 83

  28. What is Numeracy? • It’s about making sense of numbers. • It’s about problem solving with numbers. • It’s about understanding base 10. • It’s about learning with meaning. • It’s about preparing for algebra

  29. 47 83 47 83 Solving Equations 47 + = 83

  30. Solving Equations 53 - x = 27 53 - 53 - x = 27 - 53 - x = -26 x = -26 ÷ -1 x = 26

  31. Solving Equations 53 - x = 27 53 - x +x = 27 +x 53 = 27 +x 53 - 27 = 27 -27+x 26 = x

  32. 27 53 Solving Equations 53 - = 27 53 27

  33. Solving Equations 2X + 1 = X + 7 X X 1 X 7

  34. X X 1 Solving Equations 2X + 1 = 7 7

  35. A Teaching Progression Start by: • Using materials, diagrams to illustrate and solve the problem Progress to: • Developing mental images to help solve the problem Extend to: • Working abstractly with the property

  36. Solving Equations 2X - 1 = X + 7 X X X 7 1

  37. Solving Equations X - 1 = 2X - 7 7 X X X 1

  38. Solving Equations X - 1 = 2X - 7 7 X X X 1 7 = X + 1 X = 6

  39. Solving Equations 2X - 1 = 8 - X X X X 8 1

  40. Solving Equations 2(X + 1) = 18 X 1 X 1 18

  41. 9 9 Solving Equations 2(X + 1) = 18 X 1 X 1

  42. Solving Equations 2(X + 1) = 18 X X 1 1 18

  43. Solving Equations X + 3 = 2 X 3 2

  44. Solving Equations X 4 10

  45. 10 10 10 Solving Equations X 4

  46. What is Numeracy? • It’s about making sense of numbers. • It’s about problem solving with numbers. • It’s about understanding base 10. • It’s about learning with meaning. • It’s about preparing for algebra

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