The Numeracy Professional Development Project in Secondary Schools
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Transcript of The Numeracy Professional Development Project in Secondary Schools
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The Numeracy Professional Development Project in Secondary Schools
Kevin Hannah
National Coordinator,
Secondary Numeracy Project
Addition and Subtraction Strategies
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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
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Strategy Framework0 Emergent1 One-to-one counting2 Counting from one with materials3 Counting from one by imaging4 Counting on5 Early Part-Whole6 Advanced Part-Whole7 Advanced Multiplicative8 Advanced Proportional
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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.
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Answers Only Please
1. 46 + 19
2. 61 – 27
3. 14 + ? = 101
4. 78 + 124
5. 9000 – 8985
6. 403 - 98
7. 47 + y = 838. 53 - m = 279. 2x + 1 = x +
710. 2x - 1 = 8 - x11. 26 + 7 = ? +
1212. 88 + x = 120
+ ?
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A Teaching ProgressionStart by: Using materials, diagrams to illustrate and
solve the problemProgress to: Developing mental images to help solve
the problemExtend to: Working abstractly with the number
property
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Using Materials
46 + = 83
10 20 30 40 50 60 70 80 900 100
46 83
410 10 10
3
37
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Using Materials
48 + = 81 33
10 20 30 40 50 60 70 80 900 10048
210 10 10
1
81
29 + = 75 46
10 20 30 40 50 60 70 80 900 10029
140 5
75
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Encouraging Imaging
39 + = 63
39 63
110 3
24
30 40 50 60 70
10
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Encouraging Imaging
28 + = 54 26
20 40 6028
210 4
30 50
10
54
16 + = 73 57
16
450 3
20 70 73
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Using Number Properties
18 + = 62 44
From 18: add 2 to get to 20add 40 to get to 60add 2 to get to 62
Total: add 44
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Using Number Properties
39 + = 93
27 + = 52
46 + = 82
55 + = 72
17 + = 64
54
25
36
17
47
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Where to from here? A subtraction strategy Other strategies on number line Link to Algebra - solving equations
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Using Materials- subtraction
81 - 47 =
10 20 30 40 50 60 70 80 900 100
47 81
310 10 10
1
34
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Imaging - subtraction
37 64
310 4
30 40 50 60 70
10
64 - 37 =27
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Imaging - subtraction
83 - 26 =57
26
450 3
30 80 83
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Using Number Properties
From 17: add 3 to get to 20add 60 to get to 80add 2 to get to 82
Total: add 65
82 - 17 =65
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Other strategies & problems
10 20 30 40 50 60 70 80 900 100
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.
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Other subtraction strategies
81 - 47 =
10 20 30 40 50 60 70 80 900 100
41 81
6 10 10 101
34
10
34
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Other subtraction strategies
81 - 47 =
10 20 30 40 50 60 70 80 900 100
31 81
3
10 10 10
34
10
34
10
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Other subtraction problems
92 - = 65
10 20 30 40 50 60 70 80 900 100
27 92
10 10
27
5 10101010
92 - 65 =
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Other subtraction problems
92 - = 65
10 20 30 40 50 60 70 80 900 100
65 92
10 10
27
5 2
65+ = 92
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Other subtraction problems
- 18 = 43
10 20 30 40 50 60 70 80 900 100
43 61
8
61
10
= 43 + 18 61
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Other subtraction problems
- 18 = 43
10 20 30 40 50 60 70 80 900 100
18 61
3
61
10
18 + 43 = 61
10 10 10
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Other addition problems
+ 27 = 72
10 20 30 40 50 60 70 80 900 100
27 72
10 10
45
51010
+ 27 = 27 +
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Other addition problems
+ 27 = 72
10 20 30 40 50 60 70 80 900 100
45 72
10 10
45
7
= 72 - 27 45
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Other addition problems
57 + 26 =
10 20 30 40 50 60 70 80 900 100
57 83
83
1010 6
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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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Solving Equations
47 + = 83
47
83
47 83
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Solving Equations
53 - x = 27
53 - 53 - x = 27 - 53 - x = -26 x = -26 ÷ -1 x = 26
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Solving Equations
53 - x = 27
53 - x +x = 27 +x 53 = 27 +x 53 - 27 = 27 -27+x 26 = x
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Solving Equations
53 - = 27
27
53
27 53
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Solving Equations
2X + 1 = X + 7
7 X
X X 1
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Solving Equations
2X + 1 = 7
7
X X 1
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A Teaching ProgressionStart by: Using materials, diagrams to illustrate and
solve the problemProgress to: Developing mental images to help solve
the problemExtend to: Working abstractly with the property
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Solving Equations
2X - 1 = X + 7
7
X
1
X
X
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Solving Equations
X - 1 = 2X - 7
7
1
X
X X
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Solving Equations
X - 1 = 2X - 7
7
1
X
X X
7 = X + 1
X = 6
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Solving Equations
2X - 1 = 8 - X
X
1 8
X X
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Solving Equations
2(X + 1) = 18
X
18
X 1 1
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Solving Equations
2(X + 1) = 18
X X 1 1
9 9
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Solving Equations
2(X + 1) = 18
X
18
X 1 1
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Solving Equations
X + 3 = 2
X
2
3
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10
X
4
€
x3+ 4 =10
€
x3
€
x3
€
x3
Solving Equations
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X 4
€
x+43
=10
10 10 10
Solving Equations
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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