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The Numeracy Professional Development Project in Secondary Schools
Kevin Hannah
National Coordinator,
Secondary Numeracy Project
Addition and Subtraction Strategies
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
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
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.
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
+ ?
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
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
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
Where to from here? A subtraction strategy Other strategies on number line Link to Algebra - solving equations
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
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.
Other subtraction problems
92 - = 65
10 20 30 40 50 60 70 80 900 100
27 92
10 10
27
5 10101010
92 - 65 =
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
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
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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