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 Framework 0Emergent 1One-to-one counting 2Counting from one with materials 3Counting from one by imaging 4Counting on 5Early Part-Whole 6Advanced Part-Whole 7Advanced Multiplicative 8Advanced 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 – ? = – y = m = x + 1 = x x - 1 = 8 - x = ? x = ?

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

Using Materials 46 + =

Using Materials 48 + = =

Encouraging Imaging 39 + =

Encouraging Imaging 28 + = =

Using Number Properties 18 + = 6244 From 18:add 2 to get to 20 add 40 to get to 60 add 2 to get to 62 Total:add 44

Using Number Properties 39 + = = = = =

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

Using Materials- subtraction =

Imaging - subtraction =27

Imaging - subtraction =

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

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.

Other subtraction strategies =

Other subtraction strategies =

Other subtraction problems 92 - = =

Other subtraction problems 92 - = = 92

Other subtraction problems - 18 = =

Other subtraction problems - 18 = = 61 10

Other addition problems + 27 = = 27 +

Other addition problems + 27 = =

Other addition problems =

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

Solving Equations 47 + =

Solving Equations 53 - x = x = x = -26 x = -26 ÷ -1 x = 26

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

Solving Equations 53 - =

Solving Equations 2X + 1 = X + 7 7X XX1

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

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

Solving Equations 2X - 1 = X X 1 X X

Solving Equations X - 1 = 2X X X X

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

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

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

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

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

Solving Equations X + 3 = 2 X 2 3

10 X 4 Solving Equations

X4 10 Solving Equations

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