Addition & Subtraction. Strategy Framework Revision 11-1One-to-One Counting 2CACounting From One on Materials 3CACounting From One by Imaging 4ACAdvanced.

Addition & Subtraction

Strategy Framework Revision

• 1 1-1 One-to-One Counting• 2 CA Counting From One on Materials• 3 CA Counting From One by Imaging• 4 AC Advanced Counting• 5 EA Early Additive• 6 AA Advanced Additive• 7 AM Advanced Multiplicative• 8 AP Advanced Proportional

A Teaching ProgressionStart 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

The

Uni

vers

ity

of A

uckl

and

New

Zea

land

2006

Using Number Properties

Using Imaging

Using Materials

New Knowledge & Strategies

Existing Knowledge & Strategies

Using Materials

The Strategy Teaching Model

Using Materials and Imaging

Hands Tens frames

Abacus Place Value Material

Number Lines

37 87 90

+ 50+ 3

1010

1223

Stage 5 EAEarly Additive

Aim: to partition, re-group numbers and use known facts to solve problems

The next slides show different strategies with diagrams. Try them out with multilink cubes

14 - 6 14 - 4 - 2 = 814 – 6

43 - 7

43 - 3 - 4 = 36

Why is this important?

Why bother teaching mental strategies, why can’t I just learn the written form?

• Merely following a procedure - rule following

• Lack of real understanding - mistakes are made or wrongly applied to problem solving

• Need mental ability to estimate & check answers

• It is often quicker to work something out mentally

Stage 6 AA

Advanced Additive

Solve 53 - 29

53 - 29

Tidy Numbers using Compensation

53 - 30 + 1= 24

53 - 29

Place Value Partitioning

53 - 20 - 3 - 6 = 24

53 - 29

Reversibility29 + 1 + 20 + 3 = 53

53 - 29

Equal Additions

5329

1

1

5430

= 24

Summary of StrategiesTidy numbers using

Compensation

53 - 20 + 1

53 - 29

Place Value Partitioning

53 - 20 - 9

Equal Additions54 - 30

Reversibility29 + ? = 53

So, which strategy is best?

It depends on what the question is!!

Try finding different strategies for

these?385 - 99

478 - 56

1002 - 987

Stage 7 AM

Advanced Multiplicative

An extension of the strategies and written form used in Stage 6 but working with decimal numbers.

Objectives• Understand the teaching model used for

teaching strategy: Numeracy Book 5

Eg page 35 or 38. Two activities: choose one and plan a short lesson around this.

Numeracy books are available in school, materials masters on NZ Maths.

Warming down

Have a go, in pairs

1: Additions/Subtraction Strategy Understandings

2: The blue loopy

3: Look at NZC. How do the AOs for number link to the numeracy stages?

Thought for the day “And, if it all just seems too

much…..

STRESSEDbackwards spells

DESSERTS!