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
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ity
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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!