Addition & Subtraction

Strategy Framework Revision 11-1One-to-One Counting 2CACounting From One on Materials 3CACounting From One by Imaging 4ACAdvanced Counting 5EAEarly Additive 6AAAdvanced Additive 7AMAdvanced Multiplicative 8APAdvanced Proportional

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

The University of Auckland New Zealand 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 AbacusPlace Value Material Number Lines

Stage 5 EA Early 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

= 8 14 – 6

= 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

Tidy Numbers using Compensation = 24

Place Value Partitioning = 24

Reversibility = 53

Equal Additions = 24

Summary of Strategies Tidy numbers using Compensation Place Value Partitioning Equal Additions Reversibility 29 + ? = 53

So, which strategy is best? It depends on what the question is!!

Try finding different strategies for these?

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….. STRESSED backwards spells DESSERTS!