1. Addition & Subtraction

2. 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

3. 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

4. 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

5. Using Materials and Imaging Hands Tens frames AbacusPlace Value Material Number Lines 378790 + 50 + 3 10 1223

6. 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

7. 14 - 6 14 - 4 - 2 = 8 14 – 6

8. 43 - 7 43 - 3 - 4 = 36

9. 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

10. Stage 6 AA Advanced Additive Solve 53 - 29

11. 53 - 29 Tidy Numbers using Compensation 53 - 30 + 1= 24

12. 53 - 29 Place Value Partitioning 53 - 20 - 3 - 6 = 24

13. 53 - 29 Reversibility 29 + 1 + 20 + 3 = 53

14. 53 - 29 Equal Additions 53 29 1 1 54 30 = 24

15. Summary of Strategies Tidy numbers using Compensation 53 - 20 + 1 53 - 29 Place Value Partitioning 53 - 20 - 9 Equal Additions 54 - 30 Reversibility 29 + ? = 53

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

17. Try finding different strategies for these? 385 - 99 478 - 56 1002 - 987

18. Stage 7 AM Advanced Multiplicative An extension of the strategies and written form used in Stage 6 but working with decimal numbers.

19. 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.

20. 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?

21. Thought for the day “And, if it all just seems too much….. STRESSED backwards spells DESSERTS!