2. Addition and Subtraction Workshop Susan McDougall and Amanda Caldwell (With thanks to Fiona Fox and Charlotte Rawcliffe) Numeracy Facilitators

3. Addition and Subtraction Workshop Susan McDougall and Amanda Caldwell (With thanks to Fiona Fox and Charlotte Rawcliffe) Numeracy Facilitators

4. Whakatauki E tu kahikatea, hei whakapae ururoa Awhi mai, awhi atu, tatou, tatou e. Kahikatea stand together, their roots intertwine, strengthening each other. We all help one another and together we will be strong.

5. Knowledge Warm-up: No Name Game

6. Objectives: Revise the Strategy framework stages. Understand the teaching model used for teaching strategy. Explore equipment and activities used to teach addition & subtraction strategies. Know how to use planning sheets, Numeracy Book 5 and other supportive resources to help teach addition & subtraction.

7. Reflection: Reflect on your numeracy lessons, routines and classroom organisation. Share with the person beside you: One thing you have started doing One thing you have stopped doing One thing you would like to do in your maths programmes

8. This strategy - What stage? How wou ld you solve these? 3 + 5 = 7 + 9 = 42 - 7 27 + 54

9. 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

10. Using Number Properties Using Imaging Using Materials New Knowledge & Strategies Existing Knowledge & Strategies Using Materials The Strategy Teaching Model

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

12. Imaging Phases: First Phase of Imaging; Look but don’t touch! Second Phase of Imaging: Shielding materials,scaffolding. Third Phase of Imaging: No materials at all.

13. A lesson using the teaching model: Watch the DVD of a lesson using the teaching model. In your thinking groups answer the following questions: What did you notice about how the teaching model was utilised? How was folding back evident in the lesson? How were children’s misconceptions addressed during the lesson?

14. Rachel’s Millions

15. Importance of Place Value: What is place value? Where does place value start? What place value equipment have you currently got in your school? Order the equipment from least abstract to most abstract.

16. Introduction to Book 5: Each strategy stage is separated into 2 parts: Learning experiences to move from one stage to next and learning experiences for each stage. Refer to the required knowledge check before transitioning students. If the group are not ready to move from one stage to the next you may need to broaden their experiences. Refer to the teaching model progression for each lesson.

17. A Strategy Teaching Lesson: Start of Lesson Consider strategy stage of group - Required knowledge check - Diagnostic Snapshot (Can they already do it?) Teaching - Teaching Model (materials, imaging, number properties) - Consider thinking groups & modelling book End of Lesson - Feedback: Who’s got it? Who hasn’t? Set practice. - Consider next teaching and learning steps.

18. A Strategy Lesson…. Break into two groups to explore an add/sub lesson… Junior Teachers Senior Teachers Stage 4 Stage 6 Stage 5 Stage 7

19. Practice - 10 days of activities Questions on the board / Modeling Book Create a game (Snakes & Chances, Jigsaw, Bingo) Play each others games Diary writing / class book entry Solving story problems Writing and checking story problems Swapping story problems Resource Book e.g. Figure it Out Worksheet If this is the answer - what could the question be?

20. Stage 6 AA Advanced Additive There are 53 people on the bus. 29 people get off How many people are now on the bus?

21. 53 - 30 + 1= 24 53 - 29 Tidy Numbers using Compensation

22. 53 - 20 - 3 - 6 = 24 53 - 29 Place Value Partitioning

23. 29 + 1 + 20 + 3 = 53 53 - 29 Reversibility

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

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

26. Maths Thinking Groups: What is the purpose of a thinking group? Each person is given a chance to share their thinking and solution to a problem. Group members listen to each other. Only one person talks at a time. Everyone must be able to understand and explain others thinking and solutions. Group members must be prepared to explain their own thinking.

27. Why bother teaching mental strategies, why can’t I just learn the written form? written form is following a procedure - rule following - some students just learn method without understanding mistakes are made or wrongly applied to problem solving Need mental ability to estimate & check answers first It is often quicker to work something out mentally Written form sometimes is the most suitable way but not always Why are mental strategies important?

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

29. ? 385 - 99 478 - 56 1002 - 987

30. Stage 8 AP: Advanced Proportional To use a range of mental partitioning strategies to solve proportion (fraction), ratio and decimal problems.

31. Proportional Problem: If 30 children pay a total of 75 dollars in entry fees to Rainbows End, how much money will 18 children pay?”

32. 30:18 = 10/6 10 parts of 75 =7.5 p/ part 6 parts @ 7.5 p/part = 45 18 /30 is the same as 3/5 so it is 3/5 of 75 which is 45 because 1/5 is 15 30 children gives $75 1 child gives $2.50 18 x 2.5 18 children gives $45.00 30:75 is the same as 2:5 therefore multiply both by 9 18:45 Strategies for solving Proportional problems:

33. Long term unit plans (Bk 3, pg.16). AC- EA This would be appropriate for children who are transitioning from AC to EA, OR Those who need to broaden the EA stage before moving onto the next stage. In other words, AC - EA implies the EA stage Where would you start each of your groups?

34. Objectives: Revise the Strategy framework stages. Understand the teaching model used for teaching strategy Explore equipment and activities used to teach addition & subtraction strategies Know how to use planning sheets, numeracy book 5 and other supportive resources to help teach addition & subtraction.

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