Addition and Subtraction Workshop

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

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

3. 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.

4. Knowledge Warm-up: No Name Game

5. 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.

6. 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

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

8. 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

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

10. 12 23 10 10 + 50 + 3 37 87 90 Using Materials and Imaging: Hands Tens frames Abacus Place Value Material Number Lines

11. 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.

12. 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?

13. Rachel’s Millions

14. 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.

15. 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.

16. A Strategy Teaching Lesson: Start of LessonConsider 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.

17. 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

18. 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?

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

20. 53 - 29 Tidy Numbers using Compensation 53 - 30 + 1= 24

21. 53 - 29 • Place Value Partitioning 53 - 20 - 3 - 6 = 24

22. 53 - 29 29 + 1 + 20 + 3 = 53 • Reversibility

23. 1 1 53 54 29 30 53 - 29 • Equal Additions = 24

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

25. 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.

26. Why are mental strategies important? 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

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

28. ? 385 - 99 478 - 56 1002 - 987

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

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

31. 30:75 is the same as 2:5 therefore multiply both by 9 18:45 30:18 = 10/6 10 parts of 75 =7.5 p/ part 6 parts @ 7.5 p/part = 45 30 children gives $75 1 child gives $2.50 18 x 2.5 18 children gives $45.00 18 /30 is the same as 3/5 so it is 3/5 of 75 which is 45 because 1/5 is 15 Strategies for solving Proportional problems:

32. 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?

33. 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.

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