Developing Additive Thinking 2011

1. Developing Additive Thinking 2011 Lisa Heap and Alison Howard Numeracy Facilitators .

2. Rocket:

3. Objectives: • Revise the Strategy framework stages. • Develop an understanding and awareness of how to analyse data to form Maths groups • Identify knowledge hotspots for the whole class and in groups. • Understand the teaching model. • Explore problem progressions, equipment and activities used to teach addition & subtraction strategies. • Explore a range of addition and subtraction strategies.

4. Using assessment data… • What strengths do your students have? • What learning needs do your students have? • How can you group according to needs? • What implications does this have for your teaching programme?

5. Equipment Animations • Use www.nzmaths.co.nz to find out how to… • Use equipment • Learn key ideas • Reinforce your learning

6. Book 3: Homework follow up; Key ideas Elements of an effective programme How can your organise your class? What does a numeracy lesson look like?

7. Activity: What could an ‘activity’ be? • Share in your thinking group an idea you have tried in your class. • What else did you add to your sheet?

8. Group Boxes: In pairs select a group box activity to explore. As you are playing think about….. What knowledge are you practicing? What stage is the activity suitable for? How could you adapt the activity to make it either harder or easier? Now share your activity and what you have discovered with another pair.

9. How would a child at Stage 3, 4 or 5 solve this problem? these? I have seven toy cars and Tom has nine toy cars. How many cars do we have altogether?

10. Hw would you solve these? How would a child at Stage 4 or 5 solve this problem? 42 - 7 = What would this look like as a word problem?

11. How would a child at Stage 6 solve this problem? How would you solve these? 92 - 39 = Change this calculation into a Stage 7 word problem.

12. Stage 1 and 2: ? Create a word problem and discuss how it could be solved.

13. The Teaching Model: Existing Knowledge & Strategies • Using Number Properties Using Imaging Using Materials Using Materials New Knowledge & Strategies

14. 12 23 10 10 + 50 + 3 37 87 90 Using Materials and Imaging: Hands Tens frames Abacus Place Value Material Number Lines

15. 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.

16. A lesson using the teaching model: • Watch the DVD of a lesson using the teaching model. • In your thinking groups discuss the following questions: How was the teaching model utilised? How were children’s misconceptions addressed during the lesson?

17. 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.

18. Using Thinking Groups “If you teach without observing and reacting to the children, you are teaching a programme, you are not teaching the kids.” Peter Hughes

19. Introduction to Book 5: • Each strategy stage is separated into 2 parts: Learning experiences to move from one stage to the next. Learning experiences for each stage. • Refer to the required knowledge check before transitioning students. • Ask a diagnostic question to find out what your students know.

20. A Strategy Lesson…. Break into the following groups to explore an add/sub lesson… • Stage 2-3: Ones and Tens p11 • Stage 4-5: Adding in parts p29 • Stage 5-6: Jumping the Number Line p33

21. Why are strategies 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 it out mentally

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

23. Next time… Wednesday, 5th October (Week 10) 9.15am – 2.30pm Bring: Book 1, Book 6 and an example of a Modeling book. Try: Introducing a new strategy (rounding & compensating, place value, equal addition or reversibility); be ready to tell us how it went.