Blips Blops and Blaps

2. Blips Blops and Blaps

3. Blips column Blops column Blaps column Can you write 789 in terms of Blips, Blops and Blaps? 7 Blips + 8 Blops + 9 Blaps So what's the difference between 7 hundreds + 8 tens + 9 units?

4. What does this tell us about your understanding of Place Value?

5. Hello Earthling I am a Snopsitswat. I live on planet Shekle. Our number system is all BASE 8 Everything you now do is to be done in base 8!!!!

6. So what is base 8? 83 82 81 80 512 64 8 1

7. 83 82 81 80 512 64 8 1 1. Write the number 84 in base 8? 124 2. Write the number 1394 in base 8? 2561

8. What is the number 4357base 8 in base 10 4 x 512 = 2024, 3 x 64 = 192, 8 x 5 = 40, 7 x 1 = 7 2263

9. What is the number 7632 base 8 in base 10 7 x 512 = 3584, 6 x 64 = 384, 3 x 8 = 24, 1 x 2 = 2 3994

10. How did you feel working with base 8?

11. How do you think some of the students feel when we are doing base 10?

12. What do students need to know before Place Value? • Fractions Level 3 & decimals Level 4 New Curriculum

13. Material and imaging Check out the 10 A2 sheets of paper

14. Get the students to work with their own decimat.

15. Once students have had cut out the decimat get them to use the squares in their books and draw egs of 1. 0.32 2. 0.95 3. 1.30 etc This keeps them imaging beyond the decimat.

16. 1.40 vs 1.4 They could draw this in their books.

17. Number Fans

18. Some important phrases Remember ty on the end of a word means ‘tens’ eg 80(eighty) means 8 tens 30 (thirty) means 3 tens

19. Express any fractions as follows: 65% = 65 100 Read this as 65 hundredths

20. How do you think our girls would answer this? Pick the most appropriate answer 0.30 is • 3 tens B. 3 ones C. 3 tenths D. 3 hundredths E. None of the above

21. Use words zero wholes and three tenths and zero hundredths ( leave out 0 hundredths as meaningless.)

22. Add/Sub

23. Strategy framework for addition and subtraction Stage and behavioural indicator 0 Emergent The student has no reliable strategy to count an unstructured collection of items • One to One Counting The student has a reliable strategy to count an unstructured collection of items • Counting from One on Materials The student’s most advanced strategy is counting from one on materials to solve addition problems • Counting from One by Imaging The student’s most advanced strategy is counting from one without the use of materials to solve addition problems • Advanced Counting The student’s most advanced strategy is counting on or counting back to solve addition and subtraction tasks • Early Additive Part-Whole The student shows any part-whole strategy to solve addition or subtraction problems mentally by reasoning the answer from basic facts and/or place value knowledge • Advanced Additive Part-Whole The student is able to use at least 2 different mental strategies to solve addition and subtraction problems with multi-digit numbers • Advanced Multiplicative Part-Whole The student is able to use at least two different advanced mental strategies to solve addition or fraction problems with decimals and fractions with related denominators

24. How the stages operate Each stage says what students should be able to do In the books there are: Activities to consolidate knowledge/strategies at the stage Then Activities to move students to the next stage Note: Some students who have just reached a stage have more in common with those who are ready to make the transition that those who are proficient at the stage…

25. In the teaching of strategy, one of the critical concepts to develop is when it is appropriate to use a certain strategy

26. Focus of SNP • PROGRESSIONS • PEDAGOGY • PARTICIPATION

27. Progression Step 1: • Identify and build the computational strategies of students using a framework. Step 2: • Exploit what the students are using computationally and formalise it to develop algebra.

28. Pedagogy Building on the experience of teachers in the department and developing a broad understanding of how to teach mathematics. Use a concrete representation Encourage imaging and visualisation Push to the inherent property and generalisation

29. Participation • Who asks the questions? • Who answers the questions? • Who explains the reasoning behind a method? • Who explains the key ideas? • Who does the most talking? • Who checks the work? • Who decides if the answers are correct?

30. The teaching model 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

31. Lesson planning • Work in groups of twos or threes (relating to the ability of the class you teach) to plan a lesson on whole number add/sub. 9H/9ARM top work on stage 7 9PT top & mid 9ARM stage 6 9ARM/9PT low stage 5 • Plan lesson 1 for Add/sub (Use SNP books/FIO/internet) • Starter • Materials -> Imaging -> Abstraction • How many lessons would you expect the progression to take? • Present Overview to the group?????

36. Written Recording • Students are expected to record their mental calculations in a appropriate manner • Models of appropriate recording need to be carefully taught • Students will interact with written material a great deal while working on practice activities

37. Approaching problems First port of call: Is there a quick mental strategy that I can use? Second Stop: Informal jottings – “memory joggers” that will help me think through the problem Empty number line Third stop: A written algorithm Question: What do I need to write down so others can see what I have done?