Building Fluency

1. Building Fluency Geri, the following is the feedback link for your session that we ask you provide to participants! http://erlc.ca/programs/district-day-survey/?code=19-DD-PSD-GL-122

2. IF we want to impact achievement for ALL students….Geri Lorway Thinking101.ca

3. 40 years of research…

4. It’s not the curriculum…

5. It’s the teaching!

6. EVOLVE or go EXTINCT

7. Focus on number “sense” before number facts……. Build a foundation for recall and transfer.

8. BUILD EXPLAIN REPRESENT COMPARE SELF ASSESS SYNTHESIS

9. Number Sense: Learners who have a well-developed Number Sense are able to succeed in early math (and beyond), while children who don’t are at much greater risk of falling increasingly further behind.  They also demonstrated that virtually any child could develop Number Sense (Case, Griffin, and Siegler,1994; Griffin, 2004).

10. EXPRESS Number Identify and name multiple ways Trust the Count additive composition vs equal units MAGNITUDE & DENSITY Components of Number Sense: EQUAL compare expressions using the equal sign more, less , equal, not equal number properties emerge INVERSE RELATIONSHIPS

11. Grade one: Number 6 to 10 Number 11 to 20 Equal Equal parts (multiplicative reasoning) Sort one attribute Trust and repeat core forward and backward: predict Examine, explore, replicate 3 D objects Direct compare measures Grade 2: Number facts 6 to 10 Number sense 11 to 20 Number Sense to 100 Equality Inequality commutative and associative properties Zero & One Sort 2 attributes Growth patterns (move pattern to number) Match 2D to 3D: build vocabulary for attributes and properties Iterate the unit to measure Compare size of units (multiplicative reasoning) Grade 3: Number facts to 20 Inverse fluency to 100 Number sense to 1000 Reasoning about missing parts (symbol) Sort 2 or more attributes increasing & decreasing patterns: link to number Multiplicative reasoning: fraction sense, multiplication sense (division) place value sense standard units of measure 1 to 100 1 to 1000 Reason about 3D objects Reason about polygons

12. Number Sense is not addition and subtraction facts. It begins with automatic recognition of quantity and the ability to express a given number multiple ways.  Subitizing forms the foundation, not the counting sequence.

13. Your brain knows small collection without the need to count: 2, 3, 5 (if arranged to see 2 and 3) 4 because 2 twos. With practice and attention students learn to trust and use these. Seven becomes 5 plus 2 or 4 plus 3 both of which are related to 2 + 3 + 2 if you know number properties.

14. Push and circle 2, 3 and 5 to link fingers to brain in a positive way. Make it automatic.

15. Use the subitize quantities to recognize and name collections to and including ten. Additive Composition comes before equations. Build tens to introduce the 10 frame, then use the ten frame as one way to explore magnitude & inverses as you practice “facts”.

16. READY? What do you see? 2s, 3s, 5s or a total. Discuss both.

21. 6 + 2 3 + 3 + 1 + 1 5 + 3 2 + 2 + 2 + 2 7 + 1 2 + 6 4 + 4 3 + 5 3 + 3 + 2 8 Here are the ones I found. Compare to your list.

24. Build 8 with your chips.

25. 5 + 3 Find this expression in your collection. Slide the 3 in one move.

26. 5 + 3 3 + 5 Read this as 5 + 3 or 3 + 5. The order does not change there is still 8.

27. Label the parts

28. 5 + 3 = 3 + 5

29. 5 + 3 = 3 + 5 commutative property

31. 6 + 2

32. 6 + 2 2 + 6

33. 6 + 2 = 2 + 6

34. commutative property 6 + 2 = 2 + 6

36. 4 + 4

37. 4 + 4

38. 4 + 4

39. 4 + 4 = 4 + 4

40. 4 + 4 = 4 + 4 Commutative property

42. 1 + 7

43. 7 + 1 1 + 7

44. 7 + 1 = 1 + 7

45. 6 + 2 5 + 3 2 + 2 + 2 + 2 7 + 1 4 + 4 3 + 3 + 2 These expressions are all related. Let’s see…

46. 6 + 2 is the same amount as 5 + 3, watch.

47. Slide one from the 6 to the 2, now you have 5 + 3.

48. 6 + 2 = 5 + 3

49. 4 + 4 is the same amount as 5 + 3

50. 4 + 4 is the same amount as 5 + 3