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# Day 1, Session 1 - The Progression of Counting and Quantity - Sudbury Catholic District School Board (SCDSB)

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Slide deck from Sudbury Catholic District School Board (SCDSB) on the Progression of Counting and Quantity during our morning of learning on August 23rd, 2017.

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### Day 1, Session 1 - The Progression of Counting and Quantity - Sudbury Catholic District School Board (SCDSB)

1. 1. Progression of Counting and Quantity @MathletePearcewww.tapintoteenminds.com tapintoteenminds.com/sudbury
3. 3. Shared By: Jo Boaler
4. 4. How Did You The Dots? SEE
5. 5. Shared By: Jo Boaler
6. 6. Shared By: Jo Boaler
7. 7. Shared By: Jo Boaler
8. 8. Shared By: Jo Boaler
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10. 10. Shared By: Jo Boaler
11. 11. Shared By: Jo Boaler
12. 12. Shared By: Jo Boaler
13. 13. Shared By: Jo Boaler
14. 14. Shared By: Jo Boaler
15. 15. Shared By: Jo Boaler
16. 16. Shared By: Jo Boaler
17. 17. Shared By: Jo Boaler
18. 18. Shared By: Jo Boaler
19. 19. Shared By: Jo Boaler
20. 20. SPATIAL REASONING? What is
21. 21. “Spatial thinking, or reasoning, involves the location and movement of objects and ourselves, either mentally or physically, in space. It is not a single ability or process but actually refers to a considerable number of concepts, tools and processes.” (National Research Council, 2006)
22. 22. “The relation between spatial ability and mathematics is so well established that it no longer makes sense to ask whether they are related…” “…moreover, spatial thinking was a better predictor of mathematics success than either verbal or mathematical skills.”
23. 23. Activities to Develop Geometric and Spatial Thinking visualizing diagramming designing (Davis, Okamoto & Whiteley, 2015)  orienting locating perspective taking sliding rotating reﬂecting modeling exploring symmetry composing decomposing scaling map-making
24. 24. Counting Principles
25. 25. Stable-Order Order Irrelevance Conservation One-to-One Correspondence Abstraction Movement is MagnitudeSubitizing Unitizing Cardinality Counting Principles
26. 26. Stable-Order The list of words used to count must be in a repeatable order. This “stable list” must be at least as long as the number of items to be counted. Counting Principles
27. 27. Stable-Order The list of words used to count must be in a repeatable order. This “stable list” must be at least as long as the number of items to be counted. 1 2 3 4 5 6 7 8 9 10
28. 28. Stable-Order The list of words used to count must be in a repeatable order. This “stable list” must be at least as long as the number of items to be counted. 1 2 3 4 5 6
29. 29. Order Irrelevance The order in which items are counted is irrelevant. 1 2 3 4 5 6 1 2 3 4 5 6
30. 30. Conservation Understanding that the count for a set group of objects stays the same no matter whether they are spread out or close together. 7 8 9 10 1 2 3 4 5 6
31. 31. Conservation Understanding that the count for a set group of objects stays the same no matter whether they are spread out or close together. 7 8 9 10 1 2 3 4 5 6
32. 32. … the quantity of five large things is the same count as a quantity of five small things or a mixed group of five small and large things. Abstraction …we can count any collection of objects, whether tangible or not. 1 2 3 4 5 1 2 3 4 5
33. 33. One-to-One Correspondence 1 2 3 4 5 Understanding that each object in a group can be counted once and only once. It is useful in the early stages for children to actually tag or touch each item being counted and to move it out of the way as it is counted.
34. 34. One-to-One Correspondence 1 2 3 4 5 Understanding that each object in a group can be counted once and only once. It is useful in the early stages for children to actually tag or touch each item being counted and to move it out of the way as it is counted.
35. 35. Understanding that the last count of a group of objects represents how many are in the group. A child who recounts when asked how many candies are in the set that they just counted, has not understood the cardinality principle. Cardinality 1 2 3 4 5 6
36. 36. The ability to 'see' a small amount of objects and know how many there are without counting. Subitizing “5”
37. 37. The ability to 'see' a small amount of objects and know how many there are without counting. Subitizing “5” Perceptual The ability to 'see' groups of small amounts of objects as parts of a whole; often beyond 5. Conceptual “7”
38. 38. Understanding that as you move up the counting sequence (or forwards), the quantity increases by one and as you move down (or backwards), the quantity decreases by one or whatever quantity you are going up/down by. Movement is Magnitude 1 2 3 4
39. 39. @MathletePearceTapintoTeenMinds.com Unitizing Understanding that every quantity we measure is relative to another pre-measured group we call a unit. 4 twos For example, counting equal groups of 2.
40. 40. @MathletePearceTapintoTeenMinds.com Unitizing threes For example, counting equal groups of 3. Understanding that every quantity we measure is relative to another pre-measured group we call a unit. 4
41. 41. @MathletePearceTapintoTeenMinds.com Unitizing tens ones 2 01 1 For example, our base ten place value system. Understanding that every quantity we measure is relative to another pre-measured group we call a unit.
42. 42. @MathletePearcewww.tapintoteenminds.com 0 4 91 2 3 5 6 7 8 Counting, Quantity and Number Lines Stable Order and Movement is Magnitude
43. 43. More Fun With Dots
44. 44. More Fun With Dots
45. 45. More Fun With Dots How Many?
46. 46. More Fun With Dots
47. 47. More Fun With Dots
48. 48. More Fun With Dots
49. 49. More Fun With Dots How Many?
50. 50. More Fun With Dots