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.

1. Progression of Counting
and Quantity
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2. GET
READY

3. Shared By: Jo Boaler

4. How Did You
The Dots?
SEE

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18. Shared By: Jo Boaler

19. Shared By: Jo Boaler

20. SPATIAL REASONING?
What is

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. “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. 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

29. Counting
Principles

30. Stable-Order Order Irrelevance
Conservation
One-to-One
Correspondence
Abstraction
Movement is
MagnitudeSubitizing
Unitizing
Cardinality
Counting
Principles

31. 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

32. 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

33. 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

34. Order Irrelevance
The order in which items are counted is irrelevant.
1 2 3 4 5 6
1 2 3 4 5 6

35. 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

36. 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

37. … 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

38. 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.

39. 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.

40. 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

41. The ability to 'see' a small amount of objects and know how
many there are without counting.
Subitizing
“5”

42. 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”

43. 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

44. @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.

45. @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

46. @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.

56. @MathletePearcewww.tapintoteenminds.com
0 4 91 2 3 5 6 7 8
Counting, Quantity and Number Lines
Stable Order and Movement is Magnitude

57. More Fun With Dots

58. More Fun With Dots

59. More Fun With Dots
How Many?

60. More Fun With Dots

61. More Fun With Dots

62. More Fun With Dots

63. More Fun With Dots
How Many?

64. More Fun With Dots