GECDSB Mathematics Learning Teams (MLT) Session #1

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School Math
Learning Teams

AGENDA
MATH VISION
What does it mean to be good at math?
Burning questions
EARLY MATH LEARNING
Counting and Quantity
JUNIO...

TODAY’S LEARNING
We are:
• Extending our understanding of the GECDSB:
Mathematics Vision and Mathematical Proficienci...

THE MATHEMATICS JOURNEY
• Mathematics journey is unlike many others
• It is not an implementation of a program or process...

The Work: Ambitious and Necessary
Enact the Vision
“The GECDSB provides mathematics education that engages and
empowers st...

SCHOOL MATH TEAM
Click to
add text
Session 1 October
Session 2 November
Session 3 January
Session 4 & 5 February and Marc...

What does it mean to be good
at mathematics?

What does it mean to be good at math?
Enjoy learning math
Develop persistence and tenacity
Learn to use math to solve prob...

GECDSB: A Vision for Mathematics
Strategic Competence
Procedural Fluency
Conceptual Understanding
Adaptive Reasoning
Produ...

Math Task Force Data
What does it mean to be good at math?
Math as a functional skill
Math as applied to a profession
Math...

Math Vision:
Understanding Proficiency
Strategic Competence
Procedural Fluency
Conceptual Understanding
Adaptive Reasoning...

Math Task
Click to
add text
How Close to 100?
Instructions can be found at
https://www.youcubed.org/
task/how-to-close-...

Math Task: Consolidation
How do you see this math task
connected to the development of
mathematical proficiency?
Is ther...

Does this change your definition of what it
means to be good at math?

The Work: Guided By Our Questions
We have many questions about mathematics education.
Table Talk…
With the learners at you...

COFFEE BREAK

Early Mathematics
In 2007, it was found that mathematics skills among children in Kindergarten were the
best predictor o...

Early Mathematics
As educators we must constantly ask ourselves:
Why this learning,
for this student,
at this time?

Early Mathematics
What mathematical skills do you think our young learners need?
Number Sense
• Counting
• Quantity Relati...

Counting and Quantity
Conservation
One-to-one
Correspondence
Cardinality
Stable Order
Order
Irrelevance
Abstraction
Movem...

Case Study
• What principles of quantity and counting
does the child understand?
• What might be the next step(s) for lea...

Early Mathematics Connections

Mathematics
Learning
Teams
M
L
T

Counting
and
Quantity
Stable-Order Order Irrelevance
Conservation
One-to-One
Correspondence
Abstraction
Movement is
Magnit...

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...

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

Conservation
Understanding thatthe count for a set group of objects
stays the same no matterwhether they are spread out or...

Conservation
Understanding thatthe count for a set group of objects
stays the same no matterwhether they are spread out or...

… the quantityof five large things is the samecount as a
quantityof five small things or a mixed group of fivesmall
and la...

Understanding thateach object being counted must be
given one count and only one count. It is useful in the early
stages f...

Understanding thatthe last count of a group of objects
represents how many are in the group. A child who
recounts when ask...

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

Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (o...

Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (o...

Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (o...

Understanding thatas you move up the counting sequence
(or forwards), the quantityincreases by one and as you
move down (o...

Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when...

Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when...

Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when...

Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when...

Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when...

Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when...

Understanding thatin our base ten system objects are
grouped into tens once the count exceeds 9 (and intotens
of tens when...

PROCEDURAL FLUENCY
STRATEGIC COMPETENCE
ADAPTIVE REASONING
PRODUCTIVE DISPOSITION
CONCEPTUAL
UNDERSTANDING
kylep.ca/gecdsb...

PRODUCTIVE
DISPOSITION
Ability to formulate, represent & solve
mathematical problems using an effective strategy
STRATEGIC...

@MathletePearcewww.tapintoteenminds.com
LAST TIME

@MathletePearcewww.tapintoteenminds.com

@MathletePearcewww.tapintoteenminds.com
Array
Multiplication

Array

Array

Array

Array

Array

3 x 2

3 x 2
“3 groups of 2”

3 x 2
“3 groups of 2”
1 1

3 x 2
“3 groups of 2”
1 1
1 1

3 x 2
“3 groups of 2”
1 1
1 1
1 1

3 x 2
“3 groups of 2”
1 1
1 1
1 1
1 1
1 1
1
1or

4 x 3

4 x 3
“4 groups of 3”

4 x 3
“4 groups of 3”
1 1 1

4 x 3
“4 groups of 3”
1 1
1 1
1
1

4 x 3
“4 groups of 3”
1 1
1 1
1 1
1
1
1

4 x 3
“4 groups of 3”
1 1
1 1
1 1
1
1
1
1 1 1

4 x 3
“4 groups of 3”
1 1
1 1
1 1
1 1
1 1
1
1or
1
1
1
1 1 1
1
1
1 1 1 1

5 x 3 = ?
“5 groups of 3”

5 x 3
“5 groups of 3”
1 1
1 1
1 1
= ?
1
1
1
1 1
1 1
1
1

Virtual Manipulatives
catalog.mathlearningcenter.org/apps

Virtual Manipulatives

Virtual Manipulatives

Virtual Manipulatives

5 x 6
“5 groups of 6”
= ?

5 x 6
“5 groups of 6”
= ?
1
1
1
1
1

5 x 6
“5 groups of 6”
= ?
1
1
1
1
1
1 1 1 1 1 1

5 x 6
“5 groups of 6”
= ?
1
1
1
1
1
1 1 1 1 1 1
1 1 1 11 1 6

5 x 6
“5 groups of 6”
= ?
1
1
1
1
1
1 1 1 1 1 1
1 1 1 11 1
1 1 1 11 1
6
12

5 x 6
“5 groups of 6”
= ?
1
1
1
1
1
1 1 1 1 1 1
1 1 1 11 1
1 1 1 11 1
1 1 1 11 1
6
12
18

5 x 6
“5 groups of 6”
= ?
1
1
1
1
1
1 1 1 1 1 1
1 1 1 11 1
1 1 1 11 1
1 1 1 11 1
1 1 1 11 1
6
12
18
24

5 x 6
“5 groups of 6”
= ?
1
1
1
1
1
1 1 1 1 1 1
1 1 1 11 1
1 1 1 11 1
1 1 1 11 1
1 1 1 11 1
1 1 1 11 1
6
12
18
24
30

1
1
1
3 x 6
“3 groups of 6”
1 1 1 1
= ?
1 1
1 1 1 11 1
1 1 1 11 1
1 1 1 1 1 1

1 1
1
1
1
5 x 5
“5 groups of 5”
1 1 1 1
= ?
1
1
1
1
1 1 1 11
1 1 1 11
1 1 1 11
1 1 1 11
1 1

5 x 5
“5 groups of 5”
1 1 1 1
= 25
1
1 1 1 11
1 1 1 11
1 1 1 11
1 1 1 11

5 x 5
“5 groups of 5”
1 1 1 1
= 25
1
1 1 1 11
1 1 1 11
1 1 1 11
1 1 1 11

5 x 5
“5 groups of 5”
1 1 1 1
= 25
1
1 1 1 11
1 1 1 11
1 1 1 11
1 1 1 11
PERFECT
SQUARE

6 x 6
“6 groups of 6”
1 1 1 1
= ?
1
1 1 1 11
1 1 1 11
1 1 1 11
1 1 1 11

6 x 6
“6 groups of 6”
1 1 1 1
= 36
1
1 1 1 11
1 1 1 11
1 1 1 11
1 1 1 11
1
1
1
1
1
1 1 1 11 1

What’s the Length of the Pool?
?

1
1
1
1
What’s the Length of the Pool?
?

1
1
1
1
What’s the Length of the Pool?
1 1 1 1

1
1
1
1
What’s the Length of the Pool?
1 1 1 1 1 1 1 1

1
1
1
1
What’s the Length of the Pool?
1 1 1 1 1 1 1 1 1 1 1 1

1
1
1
1
What’s the Length of the Pool?
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?

1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?

1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?

1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?

1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?

1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
1 1 1
1 1 1
1 1 1
1
1
1
1 1 1 1

1 1 1
1 1 1
1 1 1
1
1
1
1 1 1 1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 16 16 16

1 1 1
1 1 1
1 1 1
1
1
1
1 1 1 1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 16 16 1664

1 1 1
1 1 1
1 1 1
1
1
1
1 1 1 1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 16 16 1664 square-...

1 1 1
1 1 1
1 1 1
1
1
1
1 1 1 1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 16
1 1 1
1 1 1
1 1...

“Spatial thinking, or reasoning,
involves the location and
movement of objects and
ourselves, either mentally or
physicall...

“The relation between spatial
ability and mathematics is so
well established that it no longer
makes sense to ask whether
...

Activities to Develop Geometric
and Spatial Thinking
visualizing diagramming
designing
(Davis, Okamoto & Whiteley, 2015)
o...

1
1
1
3 x 6
“3 groups of 6”
1
= ?
1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1

= 18
1
1
1
3 x 6
“3 groups of 6”
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1

= 18
1
1
1
3 x 6
“3 groups of 6”
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1

= 18
1
1
1
3 x 6
“Splitting the Array”
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1

= 18
1
1
1
3 x 6
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1
3 x 4=

= 18
1
1
1
3 x 6
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1
3 x 4=

= 18
1
1
1
3 x 6
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1
3 x 4= + 3 x 2

= 18
1
1
1
3 x 6
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1
3 x 4= + 3 x 2
12= + 6

= 18
1
1
1
3 x 6
1 1
1 1
1
1 1 11
1 1 11
1 1 11 1
1 1 1 1 1 1
3 x 4= + 3 x 2
12= + 6
3(= +4 2)

@MathletePearcewww.tapintoteenminds.com
=6 x 7 ?

@MathletePearcewww.tapintoteenminds.com
6 x 7 = ?

@MathletePearcewww.tapintoteenminds.com
6 x 7 = ?

@MathletePearcewww.tapintoteenminds.com
6 x 7 = ?

@MathletePearcewww.tapintoteenminds.com
6 x 7 = ?

@MathletePearcewww.tapintoteenminds.com
6 x 7 = ?

@MathletePearcewww.tapintoteenminds.com
= 426 x 7

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7
5
6

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7
5
6 30

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7
5
6 30
= 6 x 5

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7
5
6 30
= 6 x 5
2

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7
5
6 30
= 6 x 5
2
12
+ 6 x 2

@MathletePearcewww.tapintoteenminds.com
6 x 7
5
6 30
= 6 x 5
2
12
+ 6 x 2
= 30 + 12
= 42

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7

@MathletePearcewww.tapintoteenminds.com
= ?6 x 7

@MathletePearcewww.tapintoteenminds.com
=
5
5
2
1
6 x 7

@MathletePearcewww.tapintoteenminds.com
=
5
5
2
1
5 x 5 5 x 2 1 x 5 1 x 2+ + +
6 x 7

@MathletePearcewww.tapintoteenminds.com
6 x 7
=
5
5 25
2
10
1
5 x 5 5 x 2 1 x 5 1 x 2+ + +
= 25 10 5 2+ + +
5 2

5 x 14 = ?
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1

5 x 14 = ?
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
...

5 x 14 = ?
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
...

5 x 14 = ?
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
...

5 x 14 =
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 ...

5 x 14 =
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 ...

5 x 14 =
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 ...

5 x 14 =
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 ...

@MathletePearcewww.tapintoteenminds.com
BASE 10 BLOCKS
1001,000 10 1

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

5 x 14 = ?
“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”
or
1 1 1 1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
1
1
1...

1 1 1 1
5 x 14 = ?
“5 groups of 14”
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
“5 groups of 10 plus 5 groups of 4”
or
1
1
1...

4 x 12 = ?
“4 groups of 12”
“4 groups of 10 plus 4 groups of 2”
or
1 1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110
1
1
1
1

4 x 12 = ?
“4 groups of 12”
“4 groups of 10 plus 4 groups of 2”
or
1 1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110
1
1
1
1
1 110
1 1...

@MathletePearcewww.tapintoteenminds.com
13 x 14 = ?

@MathletePearcewww.tapintoteenminds.com
13 x 14 = ?
1 110 1 1
10
1
1
1

@MathletePearcewww.tapintoteenminds.com
13 x 14 = ?
1 110 1 1
10
1
1
1
100

@MathletePearcewww.tapintoteenminds.com
13 x 14 = ?
1 110 1 1
10
1
1
1
100 10 10 10 10

@MathletePearcewww.tapintoteenminds.com
13 x 14 = ?
1 110 1 1
10
1
1
1
100 10 10 10 10
10
10
10

@MathletePearcewww.tapintoteenminds.com
13 x 14 = ?
1 110 1 1
10
1
1
1
100 10 10 10 10
10
10
10
1 1 1 1
1 1 1 1
1 1 1 1

@MathletePearcewww.tapintoteenminds.com
13 x 14 = 182
1 110 1 1
10
1
1
1
100 10 10 10 10
10
10
10
1 1 1 1
1 1 1 1
1 1 1 1

@MathletePearcewww.tapintoteenminds.com
12 x 15 = ?
1 110 1 1 1
10
1
1

@MathletePearcewww.tapintoteenminds.com
1 110 1 1 1
10
1
1
100
12 x 15 = ?

@MathletePearcewww.tapintoteenminds.com
1 110 1 1 1
10
1
1
100 10 10 10 10 10
12 x 15 = ?

@MathletePearcewww.tapintoteenminds.com
1 110 1 1 1
10
1
1
100 10 10 10 10 10
10
10
12 x 15 = ?

@MathletePearcewww.tapintoteenminds.com
1 110 1 1 1
10
1
1
100 10 10 10 10 10
10
10
1 1 1 1 1
1 1 1 1 1
12 x 15 = ?

@MathletePearcewww.tapintoteenminds.com
1 110 1 1 1
10
1
1
100 10 10 10 10 10
10
10
1 1 1 1 1
1 1 1 1 1
12 x 15 = 180

@MathletePearcewww.tapintoteenminds.com
17 x 23 = ?

@MathletePearcewww.tapintoteenminds.com
17 x 23 = ?

@MathletePearcewww.tapintoteenminds.com
17 x 23 = ?

@MathletePearcewww.tapintoteenminds.com
17 x 23 = ?

@MathletePearcewww.tapintoteenminds.com
17 x 23 = ?

@MathletePearcewww.tapintoteenminds.com
17 x 23 = 391

22 x 26= ?

22 x 26= ?

22 x 26= ?

22 x 26= ?

22 x 26= ?

2
2x
2
6
The “Standard” Algorithm

2
2x
2
6
The “Standard” Algorithm

2
2x
2
6
2
1
The “Standard” Algorithm

2
2x
2
6
2
1
The “Standard” Algorithm

2
2x
2
6
2
1
The “Standard” Algorithm

2
2x
2
6
2
1
12
The “Standard” Algorithm

2
2x
2
6
1
213
The “Standard” Algorithm

2
2x
2
6
1
213
The “Standard” Algorithm

2
2x
2
6
1
213
The “Standard” Algorithm

2
2x
2
6
1
0
213
The “Standard” Algorithm

2
2x
2
6
1
04
213
The “Standard” Algorithm

2
2x
2
6
1
04
213
The “Standard” Algorithm

2
2x
2
6
2
1
1
04
3
The “Standard” Algorithm

2
2x
2
6
2
1
1
04
3
The “Standard” Algorithm

2
2x
2
6
1
044
213
The “Standard” Algorithm

2
2x
2
6
1
044
213
The “Standard” Algorithm
+

2
2x
2
6
1
044
213
The “Standard” Algorithm
+
275

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
132

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
13222
6

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
132

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
132

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
132

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
132440

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
13244022
20

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
13244022
20 6

The “Standard”
Algorithm
Arrays &
Area Models
2
2x
2
6
1
044
213
+
275
13244022
206
572
26

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
The “Standard”
Algorithm
2
2x
2
6
1
044
21 3
+
275

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
The “Standard”
Algorithm
2
2x
2
6
1
044
21 3
+
275

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
The “Standard”
Algorithm
2
2x
2
6
1
044
21 3
+
275

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
(6 x 20)
The “Standard”
Algorithm
2
2x
2
6
1
044
21 3
+
...

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
120 (6 x 20)
The “Standard”
Algorithm
2
2x
2
6
1
044
21 ...

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
120 (6 x 20)
(20 x 2)
The “Standard”
Algorithm
2
2x
2
6
...

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
The “Standard”
Algorithm
2
2x
2...

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
(20 x 20)
The “Standard”
Algori...

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
400 (20 x 20)
The “Standard”
Al...

Arrays & Area
Models
A “Conceptual“
Algorithm
2
2x
2
6
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
400 (20 x 20)
572
+
The “Standa...

9 x 12 = ?
“9 groups of 12”
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 1

9 x 12 = ?
“9 groups of 12” 1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
“5 groups of 10
plus
4 groups of 2”
or

9 x 12 = ?
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
“9 groups of 12”
“5 groups of 10
plus
4 groups of 2”
or

9 x 12 = ?
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
? ?
“9 groups of 12”
“5 groups of 10
plus
4 groups of 2”
or

9 x 12 = ?
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
?
?
“9 groups of 12”
“5 groups of 10
plus
4 groups of 2”
or

9 x 12 = ?
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
?
?
?
“9 groups of 12”
“5 groups of 10
plus
4 groups of 2”
...

9 x 12 = ?
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
?
?
?
“9 groups of 12”
“5 groups of 10
plus
4 groups of 2”
...

9 x 12 = ?
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
50
40
10
8
“9 groups of 12”
“5 groups of 10
plus
4 groups of ...

9 x 12 = ?
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
50
40
10
8
“9 groups of 12”
“5 groups of 10
plus
4 groups of ...

= (5 + 4)(10 + 2)

= (5 + 4)(10 + 2)

= (5 + 4)(10 + 2)

= (5 + 4)(10 + 2)

= (5 + 4)(10 + 2)
First

= (5 + 4)(10 + 2)
First
Outside

= (5 + 4)(10 + 2)
First
Outside
Inside

= (5 + 4)(10 + 2)
First
Outside
Inside
Last

= (5 + 4)(10 + 2)
First
Outside
Inside
Last“FOIL”

= (5 + 4)(10 + 2)
First
Outside
Inside
Last
“FOIL”
“BEDMAS”

= (5 + 4)(10 + 2)
First
Outside
Inside
Last
“FOIL”
“BEDMAS”

9 x 12
1
1
1
1
1
1
1
1
1
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
50
40
10
8
= (5 + 4)(10 + 2)
= (5 + 4)(10 + 2)
First
Outside
Insi...

What’s My Area Equation?

What’s My Area Equation?
x x x x

What’s My Area Equation?
x x x x
1
1
1

What’s My Area Equation?
x x x x
1
1
1

What’s My Area Equation?
x x x x
1
1
1
Area = 3( )4x

What’s My Area Equation?
x x x x
1
1
1
x x x x
x x x x
x x x x
Area = 3( )4x
= 12x units2

x x x xx
Area = 2x ( )3x

x x x xx
x2
Area = 2x ( )3x

x2
x x x xx
x2
Area = 2x ( )3x

x2x2
x x x xx
x2
Area = 2x ( )3x

x x x xx
x2 x2 x2
x2 x2 x2
Area = 2x ( )3x

x x x xx
x2 x2 x2
x2 x2 x2
Area = 2x ( )3x

x x x xx
x2 x2 x2
x2 x2 x2
Area = 2x ( )3x

x x x xx
x2 x2 x2
x2 x2 x2
6x2Area = 2x ( )3x =

What’s My Area Equation?x
1 1
1
1
x
1
x x

Area = (x + 3)(3x + 2)x
1 1
1
1
x
1
x x

x
1 1
1
1
x
1
x x
x2 x2 x2
x x x
x x x
x x x
x
x
1
1
1
1
1
1
Area = (x + 3)(3x + 2)

x
1 1
1
1
x
1
x x
x2 x2 x2
x x x
x x x
x x x
x
x
1
1
1
1
1
1
Area = (x + 3)(3x + 2) = 3x2 + 11x + 6

Concreteness Fading
1 2 3
Enactive
Concrete
Iconic
Visual
Symbolic
Abstract

Concreteness Fading
1 2 3Enactive
Concrete
Iconic
Visual
Symbolic
Abstract

Concreteness Fading
1 2 3Enactive
Concrete
Iconic
Visual
Symbolic
Abstract

Concreteness Fading
1 2 3Enactive
Concrete
Iconic
Visual
Symbolic
Abstract
2
2x
2
6
1
04
004
21 3
+
275

PROCEDURAL FLUENCY
STRATEGIC COMPETENCE
ADAPTIVE REASONING
PRODUCTIVE DISPOSITION
CONCEPTUAL
UNDERSTANDING
kylep.ca/gecdsb...

PRODUCTIVE
DISPOSITION
Ability to formulate, represent & solve
mathematical problems using an effective strategy
STRATEGIC...

Leading Mathematics Learning:
Building Confidence
What’s your next best move?

In Math Class
Table Talk…
What would we see, hear and feel in an exemplary
math class?
Write one idea per sticky note.
Ide...

Pedagogical System
Non-threatening
Classroom
Environment
Instructional
Task
Tools and
Representations
Classroom
Discou...

In Math Class
Table Talk…
Fold the chart paper into quarters to reflect the
4 aspects of the pedagogical system.
Do your i...

Pedagogical System: Understanding
Task
What is a Math Task?
Anyproblem or set of problemsthat focuses students'attention o...

A task by itself is not rich;
it is what we do with the task and
how it connects to the pedagogical
system that makes it r...

Bump It Up
Bump up a task as an Assessmentfor Learning
• Use the Task Cards at your table
• Grade, Topic, Overall Expectat...

Task: Assessment for Learning
Tom Schimmer’s (Grading From the Inside Out, 2016) premise is that
all assessment practices...

Understanding Math Tasks
Grade 2
Topic: Counting
Overall Expectations: read, represent, compare, and order whole
numbers...

What was your task?
What did you notice about the curriculum?
What/How can the task be modified, refined, extended to sup...

Understanding Math Tasks
If you deny students the opportunity to
engage in this activity – to pose their own
problems, to ...

Understanding Math Tasks
Quotations about mathematics by mathematicians.
• Choose 1 that connects with your thinking
• Exp...

Bring student work based on a mathematics task.
Consider
Curriculum expectation
Assessment for Learning
We will analyze ...

What was one (or more) key learning(s) from today?
What was one thing you would have changed in the day?
What questions do...

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