Making Math Contextual, Visual, and Concrete
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Making Math Contextual, Visual,
and Concretetapintoteenminds.com/prma
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PROBLEM
ENGAGED YET?
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ENGAGED YET?
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ENGAGEMENT“There are several types/categories of engagement – academic, cognitive, intellectual, institutional, emotional, behavioural, social, psychological, to name a few.”
Parsons, J., & Taylor, L. (2011). Student Engagement: What do we know and what should we do? University Partners (pp 3). University of Alberta.
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Math Class
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MathClass
1. Take Up Homework
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Math Class
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2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class
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3. Examples
2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class
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4. Homework
3. Examples
2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class
Example 1(a) List all combinations of three out of the four colours: red, blue, white, and green.
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My Result:
Successfulin Math
Unsuccessfulin Math
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A Perception Develops
Good atMath
Poor atMath
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Not
Confident in Math Class
Doubtful inMath Class
Students Feel…
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Not
EnjoyingMathematics
Disliking Mathematics
This May Lead To…
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Not
Willingnessto Engage InMath Class
Unwillingness to Engage In Math Class
This May Lead To…
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Not
Moving Ahead Falling Behind
This May Lead To…
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Two Groups of Students
Not
Good atMath
Poor atMath
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Two Groups of Students
Good at Math
Poor atMath
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Two Groups of Students
Good at Math
Poor atMath
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Two Groups of StudentsStruggle with
unfamiliarproblems
Good at Math
Poor atMath
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A VISION FOR MATHEMATICS
EDUCATION
VISION
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Contextual
VISION
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Visual and ConcreteContextual
VISION
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Interconnected
Visual and ConcreteContextual
VISION
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Interconnected
Visual and ConcreteContextual
CONFIDENCE
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Interconnected
Visual and ConcreteContextual
PERCEPTION
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Interconnected
Visual and ConcreteContextual
STUDENT SUCCESS
Change
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Change
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Change
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Immune to
http://www.vancouversun.com/life/From+geek+chic/6296707/story.htmlPhotograph by: Maggie Wong
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http://www.wykamath.com/
entertainment
engagement=
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algorithm
what’sthis?
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algorithms
algorithms
engagement=
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algorithms
engagement=
understandingor
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playkh.complaykh.comGo to:
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wiz623
Notice? Wonder?
How many packs of paper would it take to reach the ceiling?
4. Consolidate3. Connections
2. Inquiry
OUR FIRST QUESTION:
QUESTIONSPREDICTIONS
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PREDICTIONS
wiz623
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REQUEST INFORMATION
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How many packs of paper will it take to reach a
height of 273 cm?
height
273
cm24.7
5 cm
wiz623
QUESTION
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QUESTION
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper vertically against a wall. If the height of 5 reams is 24.75 cm and the height of the room is
273 cm, how many reams of paper would he need to reach the ceiling?
Answer Key: 55.15
QUESTION
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper vertically against a wall. If the height of 5 reams is 24.75 cm and the height of the room is
273 cm, how many reams of paper would he need to reach the ceiling?FUN, RIGHT?
Answer Key: 55.15QUESTION
@MathletePearcewww.tapintoteenminds.com
Mr. Pearce stacks reams of paper vertically against a wall. If the height of 5 reams is 24.75 cm and the height of the room is
273 cm, how many reams of paper would he need to reach the ceiling?
Answer Key: 55.15
Making Connections
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@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take to reach a
height of 273 cm?
height 273
cm24.7
5 cm
@MathletePearcewww.tapintoteenminds.com
273
cm
24.7
5 cm
=24
.75
cm24
.75
cm
@MathletePearcewww.tapintoteenminds.com
273
cm=
24.7
5 cm
24.7
5 cm
24.7
5 cm
@MathletePearcewww.tapintoteenminds.com
273
cm
=
24.7
5 cm
24.7
5 cm
24.7
5 cm
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273
cm
=
25 c
m
25 c
m
25 c
m
Friendly Numbers
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275
cm
=
25 c
m
25 c
m
25 c
m
Friendly Numbers
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
25 cm
Friendly Numbers
Height
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
25 cm25 cm
Height
50 cm
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
25 cm25 cm
Height
25 cm
75 cm
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
25 cm25 cm
Height
25 cm25 cm
100 cm
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
25 cm25 cm
Height
25 cm25 cm
200 cm
25 cm25 cm
25 cm25 cm
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers100 cm
Height
300 cm
100 cm
100 cm
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers100 cm
Height
275 cm
100 cm
75 cm
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers100 cm
Height
275 cm
100 cm
75 cm
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers“Array”
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275
cm
=
25 c
m
25 c
m
Friendly NumbersArea Model
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275
cm
=
25 c
m
25 c
m
Friendly Numbers
5 pa
cks
11 groupsArea Model
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
5 pa
cks
11 groups
55 packs
Area Model
5 pa
cks
11 groups
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
5 pa
cks
11 groups
55 packs
5 pa
cks
11 groups
55 packs
Area Model
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
5 pa
cks
11 groups
55 packs
5 pa
cks
11 groups
55 packs
25 c
m
11 groups
Area ModelDouble
@MathletePearcewww.tapintoteenminds.com
275
cm
=
25 c
m
25 c
m
Friendly Numbers
5 pa
cks
11 groups
55 packs
5 pa
cks
11 groups
55 packs
25 c
m
11 groups
275 cm
Area ModelDouble
@MathletePearcewww.tapintoteenminds.com
275
cm
25 c
m
Friendly NumbersDouble Number Line
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25
Number of Packs
Total Height
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25 50
10
Number of Packs
Total Height
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25 50
10
75
15
250
50
Number of Packs
Total Height
20
100 125
25
150
30 35
175 200
40
225
45 55
275
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25 50
10
Number of Packs
Total Height
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25 50
10
Number of Packs
Total Height
20
100
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25 50
10
Number of Packs
Total Height
20
100 200
40
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25 50
10
Number of Packs
Total Height
20
100 200
40
250
50
225
45 55
275
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
5
25 50
10
Number of Packs
Total Height
20
100 200
40
250
50
225
45 55
275275
5
25
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
275
x
275
5
25
5
25
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
275
x5
25
5
?x27525
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
275
x
275
5
25
5
25
?x
= 11111111
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
275
x
275
5
25
5
25
x
= 1111
11
11
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
275
x
275
5
25
5
25
x
= 11 11
11
x 11
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
275
x
275
5
25
525
x
= 1111
11
x11x = 5555
Friendly NumbersDouble Number Line
275
cm
25 c
m
0
0
Number of Packs
Total Height
275
275
5
25
525
x
= 1111
11
x11x = 55
55
How many packs of paper would it take to reach the ceiling?
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many packs of paper will it take to reach a
height of 273 cm?3. Connections
packs of paper
height 273
cm
4.95 cm
How many packs of paper would it take to reach the ceiling?
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson
How many packs of paper will it take to reach a
height of 273 cm? 4. Consolidate3. Connections
packs of paper
height 273
cm
4.95 cm
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-Part Math Lesson
4. Consolidate3. Connections
2. Inquirypacks of paper heightIndependent Dependent
273
cm
4.95 cm
40
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-Part Math Lesson
4. Consolidate3. Connections
0 0
packs of paper heightIndependent Dependent
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-Part Math Lesson
4. Consolidate3. Connections
0 01 4.95
packs of paper heightIndependent Dependent
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-Part Math Lesson
4. Consolidate3. Connections
0 01 4.952 9.9
packs of paper heightIndependent Dependent
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-Part Math Lesson
4. Consolidate3. Connections
0 01 4.952 9.9
packs of paper heightIndependent Dependent
4 19.8
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-Part Math Lesson
4. Consolidate3. Connections
0 01 4.952 9.9
packs of paper heightIndependent Dependent
4 19.840 198
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-Part Math Lesson
4. Consolidate3. Connections
0 01 4.952 9.9
packs of paper heightIndependent Dependent
4 19.840 198
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packs of paper height:
@MathletePearcewww.tapintoteenminds.com
packs of paper
height
@MathletePearcewww.tapintoteenminds.com
packs of paper
height24.75 cm
5 reams= =
@MathletePearcewww.tapintoteenminds.com
24.75 cm
5 reams= =
273 cm
How Many?
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5 reams= =
x
24.75 cm 273 cm
x ??
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5 reams= =
x
24.75 cm 273 cm
x ??
@MathletePearcewww.tapintoteenminds.com
5 reams= =
x24.75 cm
273 cm
x ??
@MathletePearcewww.tapintoteenminds.com
5 reams= =
x24.75 cm
273 cm
x ??
11.03
@MathletePearcewww.tapintoteenminds.com
24.75 cm
5 reams= =
273 cm
11.03x
x
@MathletePearcewww.tapintoteenminds.com
24.75 cm
5 reams= =
273 cm
55.15 reams
11.03
x 11.03
x
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VISIONVisual and Concrete
ContextualTASKS
Visual and ConcreteContextualTASKS
INQUIRYConstruct Conceptual
UnderstandingVISION
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Connect to Prior Knowledge
Visual and ConcreteContextualTASKS
CONNECTIONS
INQUIRYConstruct Conceptual
UnderstandingVISION
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Visual and ConcreteContextualTASKS
CONSOLIDATE INQUIRYMove Towards
Procedural Fluency
Connect to Prior Knowledge
CONNECTIONS
Construct Conceptual Understanding
VISION
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TapFollow the Math
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The CN Tower has a height of 553 m and your stack of 5 packages of paper have a height of approximately 0.25 m.
Approximately how many packages of paper would you need to stack up to the height of the CN Tower?
24.7
5 cm
wiz623
Making Math Contextual, Visual, and Concrete
@MathletePearcewww.tapintoteenminds.com
tapintoteenminds.com/prma
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