EdTechTeacher iPad Summit: Boston Slide Deck
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Making Math Contextual, Visual, and Concrete
@MathletePearce
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Get to thinking about our practice!
ABOUT ME
Belle River, ONMath Teacher / Instructional CoachApple Distinguished EducatorApple Education Trainer
@MathletePearcewww.tapintoteenminds.com
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ENGAGED YET?
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ENGAGED YET?
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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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Two Groups of Students
Result
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Two Groups of Students
Good atMath
NotGood at
Math
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Two Groups of Students
Good atMath
NotGood at
Math
Know:terminology
procedures
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Two Groups of Students
Not
Good at Memorization
Not Good at Memorization
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Two Groups of Students
Good at Memorization
Not Good at Memorization
Struggle withunfamiliarproblems
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A VISION FOR MATHEMATICS
EDUCATION
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
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“He’s Crazy”
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Change
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Immune toChange
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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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entertainment
engagement=
algorithm
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what’sthis?
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algorithms
engagement
algorithm
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s
engagement=
algorithm
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s
understanding=
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Interconnected
Visual and ConcreteContextual
VISION
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Tap
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Tap
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Tap
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Tap, then wait.
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Tap
QUESTIONS
-Part Math Lesson
How many packs of paper would it take to reach the ceiling?
4. Consolidate3. Connections
2. InquiryOUR FIRST QUESTION:QUESTIONSPREDICTIONS
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PREDICTIONS
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REQUEST INFORMATION
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How many packs of paper would it take to reach the ceiling?
4. Consolidate3. Connections 273
cm
24.7
5 cm
QUESTION
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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
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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
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Extensions
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Interconnected
Visual and ConcreteContextual
VISION
The Next Day…
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How tall is the table?
4.95 cm130
.75
cm
?
130
.75
cm
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4.95 cm
130
.75
cm packs5 x = 24.75 cm
130.75 cm24.75 cm-
106 cm
106
cm
How tall is the table?
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-Part Math Lesson
4. Consolidate
Minds On
Inquiry2. -Part Math Lesson
Making Connections
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x = 24.75 cm
130.75 cm 24.75 cm 106 cm= +
5 = 24.75 cm
130.75 cm
24.75 cm
106 cm= +
height initial height of table= +
4.95 cm13
0.7
5 c
m13
0.7
5
106
cm
packs
y b= +m x
number of packs
height of a pack )( )(
4.95 cm ( packs5 )( )
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How tall is the table?13
0.7
5 c
m
packs of paper heightIndependent Dependent
5packs
130.755
4.95 cmSlope )x y(
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How tall is the table?13
0.7
5 c
mpacks of
paper height
130.7554.95 cm
Slope )x y
( ,
y = mIn
itia
l Val
ue
y -i
nter
cep
t
5 packs
130.75130.75 =)(
130.75 = b+b+ b+
x55 )(
)(55)(4.95
b+ b+
54.9524.7524.75-24.75-
106 = b0 +
In the past…
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4. Consolidate
ExampleConsolidation
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Task #1:
Minds On
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How tall is the table?
packs of paper heightIndependent Dependent
5packs
130.755( )x y4.95 cmSlope
2 1 51 513
0.7
5 c
m
Minds On
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How tall is the table?
packs of paper heightIndependent Dependentpacks
( )x ySlope
2 1 51 51
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What does the point (1, 5) represent in the context of the Stacking Paper task?
packs of paper heightIndependent Dependentpacks
( )x ySlope
2 1 51 51
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What does the slope of 2 represent in the context of the Stacking Paper task?
packs of paper heightIndependent Dependentpacks
( )x ySlope
2 1 51 51
1pack
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packs of paper heightIndependent Dependentpacks
( )x y
2 1 51 51
5
5
2()
1
1y = +b()5 2-2-22
3
3y = 2x + 3
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Two Groups of StudentsStruggle with
unfamiliarproblems
Good at Math
Not Good at Math
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Two Groups of Students
Good at Math
Not Good at Math
Struggle withunfamiliarproblems
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Struggle withunfamiliarproblemsDigging Deeper…
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142
.75
cm
100
.75
cm
How tall is the table?
?142
.75
100
.75
?
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142
.75
cm
100
.75
cm
How tall is the table?
?
142.75 100.75
?
-=
42 cm
42
cm
12p
ack
s
5p
ack
s12 packs 5 packs-
=
7 packs7
pa
cks
6 cm
1 packs
= 6 cmSlope m,
100.75
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142
.75
cm
100
.75
cm
??
42
cm
12p
ack
s
5p
ack
s7
pa
cks
= 6 cmSlope m,packs of
paper height
5 )x y
( ,
5
y b= +mx100.75 6100.75 = )( )( 5 b+
5100.75 6100.75 = b+3030-30-
70.75 = b0 +
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142
.75
cm
100
.75
cm
?
142.75100.75
?
packs of paper height
)( ,packs of
paper height
)x1 y1
( ,12
pa
cks 5
pa
cks
142.75100.75 12
512
5
POINT 1 POINT 2
x2 y2142.75100.75
x1
y1
x2
y2
142.75 100.75- 42 cm
12 packs 5 packs- 7 packs
--
Slope m, =
= ==6 cm
1 packs==
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142
.75
cm
100
.75
cm
?
142.75100.75
?
)( ,)x1 y1
( ,12
pa
cks
5
pa
cks
142.75100.75 12
5
POINT 1 POINT 2
x2 y2142.75100.75
Slope m, = 6 cm
y b= +mx b+NOW, SUBSTITUTE
SLOPE (m) and EITHER POINT TO FIND INITIAL VALUE/Y-INTERCEPT!
b+
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142
.75
cm
100
.75
cm
142.75100.75 )( ,)x1 y1
( ,12
pa
cks
5
pa
cks
142.75100.75 12
5
POINT 1 POINT 2
x2 y2142.75100.75
Slope m, = 6 cm
y b= +mx b+
b12142.75 = 6 )( )( b+
12142.75 = 6 b+7272-72-
70.75 = b0 +
6
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142
.75
cm
100
.75
cm
142.75100.75 )( ,)x1 y1
( ,12
pa
cks
5
pa
cks
142.75100.75 12
5
POINT 1 POINT 2
x2 y2142.75100.75
Slope m, = 6 cm
y b= +mx b+b 70.75b6
Therefore, the equation of the line is:
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Interconnected
Visual and ConcreteContextual
MATH
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Interconnected
Visual and ConcreteContextualTASKS
CONNECTIONS
MATH
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Interconnected
Visual and ConcreteContextual
MATH
TASKS
INQUIRY
CONNECTIONS
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Interconnected
Visual and ConcreteContextual
MATH
TASKS
CONNECTIONS
INQUIRYCONSOLIDATE
iBooks
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iBooks Author
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iBooks Author
Available on iTunes and…
iBooks
3 Act Math Tasks
iTunes U
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iTunes U
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kylep.ca/curiousmath1p
iTunes U
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kylep.ca/curiousmath1p
iTunes U
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TapFollow the Math
Twitter Blogosphere
Interconnected
Visual and ConcreteContextual
MATH
TASKS
CONNECTIONS
INQUIRYCONSOLIDATE
@MathletePearcekylep.ca/curiousmath1p
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“He’s Crazy”every
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“He’s Crazy” thing.every
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“He’s Crazy” thing.every
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one thing.
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step.one
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one vision.
thing.
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one
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AMAZINGthing .s
NEXT
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?
BIGGERand
better
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thingNEXT
what will be your
AMAZING
BIGGERbetter
#MTBoS
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