EdTechTeacher iPad Summit: Boston Slide Deck

Making Math Contextual,
Visual, and Concrete
@MathletePearce
tapintoteenminds.com
tapintoteenminds.com/ettipad

ABOUT ME
Belle River, ON
Math Teacher /
Instructional Coach
Apple Distinguished
Educator
Apple Education Trainer
@MathletePearcewww.tapintoteenminds.com

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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.

Two Groups of
Students
Result

Two Groups of Students
Good at
Math
Not
Good at
Math

Good at
Math
Not
Good at
Math
Know:
terminology
procedures

Good at
Memorization
Not Good at
Memorization

Good at
Memorization
Not Good at
Memorization
Struggle with
unfamiliar
problems

A VISION FOR
MATHEMATICS
EDUCATION
VISION

Interconnected
Visual and Concrete
Contextual
VISION

Interconnected
Visual and Concrete
Contextual
CONFIDENCE

Interconnected
Visual and Concrete
Contextual
PERCEPTION

Interconnected
Visual and Concrete
Contextual
STUDENT
SUCCESS

“He’s Crazy”

Change

Immune to
Change

http://www.vancouversun.com/life/From+geek+chic/6296707/story.html
Photograph by: Maggie Wong

@MathletePearcewww.tapintoteenminds.com https://mathstrategies.wordpress.com/tag/numb3rs/

http://www.wykamath.com/

entertainment
engagement
=

algorithm

what’s
this?

algorithm

algorithm
s
engagement
=

algorithm
s
understanding
=

playkh.complaykh.comGo to:

Tap

Tap, then wait.

How many packs of paper would it take to
reach the ceiling?
OUR FIRST QUESTION:

PREDICTIONS

REQUEST
INFORMATION

How many packs of paper would
it take to reach the ceiling?
273cm
24.75cm

QUESTION
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?

AnswerKey:55.15
QUESTION
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?

Extensions

The Next Day…

How tall is the table?
4.95 cm
130.75cm
?
130.75cm

4.95 cm
130.75cm
packs5 x = 24.75 cm
130.75 cm
24.75 cm-
106 cm
106cm

Making Connections

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 cm
130.75cm130.75
106cm
packs
y b= +mx
number
of packs
height of
a pack
)( )(
4.95 cm ( packs5 )( )

How tall is the table?130.75cm
packs of paper height
Independent Dependent
5
packs
130.755
4.95 cm
Slope
)x y
(

130.75cm
packs of
paper
height
130.755
4.95 cm
Slope
)x y
( ,
y = m
InitialValue
y-intercept
5 packs
130.75130.75 =
)(
130.75 = b+
b+ b+
x
55 )(
)(
55)(4.95
b+ b+
54.9524.75
24.75-24.75-
106 = b0 +

In the past…

Example
Consolidation
Task #1:

5
packs
130.755( )x y4.95 cm
Slope
2 1515
130.75cm

packs
( )x y
2 15151

What does the point (1, 5) represent in
the context of the Stacking Paper task?
packs
( )x y
2 15151

What does the slope of 2 represent in
the context of the Stacking Paper task?
packs
( )x y
2 15151

1pack
packs
( )x y
2 15151
5
5
2()
1
1y = +b()5 2-2-2
2
3
3
y = 2x + 3

Struggle with
unfamiliar
problems
Good at
Math
Not Good
at Math

Good at
Math
Not Good
at Math
Struggle with
unfamiliar
problems

Digging Deeper…

142.75cm
100.75cm
?
142.75
100.75?

142.75cm
100.75cm
?
142.75 100.75
?
-
=
42 cm
42cm
12packs
5
packs
12 packs 5 packs-
=
7 packs
7packs
6 cm
1 packs
= 6 cmSlope m,

100.75
142.75cm
100.75cm??
42cm
12packs
5
packs7packs
= 6 cmSlope m,
packs of
paper
height
5 )x y
( ,
5
y b= +mx
100.75 6100.75 = )( )(5 b+
5100.75 6100.75 = b+30
30-30-
70.75 = b0 +

142.75cm
100.75cm?
142.75100.75
?
packs of
paper
height
)( ,
packs of
paper
height
)x1 y1
( ,12packs
5
packs
142.75100.75 12
512
5
POINT 1 POINT 2
x2 y2
142.75100.75
x1
y1
x2
y2
142.75 100.75- 42 cm
12 packs 5 packs- 7 packs
-
-
Slope m, =
= ==
6 cm
1 packs
==

142.75cm
100.75cm?
142.75100.75
?
)( ,)x1 y1
( ,
12packs
5
packs
142.75100.75 12
5
POINT 1 POINT 2
x2 y2
142.75100.75
Slope m, = 6 cm
y b= +mx b+
NOW, SUBSTITUTE
SLOPE (m) and EITHER
POINT TO FIND INITIAL
VALUE/Y-INTERCEPT!
b+

142.75cm
100.75cm
142.75100.75 )( ,)x1 y1
( ,
12packs
5
packs
142.75100.75 12
5
POINT 1 POINT 2
x2 y2
142.75100.75
Slope m, = 6 cm
y b= +mx b+
b
12142.75 = 6 )( )( b+
12142.75 = 6 b+72
72-72-
70.75 = b0 +
6

142.75cm
100.75cm
142.75100.75 )( ,)x1 y1
( ,
12packs
5
packs
142.75100.75 12
5
POINT 1 POINT 2
x2 y2
142.75100.75
Slope m, = 6 cm
y b= +mx b+b 70.75b6
Therefore, the
equation of the line is:

Interconnected
Visual and Concrete
Contextual
MATH

Interconnected
Visual and Concrete
Contextual
TASKS
CONNECTIONS
MATH

Interconnected
Visual and Concrete
Contextual
MATH
TASKS
INQUIRY
CONNECTIONS

Interconnected
Visual and Concrete
Contextual
MATH
TASKS
CONNECTIONS
INQUIRYCONSOLIDATE

iBooks
iBooks Author

iBooks Author
Available on iTunes and…
iBooks

3 Act Math Tasks
iTunes U
kylep.ca/curiousmath1p

iTunes U

iTunes U
Tap

Interconnected
Visual and Concrete
Contextual
MATH
TASKS
CONNECTIONS
INQUIRYCONSOLIDATE
@MathletePearcekylep.ca/curiousmath1p

thing.every

one thing.

step.one

one vision.

thing.
one

AMAZING
thing .s

BIGGERand
better

?
thing
NEXT
what will be your
AMAZING

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Visual, and Concrete
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EdTechTeacher iPad Summit: Boston Slide Deck

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