EdTechTeacher iPad Summit: Boston Slide Deck

Making Math Contextual, Visual, and Concrete

@MathletePearce

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Belle River, ONMath Teacher / Instructional CoachApple Distinguished EducatorApple Education Trainer

@MathletePearcewww.tapintoteenminds.com


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Class


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



Good atMath

NotGood at

Math



Good atMath

NotGood at

Math

Know:terminology

procedures



Not

Good at Memorization

Not Good at Memorization



Good at Memorization

Not Good at Memorization

Struggle withunfamiliarproblems


A VISION FOR MATHEMATICS

EDUCATION

VISION


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Visual and ConcreteContextual

VISION


Interconnected


CONFIDENCE


Interconnected


PERCEPTION


Interconnected


STUDENT SUCCESS


“He’s Crazy”


Change


Immune toChange


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

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


http://www.wykamath.com/

entertainment

engagement


entertainment

engagement=

algorithm




what’sthis?





algorithms

engagement

algorithm


s

engagement=

algorithm


s

understanding=


Interconnected


VISION


playkh.complaykh.comGo to:

http://playkh.com

http://playkh.com



Tap


Tap


Tap


Tap, then wait.


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


PREDICTIONS


REQUEST INFORMATION


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

4. Consolidate3. Connections 273

cm

24.7

5 cm

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?

Answer Key: 55.15QUESTION


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


Extensions


Interconnected


VISION

The Next Day…



How tall is the table?

4.95 cm130

.75

cm

?

130

.75

cm


4.95 cm

130

.75

cm packs5 x = 24.75 cm

130.75 cm24.75 cm-

106 cm

106

cm



-Part Math Lesson

4. Consolidate

Minds On

Inquiry2. -Part Math Lesson

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 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 )( )


How tall is the table?13

0.7

5 c

m

packs of paper heightIndependent Dependent

5packs

130.755

4.95 cmSlope )x y(


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…



4. Consolidate

ExampleConsolidation


Task #1:

Minds On



packs of paper heightIndependent Dependent

5packs

130.755( )x y4.95 cmSlope

2 1 51 513

0.7

5 c

m

Minds On



packs of paper heightIndependent Dependentpacks

( )x ySlope

2 1 51 51


What does the point (1, 5) represent in the context of the Stacking Paper task?


( )x ySlope

2 1 51 51


What does the slope of 2 represent in the context of the Stacking Paper task?


( )x ySlope

2 1 51 51

1pack



( )x y

2 1 51 51

5

5

2()

1

1y = +b()5 2-2-22

3

3y = 2x + 3



Two Groups of StudentsStruggle with

unfamiliarproblems

Good at Math

Not Good at Math



Good at Math

Not Good at Math

Struggle withunfamiliarproblems


Struggle withunfamiliarproblemsDigging Deeper…


142

.75

cm

100

.75

cm


?142

.75

100

.75

?


142

.75

cm

100

.75

cm


?

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


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 +


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==


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+


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


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:


Interconnected


MATH


Interconnected

Visual and ConcreteContextualTASKS

CONNECTIONS

MATH


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MATH

TASKS

INQUIRY

CONNECTIONS


Interconnected


MATH

TASKS

CONNECTIONS

INQUIRYCONSOLIDATE

iBooks


iBooks Author


iBooks Author

Available on iTunes and…

iBooks

3 Act Math Tasks

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TASKS

CONNECTIONS

INQUIRYCONSOLIDATE

@MathletePearcekylep.ca/curiousmath1p


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one thing.


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one


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