Making Math Contextual, Visual and Concrete with Technology

Making Math Contextual, Visual, and Concrete

kylep.ca/curiousmath1p khmath.com

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ABOUT MEBelle River, ONMath Teacher / Instructional Coach at Greater Essex County District School BoardApple Distinguished EducatorApple Education TrainerGoogle Certified Teacher

PROBLEM

ENGAGED YET?

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.

Class@MathletePearcewww.tapintoteenminds.com

Math Class

MathClass

1. Take Up Homework

Math Class

2. Definitions, Formulae, Procedures/Algorithms

1. Take Up Homework

Math Class

3. Examples

1. Take Up Homework

Math Class

4. Homework

3. Examples

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

Good at Memorization

Not Good at Memorization

Struggle withunfamiliarproblems

A VISION FOR MATHEMATICS

EDUCATION

VISION

Contextual

VISION

Visual and ConcreteContextual

VISION

Interconnected

VISION

Interconnected

CONFIDENCE

Interconnected

PERCEPTION

Interconnected

STUDENT SUCCESS

Change

Immune to

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entertainment

engagement=

algorithm

what’sthis?

algorithm

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algorithms

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algorithms

engagement=

algorithms

engagement=

understandingor

iBooks

iBooks Author

Available on iTunes and…

iBooks

3 Act Math Tasks

iTunes U

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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

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?

Answer Key: 55.15

QUESTION

273 cm, how many reams of paper would he need to reach the ceiling?FUN, RIGHT?

Answer Key: 55.15QUESTION

273 cm, how many reams of paper would he need to reach the ceiling?

Answer Key: 55.15

Extensions

Interconnected

VISION

Interconnected

VISION

Interconnected

VISION

The Next Day…

How tall is the table?

4.95 cm130

4.95 cm

packs5

4.95 cm

packs5 x = 24.75 cm

cm 24.75 cm

4.95 cm

packs5 x = 24.75 cm

130.75 cm24.75 cm-

4.95 cm

packs5 x = 24.75 cm

130.75 cm24.75 cm-

106 cm106 cm

4.95 cm

cm packs5 x = 24.75 cm

130.75 cm24.75 cm-

106 cm

-Part Math Lesson

4. Consolidate

Minds On

Inquiry2. -Part Math Lesson

Making Connections

4.95 cm

cm packs5 x = 24.75 cm

130.75 cm24.75 cm-

106 cm

How tall is the table?4.95 cmpacks5 x = 24.75 cm

4.95 cmx = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

packs5 4.95 cmx = 24.75 cmpacks5

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

packs5

4.95 cm (

= 24.75 cm

packs5

130.75 cm 24.75 cm 106 cm= +

4.95 cm

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

packs5 = 24.75 cm

130.75 cm

24.75 cm

106 cm= +

4.95 cm

4.95 cm ( packs5 )( )

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

packs5 = 24.75 cm

130.75 cm

24.75 cm

106 cm= +

height initial height of table= +number

of packs

4.95 cm

height of a pack )

cm ( )(

4.95 cm ( packs5 )( )

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

packs5 = 24.75 cm

130.75 cm

24.75 cm

106 cm= +

height initial height of table= +

4.95 cm13

cm number

of packsheight of

a pack )( )(

4.95 cm ( packs5 )( )

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

5 = 24.75 cm

130.75 cm

24.75 cm

106 cm= +

4.95 cm13

number of packs

height of a pack )( )(

4.95 cm ( packs5 )( )

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

5 = 24.75 cm

130.75 cm

24.75 cm

106 cm= +

4.95 cm13

number of packs

4.95 cm ( packs5 )( )

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

5 = 24.75 cm

130.75 cm

24.75 cm

106 cm= +

4.95 cm13

number of packs

4.95 cm ( packs5 )( )

x = 24.75 cm

130.75 cm 24.75 cm 106 cm= +

5 = 24.75 cm

130.75 cm

24.75 cm

106 cm= +

4.95 cm13

y b= +m x

number of packs

4.95 cm ( packs5 )( )

Minds On

-Part Math Lesson13

packs of paper heightIndependent Dependent

5packs13

4.95 cm

How tall is the table?13

5packs13

4.95 cmSlope

5packs

130.755

4.95 cmSlope

5packs

130.755

4.95 cmSlope )x y(

mpacks of

paper height5 packs130.7554.95 cm

mpacks of

paper height

130.7554.95 cmSlope

y b= +mxInit

5 packs5130.7554.95

mpacks of

paper height

130.7554.95 cmSlope

y b= +mxInit

5 packs5

130.75

mpacks of

paper height

130.7554.95 cmSlope

y b= +m xInit

5 packs5

130.75

130.75 = )()( b+

mpacks of

paper height

130.7554.95 cmSlope

y b= +m xInit

5 packs

5130.75 5130.75 =)(

)()( b+

55)(4.95

mpacks of

paper height

130.7554.95 cmSlope

y = mInit

5 packs

130.75130.75 =)(

b+130.75 = b+x55 )(

)(55)(4.95

b+ b+54.95

mpacks of

paper height

130.7554.95 cmSlope

y = mInit

5 packs

130.75130.75 =)(

130.75 = b+24.75b+ b+

x55 )(

)(55)(4.95

mpacks of

paper height

130.7554.95 cmSlope

y = mInit

5 packs

130.75130.75 =)(

130.75 = b+b+ b+

x55 )(

)(55)(4.95

54.9524.7524.75-

mpacks of

paper height

130.7554.95 cmSlope

y = mInit

5 packs

130.75130.75 =)(

130.75 = b+b+ b+

x55 )(

)(55)(4.95

54.9524.7524.75-24.75-

mpacks of

paper height

130.7554.95 cm

Slope )x y

y = mIn

5 packs

130.75130.75 =)(

130.75 = b+b+ b+

x55 )(

)(55)(4.95

54.9524.7524.75-24.75-

106 = b0 +

In the past…

4. Consolidate

ExampleConsolidation

Task #1:

Minds On

5packs

130.755( )x y4.95 cmSlope

2 1 51 513

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

( )x y1

2 1 51 51

( )x y

2 1 51 5

y = m x + b

( )1 pack

( )x y

2 1 51 51 55

2 2( )

1y = m + b( )

51 pack

( )x y

2 1 51 51

2 2( )

1y = m + b( )51 pack

( )x y

2 1 51 51

1y = + b()5 2

( )x y

2 1 51 51

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

( )x y

2 1 51 51

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

( )x y

2 1 51 51

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

3y = 2x + 3

Two Groups of StudentsStruggle with

unfamiliarproblems

Good at Math

Not Good at Math

Good at Math

Not Good at Math

Struggle withunfamiliarproblemsDigging Deeper…

142.75 100.75

- = 42 cm42 cm

142.75 100.75

- = 42 cm42

142.75 100.75

- = 42 cm42

142.75 100.75

- = 42 cm42

s12 packs 5 packs-

142.75 100.75

- = 42 cm42

s12 packs 5 packs- = 7 packs7 packs

142.75 100.75

- = 42 cm42

s12 packs 5 packs- = 7 packs

142.75 100.75

- = 42 cm42

s12 packs 5 packs- = 7 packs

142.75 100.75

42 cm42

s12 packs 5 packs-

=7 packs

142.75 100.75

42 cm42

s12 packs 5 packs-

7 packs7

1 packs=

142.75 100.75

s12 packs 5 packs-

7 packs7

1 packs

= 6 cmSlope m,

= 6 cmSlope m,packs of

paper height

100.75

paper height

5 )x y

( ,5 100.75

100.75

paper height

5 )x y

y b= +mx

100.75

paper height

5 )x y