SERCC - Making Math Contextual, Visual and Concrete

Making Math Contextual, Visual, and Concrete in

Grade 7-12

@MathletePearcewww.tapintoteenminds.com


Making Math Contextual, Visual,

and Concrete in Grade 7-12


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.

[email protected]


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.


My Result:

Successfulin Math

Unsuccessfulin Math


A Perception Develops

Good atMath

Poor atMath


Not

Confident in Math Class

Doubtful inMath Class

Students Feel…


Not

EnjoyingMathematics

Disliking Mathematics

This May Lead To…


Not

Willingnessto Engage InMath Class

Unwillingness to Engage In Math Class

This May Lead To…


Not

Moving Ahead Falling Behind

This May Lead To…


Two Groups of Students

Not

Good atMath

Poor atMath


Two Groups of Students

Good at Math

Poor atMath


Two Groups of StudentsStruggle with

unfamiliarproblems

Good at Math

Poor atMath


A VISION FOR MATHEMATICS

EDUCATION

VISION


Contextual

VISION


Visual and ConcreteContextual

VISION


Interconnected


VISION


Interconnected


CONFIDENCE


Interconnected


PERCEPTION


Interconnected


STUDENT SUCCESS

Change


Change


Immune to

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=



algorithm

what’sthis?

algorithm

s

[email protected]

algorithms

[email protected]

algorithms

engagement=


algorithms

engagement=

understandingor


Notice? Wonder?

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

4. Consolidate3. Connections

2. Inquiry

OUR FIRST QUESTION:

QUESTIONSPREDICTIONS


PREDICTIONS


REQUEST INFORMATION


How many packs of paper will it take to reach a

height of 273 cm?

height 273

cm24.7

5 cm

QUESTION


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

Making Connections




height of 273 cm?

height 273

cm24.7

5 cm


273

cm

24.7

5 cm

=24

.75

cm24

.75

cm


273

cm=

24.7

5 cm

24.7

5 cm

24.7

5 cm


273

cm

=

24.7

5 cm

24.7

5 cm

24.7

5 cm


273

cm

=

25 c

m

25 c

m

25 c

m

Friendly Numbers


275

cm

=

25 c

m

25 c

m

25 c

m

Friendly Numbers


275

cm

=

25 c

m

25 c

m

25 cm

Friendly Numbers

Height


275

cm

=

25 c

m

25 c

m

Friendly Numbers

25 cm25 cm

Height

50 cm


275

cm

=

25 c

m

25 c

m

Friendly Numbers

25 cm25 cm

Height

25 cm

75 cm


275

cm

=

25 c

m

25 c

m

Friendly Numbers

25 cm25 cm

Height

25 cm25 cm

100 cm


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


275

cm

=

25 c

m

25 c

m

Friendly Numbers100 cm

Height

300 cm

100 cm

100 cm


275

cm

=

25 c

m

25 c

m

Friendly Numbers100 cm

Height

275 cm

100 cm

75 cm


275

cm

=

25 c

m

25 c

m

Friendly Numbers“Array”


275

cm

=

25 c

m

25 c

m

Friendly NumbersArea Model


275

cm

=

25 c

m

25 c

m

Friendly Numbers

5 pa

cks

11 groupsArea Model


275

cm

=

25 c

m

25 c

m

Friendly Numbers

5 pa

cks

11 groups

55 packs

Area Model

5 pa

cks

11 groups


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


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


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


275

cm

25 c

m

Friendly NumbersDouble Number Line


275

cm

25 c

m

0

0


275

cm

25 c

m

0

0

Number of Packs

Total Height


275

cm

25 c

m

0

0

5

25

Number of Packs

Total Height


275

cm

25 c

m

0

0

5

25 50

10

Number of Packs

Total Height


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


275

cm

25 c

m

0

0

5

25 50

10

Number of Packs

Total Height


275

cm

25 c

m

0

0

5

25 50

10

Number of Packs

Total Height

20

100


275

cm

25 c

m

0

0

5

25 50

10

Number of Packs

Total Height

20

100 200

40


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


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


275

cm

25 c

m

0

0

Number of Packs

Total Height

275

x

275

5

25

5

25


275

cm

25 c

m

0

0

Number of Packs

Total Height

275

x5

25

5

?x27525


275

cm

25 c

m

0

0

Number of Packs

Total Height

275

x

275

5

25

5

25

?x

= 11111111


275

cm

25 c

m

0

0

Number of Packs

Total Height

275

x

275

5

25

5

25

x

= 1111

11

11


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


275

cm

25 c

m

0

0

Number of Packs

Total Height

275

x

275

5

25

525

x

= 1111

11

x11x = 5555


275

cm

25 c

m

0

0

Number of Packs

Total Height

275

275

5

25

525

x

= 1111

11

x11x = 55

55



-Part Math Lesson


height of 273 cm?3. Connections

packs of paper

height 273

cm

4.95 cm



-Part Math Lesson


height of 273 cm? 4. Consolidate3. Connections

packs of paper

height 273

cm

4.95 cm


-Part Math Lesson


2. Inquirypacks of paper heightIndependent Dependent

273

cm

4.95 cm

40


-Part Math Lesson


0 0

packs of paper heightIndependent Dependent


-Part Math Lesson


0 01 4.95



-Part Math Lesson


0 01 4.952 9.9



-Part Math Lesson


0 01 4.952 9.9


4 19.8


-Part Math Lesson


0 01 4.952 9.9


4 19.840 198


packs of paper height:


packs of paper

height


packs of paper

height24.75 cm

5 reams= =


24.75 cm

5 reams= =

273 cm

How Many?


5 reams= =

x

24.75 cm 273 cm

x ??


5 reams= =

x24.75 cm

273 cm

x ??


5 reams= =

x24.75 cm

273 cm

x ??

11.03


24.75 cm

5 reams= =

273 cm

11.03x

x


24.75 cm

5 reams= =

273 cm

55.15 reams

11.03

x 11.03

x


VISIONVisual and Concrete

ContextualTASKS

Visual and ConcreteContextualTASKS

INQUIRYConstruct Conceptual

UnderstandingVISION


Connect to Prior Knowledge


CONNECTIONS

INQUIRYConstruct Conceptual

UnderstandingVISION



CONSOLIDATE INQUIRYMove Towards

Procedural Fluency

Connect to Prior Knowledge

CONNECTIONS

Construct Conceptual Understanding

VISION


3 Act Math Tasks

iTunes U

kylep.ca/[email protected]

kylep.ca/curiousmath1p

iTunes U


kylep.ca/curiousmath1p

iTunes U


TapFollow the Math

Twitter Blogosphere

3 Act Math Taskstapintoteenminds.com/3act-math


fishing4tech.com/mtbos.html

http://tapintoteenminds.com/3act-math

http://fishing4tech.com/mtbos.html


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

Concreteness Fading

Concreteness Fading

1Enactive

Concreteness Fading

1Enactive

Concrete

Concreteness Fading

1 2Enactive

Concrete

Iconic

Concreteness Fading

1 2Enactive

Concrete

Iconic

Visual

Concreteness Fading

1 2 3Enactive

Concrete

Iconic

Visual

Symbolic

Concreteness Fading

1 2 3Enactive

Concrete

Iconic

Visual

Symbolic

Abstract

Concreteness Fading

1 2 3Enactive

Concrete

Iconic

Visual

Symbolic

Abstract

22x

26

1

04421 3

+

275

Making Math Contextual, Visual, and Concrete


SERCC - Making Math Contextual, Visual and Concrete

Education

Transcript of SERCC - Making Math Contextual, Visual and Concrete