otf connect webinar - exploring proportional reasoning through a 4-part math lesson

Exploring Proportional Reasoning Through a 4-Part Math Lesson

@MathletePearce

tapintoteenminds.com

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http://tapintoteenminds.com

http://kylep.ca/peelpd

[email protected]

Class

@MathletePearcewww.tapintoteenminds.com

Math Class

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.

Example 1(a) List all combinations of three out of the four colours: red, blue, white, and green.

(b) Considering the colour combinations as arrangements with indistinguishable elements, check the number of combinations of three out of four items.


Result


Two Groups of Students

Result



Good atMath

NotGood at

Math



Good atMath

NotGood at

Math

Know:



Good atMath

NotGood at

Math

Know:terminology



Good atMath

NotGood at

Math

Know:terminology

procedures



Good atMath

NotGood at

Math

Know: Know:terminology

procedures

terminology

procedures



Good atMath

NotGood at

Math



Good atMath

NotGood at

Math

Struggle withunfamiliarproblems



Good atMath

NotGood at

Math



CanMemorize

CannotMemorize

A VISION FOR MATHEMATICS

EDUCATION


A VISION FOR MATHEMATICS

EDUCATION

VISION


VISION


1. Contextual

VISION


2. Visual and Concrete1. Contextual

VISION


3. Interconnected2. Visual and Concrete1. Contextual

VISION


3. Interconnected

1. Contextual

2. Visual and Concrete

ConfidencePerception


3. Interconnected

1. Contextual


PerceptionStudent Success


3. Interconnected

1. Contextual


Student Success

4 -Part Math Lesson


3

Inquiry

Consolidation

Inquiry 1.


Minds On

Consolidation

-Part Math Lesson4

Minds On Inquiry1.


2.

Consolidation

-Part Math Lesson4

Minds On

Consolidate

Inquiry1.


2.

3. Connections

-Part Math Lesson4

Connections

Minds On

Consolidate

Inquiry1.


2.

3. 4.

-Part Math Lesson4


-Part Math Lesson

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

4. Consolidate3. Connections

2. Inquiry

Stacking Paper

273

cm

4.95

cm


Stacking Paper - Act 3

ORIGINAL QUESTION


ORIGINAL 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

ORIGINAL QUESTION



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

Answer Key: 55.15

ORIGINAL QUESTION




Answer Key: 55.15



ACT 1:


ACT 2:


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?

ACT 3:





Answer Key: 55.15

ACT 3:






-Part Math Lesson


3. Connections

Deconstructing the Task

4.95

cm


-Part Math Lesson


3. Connections

Deconstructing the Task

4.95

cm

273

cm

4.95

cm


-Part Math LessonHow many packs of paper would it

take to reach the ceiling?


2. Inquiry

Previous Day

273 cm

4.95 cm


-Part Math LessonHow many packs of paper would it

take to reach the ceiling?


2. Inquiry

Previous Day

273 cm

4.95 cm= 55.15

How many packs of paper will it take to reach

a height of 273 cm?



-Part Math Lesson

How many packs of paper will it take to reach a

height of 273 cm? 4. Consolidate3. Connections

2. Inquirypacks of paper

height


-Part Math LessonHow many packs of paper will it take

to reach a height of 273 cm?


2. Inquirypacks of paper height

Independent Dependent







0 0







0 01 4.95







0 01 4.952 9.9







0 01 4.952 9.9… …





2. Inquiry

packs of paperheight :





2. Inquiry

packs of paper

height

4.95

cm





2. Inquiry

packs of paper

height4.95 cm

1 pack

273

cm

How many





2. Inquiry4.95 cm

1 pack= 273 cm

How many?x


-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?


2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x ?




2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x 55.15




2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x 55.15

x ?




2. Inquiry4.95 cm

1 pack= 273 cm

How many?x

x 55.15

x 55.15




2. Inquiry4.95 cm

1 pack= 273 cm

How many?55.15

x 55.15

x 55.15packs

4 -Part Math Lesson


3

2. Inquiry

4. Consolidation


1. Minds On

-Part Math Lesson42. Inquiry

4. Consolidation


-Part Math Lesson41. Minds On 2. Inquiry

4. Consolidate



3. Connections4. Consolidate



3. Connections 4. Consolidate

Consolidate


-Part Math Lesson

1. Minds On

1. Minds On

Consolidate


-Part Math Lesson

Consolidate


-Part Math Lesson

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

1. Minds On

Consolidate


-Part Math Lesson


1. Minds On6

cm


-Part Math Lesson

How many ‘thick’ packs of paper would it take to reach

the ceiling?

1. Minds On6

cm


2. Inquiry


2. Inquiry1. Minds On


-Part Math Lesson4


2. Inquiry


-Part Math Lesson

4. Consolidate

2. Inquiry


-Part Math Lesson

How tall is the table?

4. Consolidate

Minds On


-Part Math LessonHow tall is the table?

2. Inquiry

Minds On

Inquiry2. -Part Math Lesson




-Part Math Lesson4

Minds On


-Part Math Lesson

3. Connections

Minds On


-Part Math LessonHow tall is the table?

3. Connections13

0.7

5 c

m

Minds On


-Part Math LessonHow tall is the table?13

0.7

5 c

m

packs of paper heightIndependent Dependent

Minds On



0.7

5 c

m


5packs13

0.7

55

Minds On



0.7

5 c

m


5packs

5

130

.75

Minds On



0.7

5 c

m


5packs

130.755

Minds On



0.7

5 c

m


5packs

130.755 )x y(

Minds On



0.7

5 c

m


5packs

130.755( )x ySlope

3. Connections





-Part Math Lesson4

4. Consolidate





-Part Math Lesson4

GoodNotes 4


The Next Day…

GoodNotes 4


The Next Day…

GoodNotes 4

How tall is this table?


The Next Day…

GoodNotes 4


142

.75

cm


The Next Day…

GoodNotes 4


142

.75

cm

100

.75

cm


The Next Day…

GoodNotes 4


142

.75

cm

100

.75

cm

6 c

m

142

.75

cm

100

.75

cm

Equations Given 2 Points

Your Turn…


Your Turn…


Think of an example involving proportional reasoning that you could introduce using context and visuals.

Your Turn…



ratios rates fractions percentagesunit rates



ratios rates fractions percentagesunit rates


2. Inquiry1. Minds On -Part Math Lesson4

Share…


Questions?


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otf connect webinar - exploring proportional reasoning through a 4-part math lesson

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