OTF Connect Webinar - Exploring Proportional Reasoning Through a 4-Part Math Lesson

Exploring Proportional
Reasoning Through a
4-Part Math Lesson
@MathletePearce
tapintoteenminds.com
kylep.ca/dvc

Math
@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

Two Groups of Students
Good at
Math
Not
Good at
Math

Good at
Math
Not
Good at
Math
Know:

Good at
Math
Not
Good at
Math
Know:
terminology

Good at
Math
Not
Good at
Math
Know:
terminology
procedures

Good at
Math
Not
Good at
Math
Know: Know:
terminology
procedures
terminology
procedures

Good at
Math
Not
Good at
Math
Struggle with
unfamiliar
problems

Can
Memorize
Cannot
Memorize

A VISION FOR
MATHEMATICS
EDUCATION
VISION

VISION

1. Contextual
VISION

2. Visual and Concrete
1. Contextual
VISION

3. Interconnected
1. Contextual
VISION

3. Interconnected
1. Contextual
Conﬁdence

3. Interconnected
1. Contextual
Perception

3. Interconnected
1. Contextual
Student Success

4-Part Math Lesson
3

1.
Minds On
-Part Math Lesson4

Minds On Inquiry1.
2.
-Part Math Lesson4

Minds On Inquiry1.
2.
3. Connections
-Part Math Lesson4

Connections
Minds On
Consolidate
Inquiry1.
2.
3. 4.
-Part Math Lesson4

How many packs of paper would
it take to reach the ceiling?
Stacking Paper
273cm
4.95cm

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?

ORIGINAL QUESTION
he need to reach the ceiling?FUN, RIGHT?
AnswerKey:55.15

ORIGINAL QUESTION
AnswerKey: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:
AnswerKey:55.15

ACT 3:

Deconstructing the Task
4.95cm

Deconstructing the Task
4.95cm
273cm
4.95cm

How many packs of paper would it
take to reach the ceiling?
Previous Day
273 cm
4.95 cm

Previous Day
273 cm
4.95 cm
= 55.15
How many packs of
paper will it take to reach
a height of 273 cm?

How many packs of paper
will it take to reach a
height of 273 cm?
packs of paper
height

How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent

0 0

0 0
1 4.95

0 0
1 4.95
2 9.9

0 0
1 4.95
2 9.9
… …

packs of paperheight :

packs of paper
height
4.95cm

packs of paper
height4.95 cm
1 pack
273cm
How many

4.95 cm
1 pack
=
273 cm
How many?
x

4.95 cm
1 pack
=
273 cm
How many?x

4.95 cm
1 pack
=
273 cm
How many?x
x ?

4.95 cm
1 pack
=
273 cm
How many?x
x 55.15

4.95 cm
1 pack
=
273 cm
How many?x
x 55.15
x ?

4.95 cm
1 pack
=
273 cm
How many?x
x 55.15
x 55.15

4.95 cm
1 pack
=
273 cm
How many?55.15
x 55.15
x 55.15
packs

1. Minds On
-Part Math Lesson4

-Part Math Lesson4
1. Minds On 2. Inquiry

-Part Math Lesson4
3. Connections

-Part Math Lesson4
3. Connections 4. Consolidate

1. Minds On

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

How many ‘thick’ packs of paper
would it take to reach the ceiling?
1. Minds On
6cm

How many ‘thick’ packs of
paper would it take to reach
the ceiling?
1. Minds On
6cm

4. Consolidate3. Connections
2. Inquiry1. Minds On
-Part Math Lesson4

2. Inquiry

2. Inquiry
How tall is the table?

2. Inquiry

3. Connections

3. Connections130.75cm

How tall is the table?130.75cm

5
packs130.75 5

5
packs
5
130.75

5
packs
130.755

5
packs
130.755 )x y
(

5
packs
130.755( )x y
Slope

3. Connections

4. Consolidate

The Next Day…

The Next Day…
How tall is
this table?

The Next Day…
How tall is
this table?
142.75cm

The Next Day…
How tall is
this table?
142.75cm
100.75cm

The Next Day…
How tall is
this table?
142.75cm
100.75cm
6cm

142.75cm
100.75cm
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
4. Consolidate3. Connections
2. Inquiry1. Minds On
-Part Math Lesson4

Share…

Questions?

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