otf connect webinar - exploring proportional reasoning through a 4-part math lesson
TRANSCRIPT
Exploring Proportional Reasoning Through a 4-Part Math Lesson
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Class
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Math Class
1. Take Up Homework
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Math Class
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2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class
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3. Examples
2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class
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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.
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.
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Result
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Two Groups of Students
Result
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Two Groups of Students
Good atMath
NotGood at
Math
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Two Groups of Students
Good atMath
NotGood at
Math
Know:
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Two Groups of Students
Good atMath
NotGood at
Math
Know:terminology
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Two Groups of Students
Good atMath
NotGood at
Math
Know:terminology
procedures
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Two Groups of Students
Good atMath
NotGood at
Math
Know: Know:terminology
procedures
terminology
procedures
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Two Groups of Students
Good atMath
NotGood at
Math
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Two Groups of Students
Good atMath
NotGood at
Math
Struggle withunfamiliarproblems
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Two Groups of Students
Good atMath
NotGood at
Math
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Two Groups of Students
CanMemorize
CannotMemorize
A VISION FOR MATHEMATICS
EDUCATION
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A VISION FOR MATHEMATICS
EDUCATION
VISION
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VISION
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1. Contextual
VISION
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2. Visual and Concrete1. Contextual
VISION
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3. Interconnected2. Visual and Concrete1. Contextual
VISION
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3. Interconnected
1. Contextual
2. Visual and Concrete
ConfidencePerception
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3. Interconnected
1. Contextual
2. Visual and Concrete
PerceptionStudent Success
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3. Interconnected
1. Contextual
2. Visual and Concrete
Student Success
4 -Part Math Lesson
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3
Inquiry
Consolidation
Inquiry 1.
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Minds On
Consolidation
-Part Math Lesson4
Minds On Inquiry1.
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2.
Consolidation
-Part Math Lesson4
Minds On
Consolidate
Inquiry1.
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2.
3. Connections
-Part Math Lesson4
Connections
Minds On
Consolidate
Inquiry1.
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2.
3. 4.
-Part Math Lesson4
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-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
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Stacking Paper - Act 3
ORIGINAL QUESTION
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ORIGINAL QUESTION
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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
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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: 55.15
ORIGINAL QUESTION
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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
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 1:
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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 1:
ACT 2:
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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:
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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
ACT 3:
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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?
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-Part Math Lesson
How many packs of paper would it take to reach the ceiling?
3. Connections
Deconstructing the Task
4.95
cm
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-Part Math Lesson
How many packs of paper would it take to reach the ceiling?
3. Connections
Deconstructing the Task
4.95
cm
273
cm
4.95
cm
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-Part Math LessonHow many packs of paper would it
take to reach the ceiling?
4. Consolidate3. Connections
2. Inquiry
Previous Day
273 cm
4.95 cm
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-Part Math LessonHow many packs of paper would it
take to reach the ceiling?
4. Consolidate3. Connections
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?
How many packs of paper would it take to reach the ceiling?
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-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
How many packs of paper would it take to reach the ceiling?
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-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
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 0
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.95
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.952 9.9
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.952 9.9… …
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquirypacks of paper height
Independent Dependent
0 01 4.952 9.9… …
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry
packs of paperheight :
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry
packs of paper
height
4.95
cm
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry
packs of paper
height4.95 cm
1 pack
273
cm
How many
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
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-Part Math LessonHow many packs of paper will it take
to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
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-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x ?
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-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x 55.15
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-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x 55.15
x ?
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-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?x
x 55.15
x 55.15
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-Part Math Lesson How many packs of paper will it take to reach a height of 273 cm?
4. Consolidate3. Connections
2. Inquiry4.95 cm
1 pack= 273 cm
How many?55.15
x 55.15
x 55.15packs
4 -Part Math Lesson
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3
2. Inquiry
4. Consolidation
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1. Minds On
-Part Math Lesson42. Inquiry
4. Consolidation
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-Part Math Lesson41. Minds On 2. Inquiry
4. Consolidate
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-Part Math Lesson41. Minds On 2. Inquiry
3. Connections4. Consolidate
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-Part Math Lesson41. Minds On 2. Inquiry
3. Connections 4. Consolidate
Consolidate
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-Part Math Lesson
1. Minds On
1. Minds On
Consolidate
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-Part Math Lesson
Consolidate
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-Part Math Lesson
How many ‘thick’ packs of paper would it take to reach the ceiling?
1. Minds On
Consolidate
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-Part Math Lesson
How many ‘thick’ packs of paper would it take to reach the ceiling?
1. Minds On6
cm
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-Part Math Lesson
How many ‘thick’ packs of paper would it take to reach
the ceiling?
1. Minds On6
cm
4. Consolidate3. Connections
2. Inquiry
4. Consolidate3. Connections
2. Inquiry1. Minds On
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-Part Math Lesson4
How many ‘thick’ packs of paper would it take to reach the ceiling?
2. Inquiry
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-Part Math Lesson
4. Consolidate
2. Inquiry
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-Part Math Lesson
How tall is the table?
4. Consolidate
Minds On
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-Part Math LessonHow tall is the table?
2. Inquiry
Minds On
Inquiry2. -Part Math Lesson
4. Consolidate3. Connections
2. Inquiry1. Minds On
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-Part Math Lesson4
Minds On
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-Part Math Lesson
3. Connections
Minds On
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-Part Math LessonHow tall is the table?
3. Connections13
0.7
5 c
m
Minds On
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-Part Math LessonHow tall is the table?13
0.7
5 c
m
packs of paper heightIndependent Dependent
Minds On
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-Part Math LessonHow tall is the table?13
0.7
5 c
m
packs of paper heightIndependent Dependent
5packs13
0.7
55
Minds On
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-Part Math LessonHow tall is the table?13
0.7
5 c
m
packs of paper heightIndependent Dependent
5packs
5
130
.75
Minds On
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-Part Math LessonHow tall is the table?13
0.7
5 c
m
packs of paper heightIndependent Dependent
5packs
130.755
Minds On
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-Part Math LessonHow tall is the table?13
0.7
5 c
m
packs of paper heightIndependent Dependent
5packs
130.755 )x y(
Minds On
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-Part Math LessonHow tall is the table?13
0.7
5 c
m
packs of paper heightIndependent Dependent
5packs
130.755( )x ySlope
3. Connections
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4. Consolidate3. Connections
2. Inquiry1. Minds On
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-Part Math Lesson4
4. Consolidate
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4. Consolidate
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4. Consolidate3. Connections
2. Inquiry1. Minds On
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-Part Math Lesson4
GoodNotes 4
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The Next Day…
GoodNotes 4
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The Next Day…
GoodNotes 4
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The Next Day…
GoodNotes 4
How tall is this table?
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The Next Day…
GoodNotes 4
How tall is this table?
142
.75
cm
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The Next Day…
GoodNotes 4
How tall is this table?
142
.75
cm
100
.75
cm
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The Next Day…
GoodNotes 4
How tall is this table?
142
.75
cm
100
.75
cm
6 c
m
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
142
.75
cm
100
.75
cm
Equations Given 2 Points
Your Turn…
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Your Turn…
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Think of an example involving proportional reasoning that you could introduce using context and visuals.
Your Turn…
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Think of an example involving proportional reasoning that you could introduce using context and visuals.
ratios rates fractions percentagesunit rates
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Think of an example involving proportional reasoning that you could introduce using context and visuals.
ratios rates fractions percentagesunit rates
4. Consolidate3. Connections
2. Inquiry1. Minds On -Part Math Lesson4
Share…
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Questions?
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