1.
Exploring Proportional
Reasoning Through a
4-Part Math Lesson
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kylep.ca/dvc

2.
Math
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3.
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Math Class

4.
1. Take Up Homework
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Math Class

5.
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2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class

6.
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3. Examples
2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class

7.
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4. Homework
3. Examples
2. Definitions, Formulae, Procedures/Algorithms
1. Take Up Homework
Math Class

8.
Example 1
(a) List all combinations of three out of
the four colours: red, blue, white, and
green.

9.
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.

10.
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Result

11.
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Two Groups of
Students
Result

12.
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Two Groups of Students
Good at
Math
Not
Good at
Math

13.
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Two Groups of Students
Good at
Math
Not
Good at
Math
Know:

14.
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Two Groups of Students
Good at
Math
Not
Good at
Math
Know:
terminology

15.
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Two Groups of Students
Good at
Math
Not
Good at
Math
Know:
terminology
procedures

16.
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Two Groups of Students
Good at
Math
Not
Good at
Math
Know: Know:
terminology
procedures
terminology
procedures

17.
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Two Groups of Students
Good at
Math
Not
Good at
Math

18.
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Two Groups of Students
Good at
Math
Not
Good at
Math
Struggle with
unfamiliar
problems

19.
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Two Groups of Students
Good at
Math
Not
Good at
Math

20.
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Two Groups of Students
Can
Memorize
Cannot
Memorize

21.
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A VISION FOR
MATHEMATICS
EDUCATION
VISION

22.
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VISION

23.
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1. Contextual
VISION

24.
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2. Visual and Concrete
1. Contextual
VISION

25.
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3. Interconnected
2. Visual and Concrete
1. Contextual
VISION

26.
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3. Interconnected
1. Contextual
2. Visual and Concrete
Confidence

27.
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3. Interconnected
1. Contextual
2. Visual and Concrete
Perception

28.
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3. Interconnected
1. Contextual
2. Visual and Concrete
Student Success

29.
4-Part Math Lesson
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3

30.
1.
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Minds On
-Part Math Lesson4

31.
Minds On Inquiry1.
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2.
-Part Math Lesson4

32.
Minds On Inquiry1.
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2.
3. Connections
-Part Math Lesson4

33.
Connections
Minds On
Consolidate
Inquiry1.
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2.
3. 4.
-Part Math Lesson4

34.
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35.
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How many packs of paper would
it take to reach the ceiling?
Stacking Paper
273cm
4.95cm

36.
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Stacking Paper - Act 3

37.
ORIGINAL QUESTION
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38.
ORIGINAL QUESTION
@MathletePearcewww.tapintoteenminds.com
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?

39.
ORIGINAL QUESTION
@MathletePearcewww.tapintoteenminds.com
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?
AnswerKey:55.15

40.
ORIGINAL QUESTION
@MathletePearcewww.tapintoteenminds.com
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?
AnswerKey:55.15

41.
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:
@MathletePearcewww.tapintoteenminds.com

42.
@MathletePearcewww.tapintoteenminds.com
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:

43.
ACT 2:
@MathletePearcewww.tapintoteenminds.com
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?

44.
ACT 3:
@MathletePearcewww.tapintoteenminds.com
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?
AnswerKey:55.15

45.
ACT 3:
@MathletePearcewww.tapintoteenminds.com
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?

46.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper would
it take to reach the ceiling?
Deconstructing the Task
4.95cm

47.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper would
it take to reach the ceiling?
Deconstructing the Task
4.95cm
273cm
4.95cm

48.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper would it
take to reach the ceiling?
Previous Day
273 cm
4.95 cm

49.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper would it
take to reach the ceiling?
Previous Day
273 cm
4.95 cm
= 55.15
How many packs of
paper will it take to reach
a height of 273 cm?

50.
How many packs of paper would it
take to reach the ceiling?
@MathletePearcewww.tapintoteenminds.com
How many packs of paper
will it take to reach a
height of 273 cm?
packs of paper
height

51.
How many packs of paper would it
take to reach the ceiling?
@MathletePearcewww.tapintoteenminds.com
How many packs of paper
will it take to reach a
height of 273 cm?
packs of paper
height

52.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent

53.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent
0 0

54.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent
0 0
1 4.95

55.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent
0 0
1 4.95
2 9.9

56.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent
0 0
1 4.95
2 9.9
… …

57.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper height
Independent Dependent
0 0
1 4.95
2 9.9
… …

58.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paperheight :

59.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper
height
4.95cm

60.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
packs of paper
height4.95 cm
1 pack
273cm
How many

61.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
4.95 cm
1 pack
=
273 cm
How many?
x

62.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
4.95 cm
1 pack
=
273 cm
How many?x

63.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
4.95 cm
1 pack
=
273 cm
How many?x
x ?

64.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
4.95 cm
1 pack
=
273 cm
How many?x
x 55.15

65.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
4.95 cm
1 pack
=
273 cm
How many?x
x 55.15
x ?

66.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
4.95 cm
1 pack
=
273 cm
How many?x
x 55.15
x 55.15

67.
@MathletePearcewww.tapintoteenminds.com
How many packs of paper will it take
to reach a height of 273 cm?
4.95 cm
1 pack
=
273 cm
How many?55.15
x 55.15
x 55.15
packs

68.
4-Part Math Lesson
@MathletePearcewww.tapintoteenminds.com
3

69.
@MathletePearcewww.tapintoteenminds.com
1. Minds On
-Part Math Lesson4

70.
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4
1. Minds On 2. Inquiry

71.
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4
1. Minds On 2. Inquiry
3. Connections

72.
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4
1. Minds On 2. Inquiry
3. Connections 4. Consolidate

73.
@MathletePearcewww.tapintoteenminds.com
1. Minds On

74.
1. Minds On
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75.
@MathletePearcewww.tapintoteenminds.com
How many ‘thick’ packs of paper
would it take to reach the ceiling?
1. Minds On

76.
@MathletePearcewww.tapintoteenminds.com
How many ‘thick’ packs of paper
would it take to reach the ceiling?
1. Minds On
6cm

77.
@MathletePearcewww.tapintoteenminds.com
How many ‘thick’ packs of
paper would it take to reach
the ceiling?
1. Minds On
6cm

78.
4. Consolidate3. Connections
2. Inquiry1. Minds On
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-Part Math Lesson4

79.
2. Inquiry
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80.
2. Inquiry
@MathletePearcewww.tapintoteenminds.com
How tall is the table?

81.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?
2. Inquiry

82.
Inquiry2.

83.
4. Consolidate3. Connections
2. Inquiry1. Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4

84.
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3. Connections

85.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?
3. Connections130.75cm

86.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?130.75cm
packs of paper height
Independent Dependent

87.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?130.75cm
packs of paper height
Independent Dependent
5
packs130.75 5

88.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?130.75cm
packs of paper height
Independent Dependent
5
packs
5
130.75

89.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?130.75cm
packs of paper height
Independent Dependent
5
packs
130.755

90.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?130.75cm
packs of paper height
Independent Dependent
5
packs
130.755 )x y
(

91.
@MathletePearcewww.tapintoteenminds.com
How tall is the table?130.75cm
packs of paper height
Independent Dependent
5
packs
130.755( )x y
Slope

92.
3. Connections
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93.
4. Consolidate3. Connections
2. Inquiry1. Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4

94.
4. Consolidate
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95.
4. Consolidate
@MathletePearcewww.tapintoteenminds.com

96.
4. Consolidate3. Connections
2. Inquiry1. Minds On
@MathletePearcewww.tapintoteenminds.com
-Part Math Lesson4

97.
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The Next Day…

98.
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The Next Day…

99.
@MathletePearcewww.tapintoteenminds.com
The Next Day…
How tall is
this table?

100.
@MathletePearcewww.tapintoteenminds.com
The Next Day…
How tall is
this table?
142.75cm

101.
@MathletePearcewww.tapintoteenminds.com
The Next Day…
How tall is
this table?
142.75cm
100.75cm

102.
@MathletePearcewww.tapintoteenminds.com
The Next Day…
How tall is
this table?
142.75cm
100.75cm
6cm

103.
142.75cm
100.75cm
Equations Given 2 Points

104.
142.75cm
100.75cm
Equations Given 2 Points

105.
142.75cm
100.75cm
Equations Given 2 Points

106.
142.75cm
100.75cm
Equations Given 2 Points

107.
142.75cm
100.75cm
Equations Given 2 Points

108.
Your Turn…
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109.
Your Turn…
@MathletePearcewww.tapintoteenminds.com
Think of an example involving
proportional reasoning that you could
introduce using context and visuals.

110.
Your Turn…
@MathletePearcewww.tapintoteenminds.com
Think of an example involving
proportional reasoning that you could
introduce using context and visuals.
ratios rates fractions percentagesunit rates

111.
@MathletePearcewww.tapintoteenminds.com
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

112.
Share…
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113.
Questions?
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114.
Find More Like This:
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