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

Ontario Teachers Federation (OTF) Connect Webinar - Exploring Proportional Reasoning Through a 4-Part Math Lesson Slide Deck.
Delivered on February 2nd, 2015 via webinar.

Ontario Teachers Federation (OTF) Connect Webinar - Exploring Proportional Reasoning Through a 4-Part Math Lesson Slide Deck.
Delivered on February 2nd, 2015 via webinar.

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

1. 1. Exploring Proportional Reasoning Through a 4-Part Math Lesson @MathletePearce tapintoteenminds.com kylep.ca/dvc
2. 2. Math @MathletePearcewww.tapintoteenminds.com
3. 3. @MathletePearcewww.tapintoteenminds.com Math Class
4. 4. 1. Take Up Homework @MathletePearcewww.tapintoteenminds.com Math Class
5. 5. @MathletePearcewww.tapintoteenminds.com 2. Deﬁnitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
6. 6. @MathletePearcewww.tapintoteenminds.com 3. Examples 2. Deﬁnitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
7. 7. @MathletePearcewww.tapintoteenminds.com 4. Homework 3. Examples 2. Deﬁnitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
8. 8. Example 1 (a) List all combinations of three out of the four colours: red, blue, white, and green.
9. 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. 10. @MathletePearcewww.tapintoteenminds.com Result
11. 11. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Result
12. 12. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math
13. 13. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math Know:
14. 14. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math Know: terminology
15. 15. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math Know: terminology procedures
16. 16. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math Know: Know: terminology procedures terminology procedures
17. 17. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math
18. 18. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math Struggle with unfamiliar problems
19. 19. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math
20. 20. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Can Memorize Cannot Memorize
21. 21. @MathletePearcewww.tapintoteenminds.com A VISION FOR MATHEMATICS EDUCATION VISION
22. 22. @MathletePearcewww.tapintoteenminds.com VISION
23. 23. @MathletePearcewww.tapintoteenminds.com 1. Contextual VISION
24. 24. @MathletePearcewww.tapintoteenminds.com 2. Visual and Concrete 1. Contextual VISION
25. 25. @MathletePearcewww.tapintoteenminds.com 3. Interconnected 2. Visual and Concrete 1. Contextual VISION
26. 26. @MathletePearcewww.tapintoteenminds.com 3. Interconnected 1. Contextual 2. Visual and Concrete Conﬁdence
27. 27. @MathletePearcewww.tapintoteenminds.com 3. Interconnected 1. Contextual 2. Visual and Concrete Perception
28. 28. @MathletePearcewww.tapintoteenminds.com 3. Interconnected 1. Contextual 2. Visual and Concrete Student Success
29. 29. 4-Part Math Lesson @MathletePearcewww.tapintoteenminds.com 3
30. 30. 1. @MathletePearcewww.tapintoteenminds.com Minds On -Part Math Lesson4
31. 31. Minds On Inquiry1. @MathletePearcewww.tapintoteenminds.com 2. -Part Math Lesson4
32. 32. Minds On Inquiry1. @MathletePearcewww.tapintoteenminds.com 2. 3. Connections -Part Math Lesson4
33. 33. Connections Minds On Consolidate Inquiry1. @MathletePearcewww.tapintoteenminds.com 2. 3. 4. -Part Math Lesson4
34. 34. @MathletePearcewww.tapintoteenminds.com
35. 35. @MathletePearcewww.tapintoteenminds.com How many packs of paper would it take to reach the ceiling? Stacking Paper 273cm 4.95cm
36. 36. @MathletePearcewww.tapintoteenminds.com Stacking Paper - Act 3
37. 37. ORIGINAL QUESTION @MathletePearcewww.tapintoteenminds.com
38. 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. 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. 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. 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. 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. 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. 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. 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. 46. @MathletePearcewww.tapintoteenminds.com How many packs of paper would it take to reach the ceiling? Deconstructing the Task 4.95cm
47. 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. 48. @MathletePearcewww.tapintoteenminds.com How many packs of paper would it take to reach the ceiling? Previous Day 273 cm 4.95 cm
49. 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. 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. 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. 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. 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. 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. 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. 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. 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. 58. @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? packs of paperheight :
59. 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. 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. 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. 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. 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. 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. 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. 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. 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. 68. 4-Part Math Lesson @MathletePearcewww.tapintoteenminds.com 3
69. 69. @MathletePearcewww.tapintoteenminds.com 1. Minds On -Part Math Lesson4
70. 70. @MathletePearcewww.tapintoteenminds.com -Part Math Lesson4 1. Minds On 2. Inquiry
71. 71. @MathletePearcewww.tapintoteenminds.com -Part Math Lesson4 1. Minds On 2. Inquiry 3. Connections
72. 72. @MathletePearcewww.tapintoteenminds.com -Part Math Lesson4 1. Minds On 2. Inquiry 3. Connections 4. Consolidate
73. 73. @MathletePearcewww.tapintoteenminds.com 1. Minds On
74. 74. 1. Minds On @MathletePearcewww.tapintoteenminds.com
75. 75. @MathletePearcewww.tapintoteenminds.com How many ‘thick’ packs of paper would it take to reach the ceiling? 1. Minds On
76. 76. @MathletePearcewww.tapintoteenminds.com How many ‘thick’ packs of paper would it take to reach the ceiling? 1. Minds On 6cm
77. 77. @MathletePearcewww.tapintoteenminds.com How many ‘thick’ packs of paper would it take to reach the ceiling? 1. Minds On 6cm
78. 78. 4. Consolidate3. Connections 2. Inquiry1. Minds On @MathletePearcewww.tapintoteenminds.com -Part Math Lesson4
79. 79. 2. Inquiry @MathletePearcewww.tapintoteenminds.com
80. 80. 2. Inquiry @MathletePearcewww.tapintoteenminds.com How tall is the table?
81. 81. @MathletePearcewww.tapintoteenminds.com How tall is the table? 2. Inquiry
82. 82. Inquiry2.
83. 83. 4. Consolidate3. Connections 2. Inquiry1. Minds On @MathletePearcewww.tapintoteenminds.com -Part Math Lesson4
84. 84. @MathletePearcewww.tapintoteenminds.com 3. Connections
85. 85. @MathletePearcewww.tapintoteenminds.com How tall is the table? 3. Connections130.75cm
86. 86. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent
87. 87. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent 5 packs130.75 5
88. 88. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent 5 packs 5 130.75
89. 89. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent 5 packs 130.755
90. 90. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent 5 packs 130.755 )x y (
91. 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. 92. 3. Connections @MathletePearcewww.tapintoteenminds.com
93. 93. 4. Consolidate3. Connections 2. Inquiry1. Minds On @MathletePearcewww.tapintoteenminds.com -Part Math Lesson4
94. 94. 4. Consolidate @MathletePearcewww.tapintoteenminds.com
95. 95. 4. Consolidate @MathletePearcewww.tapintoteenminds.com
96. 96. 4. Consolidate3. Connections 2. Inquiry1. Minds On @MathletePearcewww.tapintoteenminds.com -Part Math Lesson4
97. 97. @MathletePearcewww.tapintoteenminds.com The Next Day…
98. 98. @MathletePearcewww.tapintoteenminds.com The Next Day…
99. 99. @MathletePearcewww.tapintoteenminds.com The Next Day… How tall is this table?
100. 100. @MathletePearcewww.tapintoteenminds.com The Next Day… How tall is this table? 142.75cm
101. 101. @MathletePearcewww.tapintoteenminds.com The Next Day… How tall is this table? 142.75cm 100.75cm
102. 102. @MathletePearcewww.tapintoteenminds.com The Next Day… How tall is this table? 142.75cm 100.75cm 6cm
103. 103. 142.75cm 100.75cm Equations Given 2 Points
104. 104. 142.75cm 100.75cm Equations Given 2 Points
105. 105. 142.75cm 100.75cm Equations Given 2 Points
106. 106. 142.75cm 100.75cm Equations Given 2 Points
107. 107. 142.75cm 100.75cm Equations Given 2 Points