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# SERCC - Making Math Contextual, Visual and Concrete

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SERCC Conference Meeting in London, Ontario. Thursday November 10th, 2016.

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### SERCC - Making Math Contextual, Visual and Concrete

1. 1. Making Math Contextual, Visual, and Concrete in Grade 7-12 @MathletePearcewww.tapintoteenminds.com
2. 2. @MathletePearcewww.tapintoteenminds.com Making Math Contextual, Visual, and Concrete in Grade 7-12
3. 3. @MathletePearcewww.tapintoteenminds.com PROBLEM
4. 4. @MathletePearcewww.tapintoteenminds.com
5. 5. @MathletePearcewww.tapintoteenminds.com
6. 6. ENGAGED YET? @MathletePearcewww.tapintoteenminds.com
7. 7. @MathletePearcewww.tapintoteenminds.com ENGAGEMENT “There are several types/categories of engagement – academic, cognitive, intellectual, institutional, emotional, behavioural, social, psychological, to name a few.” Parsons, J., & Taylor, L. (2011). Student Engagement: What do we know and what should we do? University Partners (pp 3). University of Alberta.
8. 8. @MathletePearcewww.tapintoteenminds.com
9. 9. @MathletePearcewww.tapintoteenminds.com Math Class
10. 10. @MathletePearcewww.tapintoteenminds.com Math Class
11. 11. 1. Take Up Homework @MathletePearcewww.tapintoteenminds.com Math Class
12. 12. @MathletePearcewww.tapintoteenminds.com 2. Deﬁnitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
13. 13. @MathletePearcewww.tapintoteenminds.com 3. Examples 2. Deﬁnitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
14. 14. @MathletePearcewww.tapintoteenminds.com 4. Homework 3. Examples 2. Deﬁnitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
15. 15. Example 1 (a) List all combinations of three out of the four colours: red, blue, white, and green.
16. 16. @MathletePearcewww.tapintoteenminds.com My Result: Successful in Math Unsuccessful in Math
17. 17. @MathletePearcewww.tapintoteenminds.com A Perception Develops Good at Math Poor at Math
18. 18. @MathletePearcewww.tapintoteenminds.com Conﬁdent in Math Class Doubtful in Math Class Students Feel…
19. 19. @MathletePearcewww.tapintoteenminds.com Enjoying Mathematics Disliking Mathematics This May Lead To…
20. 20. @MathletePearcewww.tapintoteenminds.com Willingness to Engage In Math Class Unwillingness to Engage In Math Class This May Lead To…
22. 22. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
23. 23. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
24. 24. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
25. 25. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Struggle with unfamiliar problems Good at Math Poor at Math
26. 26. @MathletePearcewww.tapintoteenminds.com A VISION FOR MATHEMATICS EDUCATION VISION
27. 27. @MathletePearcewww.tapintoteenminds.com Contextual VISION
28. 28. @MathletePearcewww.tapintoteenminds.com Visual and Concrete Contextual VISION
29. 29. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual VISION
30. 30. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual CONFIDENCE
31. 31. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual PERCEPTION
32. 32. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual STUDENT SUCCESS
33. 33. Change @MathletePearcewww.tapintoteenminds.com
34. 34. Change @MathletePearcewww.tapintoteenminds.com
35. 35. Change @MathletePearcewww.tapintoteenminds.com Immune to
36. 36. http://www.vancouversun.com/life/From+geek+chic/6296707/story.html Photograph by: Maggie Wong @MathletePearcewww.tapintoteenminds.com
37. 37. @MathletePearcewww.tapintoteenminds.com https://mathstrategies.wordpress.com/tag/numb3rs/
38. 38. http://www.wykamath.com/
39. 39. entertainment engagement = @MathletePearcewww.tapintoteenminds.com
40. 40. @MathletePearcewww.tapintoteenminds.com algorithm
41. 41. what’s this?
42. 42. @MathletePearcewww.tapintoteenminds.com
43. 43. @MathletePearcewww.tapintoteenminds.com
44. 44. @MathletePearcewww.tapintoteenminds.com
45. 45. @MathletePearcewww.tapintoteenminds.com
46. 46. @MathletePearcewww.tapintoteenminds.com
47. 47. algorithm @MathletePearcewww.tapintoteenminds.com
48. 48. algorithms engagement = @MathletePearcewww.tapintoteenminds.com
49. 49. algorithms engagement = understanding or @MathletePearcewww.tapintoteenminds.com
50. 50. Notice? Wonder?
51. 51. How many packs of paper would it take to reach the ceiling? OUR FIRST QUESTION:
52. 52. @MathletePearcewww.tapintoteenminds.com PREDICTIONS
53. 53. @MathletePearcewww.tapintoteenminds.com REQUEST INFORMATION
54. 54. @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? height 273cm 24.75cm
55. 55. QUESTION @MathletePearcewww.tapintoteenminds.com
56. 56. 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?
57. 57. 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?
58. 58. AnswerKey:55.15 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?
59. 59. Making Connections @MathletePearcewww.tapintoteenminds.com
60. 60. @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? height 273cm 24.75cm
61. 61. @MathletePearcewww.tapintoteenminds.com 273cm 24.75cm = 24.75cm24.75cm
62. 62. @MathletePearcewww.tapintoteenminds.com 273cm = 24.75cm 24.75cm 24.75cm
63. 63. @MathletePearcewww.tapintoteenminds.com 273cm = 24.75cm 24.75cm 24.75cm
64. 64. @MathletePearcewww.tapintoteenminds.com 273cm = 25cm 25cm 25cm Friendly Numbers
65. 65. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm 25cm Friendly Numbers
66. 66. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm 25 cm Friendly Numbers Height
67. 67. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 50 cm
68. 68. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 75 cm
69. 69. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 25 cm 100 cm
70. 70. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 25 cm 200 cm 25 cm 25 cm 25 cm 25 cm
71. 71. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 100 cm Height 300 cm 100 cm 100 cm
72. 72. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 100 cm Height 275 cm 100 cm 75 cm
73. 73. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 100 cm Height 275 cm 100 cm 75 cm
74. 74. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers “Array”
75. 75. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers Area Model
76. 76. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groupsArea Model
77. 77. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs Area Model
78. 78. 5packs 11 groups @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs Area Model
79. 79. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs 25cm 11 groups Area ModelDouble
80. 80. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs 25cm 11 groups 275 cm Area ModelDouble
81. 81. @MathletePearcewww.tapintoteenminds.com 275cm 25cm Friendly Numbers Double Number Line
82. 82. Friendly Numbers Double Number Line 275cm 25cm 0 0
83. 83. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height
84. 84. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 Number of Packs Total Height
85. 85. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height
86. 86. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 75 15 250 50 Number of Packs Total Height 20 100 125 25 150 30 35 175 200 40 225 45 55 275
87. 87. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height
88. 88. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100
89. 89. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100 200 40
90. 90. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100 200 40 250 50 225 45 55 275
91. 91. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100 200 40 250 50 225 45 55 275275 5 25
92. 92. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25
93. 93. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x5 25 5 ?x 27525
94. 94. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 ?x = 11111111
95. 95. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 x = 1111 11 11
96. 96. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 x = 11 11 11 x 11
97. 97. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 x = 11 11 11 x 11x = 5555
98. 98. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 275 5 25 5 25 x = 11 11 11 x 11x = 55 55
99. 99. 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 273cm 4.95 cm
100. 100. 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 273cm 4.95 cm
101. 101. @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent 273cm 4.95 cm
102. 102. @MathletePearcewww.tapintoteenminds.com 0 0 packs of paper height Independent Dependent
103. 103. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 packs of paper height Independent Dependent
104. 104. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent
105. 105. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8
106. 106. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8 40 198
107. 107. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8 40 198
108. 108. @MathletePearcewww.tapintoteenminds.com packs of paper height:
109. 109. @MathletePearcewww.tapintoteenminds.com packs of paper height
110. 110. @MathletePearcewww.tapintoteenminds.com packs of paper height 24.75 cm 5 reams =
111. 111. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm How Many?
112. 112. @MathletePearcewww.tapintoteenminds.com 5 reams = x 24.75 cm 273 cm x ??
113. 113. @MathletePearcewww.tapintoteenminds.com 5 reams = x 24.75 cm 273 cm x ??
114. 114. @MathletePearcewww.tapintoteenminds.com 5 reams = x24.75 cm 273 cm x ??
115. 115. @MathletePearcewww.tapintoteenminds.com 5 reams = x24.75 cm 273 cm x ?? 11.03
116. 116. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm 11.03x x
117. 117. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm 55.15 reams 11.03 x 11.03 x
118. 118. @MathletePearcewww.tapintoteenminds.com VISION Visual and Concrete Contextual TASKS
119. 119. Visual and Concrete Contextual TASKS INQUIRY Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
120. 120. Connect to Prior Knowledge Visual and Concrete Contextual TASKS CONNECTIONS INQUIRY Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
121. 121. Visual and Concrete Contextual TASKS CONSOLIDATE INQUIRY Move Towards Procedural Fluency Connect to Prior Knowledge CONNECTIONS Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
122. 122. 3 Act Math Tasks iTunes U kylep.ca/curiousmath1p @MathletePearcewww.tapintoteenminds.com
123. 123. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
124. 124. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
125. 125. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com Tap
126. 126. 3 Act Math Tasks tapintoteenminds.com/3act-math @MathletePearcewww.tapintoteenminds.com ﬁshing4tech.com/mtbos.html
127. 127. @MathletePearcewww.tapintoteenminds.com The CN Tower has a height of 553 m and your stack of 5 packages of paper have a height of approximately 0.25 m. Approximately how many packages of paper would you need to stack up to the height of the CN Tower? 24.75cm