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Pine Ridge Mathematics Association Social Night - Making Math Contextual, Visual and Concrete

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Making Mathematics Contextual, Visual and Concrete with Kyle Pearce at Pine Ridge Math Association (PRMA) Social Night. November 24th, 2016.

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Pine Ridge Mathematics Association Social Night - Making Math Contextual, Visual and Concrete

  1. 1. Making Math Contextual, Visual, and Concrete @MathletePearcewww.tapintoteenminds.com tapintoteenminds.com/prma
  2. 2. @MathletePearcewww.tapintoteenminds.com Making Math Contextual, Visual, and Concrete tapintoteenminds.com/prma
  3. 3. @MathletePearcewww.tapintoteenminds.com PROBLEM
  4. 4. @MathletePearcewww.tapintoteenminds.com
  5. 5. ENGAGED YET? @MathletePearcewww.tapintoteenminds.com
  6. 6. @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.
  7. 7. @MathletePearcewww.tapintoteenminds.com
  8. 8. @MathletePearcewww.tapintoteenminds.com Math Class
  9. 9. @MathletePearcewww.tapintoteenminds.com Math Class
  10. 10. 1. Take Up Homework @MathletePearcewww.tapintoteenminds.com Math Class
  11. 11. @MathletePearcewww.tapintoteenminds.com 2. Definitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
  12. 12. @MathletePearcewww.tapintoteenminds.com 3. Examples 2. Definitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
  13. 13. @MathletePearcewww.tapintoteenminds.com 4. Homework 3. Examples 2. Definitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
  14. 14. Example 1 (a) List all combinations of three out of the four colours: red, blue, white, and green.
  15. 15. @MathletePearcewww.tapintoteenminds.com My Result: Successful in Math Unsuccessful in Math
  16. 16. @MathletePearcewww.tapintoteenminds.com A Perception Develops Good at Math Poor at Math
  17. 17. @MathletePearcewww.tapintoteenminds.com Confident in Math Class Doubtful in Math Class Students Feel…
  18. 18. @MathletePearcewww.tapintoteenminds.com Enjoying Mathematics Disliking Mathematics This May Lead To…
  19. 19. @MathletePearcewww.tapintoteenminds.com Willingness to Engage In Math Class Unwillingness to Engage In Math Class This May Lead To…
  20. 20. @MathletePearcewww.tapintoteenminds.com Moving Ahead Falling Behind This May Lead To…
  21. 21. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
  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 Struggle with unfamiliar problems Good at Math Poor at Math
  25. 25. @MathletePearcewww.tapintoteenminds.com A VISION FOR MATHEMATICS EDUCATION VISION
  26. 26. @MathletePearcewww.tapintoteenminds.com Contextual VISION
  27. 27. @MathletePearcewww.tapintoteenminds.com Visual and Concrete Contextual VISION
  28. 28. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual VISION
  29. 29. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual CONFIDENCE
  30. 30. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual PERCEPTION
  31. 31. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual STUDENT SUCCESS
  32. 32. Change @MathletePearcewww.tapintoteenminds.com
  33. 33. Change @MathletePearcewww.tapintoteenminds.com
  34. 34. Change @MathletePearcewww.tapintoteenminds.com Immune to
  35. 35. http://www.vancouversun.com/life/From+geek+chic/6296707/story.html Photograph by: Maggie Wong @MathletePearcewww.tapintoteenminds.com
  36. 36. @MathletePearcewww.tapintoteenminds.com https://mathstrategies.wordpress.com/tag/numb3rs/
  37. 37. http://www.wykamath.com/
  38. 38. entertainment engagement = @MathletePearcewww.tapintoteenminds.com
  39. 39. @MathletePearcewww.tapintoteenminds.com algorithm
  40. 40. what’s this?
  41. 41. @MathletePearcewww.tapintoteenminds.com
  42. 42. @MathletePearcewww.tapintoteenminds.com
  43. 43. @MathletePearcewww.tapintoteenminds.com
  44. 44. @MathletePearcewww.tapintoteenminds.com
  45. 45. @MathletePearcewww.tapintoteenminds.com
  46. 46. algorithm @MathletePearcewww.tapintoteenminds.com
  47. 47. algorithms engagement = @MathletePearcewww.tapintoteenminds.com
  48. 48. algorithms engagement = understanding or @MathletePearcewww.tapintoteenminds.com
  49. 49. @MathletePearcewww.tapintoteenminds.com playkh.complaykh.comGo to:
  50. 50. @MathletePearcewww.tapintoteenminds.com wiz623
  51. 51. Notice? Wonder?
  52. 52. How many packs of paper would it take to reach the ceiling? OUR FIRST QUESTION:
  53. 53. @MathletePearcewww.tapintoteenminds.com PREDICTIONS wiz623
  54. 54. @MathletePearcewww.tapintoteenminds.com REQUEST INFORMATION
  55. 55. @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? height 273cm 24.75cm wiz623
  56. 56. QUESTION @MathletePearcewww.tapintoteenminds.com
  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?
  58. 58. 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?
  59. 59. 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?
  60. 60. Making Connections @MathletePearcewww.tapintoteenminds.com
  61. 61. @MathletePearcewww.tapintoteenminds.com How many packs of paper will it take to reach a height of 273 cm? height 273cm 24.75cm
  62. 62. @MathletePearcewww.tapintoteenminds.com 273cm 24.75cm = 24.75cm24.75cm
  63. 63. @MathletePearcewww.tapintoteenminds.com 273cm = 24.75cm 24.75cm 24.75cm
  64. 64. @MathletePearcewww.tapintoteenminds.com 273cm = 24.75cm 24.75cm 24.75cm
  65. 65. @MathletePearcewww.tapintoteenminds.com 273cm = 25cm 25cm 25cm Friendly Numbers
  66. 66. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm 25cm Friendly Numbers
  67. 67. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm 25 cm Friendly Numbers Height
  68. 68. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 50 cm
  69. 69. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 75 cm
  70. 70. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 25 cm 25 cm Height 25 cm 25 cm 100 cm
  71. 71. @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
  72. 72. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 100 cm Height 300 cm 100 cm 100 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 100 cm Height 275 cm 100 cm 75 cm
  75. 75. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers “Array”
  76. 76. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers Area Model
  77. 77. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groupsArea Model
  78. 78. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs Area Model
  79. 79. 5packs 11 groups @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs Area Model
  80. 80. @MathletePearcewww.tapintoteenminds.com 275cm = 25cm 25cm Friendly Numbers 5packs 11 groups 55 packs 5packs 11 groups 55 packs 25cm 11 groups Area ModelDouble
  81. 81. @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
  82. 82. @MathletePearcewww.tapintoteenminds.com 275cm 25cm Friendly Numbers Double Number Line
  83. 83. Friendly Numbers Double Number Line 275cm 25cm 0 0
  84. 84. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height
  85. 85. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 Number of Packs Total Height
  86. 86. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height
  87. 87. 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
  88. 88. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height
  89. 89. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100
  90. 90. Friendly Numbers Double Number Line 275cm 25cm 0 0 5 25 50 10 Number of Packs Total Height 20 100 200 40
  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 55 275
  92. 92. 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
  93. 93. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25
  94. 94. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x5 25 5 ?x 27525
  95. 95. Friendly Numbers Double Number Line 275cm 25cm 0 0 Number of Packs Total Height 275 x 275 5 25 5 25 ?x = 11111111
  96. 96. 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
  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 11
  98. 98. 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
  99. 99. 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
  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. 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
  102. 102. @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent 273cm 4.95 cm
  103. 103. @MathletePearcewww.tapintoteenminds.com 0 0 packs of paper height Independent Dependent
  104. 104. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 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
  106. 106. @MathletePearcewww.tapintoteenminds.com 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8
  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 0 0 1 4.95 2 9.9 packs of paper height Independent Dependent 4 19.8 40 198
  109. 109. @MathletePearcewww.tapintoteenminds.com packs of paper height:
  110. 110. @MathletePearcewww.tapintoteenminds.com packs of paper height
  111. 111. @MathletePearcewww.tapintoteenminds.com packs of paper height 24.75 cm 5 reams =
  112. 112. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm How Many?
  113. 113. @MathletePearcewww.tapintoteenminds.com 5 reams = x 24.75 cm 273 cm x ??
  114. 114. @MathletePearcewww.tapintoteenminds.com 5 reams = x 24.75 cm 273 cm x ??
  115. 115. @MathletePearcewww.tapintoteenminds.com 5 reams = x24.75 cm 273 cm x ??
  116. 116. @MathletePearcewww.tapintoteenminds.com 5 reams = x24.75 cm 273 cm x ?? 11.03
  117. 117. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm 11.03x x
  118. 118. @MathletePearcewww.tapintoteenminds.com 24.75 cm 5 reams = 273 cm 55.15 reams 11.03 x 11.03 x
  119. 119. @MathletePearcewww.tapintoteenminds.com VISION Visual and Concrete Contextual TASKS
  120. 120. Visual and Concrete Contextual TASKS INQUIRY Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
  121. 121. Connect to Prior Knowledge Visual and Concrete Contextual TASKS CONNECTIONS INQUIRY Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
  122. 122. Visual and Concrete Contextual TASKS CONSOLIDATE INQUIRY Move Towards Procedural Fluency Connect to Prior Knowledge CONNECTIONS Construct Conceptual Understanding VISION @MathletePearcewww.tapintoteenminds.com
  123. 123. 3 Act Math Tasks iTunes U kylep.ca/curiousmath1p @MathletePearcewww.tapintoteenminds.com
  124. 124. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
  125. 125. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
  126. 126. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com Tap
  127. 127. 3 Act Math Tasks tapintoteenminds.com/3act-math @MathletePearcewww.tapintoteenminds.com fishing4tech.com/mtbos.html
  128. 128. @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 wiz623
  129. 129. Making Math Contextual, Visual, and Concrete @MathletePearcewww.tapintoteenminds.com tapintoteenminds.com/prma

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