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2016 05-25- HPEDSB Making Math Contextual, Visual and Concrete

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Making Math Contextual, Visual and Concrete Full Day Workshop with Hastings Prince Edward District School Board in Belleville, Ontario. Presentation took place in May 2016.

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  • That is so true. Knowing how to input algorithms is not the same as understanding. For many students, they miss the opportunity to refine and perfect their foundational mathematic skills because they do not truly understand the concepts. By having a deeper internalization of the these problems, why they occur, and how the overall relationship works, you will be able to perfect your understanding each and everyday. I haven't gotten through all of your presentation, but I am very impressed. Thank you for sharing.
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2016 05-25- HPEDSB Making Math Contextual, Visual and Concrete

  1. 1. Making Math Contextual, Visual, and Concrete @MathletePearcewww.tapintoteenminds.com
  2. 2. Making Math Contextual, Visual, and Concrete @MathletePearcewww.tapintoteenminds.com
  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 4. Homework 3. Examples 2. Definitions, Formulae, Procedures/Algorithms 1. Take Up Homework Math Class
  11. 11. Example 1 (a) List all combinations of three out of the four colours: red, blue, white, and green.
  12. 12. @MathletePearcewww.tapintoteenminds.com My Result: Successful in Math Unsuccessful in Math
  13. 13. @MathletePearcewww.tapintoteenminds.com A Perception Develops Good at Math Poor at Math
  14. 14. @MathletePearcewww.tapintoteenminds.com Confident in Math Class Doubtful in Math Class Students Feel…
  15. 15. @MathletePearcewww.tapintoteenminds.com Enjoying Mathematics Disliking Mathematics This May Lead To…
  16. 16. @MathletePearcewww.tapintoteenminds.com Willingness to Engage In Math Class Unwillingness to Engage In Math Class This May Lead To…
  17. 17. @MathletePearcewww.tapintoteenminds.com Moving Ahead Falling Behind This May Lead To…
  18. 18. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Poor at Math
  19. 19. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Struggle with unfamiliar problems Good at Math Poor at Math
  20. 20. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual VISION
  21. 21. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual CONFIDENCE
  22. 22. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual PERCEPTION
  23. 23. @MathletePearcewww.tapintoteenminds.com Interconnected Visual and Concrete Contextual STUDENT SUCCESS
  24. 24. Change @MathletePearcewww.tapintoteenminds.com Immune to
  25. 25. http://www.vancouversun.com/life/From+geek+chic/6296707/story.html Photograph by: Maggie Wong @MathletePearcewww.tapintoteenminds.com
  26. 26. @MathletePearcewww.tapintoteenminds.com https://mathstrategies.wordpress.com/tag/numb3rs/
  27. 27. http://www.wykamath.com/
  28. 28. entertainment engagement = @MathletePearcewww.tapintoteenminds.com
  29. 29. @MathletePearcewww.tapintoteenminds.com algorithm
  30. 30. what’s this?
  31. 31. @MathletePearcewww.tapintoteenminds.com
  32. 32. @MathletePearcewww.tapintoteenminds.com
  33. 33. algorithm @MathletePearcewww.tapintoteenminds.com
  34. 34. algorithms engagement = understanding or @MathletePearcewww.tapintoteenminds.com
  35. 35. LEARNING @MathletePearcewww.tapintoteenminds.com
  36. 36. NEWOLD PROGRESSIVETRADITIONAL ACTIVITYLECTURE INQUIRY BASEDDIRECT INSTRUCTION TECHNOLOGYPEN & PAPER MATH WARS @MathletePearcewww.tapintoteenminds.com
  37. 37. BALANCE NEW OLD PROGRESSIVE TRADITIONAL ACTIVITY LECTURE INQUIRY BASED DIRECT INSTRUCTION TECHNOLOGY PEN & PAPER @MathletePearcewww.tapintoteenminds.com
  38. 38. What do you notice? What do you wonder?
  39. 39. How many packs of paper would it take to reach the ceiling? OUR FIRST QUESTION:
  40. 40. @MathletePearcewww.tapintoteenminds.com PREDICTIONS
  41. 41. @MathletePearcewww.tapintoteenminds.com REQUEST INFORMATION
  42. 42. @MathletePearcewww.tapintoteenminds.com How many packs of paper would it take to reach the ceiling? 273cm 24.75cm
  43. 43. 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?
  44. 44. HOW MANY SMALL VASES WILL IT TAKE TO FILL THE TALL VASE?
  45. 45. www.estimation180.com
  46. 46. #MTBoS The Best Teacher PD is FREE on Twitter Follow the Math Twitter Blogosphere @MathletePearcewww.tapintoteenminds.com
  47. 47. 3 Act Math Tasks kylep.ca/curiousmath1p @MathletePearcewww.tapintoteenminds.com iTunes U tapintoteenminds.com
  48. 48. Visual and Concrete Contextual TASKS CONSOLIDATE INQUIRY Move Towards Procedural Fluency Connect to Prior Knowledge CONNECTIONS Construct Conceptual Understanding VISION @MathletePearcekylep.ca/curiousmath1p
  49. 49. @MathletePearcewww.tapintoteenminds.com Four Stages of Mastery COMPETENCE CONSCIOUSNESS 2 3 41
  50. 50. @MathletePearcewww.tapintoteenminds.com Four Stages of Mastery COMPETENCE CONSCIOUSNESS 2 3 4 Consciously Competent Consciously Incompetent 1 Unconsciously Incompetent Unconsciously Competent
  51. 51. @MathletePearcewww.tapintoteenminds.com Consciously Incompetent The Four Stages of Mastery COMPETENCE CONSCIOUSNESS 1 2 3 4 Unconsciously Competent Consciously Competent Unconsciously Incompetent1 2 3 4
  52. 52. 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 1 4 - 8 + 6 - 4 + 7 = - 4 + 6 - 4 + 7 = 2 - 4 + 7 = - 2 + 7 = 5
  53. 53. What equation am I? x 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  54. 54. x = 20+ 5 x 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  55. 55. x 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x = 20+ 5 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 - 5 - 5
  56. 56. x 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x = 20+ 5 + 5 + 5 1 1 1 1 1 1 1 1 1 1
  57. 57. x 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x = 20+ 5 + x + x x x
  58. 58. x 1 1 1 1 -x = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x = 20+ 5 - x - x -x
  59. 59. x = x = 9- 3 -1 -1 -1 -1 -1 -1 - -1 -1 -1 -1 -1 -1
  60. 60. x = 1 1 1 x = 9- 3 -1 -1 -1 -1 -1 -1 + 3 + 3 - -1 -1 -1 -1 -1 -1 1 1 1
  61. 61. x = x = 9- 3 -1 -1 -1 -1 -1 -1 - 3 - 3 - -1 -1 -1 -1 -1 -1-1 -1 -1 -1 -1 -1
  62. 62. x = x = 9- 3 -1 -1 -1 -1 -1 -1 + x - -1 -1 -1 -1 -1 -1 + x x x
  63. 63. x -x = x = 9- 3 -1 -1 -1 -1 -1 -1 - x - -1 -1 -1 -1 -1 -1 - x -x
  64. 64. What equation am I? x 1 1 -1 =x x 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 1
  65. 65. x 1 1 -1 =x x 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 1 3(x - 2) = 17
  66. 66. 3 x 2
  67. 67. 3 x 2 “3 groups of 2”
  68. 68. 1 1 1 3 x 2 “3 groups of 2”
  69. 69. 1 1 1 1 1 3 x 2 “3 groups of 2”
  70. 70. 1 1 1 1 1 3 x 2 “3 groups of 2” 1 1
  71. 71. 1 1 1 1 1 3 x 2 “3 groups of 2” 1 1 1 1
  72. 72. 1 1 1 1 1 3 x 2 “3 groups of 2” 1 1 1 1 1 1
  73. 73. 1 1 1 1 1 3 x 2 “3 groups of 2” 1 1 1 1 1 1 = 6
  74. 74. 1 1 1 1 1 5 x 3 = ? 1 1 1 “5 groups of 3”
  75. 75. 1 1 1 1 1 5 x 3 “5 groups of 3” 1 1 1 1 1 1 = ? 1 1 1 1 1 1 1 1 1 1 1 1
  76. 76. 1 1 1 1 1 5 x 3 “5 groups of 3” 1 1 1 1 = ? 1 1 1 1 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1 1 1 1 11 1
  77. 77. 1 1 1 1 1 5 x 3 “5 groups of 3” 1 1 1 1 = ? 1 1 1 1 1 1 1 1 11 1 1 1 1 11 1
  78. 78. 1 1 1 1 1 5 x 3 “5 groups of 3” 1 1 = ? 1 1 1 1 1 1 1 1 1
  79. 79. 5 x 14 = ? “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  80. 80. 5 x 14 = ? “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 4 5 “5 groups of 10 plus 5 groups of 4” or ?
  81. 81. 5 x 14 = ? “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 4 5 “5 groups of 10 plus 5 groups of 4” or ? ?
  82. 82. 5 x 14 = ? “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 4 5 “5 groups of 10 plus 5 groups of 4” or ? ?
  83. 83. 5 x 14 = 70 “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 4 5 “5 groups of 10 plus 5 groups of 4” or 50 20
  84. 84. 5 x 14 = 70 “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 4 5 “5 groups of 10 plus 5 groups of 4” or 20 50
  85. 85. 5 x 14 = 24 “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 4 5 “5 groups of 10 plus 5 groups of 4” or 15 9
  86. 86. 5 x 14 = 140 “5 groups of 14” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 4 5 “5 groups of 10 plus 5 groups of 4” or 70 70
  87. 87. 9 x 12 = ? “9 groups of 12” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  88. 88. 9 x 12 = ? “9 groups of 12” 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 “5 groups of 10 plus 4 groups of 2” or
  89. 89. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 ? “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  90. 90. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 ? ? “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  91. 91. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 ? ? ? “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  92. 92. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 ? ? ? ? “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  93. 93. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 ? ? ? ? “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  94. 94. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 50 40 10 8 “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  95. 95. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 15 14 7 6 “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  96. 96. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 40 50 20 8 “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  97. 97. 9 x 12 = ? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 110 2 5 4 10 8 50 40 “9 groups of 12” “5 groups of 10 plus 4 groups of 2” or
  98. 98. What equation am I? x 1 1 -1 =x x 1 1 1 1 1 1 1 1 1 1 1 -1 1 x x x -1 -1 -1 -1 -1 -1 -1 1
  99. 99. x 1 1 -1 =x x 1 1 1 1 1 1 1 1 1 1 1 -1 1 x x x -1 -1 -1 -1 -1 -1 -1 1 3(2x - 3) = 15
  100. 100. What’s My Area Equation?
  101. 101. What’s My Area Equation? x x x x
  102. 102. What’s My Area Equation? x x x x 1 1 1
  103. 103. What’s My Area Equation? x x x x 1 1 1
  104. 104. What’s My Area Equation? x x x x 1 1 1 Area = 3( )4x
  105. 105. What’s My Area Equation? x x x x 1 1 1 x x x x x x x x x x x x Area = 3( )4x = 12x units2
  106. 106. What’s My Area Equation? 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 x x x x 1 1 1 Area = 3( )4x = 45 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 units2
  107. 107. What’s My Area Equation? x x x x x 1 1 1 Area = 3( )4x = 15x units2 x x x x x x x x x x x x x x
  108. 108. What’s My Area Equation? x x x x 1 1 1 Area = 3( )4x = 10x + 15 units2 x x x x x x x x x x 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  109. 109. Find the Area of The Pool x x x 1 1 1 Area = 5( )3x 1 1
  110. 110. What’s My Area Equation?
  111. 111. x x x What’s My Area Equation?
  112. 112. x x x xx What’s My Area Equation?
  113. 113. x x x x x What’s My Area Equation?
  114. 114. x x x x x Area = 2x groups
  115. 115. x x x x x Area = 2x groups of 3x
  116. 116. x x x x x Area = 2x( )3x
  117. 117. x x x x x x2 Area = 2x( )3x
  118. 118. x2x x x x x x2 Area = 2x( )3x
  119. 119. x2x2x x x x x x2 Area = 2x( )3x
  120. 120. x x x x x x2 x2 x2 x2 x2 x2 Area = 2x( )3x
  121. 121. x x x x x x2 x2 x2 x2 x2 x2 Area = 2x( )3x
  122. 122. x x x x x x2 x2 x2 x2 x2 x2 Area = 2x( )3x
  123. 123. x x x x x x2 x2 x2 x2 x2 x2 6x2Area = 2x ( )3x =
  124. 124. x x x x x x2 x2 x2 x2 x2 x2 If the total area is 96 units2, solve for the value of x. 6x2Area = 2x( )3x =
  125. 125. x x x x x x2 x2 x2 x2 x2 x2 96 = 6x2 If the total area is 96 units2, solve for the value of x.
  126. 126. What’s My Area Equation?
  127. 127. x x x What’s My Area Equation?
  128. 128. x x x 1 1 What’s My Area Equation?
  129. 129. x x x 1 1 1 1 1 1 What’s My Area Equation?
  130. 130. Area = x x x 1 1 1 1 1 1
  131. 131. Area = x x x 1 1 1 1 1 1 4 groups
  132. 132. Area = x x x 1 1 1 1 1 1 4 ofgroups 3x + 2
  133. 133. Area = x x x 1 1 1 1 1 1 4 )( 3x + 2
  134. 134. 1 1 1 1 1 x x x 1 1 1x x x 1 1x x x 1 1x x x 1 1x x x Area = 4 )( 3x + 2 = 12x + 8
  135. 135. 1 1 1 1 1 x x x 1 1 1x x x 1 1x x x 1 1x x x 1 1x x x Area = 4 )( 3x + 2 = 12x + 8 If the total area is 80 units2, solve for the value of x.
  136. 136. 1 1 1 1 1 x x x 1 1 1x x x 1 1x x x 1 1x x x 1 1x x x = 12x + 8 If the total area is 80 units2, solve for the value of x. 80
  137. 137. What’s My Area Equation? x 1 1x x x x
  138. 138. x 1 1x x x x Area = 2x groups
  139. 139. x 1 1x x x x Area = 2x groups of 3x + 2
  140. 140. x 1 1x x x x Area = 2x( )3x + 2
  141. 141. x 1 1x x x x Area = 2x( )3x + 2
  142. 142. x2 x 1 1x x x x Area = 2x( )3x + 2
  143. 143. x2 x 1 1x x x x Area = 2x( )3x + 2
  144. 144. x2x2 x 1 1x x x x Area = 2x( )3x + 2
  145. 145. x2x2 x 1 1x x x x Area = 2x( )3x + 2
  146. 146. x2 x x x2x2 x 1 1x x x x Area = 2x( )3x + 2
  147. 147. x2 x x x2x2 x 1 1x x x x Area = 2x( )3x + 2
  148. 148. x 1 1x x x x2 x2 x2 x x x x2 x2 x2 x x Area = 2x( )3x + 2
  149. 149. x 1 1x x x x2 x2 x2 x x x x2 x2 x2 x x Area = 2x( )3x + 2 = 6x2 + 4x
  150. 150. What’s My Area Equation? x 1 1 1 1 x 1 x x
  151. 151. Area = (x + 3)(3x + 2) x 1 1 1 1 x 1 x x
  152. 152. x 1 1 1 1 x 1 x x x2 x2 x2 x x x x x x x x x x x 1 1 1 1 1 1 Area = (x + 3)(3x + 2)
  153. 153. x 1 1 1 1 x 1 x x x2 x2 x2 x x x x x x x x x x x 1 1 1 1 1 1 Area = (x + 3)(3x + 2) = 3x2 + 11x + 6
  154. 154. …NOTICE? …WONDER? What do you…
  155. 155. Visual and Concrete Contextual TASKS VISION @MathletePearcewww.tapintoteenminds.com
  156. 156. Visual and Concrete Contextual TASKS VISION INQUIRY @MathletePearcewww.tapintoteenminds.com
  157. 157. Interconnected Visual and Concrete Contextual TASKS CONNECTIONS INQUIRY VISION @MathletePearcewww.tapintoteenminds.com
  158. 158. Interconnected Visual and Concrete Contextual TASKS CONNECTIONS INQUIRY VISIONCONSOLIDATE @MathletePearcewww.tapintoteenminds.com
  159. 159. @MathletePearce@MrOrr_Geek Clap as fast as you can
  160. 160. @MathletePearce@MrOrr_Geek
  161. 161. @MathletePearce@MrOrr_Geek Notice? Wonder? INQUIRY
  162. 162. @MathletePearce@MrOrr_Geek Will he beat the record? INQUIRY
  163. 163. @MathletePearce@MrOrr_Geek Act 3
  164. 164. @MathletePearce@MrOrr_Geek CONSOLIDATE
  165. 165. Which One Doesn’t Belong?
  166. 166. wodb.ca
  167. 167. wodb.ca @MaryBourassa
  168. 168. wodb.ca
  169. 169. wodb.ca
  170. 170. wodb.ca
  171. 171. wodb.ca
  172. 172. wodb.ca
  173. 173. ?
  174. 174. Stage 1
  175. 175. Stage 2
  176. 176. ? Stage 3
  177. 177. Stage 1
  178. 178. Stage 2
  179. 179. Stage 3
  180. 180. Stage 1
  181. 181. Stage 2
  182. 182. Stage 3
  183. 183. ? Stage 4
  184. 184. Stage 1
  185. 185. Stage 2
  186. 186. Stage 3
  187. 187. ? Stage 4
  188. 188. Stage 1
  189. 189. Stage 2
  190. 190. Stage 3
  191. 191. Stage 4
  192. 192. Stage 1 Stage 2 Stage 3 Stage 4
  193. 193. Stage 1 Stage 2 Stage 3 Stage 4 Initial Value:
  194. 194. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares
  195. 195. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0
  196. 196. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change:
  197. 197. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change:
  198. 198. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change:
  199. 199. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change:
  200. 200. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change:
  201. 201. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: 4
  202. 202. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: 4 Equation:
  203. 203. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: 4 Equation: y =
  204. 204. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: 4 Equation: y = 0
  205. 205. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: 4 Equation: y = 0 + 4x
  206. 206. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0
  207. 207. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  208. 208. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  209. 209. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  210. 210. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  211. 211. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  212. 212. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  213. 213. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  214. 214. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 0 4 + 4x
  215. 215. Stage 1 Stage 2 Stage 3 Stage 4Initial Value: Stage 0 No Squares 0 Rate of Change: Equation: y = 4 4x
  216. 216. Stage 1 Stage 2 Stage 5 Stage 6 Stage 3 Stage 4 ? ?
  217. 217. Stage 1 Stage 2 Stage 5 Stage 6 Stage 3 Stage 4 ?
  218. 218. Stage 1 Stage 2 Stage 5 Stage 6 Stage 3 Stage 4
  219. 219. Stage 1 Stage 2 Stage 5 Stage 6 Stage 3 Stage 4
  220. 220. @MathletePearcewww.tapintoteenminds.com 130.75cm130.75cm
  221. 221. @MathletePearcewww.tapintoteenminds.com
  222. 222. @MathletePearcewww.tapintoteenminds.com 130.75cm130.75cm Notice? Wonder?
  223. 223. @MathletePearcewww.tapintoteenminds.com 4.95 cm 130.75cm ? 130.75cm How tall is the table?
  224. 224. @MathletePearcewww.tapintoteenminds.com 4.95 cm 130.75cm ? packs5 130.75cm How tall is the table?
  225. 225. @MathletePearcewww.tapintoteenminds.com 4.95 cm 130.75cm ? packs5 x = 24.75 cm 130.75cm 24.75 cm How tall is the table?
  226. 226. @MathletePearcewww.tapintoteenminds.com 4.95 cm 130.75cm ? packs5 x = 24.75 cm 130.75 cm 24.75 cm- How tall is the table?
  227. 227. @MathletePearcewww.tapintoteenminds.com 4.95 cm 130.75cm ? packs5 x = 24.75 cm 130.75 cm 24.75 cm- 106 cm106 cm How tall is the table?
  228. 228. @MathletePearcewww.tapintoteenminds.com 4.95 cm 130.75cm packs5 x = 24.75 cm 130.75 cm 24.75 cm- 106 cm 106cm How tall is the table?
  229. 229. @MathletePearcewww.tapintoteenminds.com
  230. 230. Inquiry2.
  231. 231. Making Connections @MathletePearcewww.tapintoteenminds.com
  232. 232. @MathletePearcewww.tapintoteenminds.com 4.95 cm 130.75cm packs5 x = 24.75 cm 130.75 cm 24.75 cm- 106 cm 106cm How tall is the table? 4.95 cmpacks5 x = 24.75 cm
  233. 233. @MathletePearcewww.tapintoteenminds.com 130.75cm130.75 4.95 cmx = 24.75 cm 130.75 cm 24.75 cm 106 cm= + packs5 4.95 cmx = 24.75 cmpacks5 106cm
  234. 234. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + packs5 4.95 cm ( = 24.75 cm packs5 130.75 cm 24.75 cm 106 cm= + 4.95 cm )( ) 130.75cm130.75 106cm
  235. 235. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + packs5 = 24.75 cm 130.75 cm 24.75 cm 106 cm= + 4.95 cm 4.95 cm ( packs5 )( ) 130.75cm130.75 106cm
  236. 236. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + packs5 = 24.75 cm 130.75 cm 24.75 cm 106 cm= + height initial height of table = + number of packs 4.95 cm height of a pack ) 130.75cm130.75 106cm ( )( 4.95 cm ( packs5 )( )
  237. 237. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + packs5 = 24.75 cm 130.75 cm 24.75 cm 106 cm= + height initial height of table = + 4.95 cm 130.75cm130.75 106cm number of packs height of a pack )( )( 4.95 cm ( packs5 )( )
  238. 238. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + 5 = 24.75 cm 130.75 cm 24.75 cm 106 cm= + height initial height of table = + 4.95 cm 130.75cm130.75 106cm packs number of packs height of a pack )( )( 4.95 cm ( packs5 )( )
  239. 239. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + 5 = 24.75 cm 130.75 cm 24.75 cm 106 cm= + height initial height of table = + 4.95 cm 130.75cm130.75 106cm packs number of packs height of a pack )( )( 4.95 cm ( packs5 )( )
  240. 240. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + 5 = 24.75 cm 130.75 cm 24.75 cm 106 cm= + height initial height of table = + 4.95 cm 130.75cm130.75 106cm packs number of packs height of a pack )( )( 4.95 cm ( packs5 )( )
  241. 241. @MathletePearcewww.tapintoteenminds.com x = 24.75 cm 130.75 cm 24.75 cm 106 cm= + 5 = 24.75 cm 130.75 cm 24.75 cm 106 cm= + height initial height of table = + 4.95 cm 130.75cm130.75 106cm packs y b= +mx number of packs height of a pack )( )( 4.95 cm ( packs5 )( )
  242. 242. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height Independent Dependent 5 packs130.75 5 4.95 cm How tall is the table?
  243. 243. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent 5 packs130.75 5 4.95 cm Slope
  244. 244. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent 5 packs 130.755 4.95 cm Slope
  245. 245. @MathletePearcewww.tapintoteenminds.com How tall is the table?130.75cm packs of paper height Independent Dependent 5 packs 130.755 4.95 cm Slope )x y (
  246. 246. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 5 packs 130.7554.95 cm Slope )x y ( , InitialValue y-intercept
  247. 247. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y b= +mx InitialValue y-intercept 5 packs5 130.7554.95 130.75
  248. 248. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y b= +mx InitialValue y-intercept 5 packs5 130.75 5 130.75 b+ 4.95
  249. 249. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y b= +m x InitialValue y-intercept 5 packs5 130.75 5 130.75 = )( )( b+ 4.95
  250. 250. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y b= +m x InitialValue y-intercept 5 packs 5130.75 5130.75 = )( )( )( b+ 55)(4.95
  251. 251. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y = m InitialValue y-intercept 5 packs 130.75130.75 = )( b+130.75 = b+ x 55 )( )( 55)(4.95 b+ b+ 54.95
  252. 252. 54.95 @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y = m InitialValue y-intercept 5 packs 130.75130.75 = )( 130.75 = b+24.75 b+ b+ x 55 )( )( 55)(4.95 b+ b+
  253. 253. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y = m InitialValue y-intercept 5 packs 130.75130.75 = )( 130.75 = b+ b+ b+ x 55 )( )( 55)(4.95 b+ b+ 54.9524.75 24.75-
  254. 254. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.7554.95 cm Slope )x y ( , y = m InitialValue y-intercept 5 packs 130.75130.75 = )( 130.75 = b+ b+ b+ x 55 )( )( 55)(4.95 b+ b+ 54.9524.75 24.75-24.75- b+
  255. 255. @MathletePearcewww.tapintoteenminds.com 130.75cm packs of paper height 130.755 4.95 cm Slope )x y ( , y = m InitialValue y-intercept 5 packs 130.75130.75 = )( 130.75 = b+ b+ b+ x 55 )( )( 55)(4.95 b+ b+ 54.9524.75 24.75-24.75- 106 = b0 +
  256. 256. In the past… @MathletePearcewww.tapintoteenminds.com
  257. 257. @MathletePearcewww.tapintoteenminds.com
  258. 258. Example Consolidation @MathletePearcewww.tapintoteenminds.com Task #1:
  259. 259. @MathletePearcewww.tapintoteenminds.com How tall is the table? packs of paper height Independent Dependent 5 packs 130.755( )x y4.95 cm Slope 2 1515 130.75cm
  260. 260. @MathletePearcewww.tapintoteenminds.com How tall is the table? packs of paper height Independent Dependent packs ( )x y 2 15151
  261. 261. @MathletePearcewww.tapintoteenminds.com What does the point (1, 5) represent in the context of the Stacking Paper task? packs of paper height Independent Dependent packs ( )x y 2 15151
  262. 262. @MathletePearcewww.tapintoteenminds.com What does the slope of 2 represent in the context of the Stacking Paper task? packs of paper height Independent Dependent packs ( )x y 151512 15151
  263. 263. @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y How tall is the table? 151512 15151
  264. 264. @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y 2 1515 1 5 1 52 y = m x + b 2 ( ) 1 pack
  265. 265. @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y 2 15151 55 2 2( ) 1 1y = m + b( ) 5 1 pack
  266. 266. @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y 2 15151 5 5 2 2( ) 1 1y = m + b( )5 1 pack
  267. 267. 1pack @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y 2 15151 5 5 2 2() 1 1y = + b()5 2
  268. 268. 1pack @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y 2 15151 5 5 2() 1 1y = + b()5 2 -2-2 2
  269. 269. 1pack @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y 2 15151 5 5 2() 1 1y = +b()5 2-2-22 3 3
  270. 270. 1pack @MathletePearcewww.tapintoteenminds.com packs of paper height Independent Dependent packs ( )x y 2 15151 5 5 2() 1 1y = +b()5 2-2-2 2 3 3 y = 2x + 3
  271. 271. @MathletePearcewww.tapintoteenminds.com
  272. 272. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Struggle with unfamiliar problems Good at Math Poor at Math
  273. 273. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Poor at Math Struggle with unfamiliar problems Good at Math
  274. 274. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  275. 275. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  276. 276. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  277. 277. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  278. 278. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  279. 279. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? 13 13
  280. 280. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  281. 281. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  282. 282. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  283. 283. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  284. 284. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  285. 285. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  286. 286. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  287. 287. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  288. 288. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6
  289. 289. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6 =
  290. 290. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6 =
  291. 291. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  292. 292. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b
  293. 293. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b 3
  294. 294. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b 3936
  295. 295. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b 3 9 3 6
  296. 296. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6
  297. 297. 6 @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6
  298. 298. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b 6 6
  299. 299. 6 @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6
  300. 300. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6 =
  301. 301. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b6 =
  302. 302. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  303. 303. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  304. 304. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  305. 305. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  306. 306. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  307. 307. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag?
  308. 308. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b3
  309. 309. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b3 =
  310. 310. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b3 b b bb b b 6
  311. 311. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? 3 bb b b 6 =+ + + b b b+ + ++
  312. 312. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? 3 bbbb 6 =+ b b b+ + ++3
  313. 313. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? 3 bbbb 6 =+ bbb4+3
  314. 314. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? 3 bbbb 6 =+ bbb4+3 3-
  315. 315. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? bbbb 6 =+ bbb4+3
  316. 316. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? bbbb 6 =+ bbb4+3 3-
  317. 317. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? bbbb 6 =+ bbb4+3 3-
  318. 318. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? bbbb 3 =+ bbb4+3
  319. 319. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? bbbb 3 =+ bbb4+3 3b-
  320. 320. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b3 =+ bbb4+
  321. 321. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b3 = bbb4+ 3b-
  322. 322. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b3 = bbb
  323. 323. @MathletePearcewww.tapintoteenminds.com How Many Are In The Bag? b3 = bbb
  324. 324. SOLVE FOR X = 172x + 5
  325. 325. DOUBLE CLOTHESLINE 17 2x + 5
  326. 326. DOUBLE CLOTHESLINE 17 2x + 5 0 0x
  327. 327. DOUBLE CLOTHESLINE 17 2x + 5 0 0x
  328. 328. DOUBLE CLOTHESLINE 17 2x + 5 0 0x
  329. 329. DOUBLE CLOTHESLINE 17 2x + 5 0 0x 2x
  330. 330. DOUBLE CLOTHESLINE 17 2x + 5 0 0x 2x
  331. 331. DOUBLE CLOTHESLINE 17 2x + 5 0 0x 2x 12
  332. 332. DOUBLE CLOTHESLINE 17 2x + 5 0 0x 2x 12 1x ?
  333. 333. DOUBLE CLOTHESLINE 17 2x + 5 0 0x 2x 12 1x 6
  334. 334. @MathletePearcewww.tapintoteenminds.com Digging Deeper…
  335. 335. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm ?142.75 100.75 ?
  336. 336. @MathletePearcewww.tapintoteenminds.com
  337. 337. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm ?142.75 100.75 ?
  338. 338. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75?
  339. 339. 142.75cm 100.75cm Equations Given 2 Points
  340. 340. 142.75cm 100.75cm Equations Given 2 Points
  341. 341. 142.75cm 100.75cm Equations Given 2 Points
  342. 342. 142.75cm 100.75cm Equations Given 2 Points
  343. 343. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? -
  344. 344. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm42 cm
  345. 345. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm
  346. 346. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12packs 5 packs
  347. 347. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12 packs 5 packs-
  348. 348. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12 packs 5 packs- = 7 packs7 packs
  349. 349. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12 packs 5 packs- = 7 packs 7packs
  350. 350. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12 packs 5 packs- = 7 packs 7packs
  351. 351. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12 packs 5 packs- = 7 packs 7packs
  352. 352. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12 packs 5 packs- = 7 packs 7packs 6 cm 1 packs = 6 cm
  353. 353. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm How tall is the table? ? 142.75 100.75 ? - = 42 cm 42cm 12packs 5 packs 12 packs 5 packs- = 7 packs 7packs 6 cm 1 packs = 6 cmSlope m,
  354. 354. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height )x y ( , 100.75 5
  355. 355. 100.75 @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height 5 )x y ( ,5 100.75 100.75 5 6 5
  356. 356. 100.75 @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height 5 )x y ( ,5 y b= +mx 100.75 100.75 5 6 b+
  357. 357. 100.75 @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height 5 )x y ( , 5 y b= +mx 100.75 6100.75 = )( )(5 b+
  358. 358. 100.75 @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height 5 )x y ( , 5 y b= +mx 100.75 6100.75 = )( )(5 b+ 5100.75 6100.75 = b+30
  359. 359. 100.75 @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height 5 )x y ( , 5 y b= +mx 100.75 6100.75 = )( )(5 b+ 5100.75 6100.75 = b+30 30-
  360. 360. 100.75 @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height 5 )x y ( , 5 y b= +mx 100.75 6100.75 = )( )(5 b+ 5100.75 6100.75 = b+30 30-30-
  361. 361. 100.75 @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm?? 42cm 12packs 5 packs7packs = 6 cmSlope m, packs of paper height 5 )x y ( , 5 y b= +mx 100.75 6100.75 = )( )(5 b+ 5100.75 6100.75 = b+30 30-30- 70.75 = b0 +
  362. 362. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75 100.75? packs of paper height )x y ( , packs of paper height )x y ( ,12packs 5 packs 142.75 100.75 12 5 12 5
  363. 363. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75 100.75 ? packs of paper height )x y ( , packs of paper height )x y ( ,12packs 5 packs 142.75 100.75 12 5 12 5
  364. 364. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75 100.75 ? packs of paper height )x y ( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75 100.75 12 5 12 5 POINT 1
  365. 365. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )x y ( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 125 12 5 POINT 1
  366. 366. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 125 12 5 POINT 1 POINT 2 x2 y2 142.75 100.75 12 5 142.75100.755 12 x1 y1 x2 y2
  367. 367. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 125 12 5 POINT 1 POINT 2 x2 y212 5 142.75100.755 12 x1 y1 x2 y2 142.75 100.75- = 42 cm packs packs
  368. 368. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 12 512 5 POINT 1 POINT 2 x2 y2 142.75100.75 x1 y1 x2 y2 142.75 100.75- = 42 cm 12 packs 5 packs- = 7 packs
  369. 369. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 12 512 5 POINT 1 POINT 2 x2 y2 142.75100.75 x1 y1 x2 y2 142.75 100.75- = 42 cm 12 packs 5 packs- = 7 packs
  370. 370. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 12 512 5 POINT 1 POINT 2 x2 y2 142.75100.75 x1 y1 x2 y2 142.75 100.75- 42 cm 12 packs 5 packs- 7 packs ==
  371. 371. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 12 512 5 POINT 1 POINT 2 x2 y2 142.75100.75 x1 y1 x2 y2 142.75 100.75- 42 cm 12 packs 5 packs- 7 packs - - ==
  372. 372. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 12 512 5 POINT 1 POINT 2 x2 y2 142.75100.75 x1 y1 x2 y2 142.75 100.75- 42 cm 12 packs 5 packs- 7 packs - - Slope m, = = == 6 cm 1 packs ==
  373. 373. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 12 512 5 POINT 1 POINT 2 x2 y2 142.75100.75 x1 y1 x2 y2 142.75 100.75- 42 cm 12 packs 5 packs- 7 packs - - Slope m, = = == 6 cm 1 packs ==
  374. 374. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? packs of paper height )( , packs of paper height )x1 y1 ( ,12packs 5 packs 142.75100.75 12 512 5 POINT 1 POINT 2 x2 y2 142.75100.75 x1 y1 x2 y2 142.75 100.75- 42 cm 12 packs 5 packs- 7 packs - - Slope m, = = == 6 cm 1 packs ==
  375. 375. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+
  376. 376. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm? 142.75100.75 ? )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+ NOW, SUBSTITUTE SLOPE (m) and EITHER POINT TO FIND INITIAL VALUE/Y-INTERCEPT! b+
  377. 377. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm 142.75100.75 )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+ b 12 142.75 6
  378. 378. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm 142.75100.75 )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+ b 12142.75 = 6 )( )( b+
  379. 379. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm 142.75100.75 )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+ b 12142.75 = 6 )( )( b+ 12142.75 = 6 b+72
  380. 380. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm 142.75100.75 )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+ b 12142.75 = 6 )( )( b+ 12142.75 = 6 b+72 72- 6
  381. 381. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm 142.75100.75 )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+ b 12142.75 = 6 )( )( b+ 12142.75 = 6 b+72 72-72- 70.75 = b0 + 6
  382. 382. @MathletePearcewww.tapintoteenminds.com 142.75cm 100.75cm 142.75100.75 )( ,)x1 y1 ( , 12packs 5 packs 142.75100.75 12 5 POINT 1 POINT 2 x2 y2 142.75100.75 Slope m, = 6 cm y b= +mx b+b 70.75b6 Therefore, the equation of the line is:
  383. 383. @MathletePearcewww.tapintoteenminds.com 2x - 4 = 8 Solve for x:
  384. 384. @MathletePearcewww.tapintoteenminds.com 2x - 4 = 8 Solve for x: + 4 + 4
  385. 385. @MathletePearcewww.tapintoteenminds.com 2x - 4 = 8 Solve for x: + 4 + 4 2x = 12
  386. 386. @MathletePearcewww.tapintoteenminds.com 2x - 4 = 8 Solve for x: + 4 + 4 2x = 12 2 2
  387. 387. @MathletePearcewww.tapintoteenminds.com 2x - 4 = 8Solve for x: + 4 + 4 2x = 12 2 2 x = 6
  388. 388. @MathletePearcewww.tapintoteenminds.com GAMIFICATION
  389. 389. Making Connections @MathletePearcewww.tapintoteenminds.com
  390. 390. @MathletePearcewww.tapintoteenminds.com
  391. 391. @MathletePearcewww.tapintoteenminds.com
  392. 392. @MathletePearcewww.tapintoteenminds.com 0 0
  393. 393. @MathletePearcewww.tapintoteenminds.com 0 0
  394. 394. @MathletePearcewww.tapintoteenminds.com 0 0 - +
  395. 395. @MathletePearcewww.tapintoteenminds.com 0 0 - +
  396. 396. @MathletePearcewww.tapintoteenminds.com 0 0 - + - +
  397. 397. @MathletePearcewww.tapintoteenminds.com 0 0 0 0
  398. 398. @MathletePearcewww.tapintoteenminds.com 0 0 0 = 0 xx
  399. 399. @MathletePearcewww.tapintoteenminds.com 0 0 x 0 = 0x+ -aa- a - +
  400. 400. @MathletePearcewww.tapintoteenminds.com 0 0 x -a +a = 00 x a a+ - b b + - +
  401. 401. @MathletePearcewww.tapintoteenminds.com 0 0 x -a +a -b +b =0 x a a+ - + 0 b b+ - c d + +
  402. 402. @MathletePearcewww.tapintoteenminds.com 0 0 -a +a -b +b x +c +d 0 x a a = 0 b b c d+ - + + - + +
  403. 403. @MathletePearcewww.tapintoteenminds.com 0 0 -a +a -b +b x +c +d 0 x a a = 0 b b c d+ - + + - + +
  404. 404. @MathletePearcewww.tapintoteenminds.com -a +a -b +b x x a a = b b c d- + - + + +c +d +0 +
  405. 405. +c +d @MathletePearcewww.tapintoteenminds.com -a+a -b +b x x aa = b b c d-+ - + + 0 0
  406. 406. +c +d @MathletePearcewww.tapintoteenminds.com -a+a -b+b x x aa = bb c d-+ - + + 0 0 0 0
  407. 407. +c +d @MathletePearcewww.tapintoteenminds.com x xaa = bbc d- - ++0 0
  408. 408. @MathletePearcewww.tapintoteenminds.com x = bbc d+
  409. 409. @MathletePearcewww.tapintoteenminds.com khmath.comGo to: HOMEWORK & GAMESHOW
  410. 410. @MathletePearcewww.tapintoteenminds.com REGISTER CREATE STUDENT ACCOUNT khmath.com
  411. 411. @MathletePearcewww.tapintoteenminds.com CREATE STUDENT ACCOUNT khmath.com
  412. 412. @MathletePearcewww.tapintoteenminds.com CREATE STUDENT ACCOUNT mojo923 khmath.com
  413. 413. @MathletePearcewww.tapintoteenminds.com mojo923 CREATE STUDENT ACCOUNT khmath.com
  414. 414. @MathletePearcewww.tapintoteenminds.com CREATE STUDENT ACCOUNT
  415. 415. @MathletePearcewww.tapintoteenminds.com CREATE STUDENT ACCOUNT
  416. 416. @MathletePearcewww.tapintoteenminds.com CREATE STUDENT ACCOUNT
  417. 417. @MathletePearcewww.tapintoteenminds.com CREATE STUDENT ACCOUNT
  418. 418. @MathletePearcewww.tapintoteenminds.com khmath.com
  419. 419. @MathletePearcewww.tapintoteenminds.com khmath.com GameShow
  420. 420. khmath.com
  421. 421. khmath.com
  422. 422. MAKE A PREDICTION!
  423. 423. MAKE A PREDICTION!
  424. 424. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Struggle with unfamiliar problems Good at Math Not Good at Math
  425. 425. @MathletePearcewww.tapintoteenminds.com Two Groups of Students Good at Math Not Good at Math Struggle with unfamiliar problems
  426. 426. Introduction to Desmos www.desmos.com www.desmos.com
  427. 427. www.desmos.com www.desmos.com teacher.desmos.com
  428. 428. WE DID: Marbleslides: Lines Counting Candy Activity Builder
  429. 429. 3 Act Math Tasks iTunes U kylep.ca/curiousmath1p @MathletePearcewww.tapintoteenminds.com
  430. 430. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
  431. 431. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com
  432. 432. kylep.ca/curiousmath1p iTunes U @MathletePearcewww.tapintoteenminds.com Tap
  433. 433. Making Math Contextual, Visual, and Concrete @MathletePearcewww.tapintoteenminds.com
  434. 434. Making Math Contextual, Visual, and Concrete kylep.ca/hpedsb-exit @MathletePearcewww.tapintoteenminds.com

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