MCTM Strategies & Games

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MCTM Strategies & Games

  1. 1. Teaching the Arithmetic Facts Using Strategies and Games by Joan A. Cotter, Ph.D. JoanCotter@RightStartMath.com MCTM May 4, 2012 Duluth, Minnesota 7 3 8 16 24 32 40PowerPoint Presentation & Handout RightStartMath.com >Resources © Joan A. Cotter, Ph.D., 2012
  2. 2. Learning the Facts © Joan A. Cotter, Ph.D., 2012
  3. 3. Learning the FactsLimited success when:• Based on counting. Whether dots, fingers, number lines, or counting words. © Joan A. Cotter, Ph.D., 2012
  4. 4. Learning the FactsLimited success when:• Based on counting. Whether dots, fingers, number lines, or counting words.• Based on rote memory. Whether by flash cards or timed tests. © Joan A. Cotter, Ph.D., 2012
  5. 5. Learning the FactsLimited success when:• Based on counting. Whether dots, fingers, number lines, or counting words.• Based on rote memory. Whether by flash cards or timed tests.• Based on skip counting for multiplication facts. © Joan A. Cotter, Ph.D., 2012
  6. 6. Counting ModelFrom a childs perspective © Joan A. Cotter, Ph.D., 2012
  7. 7. Counting Model From a childs perspectiveBecause we’re so familiar with 1, 2, 3, we’ll use letters. A=1 B=2 C=3 D=4 E = 5, and so forth © Joan A. Cotter, Ph.D., 2012
  8. 8. Counting ModelFrom a childs perspective F +E © Joan A. Cotter, Ph.D., 2012
  9. 9. Counting Model From a childs perspective F +EA © Joan A. Cotter, Ph.D., 2012
  10. 10. Counting Model From a childs perspective F +EA B © Joan A. Cotter, Ph.D., 2012
  11. 11. Counting Model From a childs perspective F +EA B C © Joan A. Cotter, Ph.D., 2012
  12. 12. Counting Model From a childs perspective F +EA B C D E F © Joan A. Cotter, Ph.D., 2012
  13. 13. Counting Model From a childs perspective F +EA B C D E F A © Joan A. Cotter, Ph.D., 2012
  14. 14. Counting Model From a childs perspective F +EA B C D E F A B © Joan A. Cotter, Ph.D., 2012
  15. 15. Counting Model From a childs perspective F +EA B C D E F A B C D E © Joan A. Cotter, Ph.D., 2012
  16. 16. Counting Model From a childs perspective F +EA B C D E F A B C D E What is the sum? (It must be a letter.) © Joan A. Cotter, Ph.D., 2012
  17. 17. Counting Model From a childs perspective F +E KA B C D E F G H I J K © Joan A. Cotter, Ph.D., 2012
  18. 18. Counting ModelFrom a childs perspective E +G Add with your fingers. © Joan A. Cotter, Ph.D., 2012
  19. 19. Counting ModelFrom a childs perspective H +DAdd without your fingers. © Joan A. Cotter, Ph.D., 2012
  20. 20. Counting Model From a childs perspectiveNow memorize the facts!! G +D © Joan A. Cotter, Ph.D., 2012
  21. 21. Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D © Joan A. Cotter, Ph.D., 2012
  22. 22. Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D D+C © Joan A. Cotter, Ph.D., 2012
  23. 23. Counting Model From a childs perspectiveNow memorize the facts!! H + G F +D D C+C +G © Joan A. Cotter, Ph.D., 2012
  24. 24. Counting Model From a childs perspective Now memorize the facts!! HE + G I F+ +D D C +C +G © Joan A. Cotter, Ph.D., 2012
  25. 25. Counting Model From a childs perspective H –ESubtract with your fingers. © Joan A. Cotter, Ph.D., 2012
  26. 26. Counting Model From a childs perspective J –FSubtract without using your fingers. © Joan A. Cotter, Ph.D., 2012
  27. 27. Counting Model From a childs perspectiveTry skip counting by B’s to T: B, D, . . . T. © Joan A. Cotter, Ph.D., 2012
  28. 28. Counting Model From a childs perspectiveTry skip counting by B’s to T: B, D, . . . T.What is D x E? © Joan A. Cotter, Ph.D., 2012
  29. 29. Memorizing Math © Joan A. Cotter, Ph.D., 2012
  30. 30. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  31. 31. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  32. 32. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  33. 33. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  34. 34. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  35. 35. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  36. 36. Memorizing MathSome research: Percentage Recall Immediately After 1 day After 4 wksRote 32 23 8Concept 69 69 58 © Joan A. Cotter, Ph.D., 2012
  37. 37. Memorizing Math 9 +7Flash cards: © Joan A. Cotter, Ph.D., 2012
  38. 38. Memorizing Math 9 +7Flash cards:• Are often used to teach rote. © Joan A. Cotter, Ph.D., 2012
  39. 39. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them. © Joan A. Cotter, Ph.D., 2012
  40. 40. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities. © Joan A. Cotter, Ph.D., 2012
  41. 41. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities.• Give the false impression that math isn’t aboutthinking. © Joan A. Cotter, Ph.D., 2012
  42. 42. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities.• Give the false impression that math isn’t aboutthinking.• Often produce stress – children under stress stoplearning. © Joan A. Cotter, Ph.D., 2012
  43. 43. Memorizing Math 9 +7Flash cards:• Are often used to teach rote.• Are liked by those who don’t need them.• Don’t work for those with learning disabilities.• Give the false impression that math isn’t aboutthinking.• Often produce stress – children under stress stoplearning.• Are not concrete – they use abstract symbols. © Joan A. Cotter, Ph.D., 2012
  44. 44. AN ALTERNATIVE: SUBITIZING and GAMES © Joan A. Cotter, Ph.D., 2012
  45. 45. Subitizing QuantitiesIdentifying without counting © Joan A. Cotter, Ph.D., 2012
  46. 46. Subitizing Quantities Identifying without counting• Five-month-old infants can subitize to 3. © Joan A. Cotter, Ph.D., 2012
  47. 47. Subitizing Quantities Identifying without counting• Five-month-old infants can subitize to 3.• Three-year-olds can subitize to 5. © Joan A. Cotter, Ph.D., 2012
  48. 48. Subitizing Quantities Identifying without counting• Five-month-old infants can subitize to 3.• Three-year-olds can subitize to 5.• Five-year-olds can subitize 6 to 10 byusing five as a subbase. © Joan A. Cotter, Ph.D., 2012
  49. 49. AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
  50. 50. AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
  51. 51. AddingName the quantity (practice subitizing). © Joan A. Cotter, Ph.D., 2012
  52. 52. Adding4+3= © Joan A. Cotter, Ph.D., 2012
  53. 53. Adding4+3= © Joan A. Cotter, Ph.D., 2012
  54. 54. Adding4+3= © Joan A. Cotter, Ph.D., 2012
  55. 55. Adding4+3=7 © Joan A. Cotter, Ph.D., 2012
  56. 56. Adding4+3= © Joan A. Cotter, Ph.D., 2012
  57. 57. Characteristics of a Good Game © Joan A. Cotter, Ph.D., 2012
  58. 58. Characteristics of a Good Game • Produces learning through playing. © Joan A. Cotter, Ph.D., 2012
  59. 59. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. © Joan A. Cotter, Ph.D., 2012
  60. 60. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. © Joan A. Cotter, Ph.D., 2012
  61. 61. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. • Encourages mental work. © Joan A. Cotter, Ph.D., 2012
  62. 62. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. • Encourages mental work. • Detects errors; provides continuous assessment. © Joan A. Cotter, Ph.D., 2012
  63. 63. Characteristics of a Good Game • Produces learning through playing. • Incorporates manipulatives. • Teaches strategies. • Encourages mental work. • Detects errors; provides continuous assessment. • Is enjoyable. © Joan A. Cotter, Ph.D., 2012
  64. 64. Go to the Dump GameObjective: To learn the facts that total 10: 1+9 2+8 3+7 4+6 5+5 © Joan A. Cotter, Ph.D., 2012
  65. 65. Go to the Dump GameObjective: To learn the facts that total 10: 1+9 2+8 3+7 4+6 5+5Object of the game: To collect the most pairs that equal ten. © Joan A. Cotter, Ph.D., 2012
  66. 66. Go to the Dump Game 6+ = 10 © Joan A. Cotter, Ph.D., 2012
  67. 67. Go to the Dump Game 6+ = 10 © Joan A. Cotter, Ph.D., 2012
  68. 68. Go to the Dump Game 6 + 4 = 10 © Joan A. Cotter, Ph.D., 2012
  69. 69. Go to the Dump Game Starting © Joan A. Cotter, Ph.D., 2012
  70. 70. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Starting © Joan A. Cotter, Ph.D., 2012
  71. 71. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  72. 72. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  73. 73. Go to the Dump Game 72 7 9 5 72 1 3 8 4 6 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  74. 74. Go to the Dump Game 72 7 9 5 4 6 72 1 3 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  75. 75. Go to the Dump Game 72 7 9 5 4 6 72 1 3 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  76. 76. Go to the Dump Game 72 7 9 5 4 6 72 1 3 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  77. 77. Go to the Dump Game 72 7 9 5 7 3 4 6 2 1 8 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  78. 78. Go to the Dump Game 72 7 9 5 2 8 4 6 1 34 9 Finding pairs © Joan A. Cotter, Ph.D., 2012
  79. 79. Go to the Dump Game 72 7 9 5 2 8 4 6 1 34 9 Playing © Joan A. Cotter, Ph.D., 2012
  80. 80. Go to the Dump Game BlueCap, do you have an3? have a 3? 72 7 9 5 2 8 4 6 1 34 9 Playing © Joan A. Cotter, Ph.D., 2012
  81. 81. Go to the Dump Game BlueCap, do you have an3? have a 3? 72 7 9 5 3 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  82. 82. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 3? 2 7 9 5 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  83. 83. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 8? 2 7 9 5 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  84. 84. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 8? 2 7 9 5 2 8 4 6 1 4 9 Go to the dump. Playing © Joan A. Cotter, Ph.D., 2012
  85. 85. Go to the Dump Game 7 3 BlueCap, do you have an3? have a 8? 2 2 7 9 5 2 8 4 6 1 4 9 Go to the dump. Playing © Joan A. Cotter, Ph.D., 2012
  86. 86. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  87. 87. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 4 9 PinkCap, do you Playing have a 6? © Joan A. Cotter, Ph.D., 2012
  88. 88. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 4 9 PinkCap, do youGo to the dump. Playing have a 6? © Joan A. Cotter, Ph.D., 2012
  89. 89. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  90. 90. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  91. 91. Go to the Dump Game 7 3 2 2 7 9 5 2 8 4 6 1 5 4 9YellowCap, doyou have a 9? Playing © Joan A. Cotter, Ph.D., 2012
  92. 92. Go to the Dump Game 7 3 2 2 7 5 2 8 4 6 1 5 4 9YellowCap, doyou have a 9? Playing © Joan A. Cotter, Ph.D., 2012
  93. 93. Go to the Dump Game 7 3 2 2 7 5 2 8 4 6 19 5 4 9YellowCap, doyou have a 9? Playing © Joan A. Cotter, Ph.D., 2012
  94. 94. Go to the Dump Game 7 3 2 2 7 5 2 1 8 9 4 6 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  95. 95. Go to the Dump Game 7 3 2 2 7 5 2 1 8 9 4 62 9 1 7 7 5 4 9 Playing © Joan A. Cotter, Ph.D., 2012
  96. 96. Go to the Dump Game 9 1 4 6 5 5 Winner? © Joan A. Cotter, Ph.D., 2012
  97. 97. Go to the Dump Game 9 1 4 6 5 Winner? © Joan A. Cotter, Ph.D., 2012
  98. 98. Go to the Dump Game 9 1 4 6 5 Winner? © Joan A. Cotter, Ph.D., 2012
  99. 99. Go to the Dump Game Play it again. © Joan A. Cotter, Ph.D., 2012
  100. 100. Fact Strategies © Joan A. Cotter, Ph.D., 2012
  101. 101. Fact Strategies• A strategy is a way to learn a new fact orrecall a forgotten fact. © Joan A. Cotter, Ph.D., 2012
  102. 102. Fact Strategies• A strategy is a way to learn a new fact orrecall a forgotten fact.• A visualizable representation is part of apowerful strategy. © Joan A. Cotter, Ph.D., 2012
  103. 103. Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
  104. 104. Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
  105. 105. Fact Strategies Complete the Ten9+5= © Joan A. Cotter, Ph.D., 2012
  106. 106. Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  107. 107. Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  108. 108. Fact Strategies Complete the Ten 9+5=Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  109. 109. Fact Strategies Complete the Ten 9 + 5 = 14Take 1 fromthe 5 and giveit to the 9. © Joan A. Cotter, Ph.D., 2012
  110. 110. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  111. 111. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  112. 112. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  113. 113. Fact Strategies Two Fives8+6= © Joan A. Cotter, Ph.D., 2012
  114. 114. Fact Strategies Two Fives8+6=10 + 4 = 14 © Joan A. Cotter, Ph.D., 2012
  115. 115. Fact Strategies Two Fives7+5= © Joan A. Cotter, Ph.D., 2012
  116. 116. Fact Strategies Two Fives7+5= © Joan A. Cotter, Ph.D., 2012
  117. 117. Fact Strategies Two Fives7 + 5 = 12 © Joan A. Cotter, Ph.D., 2012
  118. 118. Fact Strategies Going Down15 – 9 = © Joan A. Cotter, Ph.D., 2012
  119. 119. Fact Strategies Going Down15 – 9 = © Joan A. Cotter, Ph.D., 2012
  120. 120. Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  121. 121. Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  122. 122. Fact Strategies Going Down 15 – 9 =Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  123. 123. Fact Strategies Going Down 15 – 9 = 6Subtract 5;then 4. © Joan A. Cotter, Ph.D., 2012
  124. 124. Fact Strategies Subtract from 1015 – 9 = © Joan A. Cotter, Ph.D., 2012
  125. 125. Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  126. 126. Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  127. 127. Fact Strategies Subtract from 10 15 – 9 =Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  128. 128. Fact Strategies Subtract from 10 15 – 9 = 6Subtract 9from 10. © Joan A. Cotter, Ph.D., 2012
  129. 129. Fact Strategies Going Up15 – 9 = © Joan A. Cotter, Ph.D., 2012
  130. 130. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  131. 131. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  132. 132. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  133. 133. Fact Strategies Going Up 15 – 9 =Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  134. 134. Fact Strategies Going Up 15 – 9 = 1+5=6Start with 9;go up to 15. © Joan A. Cotter, Ph.D., 2012
  135. 135. Rows and Columns GameObjective: To find a total of 15 by adding 2, 3, or 4cards in row or column. © Joan A. Cotter, Ph.D., 2012
  136. 136. Rows and Columns GameObjective: To find a total of 15 by adding 2, 3, or 4cards in row or column.Object of the game: To collect the most cards. © Joan A. Cotter, Ph.D., 2012
  137. 137. Rows and Columns Game 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  138. 138. Rows and Columns Game 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  139. 139. Rows and Columns Game 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  140. 140. Rows and Columns Game 1 9 6 4 3 3 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  141. 141. Rows and Columns Game 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  142. 142. Rows and Columns Game 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  143. 143. Rows and Columns Game 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8 © Joan A. Cotter, Ph.D., 2012
  144. 144. Rows and Columns Game 1 6 4 3 3 1 5 1 3 8 8 © Joan A. Cotter, Ph.D., 2012
  145. 145. Rows and Columns Game © Joan A. Cotter, Ph.D., 2012
  146. 146. Multiplication Strategies Basic facts © Joan A. Cotter, Ph.D., 2012
  147. 147. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  148. 148. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  149. 149. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  150. 150. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  151. 151. Multiplication Strategies Basic facts6× 4=(6 taken 4 times) © Joan A. Cotter, Ph.D., 2012
  152. 152. Multiplication Strategies Basic facts9× 3= © Joan A. Cotter, Ph.D., 2012
  153. 153. Multiplication Strategies Basic facts9× 3= © Joan A. Cotter, Ph.D., 2012
  154. 154. Multiplication Strategies Basic facts9× 3=30 © Joan A. Cotter, Ph.D., 2012
  155. 155. Multiplication Strategies Basic facts9× 3=30 – 3 = 27 © Joan A. Cotter, Ph.D., 2012
  156. 156. Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
  157. 157. Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
  158. 158. Multiplication Strategies Basic facts4× 8= © Joan A. Cotter, Ph.D., 2012
  159. 159. Multiplication Strategies Basic facts4× 8=20 + 12 = 32 © Joan A. Cotter, Ph.D., 2012
  160. 160. Multiplication Strategies Basic facts7× 7= © Joan A. Cotter, Ph.D., 2012
  161. 161. Multiplication Strategies Basic facts7× 7= © Joan A. Cotter, Ph.D., 2012
  162. 162. Multiplication Strategies Basic facts7× 7=25 © Joan A. Cotter, Ph.D., 2012
  163. 163. Multiplication Strategies Basic facts7× 7=25 + 10 + 10 © Joan A. Cotter, Ph.D., 2012
  164. 164. Multiplication Strategies Basic facts7× 7=25 + 10 + 10+ 4 = 49 © Joan A. Cotter, Ph.D., 2012
  165. 165. Multiples Patterns Twos2 4 6 8 1012 14 16 18 20 © Joan A. Cotter, Ph.D., 2012
  166. 166. Multiples Patterns Twos 2 4 6 8 1012 14 16 18 20The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
  167. 167. Multiples Patterns Fours 4 8 12 16 2024 28 32 36 40The ones repeat in the second row. © Joan A. Cotter, Ph.D., 2012
  168. 168. Multiples Patterns Sixes and Eights6 12 18 24 3036 42 48 54 608 16 24 32 4048 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
  169. 169. Multiples Patterns Sixes and Eights6 12 18 24 3036 42 48 54 608 16 24 32 4048 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
  170. 170. Multiples Patterns Sixes and Eights6 12 18 24 3036 42 48 54 608 16 24 32 4048 56 64 72 80 © Joan A. Cotter, Ph.D., 2012
  171. 171. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  172. 172. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  173. 173. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  174. 174. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  175. 175. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80The ones in the 8s show the multiples of 2. © Joan A. Cotter, Ph.D., 2012
  176. 176. Multiples Patterns Sixes and Eights 6 12 18 24 30 6× 4 36 42 48 54 60 8 16 24 32 40 48 56 64 72 806 × 4 is the fourth number (multiple). © Joan A. Cotter, Ph.D., 2012
  177. 177. Multiples Patterns Sixes and Eights 6 12 18 24 30 36 42 48 54 60 8 16 24 32 40 48 56 64 72 80 8× 78 × 7 is the seventh number (multiple). © Joan A. Cotter, Ph.D., 2012
  178. 178. Multiples Patterns Nines 9 18 27 36 45 90 81 72 63 54The second row is written in reverse order.Also the digits in each number add to 9. © Joan A. Cotter, Ph.D., 2012
  179. 179. Multiples Patterns Threes 3 6 9 2 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  180. 180. Multiples Patterns Threes 3 6 9 2 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  181. 181. Multiples Patterns Threes 3 6 9 2 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  182. 182. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  183. 183. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  184. 184. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  185. 185. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  186. 186. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  187. 187. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  188. 188. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  189. 189. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Observe the ones. © Joan A. Cotter, Ph.D., 2012
  190. 190. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30 The 3s have several patterns:The tens are the same in each row. © Joan A. Cotter, Ph.D., 2012
  191. 191. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns:Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
  192. 192. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns:Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
  193. 193. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns:Add the digits in the columns. © Joan A. Cotter, Ph.D., 2012
  194. 194. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  195. 195. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  196. 196. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  197. 197. Multiples Patterns Threes 3 6 9 12 15 18 21 24 27 30The 3s have several patterns: Add the “opposites.” © Joan A. Cotter, Ph.D., 2012
  198. 198. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  199. 199. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  200. 200. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  201. 201. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70The 7s have the 1, 2, 3… pattern. © Joan A. Cotter, Ph.D., 2012
  202. 202. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  203. 203. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  204. 204. Multiples Patterns Sevens 7 14 21 28 35 42 49 56 63 70 Look at the tens. © Joan A. Cotter, Ph.D., 2012
  205. 205. Multiples Memory © Joan A. Cotter, Ph.D., 2012
  206. 206. Multiples MemoryObjective: To help the players learn themultiples patterns. © Joan A. Cotter, Ph.D., 2012
  207. 207. Multiples MemoryObjective: To help the players learn the multiples patterns.Object of the game: To be the first player to collect all tencards of a multiple in order. © Joan A. Cotter, Ph.D., 2012
  208. 208. Multiples Memory 7 14 21 28 35 42 49 56 63 70The 7s envelope contains 10 cards,each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
  209. 209. Multiples Memory 8 16 24 32 40 48 56 64 72 80The 8s envelope contains 10 cards,each with one of the numbers listed. © Joan A. Cotter, Ph.D., 2012
  210. 210. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  211. 211. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  212. 212. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  213. 213. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 63 1470 © Joan A. Cotter, Ph.D., 2012
  214. 214. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  215. 215. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  216. 216. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 40 © Joan A. Cotter, Ph.D., 2012
  217. 217. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  218. 218. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  219. 219. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
  220. 220. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  221. 221. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  222. 222. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
  223. 223. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
  224. 224. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 63 5670 8 © Joan A. Cotter, Ph.D., 2012
  225. 225. Multiples Memory 8 16 24 32 40 48 56 64 72 80 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
  226. 226. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
  227. 227. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 8 © Joan A. Cotter, Ph.D., 2012
  228. 228. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 © Joan A. Cotter, Ph.D., 2012
  229. 229. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 14 70 87 © Joan A. Cotter, Ph.D., 2012
  230. 230. Multiples Memory 7 14 21 28 35 42 49 56 63 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 14 © Joan A. Cotter, Ph.D., 2012
  231. 231. Multiples Memory 7 14 21 28 35 42 49 56 63 70 24 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 14 © Joan A. Cotter, Ph.D., 2012
  232. 232. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 40 28 35 42 48 56 64 72 80 49 56 63 70 87 14 © Joan A. Cotter, Ph.D., 2012
  233. 233. Multiples Memory 7 14 21 28 35 42 8 16 24 32 40 49 56 63 48 56 64 72 80 70 7 14 21 8 16 24 32 4028 35 42 48 56 64 72 8049 56 6370 © Joan A. Cotter, Ph.D., 2012
  234. 234. Multiplication MemoryObjective: To help the players master themultiplication facts. © Joan A. Cotter, Ph.D., 2012
  235. 235. Multiplication MemoryObjective: To help the players master themultiplication facts.Object of the game: To collect the most cards by matchingthe multiplier with the product. © Joan A. Cotter, Ph.D., 2012
  236. 236. Multiplication MemoryMaterials Needed: © Joan A. Cotter, Ph.D., 2012
  237. 237. Multiplication Memory1 2 3 4 5 6 7 8 9 10 Materials Needed: • Ten basic cards, numbered 1 to 10 © Joan A. Cotter, Ph.D., 2012
  238. 238. Multiplication Memory 31 2 3 4 5 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) © Joan A. Cotter, Ph.D., 2012
  239. 239. Multiplication Memory 31 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie note with “3 x” written on it © Joan A. Cotter, Ph.D., 2012
  240. 240. Multiplication Memory 31 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it © Joan A. Cotter, Ph.D., 2012
  241. 241. Multiplication Memory 31 2 3 4 5 3x 3 6 9 12 15 18 6 7 8 9 10 21 24 27 30 = Materials Needed: • Ten basic cards, numbered 1 to 10 • A set of product cards (3s used here) • A stickie with “3 x” written on it • A stickie with “=” written on it • A manipulative with groups of five © Joan A. Cotter, Ph.D., 2012
  242. 242. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  243. 243. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  244. 244. Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  245. 245. Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  246. 246. Multiplication Memory 53x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  247. 247. Multiplication Memory 53x =3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  248. 248. Multiplication Memory 5 213x =3 taken 5 times equals 15. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  249. 249. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  250. 250. Multiplication Memory3x = 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  251. 251. Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  252. 252. Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  253. 253. Multiplication Memory3x = 7 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  254. 254. Multiplication Memory3x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  255. 255. Multiplication Memory 213x = 7 3 taken 7 times equals 21. 3 6 9 12 15 18 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  256. 256. Multiplication Memory3x = 3 taken 7 times equals 21. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  257. 257. Multiplication Memory3x = 2 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  258. 258. Multiplication Memory3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  259. 259. Multiplication Memory3x = 2 3 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  260. 260. Multiplication Memory3x = 2 3 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  261. 261. Multiplication Memory3x = 2 3 12 3 taken 3 times equals 9. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  262. 262. Multiplication Memory3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  263. 263. Multiplication Memory3x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  264. 264. Multiplication Memory 53x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  265. 265. Multiplication Memory 53x = 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  266. 266. Multiplication Memory 53x =3 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  267. 267. Multiplication Memory 53x = 153 taken 5 times equals 15. 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  268. 268. Multiplication Memory3x =3 taken 5 times equals 15. 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  269. 269. Multiplication Memory3x = 5 15 3 6 9 12 15 18 7 21 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  270. 270. Multiplication Memory3x = 8 24 3 6 9 12 15 18 1 3 21 24 27 30 © Joan A. Cotter, Ph.D., 2012
  271. 271. Framing the Future of Mathematics in MinnesotaMath in Minnesota starts with the youngest.Let’s build on their natural ability to subitize.Keep joy in math; use games, not flash cards.Help them to use their minds to visualize. © Joan A. Cotter, Ph.D., 2012
  272. 272. Teaching the Arithmetic Facts Using Strategies and Games by Joan A. Cotter, Ph.D. JoanCotter@RightStartMath.com MCTM May 4, 2012 Duluth, Minnesota 7 3 8 16 24 32 40PowerPoint Presentation & Handout RightStartMath.com >Resources © Joan A. Cotter, Ph.D., 2012

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