A Plus 2012 The Future of Primary Math

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A Plus 2012 The Future of Primary Math

  1. 1. The Future of Primary Math: More Understanding/Less Counting Presented by Tracy Mittleider, MSEd Kathleen Lawler, MBA, MMgt Based on the work of Joan A. Cotter, Ph.D. Tracy@RightStartMath.com&Kathleen@rightstartmath.com October 23, 2012 1000 100 10 1 30 7 30 7© Activities for Learning, Inc., 2012
  2. 2. Introduction Presenter: Tracy Mittleider, MSEd Educational background: •Bachelor of Science in Elementary Education •Minor in Early Childhood Development •Master degree in Administration and Leadership •Kindergarten through 12th grade Math Endorsement Work History •Elementary title one math teacher •Preschool teacher •Math Coach •School Specialist© Activities for Learning, Inc., 2012
  3. 3. Introduction Presentation based on the work of Dr. Joan A. Cotter Educational background: •Home schooled in High School •Engineer from University of Wisconsin •Certified Montessori teacher •Master’s degree in curriculum and instruction •Ph.D. in Curriculum Math Education Work History •Middle-School Teacher •Montessori Educator •Tutor •Author Math Games •Developer of AL Abacus •Developer of RightStart Mathematics© Activities for Learning, Inc., 2012
  4. 4. Introduction Presentation based on the work of Dr. Joan A. Cotter Educational background: •Home schooled in High School •Engineer from University of Wisconsin •Certified Montessori teacher •Master’s degree in curriculum and instruction •Ph.D. in Curriculum Math Education Work History •Middle-School Teacher •Montessori Educator •Tutor •Author Math Games •Developer of AL Abacus •Developer of RightStart Mathematics© Activities for Learning, Inc., 2012
  5. 5. Verbal Counting Model© Activities for Learning, Inc., 2012
  6. 6. Verbal Counting Model From a childs perspective Because 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© Activities for Learning, Inc., 2012
  7. 7. Verbal Counting Model From a childs perspective F +E© Activities for Learning, Inc., 2012
  8. 8. Verbal Counting Model From a childs perspective F +E A© Activities for Learning, Inc., 2012
  9. 9. Verbal Counting Model From a childs perspective F +E A B© Activities for Learning, Inc., 2012
  10. 10. Verbal Counting Model From a childs perspective F +E A B C© Activities for Learning, Inc., 2012
  11. 11. Verbal Counting Model From a childs perspective F +E A B C D E F© Activities for Learning, Inc., 2012
  12. 12. Verbal Counting Model From a childs perspective F +E A B C D E F A© Activities for Learning, Inc., 2012
  13. 13. Verbal Counting Model From a childs perspective F +E A B C D E F A B© Activities for Learning, Inc., 2012
  14. 14. Verbal Counting Model From a childs perspective F +E A B C D E F A B C D E© Activities for Learning, Inc., 2012
  15. 15. Verbal Counting Model From a childs perspective F +E A B C D E F A B C D E What is the sum? (It must be a letter.)© Activities for Learning, Inc., 2012
  16. 16. Verbal Counting Model From a childs perspective F +E K A B C D E F G H I J K© Activities for Learning, Inc., 2012
  17. 17. Verbal Counting Model From a childs perspective Now memorize the facts!! G +D© Activities for Learning, Inc., 2012
  18. 18. Verbal Counting Model From a childs perspective Now memorize the facts!! G +D© Activities for Learning, Inc., 2012
  19. 19. Verbal Counting Model From a childs perspective Now memorize the facts!! G +D D +C© Activities for Learning, Inc., 2012
  20. 20. Verbal Counting Model From a childs perspective Now memorize the facts!! G +D D C +C +G© Activities for Learning, Inc., 2012
  21. 21. Verbal Counting Model From a childs perspective Now memorize the facts!! G +D D C +C +G© Activities for Learning, Inc., 2012
  22. 22. Verbal Counting Model From a childs perspective H –E Subtract with your fingers by counting backward.© Activities for Learning, Inc., 2012
  23. 23. Verbal Counting Model From a childs perspective J –F Subtract without using your fingers.© Activities for Learning, Inc., 2012
  24. 24. Verbal Counting Model From a childs perspective Try skip counting by B’s to T: B, D, . . . T.© Activities for Learning, Inc., 2012
  25. 25. Verbal Counting Model From a childs perspective Try skip counting by B’s to T: B, D, . . . T. What is DE?© Activities for Learning, Inc., 2012
  26. 26. Verbal Counting Model From a childs perspective L is written AB because it is A J and B A’s© Activities for Learning, Inc., 2012
  27. 27. Verbal Counting Model From a childs perspective L is written AB because it is A J and B A’s huh?© Activities for Learning, Inc., 2012
  28. 28. Verbal Counting Model From a childs perspective L (twelve) is written AB because it is A J and B A’s© Activities for Learning, Inc., 2012
  29. 29. Verbal Counting Model From a childs perspective L (twelve) is written AB (12) because it is A J and B A’s© Activities for Learning, Inc., 2012
  30. 30. Verbal Counting Model From a childs perspective L (twelve) is written AB (12) (one 10) because it is A J and B A’s© Activities for Learning, Inc., 2012
  31. 31. Verbal Counting Model From a childs perspective L (twelve) is written AB (12) (one 10) because it is A J and B A’s (two 1s).© Activities for Learning, Inc., 2012
  32. 32. Calendar Math August 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31© Activities for Learning, Inc., 2012
  33. 33. Calendar Math Calendar Counting August 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31© Activities for Learning, Inc., 2012
  34. 34. Calendar Math Calendar Counting August 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31© Activities for Learning, Inc., 2012
  35. 35. Calendar Math Calendar Counting August 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31© Activities for Learning, Inc., 2012
  36. 36. Calendar Math Calendar Counting August 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31© Activities for Learning, Inc., 2012
  37. 37. Calendar Math Calendar Counting August 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 This is ordinal counting, not cardinal counting.© Activities for Learning, Inc., 2012
  38. 38. Calendar Math Partial Calendar August 1 2 3 4 5 6 7 8 9 10© Activities for Learning, Inc., 2012
  39. 39. Calendar Math Partial Calendar August 1 2 3 4 5 6 7 8 9 10 Children need the whole month to plan ahead.© Activities for Learning, Inc., 2012
  40. 40. Calendar Math Calendar Patterning August 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Patterns are rarely based on 7s or proceed row by row. Patterns go on forever; they don’t stop at 31.© Activities for Learning, Inc., 2012
  41. 41. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  42. 42. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  43. 43. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  44. 44. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  45. 45. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  46. 46. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  47. 47. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  48. 48. Research on Counting Karen Wynn’s research© Activities for Learning, Inc., 2012
  49. 49. Memorizing Math Percentage Recall Rote Concept© Activities for Learning, Inc., 2012
  50. 50. Memorizing Math Percentage Recall Immediately Rote Concept© Activities for Learning, Inc., 2012
  51. 51. Memorizing Math Percentage Recall Immediately Rote 32 Concept 69© Activities for Learning, Inc., 2012
  52. 52. Memorizing Math Percentage Recall Immediately After 1 day Rote 32 Concept 69© Activities for Learning, Inc., 2012
  53. 53. Memorizing Math Percentage Recall Immediately After 1 day Rote 32 23 Concept 69 69© Activities for Learning, Inc., 2012
  54. 54. Memorizing Math Percentage Recall Immediately After 1 day After 4 wks Rote 32 23 Concept 69 69© Activities for Learning, Inc., 2012
  55. 55. Memorizing Math Percentage Recall Immediately After 1 day After 4 wks Rote 32 23 8 Concept 69 69 58© Activities for Learning, Inc., 2012
  56. 56. Memorizing Math Percentage Recall Immediately After 1 day After 4 wks Rote 32 23 8 Concept 69 69 58 Math needs to be taught so 95% is understood and only 5% memorized. Richard Skemp major pioneer in Mathematics Education who first integrated the disciplines of mathematics, education and psychology© Activities for Learning, Inc., 2012
  57. 57. Visualizing Quantities© Activities for Learning, Inc., 2012
  58. 58. Visualizing Quantities “Think in pictures, because the brain remembers images better than it does anything else.” Ben Pridmore, World Memory Champion, 2009© Activities for Learning, Inc., 2012
  59. 59. Visualizing Quantities “The role of physical manipulatives was to help the child form those visual images and thus to eliminate the need for the physical manipulatives.” Ginsberg and others© Activities for Learning, Inc., 2012
  60. 60. Visualizing Quantities Japanese criteria for manipulatives •Representative of structure of numbers. •Easily manipulated by children. •Imaginable mentally. Japanese Council of Mathematics Education© Activities for Learning, Inc., 2012
  61. 61. Visualizing Quantities Visualizing also needed in: • Reading • Sports • Creativity • Geography • Engineering • Construction© Activities for Learning, Inc., 2012
  62. 62. Visualizing Quantities Visualizing also needed in: • Reading • Architecture • Sports • Astronomy • Creativity • Archeology • Geography • Chemistry • Engineering • Physics • Construction • Surgery© Activities for Learning, Inc., 2012
  63. 63. Visualizing Quantities Ready: How many?© Activities for Learning, Inc., 2012
  64. 64. Visualizing Quantities Ready: How many?© Activities for Learning, Inc., 2012
  65. 65. Visualizing Quantities Try again: How many?© Activities for Learning, Inc., 2012
  66. 66. Visualizing Quantities Try again: How many?© Activities for Learning, Inc., 2012
  67. 67. Visualizing Quantities Early Roman numerals 1 I 2 II 3 III 4 IIII 5 V 8 VIII© Activities for Learning, Inc., 2012
  68. 68. Visualizing Quantities : Who could read the music?© Activities for Learning, Inc., 2012
  69. 69. AN ALTERNATIVE to learning place value: Subitizing (groups of five) Math Way (of number naming) Place Value Cards Trading (with 4-digit numbers)© Activities for Learning, Inc., 2012
  70. 70. Grouping in Fives Using fingers© Activities for Learning, Inc., 2012
  71. 71. Grouping in Fives Using fingers© Activities for Learning, Inc., 2012
  72. 72. Grouping in Fives Using fingers© Activities for Learning, Inc., 2012
  73. 73. Grouping in Fives Using fingers© Activities for Learning, Inc., 2012
  74. 74. Grouping in Fives Using fingers© Activities for Learning, Inc., 2012
  75. 75. Grouping in Fives Using fingers© Activities for Learning, Inc., 2012
  76. 76. Grouping in Fives Yellow is the Sun Yellow is the sun. Six is five and one. Why is the sky so blue? Seven is five and two. Salty is the sea. Eight is five and three. Hear the thunder roar. Nine is five and four. Ducks will swim and dive. Ten is five and five. –Joan A. Cotter© Activities for Learning, Inc., 2012
  77. 77. Games© Activities for Learning, Inc., 2012
  78. 78. Games Games Math© Activities for Learning, Inc., 2012
  79. 79. Games Games = Math© Activities for Learning, Inc., 2012
  80. 80. Games Games Books = Math Reading© Activities for Learning, Inc., 2012
  81. 81. Games Games Books = Math Reading Games provide interesting repetition needed for automatic responses.© Activities for Learning, Inc., 2012
  82. 82. Games Games Books = Math Reading Games provide interesting repetition needed for automatic responses. More importantly, games provide an application for the new information!© Activities for Learning, Inc., 2012
  83. 83. Finger Cards in Order© Activities for Learning, Inc., 2012
  84. 84. Finger Cards in Order© Activities for Learning, Inc., 2012
  85. 85. Finger Cards in Order© Activities for Learning, Inc., 2012
  86. 86. Finger Cards in Order© Activities for Learning, Inc., 2012
  87. 87. Grouping in Fives Recognizing 5© Activities for Learning, Inc., 2012
  88. 88. Grouping in Fives Recognizing 5© Activities for Learning, Inc., 2012
  89. 89. Grouping in Fives Recognizing 5 5 has a middle; 4 does not.© Activities for Learning, Inc., 2012
  90. 90. Grouping in Fives Tally sticks© Activities for Learning, Inc., 2012
  91. 91. Grouping in Fives Tally sticks© Activities for Learning, Inc., 2012
  92. 92. Grouping in Fives Tally sticks© Activities for Learning, Inc., 2012
  93. 93. Grouping in Fives Tally sticks© Activities for Learning, Inc., 2012
  94. 94. Grouping in Fives Tally sticks© Activities for Learning, Inc., 2012
  95. 95. Grouping in Fives Tally sticks© Activities for Learning, Inc., 2012
  96. 96. Tally Cards in Order© Activities for Learning, Inc., 2012
  97. 97. Naming Quantities Numbe r 1 Chart 2 3 4 5© Activities for Learning, Inc., 2012
  98. 98. Naming Quantities Numbe r 1 Chart 2 To help the 3 child learn the symbols 4 5© Activities for Learning, Inc., 2012
  99. 99. Naming Quantities Numbe r 1 6 Chart 2 7 To help the 3 8 child learn the symbols 4 9 5 10© Activities for Learning, Inc., 2012
  100. 100. Matching Numbers to Fingers 5 1 10© Activities for Learning, Inc., 2012
  101. 101. Matching Fingers to Numbers 9 1 10 4 6 2 3 7 8 5© Activities for Learning, Inc., 2012
  102. 102. Grouping in Fives Entering quantities© Activities for Learning, Inc., 2012
  103. 103. Grouping in Fives Entering quantities 3© Activities for Learning, Inc., 2012
  104. 104. Grouping in Fives Entering quantities 5© Activities for Learning, Inc., 2012
  105. 105. Grouping in Fives Entering quantities 7© Activities for Learning, Inc., 2012
  106. 106. Grouping in Fives Entering quantities 10© Activities for Learning, Inc., 2012
  107. 107. Grouping in Fives The stairs© Activities for Learning, Inc., 2012
  108. 108. Bead Cards in Order© Activities for Learning, Inc., 2012
  109. 109. Finger Card Memory© Activities for Learning, Inc., 2012
  110. 110. Memory with Different Sets© Activities for Learning, Inc., 2012
  111. 111. Grouping in Fives Adding© Activities for Learning, Inc., 2012
  112. 112. Grouping in Fives Adding 4+3=© Activities for Learning, Inc., 2012
  113. 113. Grouping in Fives Adding 4+3=© Activities for Learning, Inc., 2012
  114. 114. Grouping in Fives Adding 4+3=© Activities for Learning, Inc., 2012
  115. 115. Grouping in Fives Adding 4+3=© Activities for Learning, Inc., 2012
  116. 116. Grouping in Fives Adding 4+3= 7© Activities for Learning, Inc., 2012
  117. 117. Go to the Dump© Activities for Learning, Inc., 2012
  118. 118. Go to the Dump Objective: To learn and master the facts that total 10:© Activities for Learning, Inc., 2012
  119. 119. Go to the Dump Objective: To learn and master the facts that total 10: 1+9 2+8 3+7 4+6 5+5© Activities for Learning, Inc., 2012
  120. 120. Go to the Dump Objective: To learn and master the facts that total 10: 1+9 2+8 3+7 4+6 5+5© Activities for Learning, Inc., 2012
  121. 121. Go to the Dump Objective: To learn and master the facts that total 11:© Activities for Learning, Inc., 2012
  122. 122. Go to the Dump Objective: To learn and master the facts that total 11: 1 + 10 2+9 3+8 4+7 5+6© Activities for Learning, Inc., 2012
  123. 123. Swim to Ten Game© Activities for Learning, Inc., 2012
  124. 124. Swim to Ten Game Objective: To count purposefully and informally.© Activities for Learning, Inc., 2012
  125. 125. Swim to Ten Game Objective: To count purposefully and informally. To learn the number sequence 1 to 10 with an emphasis on fives.© Activities for Learning, Inc., 2012
  126. 126. Swim to Ten Game Objective: To count purposefully and informally. To learn the number sequence 1 to 10 with an emphasis on fives. To realize that the largest number is not always the best answer.© Activities for Learning, Inc., 2012
  127. 127. Swim to Ten Game Objective: To count purposefully and informally. To learn the number sequence 1 to 10 with an emphasis on fives. To realize that the largest number is not always the best answer. To mentally visualize moves.© Activities for Learning, Inc., 2012
  128. 128. Swim to Ten Game Need: Basic number cards 1 to 5© Activities for Learning, Inc., 2012
  129. 129. Swim to Ten Game Need: Basic number cards 1 to 5 Game board© Activities for Learning, Inc., 2012
  130. 130. Swim to Ten Game© Activities for Learning, Inc., 2012
  131. 131. Swim to Ten Game Setup:© Activities for Learning, Inc., 2012
  132. 132. Swim to Ten Game Setup: Each player chooses two lanes.© Activities for Learning, Inc., 2012
  133. 133. Swim to Ten Game Setup: Each player chooses two lanes. Objective of the Game:© Activities for Learning, Inc., 2012
  134. 134. Swim to Ten Game Setup: Each player chooses two lanes. Objective of the Game: To move both swimmers from the starting blocks to the last space in the lane.© Activities for Learning, Inc., 2012
  135. 135. Swim to Ten Game Setup: Each player chooses two lanes. Objective of the Game: To move both swimmers from the starting blocks to the last space in the lane. Swimmers must end exactly on the 10.© Activities for Learning, Inc., 2012
  136. 136. Swim to Ten Game© Activities for Learning, Inc., 2012
  137. 137. Swim to Ten Game© Activities for Learning, Inc., 2012
  138. 138. Swim to Ten Game© Activities for Learning, Inc., 2012
  139. 139. Swim to Ten Game 2© Activities for Learning, Inc., 2012
  140. 140. Swim to Ten Game 2© Activities for Learning, Inc., 2012
  141. 141. Swim to Ten Game 2© Activities for Learning, Inc., 2012
  142. 142. Swim to Ten Game 2© Activities for Learning, Inc., 2012
  143. 143. Swim to Ten Game 2 3© Activities for Learning, Inc., 2012
  144. 144. Swim to Ten Game 2 3© Activities for Learning, Inc., 2012
  145. 145. Swim to Ten Game 2 1 3© Activities for Learning, Inc., 2012
  146. 146. Swim to Ten Game 2 1 3© Activities for Learning, Inc., 2012
  147. 147. Swim to Ten Game 2 1 3© Activities for Learning, Inc., 2012
  148. 148. Swim to Ten Game 2 1 3© Activities for Learning, Inc., 2012
  149. 149. Swim to Ten Game 2 1 3© Activities for Learning, Inc., 2012
  150. 150. Swim to Ten Game 2 1 3© Activities for Learning, Inc., 2012
  151. 151. Swim to Ten Game 2 1 5 3© Activities for Learning, Inc., 2012
  152. 152. Swim to Ten Game 2 1 5 3© Activities for Learning, Inc., 2012
  153. 153. Swim to Ten Game 2 1 5 3 3 2© Activities for Learning, Inc., 2012
  154. 154. Swim to Ten Game 2 1 5 3 3 2© Activities for Learning, Inc., 2012
  155. 155. Swim to Ten Game 2 1 5 3 3 2© Activities for Learning, Inc., 2012
  156. 156. Swim to Ten Game 2 1 5 3 3 2© Activities for Learning, Inc., 2012
  157. 157. Swim to Ten Game 2 1 5 3 3 2© Activities for Learning, Inc., 2012
  158. 158. Swim to Ten Game 2 1 5 3 3 2© Activities for Learning, Inc., 2012
  159. 159. Swim to Ten Game 2 1 5 4 3 3 2© Activities for Learning, Inc., 2012
  160. 160. Swim to Ten Game 2 1 5 4 3 3 2© Activities for Learning, Inc., 2012
  161. 161. Swim to Ten Game 2 1 5 4 3 3 2© Activities for Learning, Inc., 2012
  162. 162. Swim to Ten Game 2 1 5 4 3 3 2© Activities for Learning, Inc., 2012
  163. 163. Swim to Ten Game Initially, allow the children to check out their moves by physically moving their swimmers.© Activities for Learning, Inc., 2012
  164. 164. Swim to Ten Game Initially, allow the children to check out their moves by physically moving their swimmers. Work towards the rule that players must move the first swimmer touched.© Activities for Learning, Inc., 2012
  165. 165. “Math” Way of Naming Numbers© Activities for Learning, Inc., 2012
  166. 166. “Math” Way of Naming Numbers 11 = ten 1© Activities for Learning, Inc., 2012
  167. 167. “Math” Way of Naming Numbers 11 = ten 1 12 = ten 2© Activities for Learning, Inc., 2012
  168. 168. “Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3© Activities for Learning, Inc., 2012
  169. 169. “Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4© Activities for Learning, Inc., 2012
  170. 170. “Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 .... 19 = ten 9© Activities for Learning, Inc., 2012
  171. 171. “Math” Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 13 = ten 3 14 = ten 4 .... 19 = ten 9© Activities for Learning, Inc., 2012
  172. 172. “Math” Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 14 = ten 4 .... 19 = ten 9© Activities for Learning, Inc., 2012
  173. 173. “Math” Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 22 = 2-ten 2 14 = ten 4 .... 19 = ten 9© Activities for Learning, Inc., 2012
  174. 174. “Math” Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 22 = 2-ten 2 14 = ten 4 23 = 2-ten 3 .... 19 = ten 9© Activities for Learning, Inc., 2012
  175. 175. “Math” Way of Naming Numbers 11 = ten 1 20 = 2-ten 12 = ten 2 21 = 2-ten 1 13 = ten 3 22 = 2-ten 2 14 = ten 4 23 = 2-ten 3 .... .... 19 = ten 9 .... 99 = 9-ten 9© Activities for Learning, Inc., 2012
  176. 176. “Math” Way of Naming Numbers 137 = 1 hundred 3-ten 7© Activities for Learning, Inc., 2012
  177. 177. “Math” Way of Naming Numbers 137 = 1 hundred 3-ten 7 or 137 = 1 hundred and 3-ten 7© Activities for Learning, Inc., 2012
  178. 178. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo- European languages are non-standard in number naming.)© Activities for Learning, Inc., 2012
  179. 179. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo- European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting.© Activities for Learning, Inc., 2012
  180. 180. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo- European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. • They understand place value in first grade; only half of U.S. children understand place value at the end of fourth grade.© Activities for Learning, Inc., 2012
  181. 181. Math Way of Naming Numbers • Only 11 words are needed to count to 100 the math way, 28 in English. (All Indo- European languages are non-standard in number naming.) • Asian children learn mathematics using the math way of counting. • They understand place value in first grade; only half of U.S. children understand place value at the end of fourth grade. • Mathematics is the science of patterns. The patterned math way of counting greatly helps children learn number sense.© Activities for Learning, Inc., 2012
  182. 182. Math Way of Naming Numbers Compared to reading:© Activities for Learning, Inc., 2012
  183. 183. Math Way of Naming Numbers Compared to reading: • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic.© Activities for Learning, Inc., 2012
  184. 184. Math Way of Naming Numbers Compared to reading: • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic. • Just as we first teach the sound of the letters, we must first teach the name of the quantity (math way).© Activities for Learning, Inc., 2012
  185. 185. Math Way of Naming Numbers “Rather, the increased gap between Chinese and U.S. students and that of Chinese Americans and Caucasian Americans may be due primarily to the nature of their initial gap prior to formal schooling, such as counting efficiency and base-ten number sense.” Jian Wang and Emily Lin, 2005 Researchers© Activities for Learning, Inc., 2012
  186. 186. Math Way of Naming Numbers Traditional names 4-ten = forty The “ty” means tens.© Activities for Learning, Inc., 2012
  187. 187. Math Way of Naming Numbers Traditional names 4-ten = forty The “ty” means tens.© Activities for Learning, Inc., 2012
  188. 188. Math Way of Naming Numbers Traditional names 6-ten = sixty The “ty” means tens.© Activities for Learning, Inc., 2012
  189. 189. Math Way of Naming Numbers Traditional names 3-ten = thirty “Thir” also used in 1/3, 13 and 30.© Activities for Learning, Inc., 2012
  190. 190. Math Way of Naming Numbers Traditional names 5-ten = fifty “Fif” also used in 1/5, 15 and 50.© Activities for Learning, Inc., 2012
  191. 191. Math Way of Naming Numbers Traditional names 2-ten = twenty Two used to be pronounced “twoo.”© Activities for Learning, Inc., 2012
  192. 192. Math Way of Naming Numbers Traditional names A word game fireplace place-fire© Activities for Learning, Inc., 2012
  193. 193. Math Way of Naming Numbers Traditional names A word game fireplace place-fire newspaper paper-news© Activities for Learning, Inc., 2012
  194. 194. Math Way of Naming Numbers Traditional names A word game fireplace place-fire newspaper paper-news box-mail mailbox© Activities for Learning, Inc., 2012
  195. 195. Math Way of Naming Numbers Traditional names ten 4 “Teen” also means ten.© Activities for Learning, Inc., 2012
  196. 196. Math Way of Naming Numbers Traditional names ten 4 teen 4 “Teen” also means ten.© Activities for Learning, Inc., 2012
  197. 197. Math Way of Naming Numbers Traditional names ten 4 teen 4 fourteen “Teen” also means ten.© Activities for Learning, Inc., 2012
  198. 198. Math Way of Naming Numbers Traditional names a one left© Activities for Learning, Inc., 2012
  199. 199. Math Way of Naming Numbers Traditional names a one left a left-one© Activities for Learning, Inc., 2012
  200. 200. Math Way of Naming Numbers Traditional names a one left a left-one eleven© Activities for Learning, Inc., 2012
  201. 201. Math Way of Naming Numbers Traditional names two left Two pronounce d “twoo.”© Activities for Learning, Inc., 2012
  202. 202. Math Way of Naming Numbers Traditional names two left twelve Two pronounce d “twoo.”© Activities for Learning, Inc., 2012
  203. 203. Rows and Columns© Activities for Learning, Inc., 2012
  204. 204. Rows and Columns Objective: To give the players practice in adding up to fifteen.© Activities for Learning, Inc., 2012
  205. 205. Rows and Columns Objective: To give the players practice in adding up to fifteen. Object of the Game: To collect the most cards in rows or columns that add up to fifteen.© Activities for Learning, Inc., 2012
  206. 206. Rows and Columns 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8© Activities for Learning, Inc., 2012
  207. 207. Rows and Columns 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8© Activities for Learning, Inc., 2012
  208. 208. Rows and Columns 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8© Activities for Learning, Inc., 2012
  209. 209. Rows and Columns 8 7 1 9 6 4 3 3 2 2 5 6 6 3 8 8© Activities for Learning, Inc., 2012
  210. 210. Rows and Columns 1 9 6 4 3 3 6 3 8 8© Activities for Learning, Inc., 2012
  211. 211. Rows and Columns 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8© Activities for Learning, Inc., 2012
  212. 212. Rows and Columns 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8© Activities for Learning, Inc., 2012
  213. 213. Rows and Columns 7 6 1 9 6 4 3 3 2 1 5 1 6 3 8 8© Activities for Learning, Inc., 2012
  214. 214. Rows and Columns 1 6 4 3 3 1 5 1 3 8 8© Activities for Learning, Inc., 2012
  215. 215. Rows and Columns 2 9 1 7 6 4 3 3 8 1 5 1 5 3 8 8© Activities for Learning, Inc., 2012
  216. 216. Corners™ 1 2 7 4© Activities for Learning, Inc., 2012
  217. 217. Corners™ 1 Purpose: 2 7 4 To practice the facts that total 5, 10, 15, and 20.© Activities for Learning, Inc., 2012
  218. 218. Corners™ 1 Purpose: 2 7 4 To practice the facts that total 5, 10, 15, and 20. To practice mental math through scoring.© Activities for Learning, Inc., 2012
  219. 219. Corners™ 1 2 7 Rules: 4© Activities for Learning, Inc., 2012
  220. 220. Corners™ 1 2 7 Rules: 4 • To score, sum must equal 5, 10, 15 or 20.© Activities for Learning, Inc., 2012
  221. 221. Corners™ 1 2 7 Rules: 4 • To score, sum must equal 5, 10, 15 or 20. • Play on the last card played, or play to any Corner (all sides must match as above).© Activities for Learning, Inc., 2012
  222. 222. Corners™ 1 2 7 4 1 3 8 10© Activities for Learning, Inc., 2012
  223. 223. Corners™ 10 1 8 3 2 7 1 4© Activities for Learning, Inc., 2012
  224. 224. Corners™ 10 1 8 3 2 7 1 4 9 3 6 4© Activities for Learning, Inc., 2012
  225. 225. Corners™ 10 1 8 3 2 7 1 4 9 3 6 4© Activities for Learning, Inc., 2012
  226. 226. Corners™ 10 1 8 3 2 7 1 4 9 3 6 4 7 8 4 2© Activities for Learning, Inc., 2012
  227. 227. Corners™ 10 1 8 3 2 7 1 4 2 9 4 8 3 6 7 4© Activities for Learning, Inc., 2012
  228. 228. Corners™ 10 1 8 3 2 7 1 4 2 9 4 8 3 6 7 4 3 7 10 1© Activities for Learning, Inc., 2012
  229. 229. Corners™ 10 1 8 3 2 7 1 4 2 9 4 8 3 6 7 4 3 7 10 1© Activities for Learning, Inc., 2012
  230. 230. Corners™ 10 1 8 3 2 7 1 4 2 9 4 8 3 3 6 7 7 10 4 1© Activities for Learning, Inc., 2012
  231. 231. Corners™ 10 1 8 3 2 7 1 4 2 1 7 9 4 8 10 3 6 7 3 4© Activities for Learning, Inc., 2012
  232. 232. Corners™ 10 1 8 3 2 7 1 4 2 1 7 9 4 8 10 3 6 7 3 4 7 2 5© Activities for Learning, Inc., 2012 8
  233. 233. Corners™© Activities for Learning, Inc., 2012
  234. 234. Corners™ Players learn the facts that total 5, 10, 15, and 20.© Activities for Learning, Inc., 2012
  235. 235. Corners™ Players learn the facts that total 5, 10, 15, and 20. Working in the 100s gives the players a better understanding of larger quantities.© Activities for Learning, Inc., 2012
  236. 236. Corners™ Players learn the facts that total 5, 10, 15, and 20. Working in the 100s gives the players a better understanding of larger quantities. Twenty variations of the game are available.© Activities for Learning, Inc., 2012
  237. 237. Corners™ Players learn the facts that total 5, 10, 15, and 20. Working in the 100s gives the players a better understanding of larger quantities. Twenty variations of the game are available. Each player benefits from doing accumulative scoring.© Activities for Learning, Inc., 2012
  238. 238. Corners™ Scoring is done 10 mentally. 25 30 40 55 65 80© Activities for Learning, Inc., 2012
  239. 239. Mental Addition 65 + 15 =© Activities for Learning, Inc., 2012
  240. 240. Mental Addition 65 + 15 = 65 + 10© Activities for Learning, Inc., 2012
  241. 241. Mental Addition 65 + 15 = 65 + 10 + 5 =© Activities for Learning, Inc., 2012
  242. 242. Composing Numbers 3-ten© Activities for Learning, Inc., 2012
  243. 243. Composing Numbers 3-ten© Activities for Learning, Inc., 2012
  244. 244. Composing Numbers 3-ten© Activities for Learning, Inc., 2012
  245. 245. Composing Numbers 3-ten 30© Activities for Learning, Inc., 2012
  246. 246. Composing Numbers 3-ten 30© Activities for Learning, Inc., 2012
  247. 247. Composing Numbers 3-ten 30© Activities for Learning, Inc., 2012
  248. 248. Composing Numbers 3-ten 7 30© Activities for Learning, Inc., 2012
  249. 249. Composing Numbers 3-ten 7 30© Activities for Learning, Inc., 2012
  250. 250. Composing Numbers 3-ten 7 30 7© Activities for Learning, Inc., 2012
  251. 251. Composing Numbers 3-ten 7 30 7© Activities for Learning, Inc., 2012
  252. 252. Composing Numbers 3-ten 7 30 7 Notice the way we say the number, represent the number, and write the number all correspond.© Activities for Learning, Inc., 2012
  253. 253. Composing Numbers 7-ten 70 Another example.© Activities for Learning, Inc., 2012
  254. 254. Composing Numbers 7-ten 8 70© Activities for Learning, Inc., 2012
  255. 255. Composing Numbers 7-ten 8 70© Activities for Learning, Inc., 2012
  256. 256. Composing Numbers 7-ten 8 70 8© Activities for Learning, Inc., 2012
  257. 257. Composing Numbers 7-ten 8 78 8© Activities for Learning, Inc., 2012
  258. 258. Composing Numbers 10-ten© Activities for Learning, Inc., 2012
  259. 259. Composing Numbers 10-ten 1 00© Activities for Learning, Inc., 2012
  260. 260. Composing Numbers 10-ten 100© Activities for Learning, Inc., 2012
  261. 261. Composing Numbers 10-ten 100© Activities for Learning, Inc., 2012
  262. 262. Composing Numbers 1 hundred© Activities for Learning, Inc., 2012
  263. 263. Composing Numbers 1 hundred 100© Activities for Learning, Inc., 2012
  264. 264. Composing Numbers 1 hundred 100© Activities for Learning, Inc., 2012
  265. 265. Composing Numbers 1 hundred 100© Activities for Learning, Inc., 2012
  266. 266. Composing Numbers 1 hundred 100© Activities for Learning, Inc., 2012
  267. 267. Composing Numbers 2 hundred© Activities for Learning, Inc., 2012
  268. 268. Composing Numbers 2 hundred© Activities for Learning, Inc., 2012
  269. 269. Composing Numbers 2 hundred 200© Activities for Learning, Inc., 2012
  270. 270. Counting by 2s and 5s© Activities for Learning, Inc., 2012
  271. 271. Counting by 2s and 5s Counting by 2s© Activities for Learning, Inc., 2012
  272. 272. Counting by 2s and 5s Counting by 2s 2© Activities for Learning, Inc., 2012
  273. 273. Counting by 2s and 5s Counting by 2s 2 4© Activities for Learning, Inc., 2012
  274. 274. Counting by 2s and 5s Counting by 2s 2 4 6© Activities for Learning, Inc., 2012
  275. 275. Counting by 2s and 5s Counting by 2s 2 4 6 8© Activities for Learning, Inc., 2012
  276. 276. Counting by 2s and 5s Counting by 2s 2 4 6 8 10© Activities for Learning, Inc., 2012
  277. 277. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12© Activities for Learning, Inc., 2012
  278. 278. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 14© Activities for Learning, Inc., 2012
  279. 279. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 14 16© Activities for Learning, Inc., 2012
  280. 280. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 14 16 18© Activities for Learning, Inc., 2012
  281. 281. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 14 16 18 20© Activities for Learning, Inc., 2012
  282. 282. Counting by 2s and 5s Counting by 5s© Activities for Learning, Inc., 2012
  283. 283. Counting by 2s and 5s Counting by 5s 5© Activities for Learning, Inc., 2012
  284. 284. Counting by 2s and 5s Counting by 5s 5 10© Activities for Learning, Inc., 2012
  285. 285. Counting by 2s and 5s Counting by 5s 5 10 15© Activities for Learning, Inc., 2012
  286. 286. Counting by 2s and 5s Counting by 5s 5 10 15 20© Activities for Learning, Inc., 2012
  287. 287. Counting by 2s and 5s Counting by 5s 5 10 15 20 25© Activities for Learning, Inc., 2012
  288. 288. Counting by 2s and 5s Counting by 5s 5 10 15 20 25 30© Activities for Learning, Inc., 2012
  289. 289. Evens and Odds Evens© Activities for Learning, Inc., 2012
  290. 290. Evens and Odds Evens Use two fingers and touch each pair in succession.© Activities for Learning, Inc., 2012
  291. 291. Evens and Odds Evens Use two fingers and touch each pair in succession.© Activities for Learning, Inc., 2012
  292. 292. Evens and Odds Evens Use two fingers and touch each pair in succession.© Activities for Learning, Inc., 2012
  293. 293. Evens and Odds Evens Use two fingers and touch each pair in succession. EVEN!© Activities for Learning, Inc., 2012
  294. 294. Evens and Odds Odds Use two fingers and touch each pair in succession.© Activities for Learning, Inc., 2012
  295. 295. Evens and Odds Odds Use two fingers and touch each pair in succession.© Activities for Learning, Inc., 2012
  296. 296. Evens and Odds Odds Use two fingers and touch each pair in succession.© Activities for Learning, Inc., 2012
  297. 297. Evens and Odds Odds Use two fingers and touch each pair in succession.© Activities for Learning, Inc., 2012
  298. 298. Evens and Odds Odds Use two fingers and touch each pair in succession. ODD!© Activities for Learning, Inc., 2012
  299. 299. Fact Strategies© Activities for Learning, Inc., 2012
  300. 300. Fact Strategies Complete the Ten 9+5=© Activities for Learning, Inc., 2012
  301. 301. Fact Strategies Complete the Ten 9+5=© Activities for Learning, Inc., 2012
  302. 302. Fact Strategies Complete the Ten 9+5=© Activities for Learning, Inc., 2012
  303. 303. Fact Strategies Complete the Ten 9+5= Take 1 from the 5 and give it to the 9.© Activities for Learning, Inc., 2012
  304. 304. Fact Strategies Complete the Ten 9+5= Take 1 from the 5 and give it to the 9.© Activities for Learning, Inc., 2012
  305. 305. Fact Strategies Complete the Ten 9+5= Take 1 from the 5 and give it to the 9.© Activities for Learning, Inc., 2012
  306. 306. Fact Strategies Complete the Ten 9 + 5 = 14 Take 1 from the 5 and give it to the 9.© Activities for Learning, Inc., 2012
  307. 307. Fact Strategies Two Fives 8+6=© Activities for Learning, Inc., 2012
  308. 308. Fact Strategies Two Fives 8+6=© Activities for Learning, Inc., 2012
  309. 309. Fact Strategies Two Fives 8+6=© Activities for Learning, Inc., 2012
  310. 310. Fact Strategies Two Fives 8+6=© Activities for Learning, Inc., 2012

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