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The Future of Primary Math: Less Counting, More Understanding
- 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. 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. 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. 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. Verbal Counting Model © Activities for Learning, Inc., 2012
- 6. Verbal Counting Model From a child's 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. Verbal Counting Model From a child's perspective F +E © Activities for Learning, Inc., 2012
- 8. Verbal Counting Model From a child's perspective F +E A © Activities for Learning, Inc., 2012
- 9. Verbal Counting Model From a child's perspective F +E A B © Activities for Learning, Inc., 2012
- 10. Verbal Counting Model From a child's perspective F +E A B C © Activities for Learning, Inc., 2012
- 11. Verbal Counting Model From a child's perspective F +E A B C D E F © Activities for Learning, Inc., 2012
- 12. Verbal Counting Model From a child's perspective F +E A B C D E F A © Activities for Learning, Inc., 2012
- 13. Verbal Counting Model From a child's perspective F +E A B C D E F A B © Activities for Learning, Inc., 2012
- 14. Verbal Counting Model From a child's perspective F +E A B C D E F A B C D E © Activities for Learning, Inc., 2012
- 15. Verbal Counting Model From a child's 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. Verbal Counting Model From a child's perspective F +E K A B C D E F G H I J K © Activities for Learning, Inc., 2012
- 17. Verbal Counting Model From a child's perspective Now memorize the facts!! G +D © Activities for Learning, Inc., 2012
- 18. Verbal Counting Model From a child's perspective Now memorize the facts!! G +D © Activities for Learning, Inc., 2012
- 19. Verbal Counting Model From a child's perspective Now memorize the facts!! G +D D +C © Activities for Learning, Inc., 2012
- 20. Verbal Counting Model From a child's perspective Now memorize the facts!! G +D D C +C +G © Activities for Learning, Inc., 2012
- 21. Verbal Counting Model From a child's perspective Now memorize the facts!! G +D D C +C +G © Activities for Learning, Inc., 2012
- 22. Verbal Counting Model From a child's perspective H –E Subtract with your fingers by counting backward. © Activities for Learning, Inc., 2012
- 23. Verbal Counting Model From a child's perspective J –F Subtract without using your fingers. © Activities for Learning, Inc., 2012
- 24. Verbal Counting Model From a child's perspective Try skip counting by B’s to T: B, D, . . . T. © Activities for Learning, Inc., 2012
- 25. Verbal Counting Model From a child's perspective Try skip counting by B’s to T: B, D, . . . T. What is DE? © Activities for Learning, Inc., 2012
- 26. Verbal Counting Model From a child's perspective L is written AB because it is A J and B A’s © Activities for Learning, Inc., 2012
- 27. Verbal Counting Model From a child's perspective L is written AB because it is A J and B A’s huh? © Activities for Learning, Inc., 2012
- 28. Verbal Counting Model From a child's perspective L (twelve) is written AB because it is A J and B A’s © Activities for Learning, Inc., 2012
- 29. Verbal Counting Model From a child's perspective L (twelve) is written AB (12) because it is A J and B A’s © Activities for Learning, Inc., 2012
- 30. Verbal Counting Model From a child's perspective L (twelve) is written AB (12) (one 10) because it is A J and B A’s © Activities for Learning, Inc., 2012
- 31. Verbal Counting Model From a child's 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. 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. 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. 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. 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. 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. 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. Calendar Math Partial Calendar August 1 2 3 4 5 6 7 8 9 10 © Activities for Learning, Inc., 2012
- 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. 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. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 42. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 43. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 44. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 45. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 46. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 47. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 48. Research on Counting Karen Wynn’s research © Activities for Learning, Inc., 2012
- 49. Memorizing Math Percentage Recall Rote Concept © Activities for Learning, Inc., 2012
- 50. Memorizing Math Percentage Recall Immediately Rote Concept © Activities for Learning, Inc., 2012
- 51. Memorizing Math Percentage Recall Immediately Rote 32 Concept 69 © Activities for Learning, Inc., 2012
- 52. Memorizing Math Percentage Recall Immediately After 1 day Rote 32 Concept 69 © Activities for Learning, Inc., 2012
- 53. Memorizing Math Percentage Recall Immediately After 1 day Rote 32 23 Concept 69 69 © Activities for Learning, Inc., 2012
- 54. Memorizing Math Percentage Recall Immediately After 1 day After 4 wks Rote 32 23 Concept 69 69 © Activities for Learning, Inc., 2012
- 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. 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. Visualizing Quantities © Activities for Learning, Inc., 2012
- 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. 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. 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. Visualizing Quantities Visualizing also needed in: • Reading • Sports • Creativity • Geography • Engineering • Construction © Activities for Learning, Inc., 2012
- 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. Visualizing Quantities Ready: How many? © Activities for Learning, Inc., 2012
- 64. Visualizing Quantities Ready: How many? © Activities for Learning, Inc., 2012
- 65. Visualizing Quantities Try again: How many? © Activities for Learning, Inc., 2012
- 66. Visualizing Quantities Try again: How many? © Activities for Learning, Inc., 2012
- 67. Visualizing Quantities Early Roman numerals 1 I 2 II 3 III 4 IIII 5 V 8 VIII © Activities for Learning, Inc., 2012
- 68. Visualizing Quantities : Who could read the music? © Activities for Learning, Inc., 2012
- 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. Grouping in Fives Using fingers © Activities for Learning, Inc., 2012
- 71. Grouping in Fives Using fingers © Activities for Learning, Inc., 2012
- 72. Grouping in Fives Using fingers © Activities for Learning, Inc., 2012
- 73. Grouping in Fives Using fingers © Activities for Learning, Inc., 2012
- 74. Grouping in Fives Using fingers © Activities for Learning, Inc., 2012
- 75. Grouping in Fives Using fingers © Activities for Learning, Inc., 2012
- 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. Games © Activities for Learning, Inc., 2012
- 78. Games Games Math © Activities for Learning, Inc., 2012
- 79. Games Games = Math © Activities for Learning, Inc., 2012
- 80. Games Games Books = Math Reading © Activities for Learning, Inc., 2012
- 81. Games Games Books = Math Reading Games provide interesting repetition needed for automatic responses. © Activities for Learning, Inc., 2012
- 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. Finger Cards in Order © Activities for Learning, Inc., 2012
- 84. Finger Cards in Order © Activities for Learning, Inc., 2012
- 85. Finger Cards in Order © Activities for Learning, Inc., 2012
- 86. Finger Cards in Order © Activities for Learning, Inc., 2012
- 87. Grouping in Fives Recognizing 5 © Activities for Learning, Inc., 2012
- 88. Grouping in Fives Recognizing 5 © Activities for Learning, Inc., 2012
- 89. Grouping in Fives Recognizing 5 5 has a middle; 4 does not. © Activities for Learning, Inc., 2012
- 90. Grouping in Fives Tally sticks © Activities for Learning, Inc., 2012
- 91. Grouping in Fives Tally sticks © Activities for Learning, Inc., 2012
- 92. Grouping in Fives Tally sticks © Activities for Learning, Inc., 2012
- 93. Grouping in Fives Tally sticks © Activities for Learning, Inc., 2012
- 94. Grouping in Fives Tally sticks © Activities for Learning, Inc., 2012
- 95. Grouping in Fives Tally sticks © Activities for Learning, Inc., 2012
- 96. Tally Cards in Order © Activities for Learning, Inc., 2012
- 97. Naming Quantities Numbe r 1 Chart 2 3 4 5 © Activities for Learning, Inc., 2012
- 98. Naming Quantities Numbe r 1 Chart 2 To help the 3 child learn the symbols 4 5 © Activities for Learning, Inc., 2012
- 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. Matching Numbers to Fingers 5 1 10 © Activities for Learning, Inc., 2012
- 101. Matching Fingers to Numbers 9 1 10 4 6 2 3 7 8 5 © Activities for Learning, Inc., 2012
- 102. Grouping in Fives Entering quantities © Activities for Learning, Inc., 2012
- 103. Grouping in Fives Entering quantities 3 © Activities for Learning, Inc., 2012
- 104. Grouping in Fives Entering quantities 5 © Activities for Learning, Inc., 2012
- 105. Grouping in Fives Entering quantities 7 © Activities for Learning, Inc., 2012
- 106. Grouping in Fives Entering quantities 10 © Activities for Learning, Inc., 2012
- 107. Grouping in Fives The stairs © Activities for Learning, Inc., 2012
- 108. Bead Cards in Order © Activities for Learning, Inc., 2012
- 109. Finger Card Memory © Activities for Learning, Inc., 2012
- 110. Memory with Different Sets © Activities for Learning, Inc., 2012
- 111. Grouping in Fives Adding © Activities for Learning, Inc., 2012
- 112. Grouping in Fives Adding 4+3= © Activities for Learning, Inc., 2012
- 113. Grouping in Fives Adding 4+3= © Activities for Learning, Inc., 2012
- 114. Grouping in Fives Adding 4+3= © Activities for Learning, Inc., 2012
- 115. Grouping in Fives Adding 4+3= © Activities for Learning, Inc., 2012
- 116. Grouping in Fives Adding 4+3= 7 © Activities for Learning, Inc., 2012
- 117. Go to the Dump © Activities for Learning, Inc., 2012
- 118. Go to the Dump Objective: To learn and master the facts that total 10: © Activities for Learning, Inc., 2012
- 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. 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. Go to the Dump Objective: To learn and master the facts that total 11: © Activities for Learning, Inc., 2012
- 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. Swim to Ten Game © Activities for Learning, Inc., 2012
- 124. Swim to Ten Game Objective: To count purposefully and informally. © Activities for Learning, Inc., 2012
- 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. 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. 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. Swim to Ten Game Need: Basic number cards 1 to 5 © Activities for Learning, Inc., 2012
- 129. Swim to Ten Game Need: Basic number cards 1 to 5 Game board © Activities for Learning, Inc., 2012
- 130. Swim to Ten Game © Activities for Learning, Inc., 2012
- 131. Swim to Ten Game Setup: © Activities for Learning, Inc., 2012
- 132. Swim to Ten Game Setup: Each player chooses two lanes. © Activities for Learning, Inc., 2012
- 133. Swim to Ten Game Setup: Each player chooses two lanes. Objective of the Game: © Activities for Learning, Inc., 2012
- 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. 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. Swim to Ten Game © Activities for Learning, Inc., 2012
- 137. Swim to Ten Game © Activities for Learning, Inc., 2012
- 138. Swim to Ten Game © Activities for Learning, Inc., 2012
- 139. Swim to Ten Game 2 © Activities for Learning, Inc., 2012
- 140. Swim to Ten Game 2 © Activities for Learning, Inc., 2012
- 141. Swim to Ten Game 2 © Activities for Learning, Inc., 2012
- 142. Swim to Ten Game 2 © Activities for Learning, Inc., 2012
- 143. Swim to Ten Game 2 3 © Activities for Learning, Inc., 2012
- 144. Swim to Ten Game 2 3 © Activities for Learning, Inc., 2012
- 145. Swim to Ten Game 2 1 3 © Activities for Learning, Inc., 2012
- 146. Swim to Ten Game 2 1 3 © Activities for Learning, Inc., 2012
- 147. Swim to Ten Game 2 1 3 © Activities for Learning, Inc., 2012
- 148. Swim to Ten Game 2 1 3 © Activities for Learning, Inc., 2012
- 149. Swim to Ten Game 2 1 3 © Activities for Learning, Inc., 2012
- 150. Swim to Ten Game 2 1 3 © Activities for Learning, Inc., 2012
- 151. Swim to Ten Game 2 1 5 3 © Activities for Learning, Inc., 2012
- 152. Swim to Ten Game 2 1 5 3 © Activities for Learning, Inc., 2012
- 153. Swim to Ten Game 2 1 5 3 3 2 © Activities for Learning, Inc., 2012
- 154. Swim to Ten Game 2 1 5 3 3 2 © Activities for Learning, Inc., 2012
- 155. Swim to Ten Game 2 1 5 3 3 2 © Activities for Learning, Inc., 2012
- 156. Swim to Ten Game 2 1 5 3 3 2 © Activities for Learning, Inc., 2012
- 157. Swim to Ten Game 2 1 5 3 3 2 © Activities for Learning, Inc., 2012
- 158. Swim to Ten Game 2 1 5 3 3 2 © Activities for Learning, Inc., 2012
- 159. Swim to Ten Game 2 1 5 4 3 3 2 © Activities for Learning, Inc., 2012
- 160. Swim to Ten Game 2 1 5 4 3 3 2 © Activities for Learning, Inc., 2012
- 161. Swim to Ten Game 2 1 5 4 3 3 2 © Activities for Learning, Inc., 2012
- 162. Swim to Ten Game 2 1 5 4 3 3 2 © Activities for Learning, Inc., 2012
- 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. 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. “Math” Way of Naming Numbers © Activities for Learning, Inc., 2012
- 166. “Math” Way of Naming Numbers 11 = ten 1 © Activities for Learning, Inc., 2012
- 167. “Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 © Activities for Learning, Inc., 2012
- 168. “Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 © Activities for Learning, Inc., 2012
- 169. “Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 © Activities for Learning, Inc., 2012
- 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. “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. “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. “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. “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. “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. “Math” Way of Naming Numbers 137 = 1 hundred 3-ten 7 © Activities for Learning, Inc., 2012
- 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. 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. 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. 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. 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. Math Way of Naming Numbers Compared to reading: © Activities for Learning, Inc., 2012
- 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. 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. 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. Math Way of Naming Numbers Traditional names 4-ten = forty The “ty” means tens. © Activities for Learning, Inc., 2012
- 187. Math Way of Naming Numbers Traditional names 4-ten = forty The “ty” means tens. © Activities for Learning, Inc., 2012
- 188. Math Way of Naming Numbers Traditional names 6-ten = sixty The “ty” means tens. © Activities for Learning, Inc., 2012
- 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. 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. Math Way of Naming Numbers Traditional names 2-ten = twenty Two used to be pronounced “twoo.” © Activities for Learning, Inc., 2012
- 192. Math Way of Naming Numbers Traditional names A word game fireplace place-fire © Activities for Learning, Inc., 2012
- 193. Math Way of Naming Numbers Traditional names A word game fireplace place-fire newspaper paper-news © Activities for Learning, Inc., 2012
- 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. Math Way of Naming Numbers Traditional names ten 4 “Teen” also means ten. © Activities for Learning, Inc., 2012
- 196. Math Way of Naming Numbers Traditional names ten 4 teen 4 “Teen” also means ten. © Activities for Learning, Inc., 2012
- 197. Math Way of Naming Numbers Traditional names ten 4 teen 4 fourteen “Teen” also means ten. © Activities for Learning, Inc., 2012
- 198. Math Way of Naming Numbers Traditional names a one left © Activities for Learning, Inc., 2012
- 199. Math Way of Naming Numbers Traditional names a one left a left-one © Activities for Learning, Inc., 2012
- 200. Math Way of Naming Numbers Traditional names a one left a left-one eleven © Activities for Learning, Inc., 2012
- 201. Math Way of Naming Numbers Traditional names two left Two pronounce d “twoo.” © Activities for Learning, Inc., 2012
- 202. Math Way of Naming Numbers Traditional names two left twelve Two pronounce d “twoo.” © Activities for Learning, Inc., 2012
- 203. Rows and Columns © Activities for Learning, Inc., 2012
- 204. Rows and Columns Objective: To give the players practice in adding up to fifteen. © Activities for Learning, Inc., 2012
- 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. 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. 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. 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. 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. Rows and Columns 1 9 6 4 3 3 6 3 8 8 © Activities for Learning, Inc., 2012
- 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. 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. 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. Rows and Columns 1 6 4 3 3 1 5 1 3 8 8 © Activities for Learning, Inc., 2012
- 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. Corners™ 1 2 7 4 © Activities for Learning, Inc., 2012
- 217. Corners™ 1 Purpose: 2 7 4 To practice the facts that total 5, 10, 15, and 20. © Activities for Learning, Inc., 2012
- 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. Corners™ 1 2 7 Rules: 4 © Activities for Learning, Inc., 2012
- 220. Corners™ 1 2 7 Rules: 4 • To score, sum must equal 5, 10, 15 or 20. © Activities for Learning, Inc., 2012
- 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. Corners™ 1 2 7 4 1 3 8 10 © Activities for Learning, Inc., 2012
- 223. Corners™ 10 1 8 3 2 7 1 4 © Activities for Learning, Inc., 2012
- 224. Corners™ 10 1 8 3 2 7 1 4 9 3 6 4 © Activities for Learning, Inc., 2012
- 225. Corners™ 10 1 8 3 2 7 1 4 9 3 6 4 © Activities for Learning, Inc., 2012
- 226. Corners™ 10 1 8 3 2 7 1 4 9 3 6 4 7 8 4 2 © Activities for Learning, Inc., 2012
- 227. Corners™ 10 1 8 3 2 7 1 4 2 9 4 8 3 6 7 4 © Activities for Learning, Inc., 2012
- 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. 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. 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. 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. 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. Corners™ © Activities for Learning, Inc., 2012
- 234. Corners™ Players learn the facts that total 5, 10, 15, and 20. © Activities for Learning, Inc., 2012
- 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. 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. 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. Corners™ Scoring is done 10 mentally. 25 30 40 55 65 80 © Activities for Learning, Inc., 2012
- 239. Mental Addition 65 + 15 = © Activities for Learning, Inc., 2012
- 240. Mental Addition 65 + 15 = 65 + 10 © Activities for Learning, Inc., 2012
- 241. Mental Addition 65 + 15 = 65 + 10 + 5 = © Activities for Learning, Inc., 2012
- 242. Composing Numbers 3-ten © Activities for Learning, Inc., 2012
- 243. Composing Numbers 3-ten © Activities for Learning, Inc., 2012
- 244. Composing Numbers 3-ten © Activities for Learning, Inc., 2012
- 245. Composing Numbers 3-ten 30 © Activities for Learning, Inc., 2012
- 246. Composing Numbers 3-ten 30 © Activities for Learning, Inc., 2012
- 247. Composing Numbers 3-ten 30 © Activities for Learning, Inc., 2012
- 248. Composing Numbers 3-ten 7 30 © Activities for Learning, Inc., 2012
- 249. Composing Numbers 3-ten 7 30 © Activities for Learning, Inc., 2012
- 250. Composing Numbers 3-ten 7 30 7 © Activities for Learning, Inc., 2012
- 251. Composing Numbers 3-ten 7 30 7 © Activities for Learning, Inc., 2012
- 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. Composing Numbers 7-ten 70 Another example. © Activities for Learning, Inc., 2012
- 254. Composing Numbers 7-ten 8 70 © Activities for Learning, Inc., 2012
- 255. Composing Numbers 7-ten 8 70 © Activities for Learning, Inc., 2012
- 256. Composing Numbers 7-ten 8 70 8 © Activities for Learning, Inc., 2012
- 257. Composing Numbers 7-ten 8 78 8 © Activities for Learning, Inc., 2012
- 258. Composing Numbers 10-ten © Activities for Learning, Inc., 2012
- 259. Composing Numbers 10-ten 1 00 © Activities for Learning, Inc., 2012
- 260. Composing Numbers 10-ten 100 © Activities for Learning, Inc., 2012
- 261. Composing Numbers 10-ten 100 © Activities for Learning, Inc., 2012
- 262. Composing Numbers 1 hundred © Activities for Learning, Inc., 2012
- 263. Composing Numbers 1 hundred 100 © Activities for Learning, Inc., 2012
- 264. Composing Numbers 1 hundred 100 © Activities for Learning, Inc., 2012
- 265. Composing Numbers 1 hundred 100 © Activities for Learning, Inc., 2012
- 266. Composing Numbers 1 hundred 100 © Activities for Learning, Inc., 2012
- 267. Composing Numbers 2 hundred © Activities for Learning, Inc., 2012
- 268. Composing Numbers 2 hundred © Activities for Learning, Inc., 2012
- 269. Composing Numbers 2 hundred 200 © Activities for Learning, Inc., 2012
- 270. Counting by 2s and 5s © Activities for Learning, Inc., 2012
- 271. Counting by 2s and 5s Counting by 2s © Activities for Learning, Inc., 2012
- 272. Counting by 2s and 5s Counting by 2s 2 © Activities for Learning, Inc., 2012
- 273. Counting by 2s and 5s Counting by 2s 2 4 © Activities for Learning, Inc., 2012
- 274. Counting by 2s and 5s Counting by 2s 2 4 6 © Activities for Learning, Inc., 2012
- 275. Counting by 2s and 5s Counting by 2s 2 4 6 8 © Activities for Learning, Inc., 2012
- 276. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 © Activities for Learning, Inc., 2012
- 277. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 © Activities for Learning, Inc., 2012
- 278. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 14 © Activities for Learning, Inc., 2012
- 279. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 14 16 © Activities for Learning, Inc., 2012
- 280. Counting by 2s and 5s Counting by 2s 2 4 6 8 10 12 14 16 18 © Activities for Learning, Inc., 2012
- 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. Counting by 2s and 5s Counting by 5s © Activities for Learning, Inc., 2012
- 283. Counting by 2s and 5s Counting by 5s 5 © Activities for Learning, Inc., 2012
- 284. Counting by 2s and 5s Counting by 5s 5 10 © Activities for Learning, Inc., 2012
- 285. Counting by 2s and 5s Counting by 5s 5 10 15 © Activities for Learning, Inc., 2012
- 286. Counting by 2s and 5s Counting by 5s 5 10 15 20 © Activities for Learning, Inc., 2012
- 287. Counting by 2s and 5s Counting by 5s 5 10 15 20 25 © Activities for Learning, Inc., 2012
- 288. Counting by 2s and 5s Counting by 5s 5 10 15 20 25 30 © Activities for Learning, Inc., 2012
- 289. Evens and Odds Evens © Activities for Learning, Inc., 2012
- 290. Evens and Odds Evens Use two fingers and touch each pair in succession. © Activities for Learning, Inc., 2012
- 291. Evens and Odds Evens Use two fingers and touch each pair in succession. © Activities for Learning, Inc., 2012
- 292. Evens and Odds Evens Use two fingers and touch each pair in succession. © Activities for Learning, Inc., 2012
- 293. Evens and Odds Evens Use two fingers and touch each pair in succession. EVEN! © Activities for Learning, Inc., 2012
- 294. Evens and Odds Odds Use two fingers and touch each pair in succession. © Activities for Learning, Inc., 2012
- 295. Evens and Odds Odds Use two fingers and touch each pair in succession. © Activities for Learning, Inc., 2012
- 296. Evens and Odds Odds Use two fingers and touch each pair in succession. © Activities for Learning, Inc., 2012
- 297. Evens and Odds Odds Use two fingers and touch each pair in succession. © Activities for Learning, Inc., 2012
- 298. Evens and Odds Odds Use two fingers and touch each pair in succession. ODD! © Activities for Learning, Inc., 2012
- 299. Fact Strategies © Activities for Learning, Inc., 2012
- 300. Fact Strategies Complete the Ten 9+5= © Activities for Learning, Inc., 2012
- 301. Fact Strategies Complete the Ten 9+5= © Activities for Learning, Inc., 2012
- 302. Fact Strategies Complete the Ten 9+5= © Activities for Learning, Inc., 2012
- 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. Fact Strategies Complete the Ten 9+5= Take 1 from the 5 and give it to the 9. © Activities for Learning, Inc., 2012
- 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. 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. Fact Strategies Two Fives 8+6= © Activities for Learning, Inc., 2012
- 308. Fact Strategies Two Fives 8+6= © Activities for Learning, Inc., 2012
- 309. Fact Strategies Two Fives 8+6= © Activities for Learning, Inc., 2012
- 310. Fact Strategies Two Fives 8+6= © Activities for Learning, Inc., 2012
- 311. Fact Strategies Two Fives 8+6= 10 + 4 = 14 © Activities for Learning, Inc., 2012
- 312. Fact Strategies Going Down 15 – 9 = © Activities for Learning, Inc., 2012
- 313. Fact Strategies Going Down 15 – 9 = © Activities for Learning, Inc., 2012
- 314. Fact Strategies Going Down 15 – 9 = Subtract 5; then 4. © Activities for Learning, Inc., 2012
- 315. Fact Strategies Going Down 15 – 9 = Subtract 5; then 4. © Activities for Learning, Inc., 2012
- 316. Fact Strategies Going Down 15 – 9 = Subtract 5; then 4. © Activities for Learning, Inc., 2012
- 317. Fact Strategies Going Down 15 – 9 = 6 Subtract 5; then 4. © Activities for Learning, Inc., 2012
- 318. Fact Strategies Subtract from 10 15 – 9 = © Activities for Learning, Inc., 2012
- 319. Fact Strategies Subtract from 10 15 – 9 = Subtract 9 from 10. © Activities for Learning, Inc., 2012
- 320. Fact Strategies Subtract from 10 15 – 9 = Subtract 9 from 10. © Activities for Learning, Inc., 2012
- 321. Fact Strategies Subtract from 10 15 – 9 = Subtract 9 from 10. © Activities for Learning, Inc., 2012