2012 A Plus AL Abacus

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2012 A Plus AL Abacus

  1. 1. Overcoming Math Obstacles through Visualizing with the AL Abacus Based on the work of Joan A. Cotter, Ph.D Presented by Tracy Mittleider, MSEd October 25, 2012© Activities for Learning, Inc., 2012
  2. 2. Introduction Presented by 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. CotterEducational 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 EducationWork 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. AL Abacus© Activities for Learning, Inc., 2012
  5. 5. AL Abacus 1000 100 10 1© Activities for Learning, Inc., 2012
  6. 6. What is the AL Abacus?© Activities for Learning, Inc., 2012
  7. 7. What is the AL Abacus? • Visual and tactile manipulative© Activities for Learning, Inc., 2012
  8. 8. What is the AL Abacus? • Visual and tactile manipulative • Develops mental images of© Activities for Learning, Inc., 2012
  9. 9. What is the AL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities© Activities for Learning, Inc., 2012
  10. 10. What is the AL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities Strategies© Activities for Learning, Inc., 2012
  11. 11. What is the AL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities Strategies Mathematical Operations© Activities for Learning, Inc., 2012
  12. 12. Quantities With Fingers© Activities for Learning, Inc., 2012
  13. 13. Quantities With Fingers© Activities for Learning, Inc., 2012
  14. 14. Quantities With Fingers© Activities for Learning, Inc., 2012
  15. 15. Quantities With Fingers© Activities for Learning, Inc., 2012
  16. 16. Quantities With Fingers© Activities for Learning, Inc., 2012
  17. 17. Counting Model How many?© Activities for Learning, Inc., 2012
  18. 18. Counting Model 1 What we see© Activities for Learning, Inc., 2012
  19. 19. Counting Model 2 What we see© Activities for Learning, Inc., 2012
  20. 20. Counting Model 3 What we see© Activities for Learning, Inc., 2012
  21. 21. Counting Model 4 What we see© Activities for Learning, Inc., 2012
  22. 22. Counting Model 1 What the young child sees© Activities for Learning, Inc., 2012
  23. 23. Counting Model 2 What the young child sees© Activities for Learning, Inc., 2012
  24. 24. Counting Model 3 What the young child sees© Activities for Learning, Inc., 2012
  25. 25. Counting Model 4 What the young child sees© Activities for Learning, Inc., 2012
  26. 26. Visualizing 8 Try to visualize 8 apples without grouping.© Activities for Learning, Inc., 2012
  27. 27. Visualizing 8 Try to visualize 8 apples without grouping.© Activities for Learning, Inc., 2012
  28. 28. Visualizing 8 Now try to visualize 5 as red and 3 as green.© Activities for Learning, Inc., 2012
  29. 29. Visualizing 8 Now try to visualize 5 as red and 3 as green.© Activities for Learning, Inc., 2012
  30. 30. Grouping by 5s© Activities for Learning, Inc., 2012
  31. 31. Grouping by 5s Early Roman grouped by 5s© Activities for Learning, Inc., 2012
  32. 32. Grouping by 5s :© Activities for Learning, Inc., 2012
  33. 33. Grouping by 5s : Who could read the music?© Activities for Learning, Inc., 2012
  34. 34. What is Visualizing?© Activities for Learning, Inc., 2012
  35. 35. What is Visualizing? To form a mental image or vision; to imagine.© Activities for Learning, Inc., 2012
  36. 36. Visualizing Needed in:© Activities for Learning, Inc., 2012
  37. 37. Visualizing Needed in: • Mathematics© Activities for Learning, Inc., 2012
  38. 38. Visualizing Needed in: • Mathematics • Botany© Activities for Learning, Inc., 2012
  39. 39. Visualizing Needed in: • Mathematics • Botany • Geography© Activities for Learning, Inc., 2012
  40. 40. Visualizing Needed in: • Mathematics • Botany • Geography • Engineering© Activities for Learning, Inc., 2012
  41. 41. Visualizing Needed in: • Mathematics • Botany • Geography • Engineering • Construction© Activities for Learning, Inc., 2012
  42. 42. Visualizing Needed in: • Mathematics • Botany • Geography • Engineering • Construction • Spelling© Activities for Learning, Inc., 2012
  43. 43. Visualizing Needed in: • • Architecture Mathematics • Botany • Geography • Engineering • Construction • Spelling© Activities for Learning, Inc., 2012
  44. 44. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Geography • Engineering • Construction • Spelling© Activities for Learning, Inc., 2012
  45. 45. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Engineering • Construction • Spelling© Activities for Learning, Inc., 2012
  46. 46. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Chemistry • Engineering • Construction • Spelling© Activities for Learning, Inc., 2012
  47. 47. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Chemistry • Engineering • Physics • Construction • Spelling© Activities for Learning, Inc., 2012
  48. 48. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Chemistry • Engineering • Physics • Construction • Surgery • Spelling© Activities for Learning, Inc., 2012
  49. 49. Entering Quantities© Activities for Learning, Inc., 2012
  50. 50. Entering Quantities© Activities for Learning, Inc., 2012
  51. 51. Entering Quantities© Activities for Learning, Inc., 2012
  52. 52. Entering Quantities 3© Activities for Learning, Inc., 2012
  53. 53. Entering Quantities© Activities for Learning, Inc., 2012
  54. 54. Entering Quantities© Activities for Learning, Inc., 2012
  55. 55. Entering Quantities© Activities for Learning, Inc., 2012
  56. 56. Entering Quantities 5© Activities for Learning, Inc., 2012
  57. 57. Entering Quantities© Activities for Learning, Inc., 2012
  58. 58. Entering Quantities© Activities for Learning, Inc., 2012
  59. 59. Entering Quantities© Activities for Learning, Inc., 2012
  60. 60. Entering Quantities 7© Activities for Learning, Inc., 2012
  61. 61. Entering Quantities© Activities for Learning, Inc., 2012
  62. 62. Entering Quantities 10© Activities for Learning, Inc., 2012
  63. 63. Entering Quantities© Activities for Learning, Inc., 2012
  64. 64. Simple Adding© Activities for Learning, Inc., 2012
  65. 65. Simple Adding 4 + 3 = ___© Activities for Learning, Inc., 2012
  66. 66. Simple Adding 4 + 3 = ___© Activities for Learning, Inc., 2012
  67. 67. Simple Adding 4 + 3 = ___© Activities for Learning, Inc., 2012
  68. 68. Simple Adding 4 + 3 = ___© Activities for Learning, Inc., 2012
  69. 69. Simple Adding 4 + 3 = ___ 7© Activities for Learning, Inc., 2012
  70. 70. Typical Worksheet© Activities for Learning, Inc., 2012
  71. 71. Facts Equaling 10© Activities for Learning, Inc., 2012
  72. 72. Facts Equaling 10© Activities for Learning, Inc., 2012
  73. 73. Facts Equaling 10© Activities for Learning, Inc., 2012
  74. 74. Facts Equaling 10© Activities for Learning, Inc., 2012
  75. 75. Facts Equaling 10© Activities for Learning, Inc., 2012
  76. 76. Facts Equaling 10© Activities for Learning, Inc., 2012
  77. 77. Facts Equaling 10© Activities for Learning, Inc., 2012
  78. 78. Facts Equaling 10© Activities for Learning, Inc., 2012
  79. 79. Facts Equaling 10© Activities for Learning, Inc., 2012
  80. 80. Go to the Dump Game© Activities for Learning, Inc., 2012
  81. 81. Go to the Dump Game A “Go Fish” type of game where the pairs are:© Activities for Learning, Inc., 2012
  82. 82. Go to the Dump Game A “Go Fish” type of game where the pairs are: 1 & 9 2 & 8 3 & 7 4 & 6 5 & 5© Activities for Learning, Inc., 2012
  83. 83. Go to the Dump Game A “Go Fish” type of game where the pairs are: 1 & 9 2 & 8 3 & 7 4 & 6 5 & 5© Activities for Learning, Inc., 2012
  84. 84. Math Way of Naming Numbers© Activities for Learning, Inc., 2012
  85. 85. 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
  86. 86. Math Way of Naming Numbers • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic.© Activities for Learning, Inc., 2012
  87. 87. Math Way of Naming Numbers • 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 first teach the name of the quantity (math way).© Activities for Learning, Inc., 2012
  88. 88. Math Way of Naming Numbers • Asian children learn mathematics using the math way of number naming.© Activities for Learning, Inc., 2012
  89. 89. Math Way of Naming Numbers • Asian children learn mathematics using the math way of number naming. • 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
  90. 90. Math Way of Naming Numbers • Asian children learn mathematics using the math way of number naming. • 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. Using the math way of number naming for a few months helps children master place value, the most important concept in arithmetic.© Activities for Learning, Inc., 2012
  91. 91. Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones.© Activities for Learning, Inc., 2012
  92. 92. Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. The pattern that is needed to make sense of tens and ones is© Activities for Learning, Inc., 2012
  93. 93. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48.© Activities for Learning, Inc., 2012
  94. 94. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48.© Activities for Learning, Inc., 2012
  95. 95. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14.© Activities for Learning, Inc., 2012
  96. 96. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  97. 97. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  98. 98. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  99. 99. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  100. 100. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  101. 101. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  102. 102. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  103. 103. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.© Activities for Learning, Inc., 2012
  104. 104. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children who understand tens remove a ten and 4 ones.© Activities for Learning, Inc., 2012
  105. 105. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children who understand tens remove a ten and 4 ones.© Activities for Learning, Inc., 2012
  106. 106. Subtracting 14 From 48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. Children who understand tens remove a ten and 4 ones.© Activities for Learning, Inc., 2012
  107. 107. Understanding Place Value 2-ten 2 0© Activities for Learning, Inc., 2012
  108. 108. Understanding Place Value 2-ten 2 0© Activities for Learning, Inc., 2012
  109. 109. Understanding Place Value 2-ten 2 0© Activities for Learning, Inc., 2012
  110. 110. Understanding Place Value 3-ten 2 0 3© Activities for Learning, Inc., 2012
  111. 111. Understanding Place Value 3-ten 2 0 3© Activities for Learning, Inc., 2012
  112. 112. Understanding Place Value 3-ten 2 0 3© Activities for Learning, Inc., 2012
  113. 113. Understanding Place Value 3-ten 7 2 0 3 7© Activities for Learning, Inc., 2012
  114. 114. Understanding Place Value 3-ten 7 3 7 2 0© Activities for Learning, Inc., 2012
  115. 115. Understanding Place Value 6-ten 2 0 6© Activities for Learning, Inc., 2012
  116. 116. Understanding Place Value 6-ten 2 2 0 6 2© Activities for Learning, Inc., 2012
  117. 117. Understanding Place Value 6-ten 2 6 2 2 0© Activities for Learning, Inc., 2012
  118. 118. Understanding Place Value 10-ten 1 0 0© Activities for Learning, Inc., 2012
  119. 119. Understanding Place Value 10-ten 1 0 0© Activities for Learning, Inc., 2012
  120. 120. Understanding Place Value 10-ten 1 0 0© Activities for Learning, Inc., 2012
  121. 121. Understanding Place Value 1 hundred 1 0 0© Activities for Learning, Inc., 2012
  122. 122. Understanding Place Value 1 hundred 1 0 0© Activities for Learning, Inc., 2012
  123. 123. Understanding Place Value 1 hundred 1 0 0© Activities for Learning, Inc., 2012
  124. 124. Understanding Place Value 1 hundred 1 0 0© Activities for Learning, Inc., 2012
  125. 125. Understanding Place Value 2 hundred 2 0 0© Activities for Learning, Inc., 2012
  126. 126. Understanding Place Value 10 hundred 1 0 0 0© Activities for Learning, Inc., 2012
  127. 127. Understanding Place Value 10 hundred 1 0 0 0© Activities for Learning, Inc., 2012
  128. 128. Understanding Place Value 10 hundred 1 0 0 0© Activities for Learning, Inc., 2012
  129. 129. Understanding Place Value 10 hundred 1 0 0 0© Activities for Learning, Inc., 2012
  130. 130. Understanding Place Value 1 thousand 1 0 0 0© Activities for Learning, Inc., 2012
  131. 131. Understanding Place Value 1 thousand 1 0 0 0© Activities for Learning, Inc., 2012
  132. 132. Understanding Place Value 1 thousand 1 0 0 0© Activities for Learning, Inc., 2012
  133. 133. Understanding Place Value 1 thousand 1 0 0 0© Activities for Learning, Inc., 2012
  134. 134. Understanding Place Value 1 thousand 1 0 0 0© Activities for Learning, Inc., 2012
  135. 135. Place Value Cards 3 0 3- ten 3 0 0 3 hun-dred 3 0 0 0 3 th- ou-sand© Activities for Learning, Inc., 2012
  136. 136. Place Value Cards 3 0 0 0 3 0 0 0 3 0 0 8 6 5 0 6 0 0 6 0 0 5 0 8 5 0 8© Activities for Learning, Inc., 2012
  137. 137. Place Value Cards 3 0 0 0 3 0 0 0 3 0 0 8 0 8 8© Activities for Learning, Inc., 2012
  138. 138. Traditional Names 4-ten = forty© Activities for Learning, Inc., 2012
  139. 139. Traditional Names 6-ten = sixty© Activities for Learning, Inc., 2012
  140. 140. Traditional Names 8-ten = eighty© Activities for Learning, Inc., 2012
  141. 141. Traditional Names A word game© Activities for Learning, Inc., 2012
  142. 142. Traditional Names A word game fireplace© Activities for Learning, Inc., 2012
  143. 143. Traditional Names A word game fireplace place-fire© Activities for Learning, Inc., 2012
  144. 144. Traditional Names A word game fireplace place-fire newspaper© Activities for Learning, Inc., 2012
  145. 145. Traditional Names A word game fireplace place-fire newspaper paper-news© Activities for Learning, Inc., 2012
  146. 146. Traditional Names A word game fireplace place-fire newspaper paper-news box-mail© Activities for Learning, Inc., 2012
  147. 147. Traditional Names A word game fireplace place-fire newspaper paper-news box-mail mailbox© Activities for Learning, Inc., 2012
  148. 148. Traditional Names© Activities for Learning, Inc., 2012
  149. 149. Traditional Names ten 4© Activities for Learning, Inc., 2012
  150. 150. Traditional Names ten 4 teen 4 “Teen” also means ten.© Activities for Learning, Inc., 2012
  151. 151. Traditional Names ten 4 teen 4 fourteen “Teen” also means ten.© Activities for Learning, Inc., 2012
  152. 152. Traditional Names© Activities for Learning, Inc., 2012
  153. 153. Traditional Names ten 7© Activities for Learning, Inc., 2012
  154. 154. Traditional Names ten 7 teen 7© Activities for Learning, Inc., 2012
  155. 155. Traditional Names ten 7 teen 7 seventeen© Activities for Learning, Inc., 2012
  156. 156. Traditional Names© Activities for Learning, Inc., 2012
  157. 157. Traditional Names a one left© Activities for Learning, Inc., 2012
  158. 158. Traditional Names a one left a left-one© Activities for Learning, Inc., 2012
  159. 159. Traditional Names a one left a left-one eleven© Activities for Learning, Inc., 2012
  160. 160. Traditional Names© Activities for Learning, Inc., 2012
  161. 161. Traditional Names two leftTwopronounced“twoo.”© Activities for Learning, Inc., 2012
  162. 162. Traditional Names two left twelveTwopronounced“twoo.”© Activities for Learning, Inc., 2012
  163. 163. Strategies A strategy is an efficient way to learn a new fact or recall a forgotten fact.© Activities for Learning, Inc., 2012
  164. 164. Strategies A strategy is an efficient way to learn a new fact or recall a forgotten fact. A visual representation is a powerful strategy.© Activities for Learning, Inc., 2012
  165. 165. Strategy: Complete the Ten 9 + 5 = ___© Activities for Learning, Inc., 2012
  166. 166. Strategy: Complete the Ten 9 + 5 = ___© Activities for Learning, Inc., 2012
  167. 167. Strategy: Complete the Ten 9 + 5 = ___© Activities for Learning, Inc., 2012
  168. 168. Strategy: Complete the Ten 9 + 5 = ___© Activities for Learning, Inc., 2012
  169. 169. Strategy: Complete the Ten 9 + 5 = ___© Activities for Learning, Inc., 2012
  170. 170. Strategy: Complete the Ten 9 + 5 = ___© Activities for Learning, Inc., 2012
  171. 171. Strategy: Complete the Ten 9 + 5 = ___ 14© Activities for Learning, Inc., 2012
  172. 172. Strategy: Complete the Ten 9 + 7 = ___© Activities for Learning, Inc., 2012
  173. 173. Strategy: Complete the Ten 9 + 7 = ___© Activities for Learning, Inc., 2012
  174. 174. Strategy: Complete the Ten 9 + 7 = ___© Activities for Learning, Inc., 2012
  175. 175. Strategy: Complete the Ten 9 + 7 = ___© Activities for Learning, Inc., 2012
  176. 176. Strategy: Complete the Ten 9 + 7 = ___ 16© Activities for Learning, Inc., 2012
  177. 177. Strategy: Two Fives 8+6=© Activities for Learning, Inc., 2012
  178. 178. Strategy: Two Fives 8+6=© Activities for Learning, Inc., 2012
  179. 179. Strategy: Two Fives 8+6=© Activities for Learning, Inc., 2012
  180. 180. Strategy: Two Fives 8+6=© Activities for Learning, Inc., 2012
  181. 181. Strategy: Two Fives 8 + 6 = 10 + 4© Activities for Learning, Inc., 2012
  182. 182. Strategy: Two Fives 8 + 6 = 10 + 4 = 14© Activities for Learning, Inc., 2012
  183. 183. Strategy: Two Fives 7+5=© Activities for Learning, Inc., 2012
  184. 184. Strategy: Two Fives 7+5=© Activities for Learning, Inc., 2012
  185. 185. Strategy: Two Fives 7+5=© Activities for Learning, Inc., 2012
  186. 186. Strategy: Two Fives 7 + 5 = 10 + 2 = 12© Activities for Learning, Inc., 2012
  187. 187. Strategy: Going Down 15 – 9 = ___© Activities for Learning, Inc., 2012
  188. 188. Strategy: Going Down 15 – 9 = ___© Activities for Learning, Inc., 2012
  189. 189. Strategy: Going Down 15 – 9 = ___ Subtract 5, then 4© Activities for Learning, Inc., 2012
  190. 190. Strategy: Going Down 15 – 9 = ___ Subtract 5, then 4© Activities for Learning, Inc., 2012
  191. 191. Strategy: Going Down 15 – 9 = ___ Subtract 5, then 4© Activities for Learning, Inc., 2012
  192. 192. Strategy: Going Down 15 – 9 = ___ 6 Subtract 5, then 4© Activities for Learning, Inc., 2012
  193. 193. Strategy: Going Down 15 – 9 = ___© Activities for Learning, Inc., 2012
  194. 194. Strategy: Going Down 15 – 9 = ___ Subtract 9 from the 10© Activities for Learning, Inc., 2012
  195. 195. Strategy: Going Down 15 – 9 = ___ Subtract 9 from the 10© Activities for Learning, Inc., 2012
  196. 196. Strategy: Going Down 15 – 9 = ___ 6 Subtract 9 from the 10© Activities for Learning, Inc., 2012
  197. 197. Strategy: Going Up 13 – 9 =© Activities for Learning, Inc., 2012
  198. 198. Strategy: Going Up 13 – 9 = Start at 9; go up to 13© Activities for Learning, Inc., 2012
  199. 199. Strategy: Going Up 13 – 9 = Start at 9; go up to 13© Activities for Learning, Inc., 2012
  200. 200. Strategy: Going Up 13 – 9 = Start at 9; go up to 13© Activities for Learning, Inc., 2012
  201. 201. Strategy: Going Up 13 – 9 = 1 + 3 Start at 9; go up to 13© Activities for Learning, Inc., 2012
  202. 202. Strategy: Going Up 13 – 9 = 1 + 3 = 4 Start at 9; go up to 13© Activities for Learning, Inc., 2012
  203. 203. AL Abacus - Side 2 1000 10 1 Cleared© Activities for Learning, Inc., 2012
  204. 204. AL Abacus - Side 2 1000 10 1 Thousands© Activities for Learning, Inc., 2012
  205. 205. AL Abacus - Side 2 1000 100 10 1 Hundreds© Activities for Learning, Inc., 2012
  206. 206. AL Abacus - Side 2 1000 100 10 1 Tens© Activities for Learning, Inc., 2012
  207. 207. AL Abacus - Side 2 1000 100 10 1 Ones© Activities for Learning, Inc., 2012
  208. 208. AL Abacus - Side 2 1000 100 10 1 8 + 6© Activities for Learning, Inc., 2012
  209. 209. AL Abacus - Side 2 1000 100 10 1 8 + 6© Activities for Learning, Inc., 2012
  210. 210. AL Abacus - Side 2 1000 100 10 1 8 + 6© Activities for Learning, Inc., 2012
  211. 211. AL Abacus - Side 2 1000 100 10 1 8 + 6 14© Activities for Learning, Inc., 2012
  212. 212. AL Abacus - Side 2 1000 100 10 1 8 + 6 14© Activities for Learning, Inc., 2012
  213. 213. AL Abacus - Side 2 1000 100 10 1 8 + 6 14© Activities for Learning, Inc., 2012
  214. 214. AL Abacus - Side 2 1000 100 10 1 8 + 6 14© Activities for Learning, Inc., 2012
  215. 215. AL Abacus - Side 2 1000 100 10 1 Why keep the two columns even?© Activities for Learning, Inc., 2012
  216. 216. AL Abacus - Side 2 1000 100 10 1© Activities for Learning, Inc., 2012
  217. 217. AL Abacus - Side 2 1000 100 10 1 Do we need to trade?© Activities for Learning, Inc., 2012
  218. 218. Bead Trading 1000 100 10 1© Activities for Learning, Inc., 2012
  219. 219. Bead Trading 1000 100 10 1 7© Activities for Learning, Inc., 2012
  220. 220. Bead Trading 1000 100 10 1 7© Activities for Learning, Inc., 2012
  221. 221. Bead Trading 1000 100 10 1 6© Activities for Learning, Inc., 2012
  222. 222. Bead Trading 1000 100 10 1 6© Activities for Learning, Inc., 2012
  223. 223. Bead Trading 1000 100 10 1 6© Activities for Learning, Inc., 2012
  224. 224. Bead Trading 1000 100 10 1 6© Activities for Learning, Inc., 2012
  225. 225. Bead Trading 1000 100 10 1 9© Activities for Learning, Inc., 2012
  226. 226. Bead Trading 1000 100 10 1 9© Activities for Learning, Inc., 2012
  227. 227. Bead Trading 1000 100 10 1 9© Activities for Learning, Inc., 2012
  228. 228. Bead Trading 1000 100 10 1 9© Activities for Learning, Inc., 2012
  229. 229. Bead Trading 1000 100 10 1 5© Activities for Learning, Inc., 2012
  230. 230. Bead Trading 1000 100 10 1 5© Activities for Learning, Inc., 2012
  231. 231. Bead Trading • To appreciate a pattern, there must be at least three examples in the sequence.© Activities for Learning, Inc., 2012
  232. 232. Bead Trading • To appreciate a pattern, there must be at least three examples in the sequence. • Bead trading helps the child experience the greater value of each column.© Activities for Learning, Inc., 2012
  233. 233. Bead Trading • To appreciate a pattern, there must be at least three examples in the sequence. • Bead trading helps the child experience the greater value of each column. • Therefore, to understand the never-ending pattern of trading, the child must trade 10 ones for 1 ten, 10 tens for 1 hundred, and 10 hundreds for 1 thousand.© Activities for Learning, Inc., 2012
  234. 234. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  235. 235. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  236. 236. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  237. 237. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  238. 238. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  239. 239. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  240. 240. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  241. 241. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  242. 242. Four Digit Addition 1000 100 10 1 3658 + 2738© Activities for Learning, Inc., 2012
  243. 243. Four Digit Addition 1000 100 10 1 3658 + 2738 6© Activities for Learning, Inc., 2012
  244. 244. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6© Activities for Learning, Inc., 2012
  245. 245. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6© Activities for Learning, Inc., 2012
  246. 246. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6© Activities for Learning, Inc., 2012
  247. 247. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96© Activities for Learning, Inc., 2012
  248. 248. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96© Activities for Learning, Inc., 2012
  249. 249. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96© Activities for Learning, Inc., 2012
  250. 250. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96© Activities for Learning, Inc., 2012
  251. 251. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96© Activities for Learning, Inc., 2012
  252. 252. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96© Activities for Learning, Inc., 2012
  253. 253. Four Digit Addition 1000 100 10 1 1 3658 + 2738 396© Activities for Learning, Inc., 2012
  254. 254. Four Digit Addition 1000 100 10 1 11 3658 + 2738 396© Activities for Learning, Inc., 2012
  255. 255. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396© Activities for Learning, Inc., 2012
  256. 256. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396© Activities for Learning, Inc., 2012
  257. 257. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396© Activities for Learning, Inc., 2012
  258. 258. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396© Activities for Learning, Inc., 2012
  259. 259. Four Digit Addition Most children who 1 1 learn to add on the 3658 AL Abacus + 2738 transition 6396 to the paper and pencil algorithm without further instruction.© Activities for Learning, Inc., 2012
  260. 260. Multiplying on the AL Abacus 6x4 (6 taken 4 times)© Activities for Learning, Inc., 2012
  261. 261. Multiplying on the AL Abacus 5x7© Activities for Learning, Inc., 2012
  262. 262. Multiplying on the AL Abacus 5x7© Activities for Learning, Inc., 2012
  263. 263. Multiplying on the AL Abacus 5x7© Activities for Learning, Inc., 2012
  264. 264. Multiplying on the AL Abacus 5x7© Activities for Learning, Inc., 2012
  265. 265. Multiplying on the AL Abacus 5x7 (30 + 5)© Activities for Learning, Inc., 2012
  266. 266. Multiplying on the AL Abacus 7x7© Activities for Learning, Inc., 2012
  267. 267. Multiplying on the AL Abacus 7x7© Activities for Learning, Inc., 2012
  268. 268. Multiplying on the AL Abacus 7x7© Activities for Learning, Inc., 2012
  269. 269. Multiplying on the AL Abacus 7x7© Activities for Learning, Inc., 2012
  270. 270. Multiplying on the AL Abacus 7x7© Activities for Learning, Inc., 2012
  271. 271. Multiplying on the AL Abacus 7 x 7 = 25 + 10 + 10 + 4© Activities for Learning, Inc., 2012
  272. 272. Multiplying on the AL Abacus 9x3 (30 – 3)© Activities for Learning, Inc., 2012
  273. 273. Commutative Property 9x3© Activities for Learning, Inc., 2012
  274. 274. Commutative Property 9x3 3x9© Activities for Learning, Inc., 2012
  275. 275. Effective Math Users “…The now well established fact that those who are mathematically effective in daily life seldom make use in their heads of the standard written methods which are taught in the classroom.” W. H. Cockroft, 1982 - renowned math educator in England© Activities for Learning, Inc., 2012
  276. 276. What is the AL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities Strategies Mathematical Operations© Activities for Learning, Inc., 2012
  277. 277. In Conclusion … Math needs to be taught so 95 percent is understood and only 5 percent memorized. Richard Skemp -- major pioneer in mathematics education© Activities for Learning, Inc., 2012
  278. 278. Overcoming Math Obstacles through Visualizing with the AL Abacus Based on the work of Joan A. Cotter, Ph.D Presented by Tracy Mittleider, MSEd October 25, 2012© Activities for Learning, Inc., 2012
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