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2012 A Plus AL Abacus
- 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. 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. 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. AL Abacus © Activitiesfor Learning, Inc., 2012
- 5. AL Abacus 1000 100 10 1 © Activities for Learning, Inc., 2012
- 6. What is theAL Abacus? © Activities for Learning, Inc., 2012
- 7. What is theAL Abacus? • Visual and tactile manipulative © Activities for Learning, Inc., 2012
- 8. What is theAL Abacus? • Visual and tactile manipulative • Develops mental images of © Activities for Learning, Inc., 2012
- 9. What is theAL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities © Activities for Learning, Inc., 2012
- 10. What is theAL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities Strategies © Activities for Learning, Inc., 2012
- 11. What is theAL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities Strategies Mathematical Operations © Activities for Learning, Inc., 2012
- 12. Quantities With Fingers ©Activities for Learning, Inc., 2012
- 13. Quantities With Fingers ©Activities for Learning, Inc., 2012
- 14. Quantities With Fingers ©Activities for Learning, Inc., 2012
- 15. Quantities With Fingers ©Activities for Learning, Inc., 2012
- 16. Quantities With Fingers ©Activities for Learning, Inc., 2012
- 17. Counting Model How many? © Activities for Learning, Inc., 2012
- 18. Counting Model 1 What we see © Activities for Learning, Inc., 2012
- 19. Counting Model 2 What we see © Activities for Learning, Inc., 2012
- 20. Counting Model 3 What we see © Activities for Learning, Inc., 2012
- 21. Counting Model 4 What we see © Activities for Learning, Inc., 2012
- 22. Counting Model 1 What the young child sees © Activities for Learning, Inc., 2012
- 23. Counting Model 2 What the young child sees © Activities for Learning, Inc., 2012
- 24. Counting Model 3 What the young child sees © Activities for Learning, Inc., 2012
- 25. Counting Model 4 What the young child sees © Activities for Learning, Inc., 2012
- 26. Visualizing 8 Try to visualize 8 apples without grouping. © Activities for Learning, Inc., 2012
- 27. Visualizing 8 Try to visualize 8 apples without grouping. © Activities for Learning, Inc., 2012
- 28. Visualizing 8 Now try to visualize 5 as red and 3 as green. © Activities for Learning, Inc., 2012
- 29. Visualizing 8 Now try to visualize 5 as red and 3 as green. © Activities for Learning, Inc., 2012
- 30. Grouping by 5s ©Activities for Learning, Inc., 2012
- 31. Grouping by 5s Early Roman grouped by 5s © Activities for Learning, Inc., 2012
- 32. Grouping by 5s : © Activities for Learning, Inc., 2012
- 33. Grouping by 5s : Who could read the music? © Activities for Learning, Inc., 2012
- 34. What is Visualizing? ©Activities for Learning, Inc., 2012
- 35. What is Visualizing? To form a mental image or vision; to imagine. © Activities for Learning, Inc., 2012
- 36. Visualizing Needed in: ©Activities for Learning, Inc., 2012
- 37. Visualizing Needed in: • Mathematics © Activities for Learning, Inc., 2012
- 38. Visualizing Needed in: • Mathematics • Botany © Activities for Learning, Inc., 2012
- 39. Visualizing Needed in: • Mathematics • Botany • Geography © Activities for Learning, Inc., 2012
- 40. Visualizing Needed in: • Mathematics • Botany • Geography • Engineering © Activities for Learning, Inc., 2012
- 41. Visualizing Needed in: • Mathematics • Botany • Geography • Engineering • Construction © Activities for Learning, Inc., 2012
- 42. Visualizing Needed in: • Mathematics • Botany • Geography • Engineering • Construction • Spelling © Activities for Learning, Inc., 2012
- 43. Visualizing Needed in: • • Architecture Mathematics • Botany • Geography • Engineering • Construction • Spelling © Activities for Learning, Inc., 2012
- 44. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Geography • Engineering • Construction • Spelling © Activities for Learning, Inc., 2012
- 45. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Engineering • Construction • Spelling © Activities for Learning, Inc., 2012
- 46. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Chemistry • Engineering • Construction • Spelling © Activities for Learning, Inc., 2012
- 47. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Chemistry • Engineering • Physics • Construction • Spelling © Activities for Learning, Inc., 2012
- 48. Visualizing Needed in: • • Architecture Mathematics • Astronomy • Botany • Archeology • Geography • Chemistry • Engineering • Physics • Construction • Surgery • Spelling © Activities for Learning, Inc., 2012
- 49. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 50. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 51. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 52. Entering Quantities 3 © Activities for Learning, Inc., 2012
- 53. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 54. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 55. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 56. Entering Quantities 5 © Activities for Learning, Inc., 2012
- 57. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 58. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 59. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 60. Entering Quantities 7 © Activities for Learning, Inc., 2012
- 61. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 62. Entering Quantities 10 © Activities for Learning, Inc., 2012
- 63. Entering Quantities © Activitiesfor Learning, Inc., 2012
- 64. Simple Adding © Activitiesfor Learning, Inc., 2012
- 65. Simple Adding 4 + 3 = ___ © Activities for Learning, Inc., 2012
- 66. Simple Adding 4 + 3 = ___ © Activities for Learning, Inc., 2012
- 67. Simple Adding 4 + 3 = ___ © Activities for Learning, Inc., 2012
- 68. Simple Adding 4 + 3 = ___ © Activities for Learning, Inc., 2012
- 69. Simple Adding 4 + 3 = ___ 7 © Activities for Learning, Inc., 2012
- 70. Typical Worksheet © Activitiesfor Learning, Inc., 2012
- 71. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 72. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 73. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 74. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 75. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 76. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 77. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 78. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 79. Facts Equaling 10 ©Activities for Learning, Inc., 2012
- 80. Go to theDump Game © Activities for Learning, Inc., 2012
- 81. Go to theDump Game A “Go Fish” type of game where the pairs are: © Activities for Learning, Inc., 2012
- 82. Go to theDump 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. Go to theDump 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. Math Way ofNaming Numbers © Activities for Learning, Inc., 2012
- 85. Math Way ofNaming 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. Math Way ofNaming Numbers • Just as reciting the alphabet doesn’t teach reading, counting doesn’t teach arithmetic. © Activities for Learning, Inc., 2012
- 87. Math Way ofNaming 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. Math Way ofNaming Numbers • Asian children learn mathematics using the math way of number naming. © Activities for Learning, Inc., 2012
- 89. Math Way ofNaming 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. Math Way ofNaming 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. Math Way ofNaming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. © Activities for Learning, Inc., 2012
- 92. Math Way ofNaming 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. Subtracting 14 From48 Task: Using 10s and 1s, ask the child to construct 48. © Activities for Learning, Inc., 2012
- 94. Subtracting 14 From48 Task: Using 10s and 1s, ask the child to construct 48. © Activities for Learning, Inc., 2012
- 95. Subtracting 14 From48 Task: Using 10s and 1s, ask the child to construct 48. Then ask the child to subtract 14. © Activities for Learning, Inc., 2012
- 96. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Subtracting 14 From48 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. Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc., 2012
- 108. Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc., 2012
- 109. Understanding Place Value 2-ten 2 0 © Activities for Learning, Inc., 2012
- 110. Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc., 2012
- 111. Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc., 2012
- 112. Understanding Place Value 3-ten 2 0 3 © Activities for Learning, Inc., 2012
- 113. Understanding Place Value 3-ten 7 2 0 3 7 © Activities for Learning, Inc., 2012
- 114. Understanding Place Value 3-ten 7 3 7 2 0 © Activities for Learning, Inc., 2012
- 115. Understanding Place Value 6-ten 2 0 6 © Activities for Learning, Inc., 2012
- 116. Understanding Place Value 6-ten 2 2 0 6 2 © Activities for Learning, Inc., 2012
- 117. Understanding Place Value 6-ten 2 6 2 2 0 © Activities for Learning, Inc., 2012
- 118. Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc., 2012
- 119. Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc., 2012
- 120. Understanding Place Value 10-ten 1 0 0 © Activities for Learning, Inc., 2012
- 121. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc., 2012
- 122. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc., 2012
- 123. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc., 2012
- 124. Understanding Place Value 1 hundred 1 0 0 © Activities for Learning, Inc., 2012
- 125. Understanding Place Value 2 hundred 2 0 0 © Activities for Learning, Inc., 2012
- 126. Understanding Place Value 10 hundred 1 0 0 0 © Activities for Learning, Inc., 2012
- 127. Understanding Place Value 10 hundred 1 0 0 0 © Activities for Learning, Inc., 2012
- 128. Understanding Place Value 10 hundred 1 0 0 0 © Activities for Learning, Inc., 2012
- 129. Understanding Place Value 10 hundred 1 0 0 0 © Activities for Learning, Inc., 2012
- 130. Understanding Place Value 1 thousand 1 0 0 0 © Activities for Learning, Inc., 2012
- 131. Understanding Place Value 1 thousand 1 0 0 0 © Activities for Learning, Inc., 2012
- 132. Understanding Place Value 1 thousand 1 0 0 0 © Activities for Learning, Inc., 2012
- 133. Understanding Place Value 1 thousand 1 0 0 0 © Activities for Learning, Inc., 2012
- 134. Understanding Place Value 1 thousand 1 0 0 0 © Activities for Learning, Inc., 2012
- 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. 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. Place Value Cards 3 0 0 0 3 0 0 0 3 0 0 8 0 8 8 © Activities for Learning, Inc., 2012
- 138. Traditional Names 4-ten = forty © Activities for Learning, Inc., 2012
- 139. Traditional Names 6-ten = sixty © Activities for Learning, Inc., 2012
- 140. Traditional Names 8-ten = eighty © Activities for Learning, Inc., 2012
- 141. Traditional Names A word game © Activities for Learning, Inc., 2012
- 142. Traditional Names A word game fireplace © Activities for Learning, Inc., 2012
- 143. Traditional Names A word game fireplace place-fire © Activities for Learning, Inc., 2012
- 144. Traditional Names A word game fireplace place-fire newspaper © Activities for Learning, Inc., 2012
- 145. Traditional Names A word game fireplace place-fire newspaper paper-news © Activities for Learning, Inc., 2012
- 146. Traditional Names A word game fireplace place-fire newspaper paper-news box-mail © Activities for Learning, Inc., 2012
- 147. Traditional Names A word game fireplace place-fire newspaper paper-news box-mail mailbox © Activities for Learning, Inc., 2012
- 148. Traditional Names © Activitiesfor Learning, Inc., 2012
- 149. Traditional Names ten 4 © Activities for Learning, Inc., 2012
- 150. Traditional Names ten 4 teen 4 “Teen” also means ten. © Activities for Learning, Inc., 2012
- 151. Traditional Names ten 4 teen 4 fourteen “Teen” also means ten. © Activities for Learning, Inc., 2012
- 152. Traditional Names © Activitiesfor Learning, Inc., 2012
- 153. Traditional Names ten 7 © Activities for Learning, Inc., 2012
- 154. Traditional Names ten 7 teen 7 © Activities for Learning, Inc., 2012
- 155. Traditional Names ten 7 teen 7 seventeen © Activities for Learning, Inc., 2012
- 156. Traditional Names © Activitiesfor Learning, Inc., 2012
- 157. Traditional Names a one left © Activities for Learning, Inc., 2012
- 158. Traditional Names a one left a left-one © Activities for Learning, Inc., 2012
- 159. Traditional Names a one left a left-one eleven © Activities for Learning, Inc., 2012
- 160. Traditional Names © Activitiesfor Learning, Inc., 2012
- 161. Traditional Names two left Two pronounced “twoo.” © Activities for Learning, Inc., 2012
- 162. Traditional Names two left twelve Two pronounced “twoo.” © Activities for Learning, Inc., 2012
- 163. Strategies A strategy is an efficient way to learn a new fact or recall a forgotten fact. © Activities for Learning, Inc., 2012
- 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. Strategy: Complete theTen 9 + 5 = ___ © Activities for Learning, Inc., 2012
- 166. Strategy: Complete theTen 9 + 5 = ___ © Activities for Learning, Inc., 2012
- 167. Strategy: Complete theTen 9 + 5 = ___ © Activities for Learning, Inc., 2012
- 168. Strategy: Complete theTen 9 + 5 = ___ © Activities for Learning, Inc., 2012
- 169. Strategy: Complete theTen 9 + 5 = ___ © Activities for Learning, Inc., 2012
- 170. Strategy: Complete theTen 9 + 5 = ___ © Activities for Learning, Inc., 2012
- 171. Strategy: Complete theTen 9 + 5 = ___ 14 © Activities for Learning, Inc., 2012
- 172. Strategy: Complete theTen 9 + 7 = ___ © Activities for Learning, Inc., 2012
- 173. Strategy: Complete theTen 9 + 7 = ___ © Activities for Learning, Inc., 2012
- 174. Strategy: Complete theTen 9 + 7 = ___ © Activities for Learning, Inc., 2012
- 175. Strategy: Complete theTen 9 + 7 = ___ © Activities for Learning, Inc., 2012
- 176. Strategy: Complete theTen 9 + 7 = ___ 16 © Activities for Learning, Inc., 2012
- 177. Strategy: Two Fives 8+6= © Activities for Learning, Inc., 2012
- 178. Strategy: Two Fives 8+6= © Activities for Learning, Inc., 2012
- 179. Strategy: Two Fives 8+6= © Activities for Learning, Inc., 2012
- 180. Strategy: Two Fives 8+6= © Activities for Learning, Inc., 2012
- 181. Strategy: Two Fives 8 + 6 = 10 + 4 © Activities for Learning, Inc., 2012
- 182. Strategy: Two Fives 8 + 6 = 10 + 4 = 14 © Activities for Learning, Inc., 2012
- 183. Strategy: Two Fives 7+5= © Activities for Learning, Inc., 2012
- 184. Strategy: Two Fives 7+5= © Activities for Learning, Inc., 2012
- 185. Strategy: Two Fives 7+5= © Activities for Learning, Inc., 2012
- 186. Strategy: Two Fives 7 + 5 = 10 + 2 = 12 © Activities for Learning, Inc., 2012
- 187. Strategy: Going Down 15 – 9 = ___ © Activities for Learning, Inc., 2012
- 188. Strategy: Going Down 15 – 9 = ___ © Activities for Learning, Inc., 2012
- 189. Strategy: Going Down 15 – 9 = ___ Subtract 5, then 4 © Activities for Learning, Inc., 2012
- 190. Strategy: Going Down 15 – 9 = ___ Subtract 5, then 4 © Activities for Learning, Inc., 2012
- 191. Strategy: Going Down 15 – 9 = ___ Subtract 5, then 4 © Activities for Learning, Inc., 2012
- 192. Strategy: Going Down 15 – 9 = ___ 6 Subtract 5, then 4 © Activities for Learning, Inc., 2012
- 193. Strategy: Going Down 15 – 9 = ___ © Activities for Learning, Inc., 2012
- 194. Strategy: Going Down 15 – 9 = ___ Subtract 9 from the 10 © Activities for Learning, Inc., 2012
- 195. Strategy: Going Down 15 – 9 = ___ Subtract 9 from the 10 © Activities for Learning, Inc., 2012
- 196. Strategy: Going Down 15 – 9 = ___ 6 Subtract 9 from the 10 © Activities for Learning, Inc., 2012
- 197. Strategy: Going Up 13 – 9 = © Activities for Learning, Inc., 2012
- 198. Strategy: Going Up 13 – 9 = Start at 9; go up to 13 © Activities for Learning, Inc., 2012
- 199. Strategy: Going Up 13 – 9 = Start at 9; go up to 13 © Activities for Learning, Inc., 2012
- 200. Strategy: Going Up 13 – 9 = Start at 9; go up to 13 © Activities for Learning, Inc., 2012
- 201. Strategy: Going Up 13 – 9 = 1 + 3 Start at 9; go up to 13 © Activities for Learning, Inc., 2012
- 202. Strategy: Going Up 13 – 9 = 1 + 3 = 4 Start at 9; go up to 13 © Activities for Learning, Inc., 2012
- 203. AL Abacus -Side 2 1000 10 1 Cleared © Activities for Learning, Inc., 2012
- 204. AL Abacus -Side 2 1000 10 1 Thousands © Activities for Learning, Inc., 2012
- 205. AL Abacus -Side 2 1000 100 10 1 Hundreds © Activities for Learning, Inc., 2012
- 206. AL Abacus -Side 2 1000 100 10 1 Tens © Activities for Learning, Inc., 2012
- 207. AL Abacus -Side 2 1000 100 10 1 Ones © Activities for Learning, Inc., 2012
- 208. AL Abacus -Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc., 2012
- 209. AL Abacus -Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc., 2012
- 210. AL Abacus -Side 2 1000 100 10 1 8 + 6 © Activities for Learning, Inc., 2012
- 211. AL Abacus -Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc., 2012
- 212. AL Abacus -Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc., 2012
- 213. AL Abacus -Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc., 2012
- 214. AL Abacus -Side 2 1000 100 10 1 8 + 6 14 © Activities for Learning, Inc., 2012
- 215. AL Abacus -Side 2 1000 100 10 1 Why keep the two columns even? © Activities for Learning, Inc., 2012
- 216. AL Abacus -Side 2 1000 100 10 1 © Activities for Learning, Inc., 2012
- 217. AL Abacus -Side 2 1000 100 10 1 Do we need to trade? © Activities for Learning, Inc., 2012
- 218. Bead Trading 1000 100 10 1 © Activities for Learning, Inc., 2012
- 219. Bead Trading 1000 100 10 1 7 © Activities for Learning, Inc., 2012
- 220. Bead Trading 1000 100 10 1 7 © Activities for Learning, Inc., 2012
- 221. Bead Trading 1000 100 10 1 6 © Activities for Learning, Inc., 2012
- 222. Bead Trading 1000 100 10 1 6 © Activities for Learning, Inc., 2012
- 223. Bead Trading 1000 100 10 1 6 © Activities for Learning, Inc., 2012
- 224. Bead Trading 1000 100 10 1 6 © Activities for Learning, Inc., 2012
- 225. Bead Trading 1000 100 10 1 9 © Activities for Learning, Inc., 2012
- 226. Bead Trading 1000 100 10 1 9 © Activities for Learning, Inc., 2012
- 227. Bead Trading 1000 100 10 1 9 © Activities for Learning, Inc., 2012
- 228. Bead Trading 1000 100 10 1 9 © Activities for Learning, Inc., 2012
- 229. Bead Trading 1000 100 10 1 5 © Activities for Learning, Inc., 2012
- 230. Bead Trading 1000 100 10 1 5 © Activities for Learning, Inc., 2012
- 231. Bead Trading • To appreciate a pattern, there must be at least three examples in the sequence. © Activities for Learning, Inc., 2012
- 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. 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. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 235. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 236. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 237. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 238. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 239. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 240. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 241. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 242. Four Digit Addition 1000 100 10 1 3658 + 2738 © Activities for Learning, Inc., 2012
- 243. Four Digit Addition 1000 100 10 1 3658 + 2738 6 © Activities for Learning, Inc., 2012
- 244. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc., 2012
- 245. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc., 2012
- 246. Four Digit Addition 1000 100 10 1 1 3658 + 2738 6 © Activities for Learning, Inc., 2012
- 247. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc., 2012
- 248. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc., 2012
- 249. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc., 2012
- 250. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc., 2012
- 251. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc., 2012
- 252. Four Digit Addition 1000 100 10 1 1 3658 + 2738 96 © Activities for Learning, Inc., 2012
- 253. Four Digit Addition 1000 100 10 1 1 3658 + 2738 396 © Activities for Learning, Inc., 2012
- 254. Four Digit Addition 1000 100 10 1 11 3658 + 2738 396 © Activities for Learning, Inc., 2012
- 255. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc., 2012
- 256. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 396 © Activities for Learning, Inc., 2012
- 257. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396 © Activities for Learning, Inc., 2012
- 258. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738 6396 © Activities for Learning, Inc., 2012
- 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. Multiplying on theAL Abacus 6x4 (6 taken 4 times) © Activities for Learning, Inc., 2012
- 261. Multiplying on theAL Abacus 5x7 © Activities for Learning, Inc., 2012
- 262. Multiplying on theAL Abacus 5x7 © Activities for Learning, Inc., 2012
- 263. Multiplying on theAL Abacus 5x7 © Activities for Learning, Inc., 2012
- 264. Multiplying on theAL Abacus 5x7 © Activities for Learning, Inc., 2012
- 265. Multiplying on theAL Abacus 5x7 (30 + 5) © Activities for Learning, Inc., 2012
- 266. Multiplying on theAL Abacus 7x7 © Activities for Learning, Inc., 2012
- 267. Multiplying on theAL Abacus 7x7 © Activities for Learning, Inc., 2012
- 268. Multiplying on theAL Abacus 7x7 © Activities for Learning, Inc., 2012
- 269. Multiplying on theAL Abacus 7x7 © Activities for Learning, Inc., 2012
- 270. Multiplying on theAL Abacus 7x7 © Activities for Learning, Inc., 2012
- 271. Multiplying on theAL Abacus 7 x 7 = 25 + 10 + 10 + 4 © Activities for Learning, Inc., 2012
- 272. Multiplying on theAL Abacus 9x3 (30 – 3) © Activities for Learning, Inc., 2012
- 273. Commutative Property 9x3 © Activities for Learning, Inc., 2012
- 274. Commutative Property 9x3 3x9 © Activities for Learning, Inc., 2012
- 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. What is theAL Abacus? • Visual and tactile manipulative • Develops mental images of Quantities Strategies Mathematical Operations © Activities for Learning, Inc., 2012
- 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. 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