1. Overcoming Math Obstaclesthrough Visualizingwith the AL AbacusBased on the work of Joan A. Cotter, Ph.DPresented by Tracy Mittleider, MSEdOctober 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. IntroductionPresentation based on the work of Dr. Joan A. CotterEducational background: Home schooled in High School Engineer from University of Wisconsin Certified Montessori teacher Masters 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. AL Abacus Activities for Learning, Inc., 2012 5. AL Abacus1000 100 10 1 Activities for Learning, Inc., 2012 6. What is the AL Abacus? Activities for Learning, Inc., 2012 7. What is the AL Abacus? Visual and tactile manipulative Activities for Learning, Inc., 2012 8. What is the AL Abacus? Visual and tactile manipulative Develops mental images of Activities for Learning, Inc., 2012 9. What is the AL Abacus? Visual and tactile manipulative Develops mental images of Quantities Activities for Learning, Inc., 2012 10. What is the AL Abacus? Visual and tactile manipulative Develops mental images of Quantities Strategies Activities for Learning, Inc., 2012 11. What is the AL 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 ModelHow many? Activities for Learning, Inc., 2012 18. Counting Model 1What we see Activities for Learning, Inc., 2012 19. Counting Model 2What we see Activities for Learning, Inc., 2012 20. Counting Model 3What we see Activities for Learning, Inc., 2012 21. Counting Model 4What we see Activities for Learning, Inc., 2012 22. Counting Model1What the young child sees Activities for Learning, Inc., 2012 23. Counting Model2What the young child sees Activities for Learning, Inc., 2012 24. Counting Model3What the young child sees Activities for Learning, Inc., 2012 25. Counting Model 4What the young child sees Activities for Learning, Inc., 2012 26. Visualizing 8Try to visualize 8 apples without grouping. Activities for Learning, Inc., 2012 27. Visualizing 8Try to visualize 8 apples without grouping. Activities for Learning, Inc., 2012 28. Visualizing 8 Now try to visualize 5 as red and 3 asgreen. Activities for Learning, Inc., 2012 29. Visualizing 8 Now try to visualize 5 as red and 3 asgreen. 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: ArchitectureMathematics Botany Geography Engineering Construction Spelling Activities for Learning, Inc., 2012 44. Visualizing Needed in: ArchitectureMathematics Astronomy Botany Geography Engineering Construction Spelling Activities for Learning, Inc., 2012 45. Visualizing Needed in: ArchitectureMathematics Astronomy Botany Archeology Geography Engineering Construction Spelling Activities for Learning, Inc., 2012 46. Visualizing Needed in: ArchitectureMathematics Astronomy Botany Archeology Geography Chemistry Engineering Construction Spelling Activities for Learning, Inc., 2012 47. Visualizing Needed in: ArchitectureMathematics Astronomy Botany Archeology Geography Chemistry Engineering Physics Construction Spelling Activities for Learning, Inc., 2012 48. Visualizing Needed in: ArchitectureMathematics Astronomy Botany Archeology Geography Chemistry Engineering Physics Construction Surgery Spelling Activities for Learning, Inc., 2012 49. Entering Quantities Activities for Learning, Inc., 2012 50. Entering Quantities Activities for Learning, Inc., 2012 51. Entering Quantities Activities for Learning, Inc., 2012 52. Entering Quantities3 Activities for Learning, Inc., 2012 53. Entering Quantities Activities for Learning, Inc., 2012 54. Entering Quantities Activities for Learning, Inc., 2012 55. Entering Quantities Activities for Learning, Inc., 2012 56. Entering Quantities5 Activities for Learning, Inc., 2012 57. Entering Quantities Activities for Learning, Inc., 2012 58. Entering Quantities Activities for Learning, Inc., 2012 59. Entering Quantities Activities for Learning, Inc., 2012 60. Entering Quantities7 Activities for Learning, Inc., 2012 61. Entering Quantities Activities for Learning, Inc., 2012 62. Entering Quantities 10 Activities for Learning, Inc., 2012 63. Entering Quantities Activities for Learning, Inc., 2012 64. Simple Adding Activities for Learning, Inc., 2012 65. Simple Adding4 + 3 = ___ Activities for Learning, Inc., 2012 66. Simple Adding4 + 3 = ___ Activities for Learning, Inc., 2012 67. Simple Adding4 + 3 = ___ Activities for Learning, Inc., 2012 68. Simple Adding4 + 3 = ___ Activities for Learning, Inc., 2012 69. Simple Adding4 + 3 = ___7 Activities for Learning, Inc., 2012 70. Typical Worksheet Activities for 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 the Dump Game Activities for Learning, Inc., 2012 81. Go to the Dump Game A Go Fish type of game where thepairs are: Activities for Learning, Inc., 2012 82. Go to the Dump Game A Go Fish type of game where thepairs are: 1 & 92 & 83 & 74 & 65 & 5 Activities for Learning, Inc., 2012 83. Go to the Dump Game A Go Fish type of game where thepairs are: 1 & 92 & 83 & 74 & 65 & 5 Activities for Learning, Inc., 2012 84. Math Way of Naming Numbers Activities for Learning, Inc., 2012 85. Math Way of Naming Numbers11 = ten 120 = 2-ten12 = ten 221 = 2-ten 113 = ten 322 = 2-ten 214 = ten 423 = 2-ten 3 ........19 = ten 9 ....99 = 9-ten 9 Activities for Learning, Inc., 2012 86. Math Way of Naming Numbers Just as reciting the alphabet doesnt teach reading, counting doesnt teach arithmetic. Activities for Learning, Inc., 2012 87. Math Way of Naming Numbers Just as reciting the alphabet doesnt teach reading, counting doesnt 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 of Naming Numbers Asian children learn mathematics using the math way of number naming. Activities for Learning, Inc., 2012 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. 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. Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. Activities for Learning, Inc., 2012 92. Math Way of Naming Numbers Children often think of 14 as 14 ones, not ten and 4 ones. The pattern that is needed tomake sense of tens and ones is Activities for Learning, Inc., 2012 93. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48. Activities for Learning, Inc., 2012 94. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48. Activities for Learning, Inc., 2012 95. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Activities for Learning, Inc., 2012 96. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 97. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 98. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 99. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 100. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 101. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 102. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 103. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children thinking of 14 as 14 ones counted 14. Activities for Learning, Inc., 2012 104. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children who understand tens remove a ten and 4 ones. Activities for Learning, Inc., 2012 105. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children who understand tens remove a ten and 4 ones. Activities for Learning, Inc., 2012 106. Subtracting 14 From 48 Task:Using 10s and 1s, askthe child to construct48.Then ask the child tosubtract 14. Children who understand tens remove a ten and 4 ones. Activities for Learning, Inc., 2012 107. Understanding Place Value2-ten 2 0 Activities for Learning, Inc., 2012 108. Understanding Place Value2-ten 2 0 Activities for Learning, Inc., 2012 109. Understanding Place Value2-ten 2 0 Activities for Learning, Inc., 2012 110. Understanding Place Value3-ten 2 03 Activities for Learning, Inc., 2012 111. Understanding Place Value3-ten 2 03 Activities for Learning, Inc., 2012 112. Understanding Place Value3-ten 2 03 Activities for Learning, Inc., 2012 113. Understanding Place Value3-ten 7 2 03 7 Activities for Learning, Inc., 2012 114. Understanding Place Value3-ten 7 3 72 0 Activities for Learning, Inc., 2012 115. Understanding Place Value6-ten 2 06 Activities for Learning, Inc., 2012 116. Understanding Place Value6-ten 2 2 06 2 Activities for Learning, Inc., 2012 117. Understanding Place Value6-ten 2 6 22 0 Activities for Learning, Inc., 2012 118. Understanding Place Value10-ten 1 0 0 Activities for Learning, Inc., 2012 119. Understanding Place Value10-ten 1 0 0 Activities for Learning, Inc., 2012 120. Understanding Place Value10-ten 1 0 0 Activities for Learning, Inc., 2012 121. Understanding Place Value1 hundred 1 0 0 Activities for Learning, Inc., 2012 122. Understanding Place Value1 hundred 1 0 0 Activities for Learning, Inc., 2012 123. Understanding Place Value1 hundred 1 0 0 Activities for Learning, Inc., 2012 124. Understanding Place Value1 hundred 1 0 0 Activities for Learning, Inc., 2012 125. Understanding Place Value2 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 03- ten3 0 0 3 hun-dred3 0 0 03 th- ou-sand Activities for Learning, Inc., 2012 136. Place Value Cards 3 0 0 03 0 0 0 3 0 0 86 5 06 0 0 6 0 05 085 08 Activities for Learning, Inc., 2012 137. Place Value Cards 3 0 0 03 0 0 0 3 0 0 8088 Activities for Learning, Inc., 2012 138. Traditional Names4-ten = forty Activities for Learning, Inc., 2012 139. Traditional Names6-ten = sixty Activities for Learning, Inc., 2012 140. Traditional Names8-ten = eighty Activities for Learning, Inc., 2012 141. Traditional Names A word game Activities for Learning, Inc., 2012 142. Traditional Names A word gamefireplace Activities for Learning, Inc., 2012 143. Traditional Names A word gamefireplace place-fire Activities for Learning, Inc., 2012 144. Traditional Names A word gamefireplace place-firenewspaper Activities for Learning, Inc., 2012 145. Traditional Names A word gamefireplace place-firenewspaper paper-news Activities for Learning, Inc., 2012 146. Traditional Names A word gamefireplace place-firenewspaper paper-newsbox-mail Activities for Learning, Inc., 2012 147. Traditional Names A word gamefireplace place-firenewspaper paper-newsbox-mailmailbox Activities for Learning, Inc., 2012 148. Traditional Names Activities for Learning, Inc., 2012 149. Traditional Namesten 4 Activities for Learning, Inc., 2012 150. Traditional Namesten 4 teen 4 Teen also means ten. Activities for Learning, Inc., 2012 151. Traditional Namesten 4 teen 4 fourteen Teen also means ten. Activities for Learning, Inc., 2012 152. Traditional Names Activities for Learning, Inc., 2012 153. Traditional Namesten 7 Activities for Learning, Inc., 2012 154. Traditional Namesten 7 teen 7 Activities for Learning, Inc., 2012 155. Traditional Namesten 7 teen 7 seventeen Activities for Learning, Inc., 2012 156. Traditional Names Activities for 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-oneeleven Activities for Learning, Inc., 2012 160. Traditional Names Activities for Learning, Inc., 2012 161. Traditional Namestwo leftTwopronouncedtwoo. Activities for Learning, Inc., 2012 162. Traditional Namestwo left twelveTwopronouncedtwoo. Activities for Learning, Inc., 2012 163. Strategies A strategy is an efficient wayto learn a new fact or recall aforgotten fact. Activities for Learning, Inc., 2012 164. Strategies A strategy is an efficient wayto learn a new fact or recall aforgotten fact. A visual representation is apowerful strategy. Activities for Learning, Inc., 2012 165. Strategy: Complete the Ten9 + 5 = ___ Activities for Learning, Inc., 2012 166. Strategy: Complete the Ten9 + 5 = ___ Activities for Learning, Inc., 2012 167. Strategy: Complete the Ten9 + 5 = ___ Activities for Learning, Inc., 2012 168. Strategy: Complete the Ten9 + 5 = ___ Activities for Learning, Inc., 2012 169. Strategy: Complete the Ten9 + 5 = ___ Activities for Learning, Inc., 2012 170. Strategy: Complete the Ten9 + 5 = ___ Activities for Learning, Inc., 2012 171. Strategy: Complete the Ten9 + 5 = ___14 Activities for Learning, Inc., 2012 172. Strategy: Complete the Ten9 + 7 = ___ Activities for Learning, Inc., 2012 173. Strategy: Complete the Ten9 + 7 = ___ Activities for Learning, Inc., 2012 174. Strategy: Complete the Ten9 + 7 = ___ Activities for Learning, Inc., 2012 175. Strategy: Complete the Ten9 + 7 = ___ Activities for Learning, Inc., 2012 176. Strategy: Complete the Ten9 + 7 = ___16 Activities for Learning, Inc., 2012 177. Strategy: Two Fives8+6= Activities for Learning, Inc., 2012 178. Strategy: Two Fives8+6= Activities for Learning, Inc., 2012 179. Strategy: Two Fives8+6= Activities for Learning, Inc., 2012 180. Strategy: Two Fives8+6= Activities for Learning, Inc., 2012 181. Strategy: Two Fives8 + 6 = 10 + 4 Activities for Learning, Inc., 2012 182. Strategy: Two Fives8 + 6 = 10 + 4 = 14 Activities for Learning, Inc., 2012 183. Strategy: Two Fives7+5= Activities for Learning, Inc., 2012 184. Strategy: Two Fives7+5= Activities for Learning, Inc., 2012 185. Strategy: Two Fives7+5= Activities for Learning, Inc., 2012 186. Strategy: Two Fives7 + 5 = 10 + 2 = 12 Activities for Learning, Inc., 2012 187. Strategy: Going Down15 9 = ___ Activities for Learning, Inc., 2012 188. Strategy: Going Down15 9 = ___ Activities for Learning, Inc., 2012 189. Strategy: Going Down15 9 = ___ Subtract 5, then 4 Activities for Learning, Inc., 2012 190. Strategy: Going Down15 9 = ___ Subtract 5, then 4 Activities for Learning, Inc., 2012 191. Strategy: Going Down15 9 = ___ Subtract 5, then 4 Activities for Learning, Inc., 2012 192. Strategy: Going Down15 9 = ___ 6 Subtract 5, then 4 Activities for Learning, Inc., 2012 193. Strategy: Going Down15 9 = ___ Activities for Learning, Inc., 2012 194. Strategy: Going Down15 9 = ___ Subtract 9 from the 10 Activities for Learning, Inc., 2012 195. Strategy: Going Down15 9 = ___ Subtract 9 from the 10 Activities for Learning, Inc., 2012 196. Strategy: Going Down15 9 = ___ 6 Subtract 9 from the 10 Activities for Learning, Inc., 2012 197. Strategy: Going Up13 9 = Activities for Learning, Inc., 2012 198. Strategy: Going Up13 9 = Start at 9; go up to 13 Activities for Learning, Inc., 2012 199. Strategy: Going Up13 9 = Start at 9; go up to 13 Activities for Learning, Inc., 2012 200. Strategy: Going Up13 9 = Start at 9; go up to 13 Activities for Learning, Inc., 2012 201. Strategy: Going Up13 9 = 1 + 3 Start at 9; go up to 13 Activities for Learning, Inc., 2012 202. Strategy: Going Up13 9 = 1 + 3 = 4Start 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 + 614 Activities for Learning, Inc., 2012 213. AL Abacus - Side 2 1000 100 10 1 8 + 614 Activities for Learning, Inc., 2012 214. AL Abacus - Side 2 1000 100 10 1 8 + 614 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 leastthree examples in the sequence. Activities for Learning, Inc., 2012 232. Bead Trading To appreciate a pattern, there must be at leastthree examples in the sequence. Bead trading helps the child experience thegreater value of each column. Activities for Learning, Inc., 2012 233. Bead Trading To appreciate a pattern, there must be at leastthree examples in the sequence. Bead trading helps the child experience thegreater value of each column. Therefore, to understand the never-endingpattern of trading, the child must trade10 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 + 27386 Activities for Learning, Inc., 2012 246. Four Digit Addition 1000 100 10 1 1 3658 + 27386 Activities for Learning, Inc., 2012 247. Four Digit Addition 1000 100 10 1 1 3658 + 273896 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 + 2738396 Activities for Learning, Inc., 2012 256. Four Digit Addition 1000 100 10 1 1 1 3658 + 2738396 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 AdditionMost children who 1 1learn to add on the 3658AL Abacus + 2738transition6396to the paper andpencil algorithmwithout furtherinstruction. Activities for Learning, Inc., 2012 260. Multiplying on the AL Abacus6x4 (6 taken 4 times) Activities for Learning, Inc., 2012 261. Multiplying on the AL Abacus5x7 Activities for Learning, Inc., 2012 262. Multiplying on the AL Abacus5x7 Activities for Learning, Inc., 2012 263. Multiplying on the AL Abacus5x7 Activities for Learning, Inc., 2012 264. Multiplying on the AL Abacus5x7 Activities for Learning, Inc., 2012 265. Multiplying on the AL Abacus5x7 (30 + 5) Activities for Learning, Inc., 2012 266. Multiplying on the AL Abacus7x7 Activities for Learning, Inc., 2012 267. Multiplying on the AL Abacus7x7 Activities for Learning, Inc., 2012 268. Multiplying on the AL Abacus7x7 Activities for Learning, Inc., 2012 269. Multiplying on the AL Abacus7x7 Activities for Learning, Inc., 2012 270. Multiplying on the AL Abacus7x7 Activities for Learning, Inc., 2012 271. Multiplying on the AL Abacus7 x 7 = 25 + 10 + 10 + 4 Activities for Learning, Inc., 2012 272. Multiplying on the AL Abacus9x3 (30 3) Activities for Learning, Inc., 2012 273. Commutative Property9x3 Activities for Learning, Inc., 2012 274. Commutative Property9x3 3x9 Activities for Learning, Inc., 2012 275. Effective Math UsersThe now well established fact thatthose who are mathematicallyeffective in daily life seldom makeuse in their heads of the standardwritten methods which are taught inthe classroom. W. H. Cockroft, 1982- renowned math educator in England Activities for Learning, Inc., 2012 276. What is the AL 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 andonly 5 percent memorized.Richard Skemp-- major pioneer inmathematics education Activities for Learning, Inc., 2012 278. Overcoming Math Obstaclesthrough Visualizingwith the AL AbacusBased on the work of Joan A. Cotter, Ph.DPresented by Tracy Mittleider, MSEdOctober 25, 2012 Activities for Learning, Inc., 2012