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- 1. Personalized Learning Bridges Middle-School Math with a Geometric Approach Presented by Tracy Mittleider, MSEd and Kathleen Lawler Based on work of Joan A. Cotter, Ph.D. Aplus+ Conference October 24, 2012© Activities for Learning, Inc., 2012
- 2. Why a Geometric Approach?© Activities for Learning, Inc., 2012
- 3. Why a Geometric Approach? Most students in “middle school” are visual learners.© Activities for Learning, Inc., 2012
- 4. Why a Geometric Approach? Most students in “middle school” are visual learners. 90% of the math topics can be explored geometrically (visually).© Activities for Learning, Inc., 2012
- 5. Why a Geometric Approach? Most students in “middle school” are visual learners. 90% of the math topics can be explored geometrically (visually). Therefore, it makes sense to teach them geometrically.© Activities for Learning, Inc., 2012
- 6. Drawing Tools Paper 11 in. by 8.5 in.© Activities for Learning, Inc., 2012
- 7. Drawing Tools Drawing board with paper© Activities for Learning, Inc., 2012
- 8. Drawing Tools Drawing board with paper© Activities for Learning, Inc., 2012
- 9. Drawing Tools T-square T-square© Activities for Learning, Inc., 2012
- 10. Drawing Tools T-square T-square© Activities for Learning, Inc., 2012
- 11. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 12. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 13. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 14. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 15. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 16. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 17. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 18. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 19. Drawing Tools T-square© Activities for Learning, Inc., 2012
- 20. Drawing Tools Pencil (mechanical) and eraser© Activities for Learning, Inc., 2012
- 21. Drawing Tools Pencil (mechanical) and eraser© Activities for Learning, Inc., 2012
- 22. Drawing Tools Pencil (mechanical) and eraser© Activities for Learning, Inc., 2012
- 23. Drawing Tools Pencil (mechanical) and eraser© Activities for Learning, Inc., 2012
- 24. Drawing Tools Pencil (mechanical) and eraser© Activities for Learning, Inc., 2012
- 25. Drawing Tools Pencil (mechanical) and eraser© Activities for Learning, Inc., 2012
- 26. Drawing Tools The 45 triangle 45° 45° 90°© Activities for Learning, Inc., 2012
- 27. Drawing Tools The 30-60 triangle (a set square) 30° 60° 90°© Activities for Learning, Inc., 2012
- 28. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 29. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 30. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 31. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 32. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 33. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 34. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 35. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 36. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 37. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 38. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 39. Drawing Tools The 30-60 triangle© Activities for Learning, Inc., 2012
- 40. © Activities for Learning, Inc., 2012
- 41. Equilateral Triangles Draw the base line© Activities for Learning, Inc., 2012
- 42. Equilateral Triangles Draw the base line© Activities for Learning, Inc., 2012
- 43. Equilateral Triangles Draw the sides© Activities for Learning, Inc., 2012
- 44. Equilateral Triangles Draw the sides© Activities for Learning, Inc., 2012
- 45. Equilateral Triangles Draw the sides© Activities for Learning, Inc., 2012
- 46. Equilateral Triangles Draw the sides© Activities for Learning, Inc., 2012
- 47. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 48. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 49. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 50. Equilateral Triangles Divide it into halves 1 1 2 2© Activities for Learning, Inc., 2012
- 51. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 52. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 53. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 54. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 55. Equilateral Triangles Divide it into halves© Activities for Learning, Inc., 2012
- 56. © Activities for Learning, Inc., 2012
- 57. Equilateral Triangles Divide it into thirds© Activities for Learning, Inc., 2012
- 58. Equilateral Triangles Divide it into thirds© Activities for Learning, Inc., 2012
- 59. Equilateral Triangles Divide it into thirds© Activities for Learning, Inc., 2012
- 60. Equilateral Triangles Divide it into thirds© Activities for Learning, Inc., 2012
- 61. Equilateral Triangles Divide it into thirds© Activities for Learning, Inc., 2012
- 62. Equilateral Triangles Divide it into thirds© Activities for Learning, Inc., 2012
- 63. Equilateral Triangles Divide it into thirds© Activities for Learning, Inc., 2012
- 64. Equilateral Triangles Divide it into thirds 1 1 3 3 1 3© Activities for Learning, Inc., 2012
- 65. Equilateral Triangles Divide it into thirds 1 3 1 1 3 3© Activities for Learning, Inc., 2012
- 66. © Activities for Learning, Inc., 2012
- 67. Equilateral Triangles Divide it into fourths© Activities for Learning, Inc., 2012
- 68. Equilateral Triangles Divide it into fourths Find the center of the base line.© Activities for Learning, Inc., 2012
- 69. Equilateral Triangles Divide it into fourths tick mark© Activities for Learning, Inc., 2012
- 70. Equilateral Triangles Divide it into fourths© Activities for Learning, Inc., 2012
- 71. Equilateral Triangles Divide it into fourths© Activities for Learning, Inc., 2012
- 72. Equilateral Triangles Divide it into fourths© Activities for Learning, Inc., 2012
- 73. Equilateral Triangles Divide it into fourths© Activities for Learning, Inc., 2012
- 74. Equilateral Triangles Divide it into fourths© Activities for Learning, Inc., 2012
- 75. Equilateral Triangles Divide it into fourths 1 4 1 1 4 1 4 4© Activities for Learning, Inc., 2012
- 76. Equilateral Triangles Divide it into fourths A B F C E D Name the rhombuses:© Activities for Learning, Inc., 2012
- 77. Equilateral Triangles Divide it into fourths A B F C E D Name the rhombuses: ABDF© Activities for Learning, Inc., 2012
- 78. Equilateral Triangles Divide it into fourths A B F C E D Name the rhombuses: ABDF, BCDF© Activities for Learning, Inc., 2012
- 79. Equilateral Triangles Divide it into fourths A B F C E D Name the rhombuses: ABDF, BCDF,© Activities for Learning, Inc., 2012 BDEF
- 80. Equilateral Triangles Divide it into fourths A B F C E D Name the trapezoids:© Activities for Learning, Inc., 2012
- 81. Equilateral Triangles Divide it into fourths A B F C E D Name the trapezoids: BCEF© Activities for Learning, Inc., 2012
- 82. Equilateral Triangles Divide it into fourths A B F C E D Name the trapezoids: BCEF, ACDF© Activities for Learning, Inc., 2012
- 83. Equilateral Triangles Divide it into fourths A B F C E D Name the trapezoids: BCEF, ACDF,© Activities for Learning, Inc., 2012 ABDE
- 84. Equilateral Triangles What if we cut this shape out….© Activities for Learning, Inc., 2012
- 85. Equilateral Triangles …and folded it on the lines….© Activities for Learning, Inc., 2012
- 86. Equilateral Triangles© Activities for Learning, Inc., 2012
- 87. Equilateral Triangles© Activities for Learning, Inc., 2012
- 88. Equilateral Triangles© Activities for Learning, Inc., 2012
- 89. Equilateral Triangles© Activities for Learning, Inc., 2012
- 90. Equilateral Triangles© Activities for Learning, Inc., 2012
- 91. Equilateral Triangles It’s a tetrahedron!© Activities for Learning, Inc., 2012
- 92. Equilateral Triangles Divide it into eighths© Activities for Learning, Inc., 2012
- 93. Equilateral Triangles Divide it into eighths© Activities for Learning, Inc., 2012
- 94. Equilateral Triangles Divide it into eighths© Activities for Learning, Inc., 2012
- 95. Equilateral Triangles Divide it into eighths© Activities for Learning, Inc., 2012
- 96. Equilateral Triangles Divide it into eighths© Activities for Learning, Inc., 2012
- 97. Equilateral Triangles Divide it into sixths© Activities for Learning, Inc., 2012
- 98. Equilateral Triangles Divide it into sixths© Activities for Learning, Inc., 2012
- 99. Equilateral Triangles Divide it into sixths© Activities for Learning, Inc., 2012
- 100. Equilateral Triangles Divide it into sixths A B F G C E D Name an acute triangle:© Activities for Learning, Inc., 2012
- 101. Equilateral Triangles Divide it into sixths A B F G C E D Name an acute triangle: ACE© Activities for Learning, Inc., 2012
- 102. Equilateral Triangles Divide it into sixths A B F G C E D Name a right triangle:© Activities for Learning, Inc., 2012
- 103. Equilateral Triangles Divide it into sixths A B F G C E D Name a right triangle: ADE© Activities for Learning, Inc., 2012
- 104. Equilateral Triangles Divide it into sixths A B F G C E D Name a right triangle: ADE, ABE© Activities for Learning, Inc., 2012
- 105. Equilateral Triangles Divide it into sixths A B F G C E D Name a right triangle: ADE, ABE, ABG© Activities for Learning, Inc., 2012
- 106. Equilateral Triangles Divide it into sixths A B F G C E D Name an obtuse triangle:© Activities for Learning, Inc., 2012
- 107. Equilateral Triangles Divide it into sixths A B F G C E D Name an obtuse triangle: GCE© Activities for Learning, Inc., 2012
- 108. Equilateral Triangles Divide it into twelfths© Activities for Learning, Inc., 2012
- 109. Equilateral Triangles Divide it into twelfths© Activities for Learning, Inc., 2012
- 110. Equilateral Triangles Divide it into twelfths© Activities for Learning, Inc., 2012
- 111. Equilateral Triangles Divide it into twelfths© Activities for Learning, Inc., 2012
- 112. Equilateral Triangles Divide it into twelfths© Activities for Learning, Inc., 2012
- 113. Equilateral Triangles Divide it into twelfths© Activities for Learning, Inc., 2012
- 114. Equilateral Triangles Divide it into twelfths Can you see the cube?© Activities for Learning, Inc., 2012
- 115. Equilateral Triangles Divide it into twelfths Can you see the cube?© Activities for Learning, Inc., 2012
- 116. Equilateral Triangles Divide it into twelfths Do you see the hexagon?© Activities for Learning, Inc., 2012
- 117. Equilateral Triangles Divide it into twelfths Do you see the hexagon?© Activities for Learning, Inc., 2012
- 118. Equilateral Triangles Ninths© Activities for Learning, Inc., 2012
- 119. Equilateral Triangles Twenty-sevenths© Activities for Learning, Inc., 2012
- 120. Equilateral Triangles Twenty-sevenths© Activities for Learning, Inc., 2012
- 121. Equilateral Triangles© Activities for Learning, Inc., 2012
- 122. Equilateral Triangles© Activities for Learning, Inc., 2012
- 123. Equilateral Triangles Thirty-seconds© Activities for Learning, Inc., 2012
- 124. Equilateral Triangles Stephanie, 6, did 256!© Activities for Learning, Inc., 2012
- 125. Equilateral Triangles© Activities for Learning, Inc., 2012
- 126. Equilateral Triangles© Activities for Learning, Inc., 2012
- 127. Equilateral Triangles© Activities for Learning, Inc., 2012
- 128. Equilateral Triangles© Activities for Learning, Inc., 2012
- 129. © Activities for Learning, Inc., 2012
- 130. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 131. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 132. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 133. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 134. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 135. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 136. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 137. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 138. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 139. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 140. Equilateral Triangles Spiral© Activities for Learning, Inc., 2012
- 141. Geometric Approach© Activities for Learning, Inc., 2012
- 142. Geometric Approach • Basis of CAD (computer aided design).© Activities for Learning, Inc., 2012
- 143. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts.© Activities for Learning, Inc., 2012
- 144. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts. • Incorporates measuring.© Activities for Learning, Inc., 2012
- 145. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts. • Incorporates measuring. • Allows independent work.© Activities for Learning, Inc., 2012
- 146. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts. • Incorporates measuring. • Allows independent work. • Excellent preparation for high school mathematics.© Activities for Learning, Inc., 2012
- 147. Geometric Approach Goals© Activities for Learning, Inc., 2012
- 148. Geometric Approach Goals • To use elementary math.© Activities for Learning, Inc., 2012
- 149. Geometric Approach Goals • To use elementary math. • To learn to read math texts.© Activities for Learning, Inc., 2012
- 150. Geometric Approach Goals • To use elementary math. • To learn to read math texts. • To prepare for more advanced mathematics.© Activities for Learning, Inc., 2012
- 151. Geometric Approach Goals • To use elementary math. • To learn to read math texts. • To prepare for more advanced mathematics. • To discover mathematics in the everyday world.© Activities for Learning, Inc., 2012
- 152. Geometric Approach Goals • To use elementary math. • To learn to read math texts. • To prepare for more advanced mathematics. • To discover mathematics in the everyday world. • To enjoy mathematics.© Activities for Learning, Inc., 2012
- 153. Why a Geometric Approach?© Activities for Learning, Inc., 2012
- 154. Why a Geometric Approach? Most students in “middle school” are visual learners.© Activities for Learning, Inc., 2012
- 155. Why a Geometric Approach? Most students in “middle school” are visual learners. 90% of the math topics can be explored geometrically (visually).© Activities for Learning, Inc., 2012
- 156. Why a Geometric Approach? Most students in “middle school” are visual learners. 90% of the math topics can be explored geometrically (visually). Therefore, it makes sense to teach them geometrically.© Activities for Learning, Inc., 2012
- 157. © Activities for Learning, Inc., 2012
- 158. Squares The 45 triangle.© Activities for Learning, Inc., 2012
- 159. Squares The 45 triangle is half of a square.© Activities for Learning, Inc., 2012
- 160. Squares© Activities for Learning, Inc., 2012
- 161. Squares© Activities for Learning, Inc., 2012
- 162. Squares© Activities for Learning, Inc., 2012
- 163. Squares© Activities for Learning, Inc., 2012
- 164. Squares© Activities for Learning, Inc., 2012
- 165. Squares© Activities for Learning, Inc., 2012
- 166. Squares© Activities for Learning, Inc., 2012
- 167. Squares© Activities for Learning, Inc., 2012
- 168. Squares© Activities for Learning, Inc., 2012
- 169. Squares Halves© Activities for Learning, Inc., 2012
- 170. Squares Fourths© Activities for Learning, Inc., 2012
- 171. Squares Eighths© Activities for Learning, Inc., 2012
- 172. Squares Sixteenths© Activities for Learning, Inc., 2012
- 173. © Activities for Learning, Inc., 2012
- 174. Squares Halves We need to find the center.© Activities for Learning, Inc., 2012
- 175. Squares Halves We need to find the center.© Activities for Learning, Inc., 2012
- 176. Squares Halves We need to find the center.© Activities for Learning, Inc., 2012
- 177. Squares Halves© Activities for Learning, Inc., 2012
- 178. Squares Halves© Activities for Learning, Inc., 2012
- 179. Squares Fourths© Activities for Learning, Inc., 2012
- 180. Squares Fourths© Activities for Learning, Inc., 2012
- 181. Squares Eighths Find the center of a small square.© Activities for Learning, Inc., 2012
- 182. Squares Eighths Find the center of a small square.© Activities for Learning, Inc., 2012
- 183. Squares Eighths Find the center of a small square.© Activities for Learning, Inc., 2012
- 184. Squares Eighths Find the center of a small square.© Activities for Learning, Inc., 2012
- 185. Squares Eighths© Activities for Learning, Inc., 2012
- 186. Squares Eighths© Activities for Learning, Inc., 2012
- 187. Squares Sixteenths© Activities for Learning, Inc., 2012
- 188. Squares Sixteenths© Activities for Learning, Inc., 2012
- 189. Squares Sixteenths© Activities for Learning, Inc., 2012
- 190. © Activities for Learning, Inc., 2012
- 191. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 192. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 193. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 194. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 195. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 196. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 197. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 198. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 199. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 200. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 201. Squares Circumscribed squares© Activities for Learning, Inc., 2012
- 202. © Activities for Learning, Inc., 2012
- 203. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 204. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 205. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 206. Squares Inscribed squares Compare the area of the squares.© Activities for Learning, Inc., 2012
- 207. Squares Inscribed squares Compare the area of the squares.© Activities for Learning, Inc., 2012
- 208. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 209. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 210. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 211. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 212. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 213. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 214. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 215. Squares Inscribed squares© Activities for Learning, Inc., 2012
- 216. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 217. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 218. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 219. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 220. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 221. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 222. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 223. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 224. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 225. Squares Right triangle spiral© Activities for Learning, Inc., 2012
- 226. © Activities for Learning, Inc., 2012
- 227. Hexagons Start with a small equilateral triangle.© Activities for Learning, Inc., 2012
- 228. Hexagons© Activities for Learning, Inc., 2012
- 229. Hexagons© Activities for Learning, Inc., 2012
- 230. Hexagons© Activities for Learning, Inc., 2012
- 231. Hexagons© Activities for Learning, Inc., 2012
- 232. Hexagons© Activities for Learning, Inc., 2012
- 233. Hexagons© Activities for Learning, Inc., 2012
- 234. Hexagons© Activities for Learning, Inc., 2012
- 235. Hexagons© Activities for Learning, Inc., 2012
- 236. Hexagons Draw all the diagonals.© Activities for Learning, Inc., 2012
- 237. Hexagons Draw all the diagonals.© Activities for Learning, Inc., 2012
- 238. Hexagons Draw all the diagonals.© Activities for Learning, Inc., 2012
- 239. Hexagons Draw all the diagonals.© Activities for Learning, Inc., 2012
- 240. Hexagons Draw all the diagonals.© Activities for Learning, Inc., 2012
- 241. Hexagons Draw all the diagonals.© Activities for Learning, Inc., 2012
- 242. Hexagons Do you see another hexagon?© Activities for Learning, Inc., 2012
- 243. Hexagons Find the figures Do you see another hexagon?© Activities for Learning, Inc., 2012
- 244. Hexagons Find the figures 2 non-congruent rectangles?© Activities for Learning, Inc., 2012
- 245. Hexagons Find the figures 2 non-congruent rectangles?© Activities for Learning, Inc., 2012
- 246. Hexagons Find the figures 2 non-congruent rectangles?© Activities for Learning, Inc., 2012
- 247. Hexagons Find the figures 3 non-congruent right triangles?© Activities for Learning, Inc., 2012
- 248. Hexagons Find the figures 3 non-congruent right triangles?© Activities for Learning, Inc., 2012
- 249. Hexagons Find the figures 3 non-congruent right triangles?© Activities for Learning, Inc., 2012
- 250. Hexagons Find the figures 3 non-congruent right triangles?© Activities for Learning, Inc., 2012
- 251. Hexagons Find the figures 2 non-congruent rhombuses?© Activities for Learning, Inc., 2012
- 252. Hexagons Find the figures 2 non-congruent rhombuses?© Activities for Learning, Inc., 2012
- 253. Hexagons Find the figures 2 non-congruent rhombuses?© Activities for Learning, Inc., 2012
- 254. Hexagons Find the figures 3 similar equilateral triangles?© Activities for Learning, Inc., 2012
- 255. Hexagons Find the figures 3 similar equilateral triangles?© Activities for Learning, Inc., 2012
- 256. Hexagons Find the figures 3 similar equilateral triangles?© Activities for Learning, Inc., 2012
- 257. Hexagons Find the figures 3 similar obtuse triangles?© Activities for Learning, Inc., 2012
- 258. Hexagons Find the figures 3 similar obtuse triangles?© Activities for Learning, Inc., 2012
- 259. Hexagons Find the figures 3 similar obtuse triangles?© Activities for Learning, Inc., 2012
- 260. Hexagons Find the figures 3 similar obtuse triangles?© Activities for Learning, Inc., 2012
- 261. Hexagons Find the figures 3 non-congruent trapezoids?© Activities for Learning, Inc., 2012
- 262. Hexagons Find the figures 3 non-congruent trapezoids?© Activities for Learning, Inc., 2012
- 263. Hexagons Find the figures 3 non-congruent trapezoids?© Activities for Learning, Inc., 2012
- 264. Hexagons Find the figures 3 non-congruent trapezoids?© Activities for Learning, Inc., 2012
- 265. Hexagons Find the figures 2 similar kites?© Activities for Learning, Inc., 2012
- 266. Hexagons Find the figures 2 similar kites?© Activities for Learning, Inc., 2012
- 267. Hexagons Find the figures 2 similar kites?© Activities for Learning, Inc., 2012
- 268. © Activities for Learning, Inc., 2012
- 269. Hexagons Constructing the small star Apothem: perpendicular line from side to center.© Activities for Learning, Inc., 2012
- 270. Hexagons Constructing the small star Apothem: perpendicular line from side to center.© Activities for Learning, Inc., 2012
- 271. Hexagons Constructing the small star Apothem: perpendicular line from side to center.© Activities for Learning, Inc., 2012
- 272. Hexagons Constructing the small star© Activities for Learning, Inc., 2012
- 273. Hexagons Constructing the small star© Activities for Learning, Inc., 2012
- 274. Hexagons Constructing the small star© Activities for Learning, Inc., 2012
- 275. Hexagons Constructing the small star© Activities for Learning, Inc., 2012
- 276. Hexagons Constructing the small star Ratio of the areas of star and hexagon?© Activities for Learning, Inc., 2012
- 277. Hexagons Constructing the small star Ratio of the areas of star and hexagon?© Activities for Learning, Inc., 2012
- 278. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 279. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 280. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 281. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 282. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 283. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 284. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 285. Hexagons Constructing the large star© Activities for Learning, Inc., 2012
- 286. The Clock 11 12 1 10 2 9 3 8 4 7 6 5© Activities for Learning, Inc., 2012
- 287. The Clock 11 12 1 10 2 9 3 8 4 7 6 5© Activities for Learning, Inc., 2012
- 288. The Clock 11 12 1 10 2 9 3 8 4 7 6 5© Activities for Learning, Inc., 2012
- 289. The Clock 11 12 1 10 2 9 3 8 4 7 6 5© Activities for Learning, Inc., 2012
- 290. The Clock 11 12 1 10 2 9 3 8 4 7 6 5© Activities for Learning, Inc., 2012
- 291. The Clock 11 12 1 10 2 9 3 8 4 7 6 5 11 12 1 10 2 9 3 8 4 7 6 5© Activities for Learning, Inc., 2012
- 292. Right Triangle Design© Activities for Learning, Inc., 2012
- 293. Right Triangle Design© Activities for Learning, Inc., 2012
- 294. Right Triangle Design© Activities for Learning, Inc., 2012
- 295. Right Triangle Design© Activities for Learning, Inc., 2012
- 296. Right Triangle Design© Activities for Learning, Inc., 2012
- 297. Right Triangle Design© Activities for Learning, Inc., 2012
- 298. Right Triangle Design© Activities for Learning, Inc., 2012
- 299. Right Triangle Design© Activities for Learning, Inc., 2012
- 300. Right Triangle Design© Activities for Learning, Inc., 2012
- 301. Right Triangle Design© Activities for Learning, Inc., 2012
- 302. © Activities for Learning, Inc., 2012
- 303. Tangrams© Activities for Learning, Inc., 2012
- 304. Tangrams© Activities for Learning, Inc., 2012
- 305. Tangrams© Activities for Learning, Inc., 2012
- 306. Tangrams© Activities for Learning, Inc., 2012
- 307. Tangrams© Activities for Learning, Inc., 2012
- 308. Tangrams© Activities for Learning, Inc., 2012
- 309. Tangrams© Activities for Learning, Inc., 2012
- 310. Tangrams Are the 3 green figures are equal in© Activities for Learning, Inc., 2012 area?
- 311. Tangrams© Activities for Learning, Inc., 2012
- 312. Tangrams The 3 green figures ARE equal in area.© Activities for Learning, Inc., 2012
- 313. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 314. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 315. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 316. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 317. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 318. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 319. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 320. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 321. Tangrams Constructing a tangram arrangement.© Activities for Learning, Inc., 2012
- 322. Tangrams© Activities for Learning, Inc., 2012
- 323. Tangram Design Symmetry Start at the left side of the paper.© Activities for Learning, Inc., 2012
- 324. Tangram Design Symmetry Start at the left side of the paper.© Activities for Learning, Inc., 2012
- 325. Tangram Design Symmetry Reflect the image vertically across the© Activities for Learning, Inc., 2012 line.
- 326. Tangram Design Symmetry Reflect the image vertically.© Activities for Learning, Inc., 2012
- 327. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 328. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 329. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 330. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 331. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 332. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 333. Tangram Design Symmetry Reflect the image horizontally.© Activities for Learning, Inc., 2012
- 334. Tangram Design Symmetry Reflect the image horizontally.© Activities for Learning, Inc., 2012
- 335. Tangram Design Symmetry The blue rotated 180° is the yellow.© Activities for Learning, Inc., 2012
- 336. Tangram Design Symmetry Reflect the image vertically.© Activities for Learning, Inc., 2012
- 337. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 338. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 339. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 340. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 341. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 342. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 343. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 344. Tangram Design Symmetry© Activities for Learning, Inc., 2012
- 345. Tangram Design Symmetry Two horizontal reflections is the original.© Activities for Learning, Inc., 2012
- 346. Tangram Design Symmetry • Such constructions require thinking ahead.© Activities for Learning, Inc., 2012
- 347. Tangram Design Symmetry • Such constructions require thinking ahead. • Each step must be justified; no guessing.© Activities for Learning, Inc., 2012
- 348. Tangram Design Symmetry • Such constructions require thinking ahead. • Each step must be justified; no guessing. • Symmetry is in everyday life.© Activities for Learning, Inc., 2012
- 349. Tangram Design Symmetry • Such constructions require thinking ahead. • Each step must be justified; no guessing. • Symmetry is in everyday life. • Symmetry is often on tests.© Activities for Learning, Inc., 2012
- 350. © Activities for Learning, Inc., 2012
- 351. Pythagorean Theorem First construct a right triangle.© Activities for Learning, Inc., 2012
- 352. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 353. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 354. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 355. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 356. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 357. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 358. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 359. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 360. Pythagorean Theorem Area of blue squares = yellow square.© Activities for Learning, Inc., 2012
- 361. Pythagorean Theorem Area of blue squares = yellow square.© Activities for Learning, Inc., 2012
- 362. Pythagorean Theorem Draw a right triangle.© Activities for Learning, Inc., 2012
- 363. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 364. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 365. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 366. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 367. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 368. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 369. Pythagorean Theorem Turn the t-square upside down.© Activities for Learning, Inc., 2012
- 370. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 371. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 372. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 373. Pythagorean Theorem Do not move the t-square.© Activities for Learning, Inc., 2012
- 374. Pythagorean Theorem Do not move the t-square.© Activities for Learning, Inc., 2012
- 375. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 376. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 377. Pythagorean Theorem© Activities for Learning, Inc., 2012
- 378. Pythagorean Theorem Area of blue squares = yellow square.© Activities for Learning, Inc., 2012
- 379. Triangle Area A B C© Activities for Learning, Inc., 2012
- 380. Triangle Area A B C Draw the altitude.© Activities for Learning, Inc., 2012
- 381. Triangle Area A B C Area is half of enclosing rectangle.© Activities for Learning, Inc., 2012
- 382. Triangle Area A B C Another altitude.© Activities for Learning, Inc., 2012
- 383. Triangle Area A B C Find the area.© Activities for Learning, Inc., 2012
- 384. Triangle Area A B C Another altitude.© Activities for Learning, Inc., 2012
- 385. Triangle Area A B C Find the area.© Activities for Learning, Inc., 2012
- 386. Triangle Area A B C Altitudes intersect at the orthocenter.© Activities for Learning, Inc., 2012
- 387. Triangle Area A B C 3 areas slightly different. Why?© Activities for Learning, Inc., 2012
- 388. Geometric Approach© Activities for Learning, Inc., 2012
- 389. Geometric Approach • Basis of CAD (computer aided design).© Activities for Learning, Inc., 2012
- 390. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts.© Activities for Learning, Inc., 2012
- 391. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts. • Incorporates measuring.© Activities for Learning, Inc., 2012
- 392. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts. • Incorporates measuring. • Allows independent work.© Activities for Learning, Inc., 2012
- 393. Geometric Approach • Basis of CAD (computer aided design). • Integrates many concepts. • Incorporates measuring. • Allows independent work. • Excellent preparation for high school mathematics.© Activities for Learning, Inc., 2012
- 394. Geometric Approach Goals© Activities for Learning, Inc., 2012
- 395. Geometric Approach Goals • To use elementary math.© Activities for Learning, Inc., 2012
- 396. Geometric Approach Goals • To use elementary math. • To learn to read math texts.© Activities for Learning, Inc., 2012
- 397. Geometric Approach Goals • To use elementary math. • To learn to read math texts. • To prepare for more advanced mathematics.© Activities for Learning, Inc., 2012
- 398. Geometric Approach Goals • To use elementary math. • To learn to read math texts. • To prepare for more advanced mathematics. • To discover mathematics in the everyday world.© Activities for Learning, Inc., 2012
- 399. Geometric Approach Goals • To use elementary math. • To learn to read math texts. • To prepare for more advanced mathematics. • To discover mathematics in the everyday world. • To enjoy mathematics.© Activities for Learning, Inc., 2012
- 400. Personalized Learning Bridges Middle-School Math with a Geometric Approach – Part 2 Presented by Tracy Mittleider, MSEd and Kathleen Lawler Based on work of Joan A. Cotter, Ph.D. Aplus+ Conference October 24, 2012© Activities for Learning, Inc., 2012

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