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Personalized Learning Bridges Middle School Math with a Geometric Approach
- 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
Editor's Notes
- Right-handed user.
- Hold pencil 2-3cm (1 in.)from tip.
- Parallel lines.
- Triangle must hug the t-square.
- This doesn’t work!
- Perpendicular lines.
- Perpendicular lines.
- Still more parallel lines.
- Intersecting lines.
- Intersecting lines.
- Maintain a margin.
- Move the t-square down.
- Draw a side.
- Flip the triangle and repeat.
- Flip the triangle and repeat.
- A bit of erasing.
- The two halves are congruent.
- Divide it in half another way.
- Divide it in half another way.
- Divide it in half another way.
- Divide it in half another way.
- A bit of erasing.
- Flip the triangle and repeat.
- Can you figure out how to do it?
- Finding the center of the base line.
- Be sure the tick mark intersects the line.
- Flip the triangle over and repeat.
- How do you draw the last line?
- The smaller triangles are similar to the larger triangle.
- Name the rhombuses:
- Name the rhombuses: ABDF,
- Name the rhombuses. ABDF, BCDF,
- Name the rhombuses: ABDF, BCDF, BDEF.
- Name the trapezoids:
- Name the trapezoids: BCEF,
- Name the trapezoids: BCEF, ACDF,
- Name the trapezoids: BCEF, ACDF, ABDE.
- Cut it out….
- and fold on the lines.
- and fold on the lines.
- and fold on the dotted lines.
- and fold on the dotted lines.
- and fold on the dotted lines.
- How could you draw eighths?
- Not very esthetic.
- Can you divide it into sixths?
- Name an acute triangle:
- Name an acute triangle: ACE.
- Name a right triangle: ADE, ABE, ABG.
- Draw the base line.
- Move the t-square down.
- Draw the sides.
- Draw the diagonal…
- or just a tick mark.
- Draw the top.
- A bit of erasing.
- Outside square is twice the size of the inscribed square.
- No tracing or measuring.
- No tracing or measuring.
- No tracing or measuring.
- No tracing or measuring.
- No tracing or measuring.
- No tracing or measuring.
- No tracing or measuring.
- No tracing or measuring.
- No tracing or measuring.
- More examples to construct.