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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
- 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
- 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
- 68. Equilateral Triangles
Divide it into fourths
Find the center of the base line.
© 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 227. Hexagons
Start with a small equilateral triangle.
© 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
- 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
- 310. Tangrams
Are the 3 green figures are equal in
© Activities for Learning, Inc., 2012 area?
- 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
- 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
- 351. Pythagorean Theorem
First construct a right triangle.
© 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
- 378. Pythagorean Theorem
Area of blue squares = yellow square.
© 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
- 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
- 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
Notas del editor
- 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.