personalized learning bridges middle school math with a geometric approach
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TRANSCRIPT
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© Activities for Learning, Inc., 2012
Personalized LearningBridges Middle-School Math with a Geometric Approach
Aplus+ ConferenceOctober 24, 2012
Presented by Tracy Mittleider, MSEd and Kathleen Lawler
Based on work of Joan A. Cotter, Ph.D.
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© Activities for Learning, Inc., 2012
Why a Geometric Approach?
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© Activities for Learning, Inc., 2012
Most students in “middle school” are visual learners.
Why a Geometric Approach?
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© Activities for Learning, Inc., 2012
Most students in “middle school” are visual learners.
90% of the math topics can be explored geometrically (visually).
Why a Geometric Approach?
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© Activities for Learning, Inc., 2012
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.
Why a Geometric Approach?
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Drawing ToolsPaper
11 in. by 8.5 in.
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Drawing ToolsDrawing board with paper
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Drawing ToolsDrawing board with paper
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Drawing ToolsT-square
T-square
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Drawing ToolsT-square
T-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsT-square
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Drawing ToolsPencil (mechanical) and eraser
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© Activities for Learning, Inc., 2012
Drawing ToolsPencil (mechanical) and eraser
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© Activities for Learning, Inc., 2012
Drawing ToolsPencil (mechanical) and eraser
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© Activities for Learning, Inc., 2012
Drawing ToolsPencil (mechanical) and eraser
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Drawing ToolsPencil (mechanical) and eraser
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© Activities for Learning, Inc., 2012
Drawing ToolsPencil (mechanical) and eraser
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Drawing ToolsThe 45 triangle
45°
45° 90°
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Drawing ToolsThe 30-60 triangle (a set square)
60°
30°
90°
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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© Activities for Learning, Inc., 2012
Drawing ToolsThe 30-60 triangle
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Equilateral TrianglesDraw the base line
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDraw the base line
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Equilateral TrianglesDraw the sides
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDraw the sides
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDraw the sides
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDraw the sides
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
12
12
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
![Page 54: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/54.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
![Page 55: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/55.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into halves
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into thirds
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into thirds
![Page 59: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/59.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into thirds
![Page 60: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/60.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into thirds
![Page 61: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/61.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into thirds
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into thirds
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into thirds
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Equilateral Triangles
13
13
13
Divide it into thirds
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© Activities for Learning, Inc., 2012
Equilateral Triangles
13
13
13
Divide it into thirds
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
Find the center of the base line.
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Equilateral Triangles
tick mark
Divide it into fourths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
14
14
14
14
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Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses:
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses: ABDF
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses: ABDF, BCDF
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the rhombuses: ABDF, BCDF, BDEF
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Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids:
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids: BCEF
![Page 82: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/82.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids: BCEF, ACDF
![Page 83: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/83.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into fourths
A
B
CD
E
F
Name the trapezoids: BCEF, ACDF, ABDE
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Equilateral Triangles
What if we cut this shape out….
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Equilateral Triangles
…and folded it on the lines….
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Equilateral Triangles
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Equilateral Triangles
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Equilateral Triangles
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Equilateral Triangles
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Equilateral Triangles
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Equilateral Triangles
It’s a tetrahedron!
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Equilateral TrianglesDivide it into eighths
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Equilateral TrianglesDivide it into eighths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into eighths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into eighths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into eighths
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Equilateral TrianglesDivide it into sixths
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Equilateral TrianglesDivide it into sixths
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Equilateral TrianglesDivide it into sixths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name an acute triangle:
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name an acute triangle: ACE
![Page 102: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/102.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name a right triangle:
![Page 103: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/103.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name a right triangle: ADE
![Page 104: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/104.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name a right triangle: ADE, ABE
![Page 105: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/105.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name a right triangle: ADE, ABE, ABG
![Page 106: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/106.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name an obtuse triangle:
![Page 107: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/107.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into sixths
A
B
CD
E
FG
Name an obtuse triangle: GCE
![Page 108: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/108.jpg)
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Equilateral TrianglesDivide it into twelfths
![Page 109: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/109.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
![Page 111: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/111.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
![Page 112: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/112.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
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© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
![Page 114: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/114.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
Can you see the cube?
![Page 115: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/115.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
Can you see the cube?
![Page 116: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/116.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
Do you see the hexagon?
![Page 117: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/117.jpg)
© Activities for Learning, Inc., 2012
Equilateral TrianglesDivide it into twelfths
Do you see the hexagon?
![Page 118: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/118.jpg)
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Equilateral Triangles
Ninths
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Equilateral Triangles
Twenty-sevenths
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Equilateral Triangles
Twenty-sevenths
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Equilateral Triangles
![Page 122: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/122.jpg)
© Activities for Learning, Inc., 2012
Equilateral Triangles
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© Activities for Learning, Inc., 2012
Equilateral Triangles
Thirty-seconds
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Equilateral Triangles
Stephanie, 6, did 256!
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Equilateral Triangles
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© Activities for Learning, Inc., 2012
Equilateral Triangles
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© Activities for Learning, Inc., 2012
Equilateral Triangles
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Equilateral Triangles
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Equilateral TrianglesSpiral
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© Activities for Learning, Inc., 2012
Equilateral TrianglesSpiral
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© Activities for Learning, Inc., 2012
Equilateral TrianglesSpiral
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© Activities for Learning, Inc., 2012
Equilateral TrianglesSpiral
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Equilateral TrianglesSpiral
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© Activities for Learning, Inc., 2012
Equilateral TrianglesSpiral
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Equilateral TrianglesSpiral
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© Activities for Learning, Inc., 2012
Equilateral TrianglesSpiral
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© Activities for Learning, Inc., 2012
Equilateral TrianglesSpiral
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© Activities for Learning, Inc., 2012
Equilateral TrianglesSpiral
![Page 140: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/140.jpg)
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Equilateral TrianglesSpiral
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Geometric Approach
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Geometric Approach
• Basis of CAD (computer aided design).
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© Activities for Learning, Inc., 2012
Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.
![Page 144: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/144.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.• Incorporates measuring.
![Page 145: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/145.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.• Incorporates measuring.• Allows independent work.
![Page 146: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/146.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.• Incorporates measuring.• Allows independent work.• Excellent preparation for
high school mathematics.
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Geometric Approach
Goals
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Geometric Approach
• To use elementary math.
Goals
![Page 149: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/149.jpg)
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Geometric Approach
• To use elementary math.• To learn to read math texts.
Goals
![Page 150: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/150.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• To use elementary math.• To learn to read math texts.• To prepare for more advanced
mathematics.
Goals
![Page 151: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/151.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• To use elementary math.• To learn to read math texts.• To prepare for more advanced
mathematics.• To discover mathematics in
the everyday world.
Goals
![Page 152: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/152.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• 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.
Goals
![Page 153: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/153.jpg)
© Activities for Learning, Inc., 2012
Why a Geometric Approach?
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Most students in “middle school” are visual learners.
Why a Geometric Approach?
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Most students in “middle school” are visual learners.
90% of the math topics can be explored geometrically (visually).
Why a Geometric Approach?
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© Activities for Learning, Inc., 2012
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.
Why a Geometric Approach?
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Squares
The 45 triangle.
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Squares
The 45 triangle is half of a square.
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Squares
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Squares
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Squares
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Squares
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Squares
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Squares
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© Activities for Learning, Inc., 2012
Squares
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© Activities for Learning, Inc., 2012
Squares
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Squares
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Squares
Halves
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Squares
Fourths
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Squares
Eighths
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Squares
Sixteenths
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SquaresHalves
We need to find the center.
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© Activities for Learning, Inc., 2012
SquaresHalves
We need to find the center.
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© Activities for Learning, Inc., 2012
SquaresHalves
We need to find the center.
![Page 177: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/177.jpg)
© Activities for Learning, Inc., 2012
SquaresHalves
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© Activities for Learning, Inc., 2012
SquaresHalves
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© Activities for Learning, Inc., 2012
SquaresFourths
![Page 180: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/180.jpg)
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SquaresFourths
![Page 181: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/181.jpg)
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SquaresEighths
Find the center of a small square.
![Page 182: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/182.jpg)
© Activities for Learning, Inc., 2012
SquaresEighths
Find the center of a small square.
![Page 183: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/183.jpg)
© Activities for Learning, Inc., 2012
SquaresEighths
Find the center of a small square.
![Page 184: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/184.jpg)
© Activities for Learning, Inc., 2012
SquaresEighths
Find the center of a small square.
![Page 185: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/185.jpg)
© Activities for Learning, Inc., 2012
SquaresEighths
![Page 186: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/186.jpg)
© Activities for Learning, Inc., 2012
SquaresEighths
![Page 187: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/187.jpg)
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SquaresSixteenths
![Page 188: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/188.jpg)
© Activities for Learning, Inc., 2012
SquaresSixteenths
![Page 189: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/189.jpg)
© Activities for Learning, Inc., 2012
SquaresSixteenths
![Page 190: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/190.jpg)
© Activities for Learning, Inc., 2012
![Page 191: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/191.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 192: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/192.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 193: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/193.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 194: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/194.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 195: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/195.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 196: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/196.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 197: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/197.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 198: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/198.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 199: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/199.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 200: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/200.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 201: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/201.jpg)
© Activities for Learning, Inc., 2012
SquaresCircumscribed squares
![Page 202: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/202.jpg)
© Activities for Learning, Inc., 2012
![Page 203: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/203.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 204: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/204.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 205: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/205.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 206: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/206.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
Compare the area of the squares.
![Page 207: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/207.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
Compare the area of the squares.
![Page 208: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/208.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 209: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/209.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 210: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/210.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 211: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/211.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 212: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/212.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 213: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/213.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 214: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/214.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 215: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/215.jpg)
© Activities for Learning, Inc., 2012
SquaresInscribed squares
![Page 216: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/216.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 217: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/217.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 218: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/218.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 219: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/219.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 220: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/220.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 221: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/221.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 222: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/222.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 223: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/223.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 224: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/224.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 225: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/225.jpg)
© Activities for Learning, Inc., 2012
SquaresRight triangle spiral
![Page 226: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/226.jpg)
© Activities for Learning, Inc., 2012
![Page 227: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/227.jpg)
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Hexagons
Start with a small equilateral triangle.
![Page 228: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/228.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 229: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/229.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 230: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/230.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 231: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/231.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 232: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/232.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 233: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/233.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 234: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/234.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 235: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/235.jpg)
© Activities for Learning, Inc., 2012
Hexagons
![Page 236: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/236.jpg)
© Activities for Learning, Inc., 2012
Hexagons
Draw all the diagonals.
![Page 237: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/237.jpg)
© Activities for Learning, Inc., 2012
Hexagons
Draw all the diagonals.
![Page 238: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/238.jpg)
© Activities for Learning, Inc., 2012
Hexagons
Draw all the diagonals.
![Page 239: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/239.jpg)
© Activities for Learning, Inc., 2012
Hexagons
Draw all the diagonals.
![Page 240: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/240.jpg)
© Activities for Learning, Inc., 2012
Hexagons
Draw all the diagonals.
![Page 241: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/241.jpg)
© Activities for Learning, Inc., 2012
Hexagons
Draw all the diagonals.
![Page 242: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/242.jpg)
© Activities for Learning, Inc., 2012
Hexagons
Do you see another hexagon?
![Page 243: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/243.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
Do you see another hexagon?
![Page 244: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/244.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 non-congruent rectangles?
![Page 245: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/245.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 non-congruent rectangles?
![Page 246: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/246.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 non-congruent rectangles?
![Page 247: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/247.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent right triangles?
![Page 248: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/248.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent right triangles?
![Page 249: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/249.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent right triangles?
![Page 250: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/250.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent right triangles?
![Page 251: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/251.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 non-congruent rhombuses?
![Page 252: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/252.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 non-congruent rhombuses?
![Page 253: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/253.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 non-congruent rhombuses?
![Page 254: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/254.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 similar equilateral triangles?
![Page 255: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/255.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 similar equilateral triangles?
![Page 256: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/256.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 similar equilateral triangles?
![Page 257: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/257.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 similar obtuse triangles?
![Page 258: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/258.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 similar obtuse triangles?
![Page 259: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/259.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 similar obtuse triangles?
![Page 260: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/260.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 similar obtuse triangles?
![Page 261: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/261.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent trapezoids?
![Page 262: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/262.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent trapezoids?
![Page 263: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/263.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent trapezoids?
![Page 264: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/264.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
3 non-congruent trapezoids?
![Page 265: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/265.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 similar kites?
![Page 266: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/266.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 similar kites?
![Page 267: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/267.jpg)
© Activities for Learning, Inc., 2012
HexagonsFind the figures
2 similar kites?
![Page 268: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/268.jpg)
© Activities for Learning, Inc., 2012
![Page 269: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/269.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
Apothem: perpendicular line from side to center.
![Page 270: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/270.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
Apothem: perpendicular line from side to center.
![Page 271: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/271.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
Apothem: perpendicular line from side to center.
![Page 272: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/272.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
![Page 273: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/273.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
![Page 274: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/274.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
![Page 275: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/275.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
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© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
Ratio of the areas of star and hexagon?
![Page 277: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/277.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the small star
Ratio of the areas of star and hexagon?
![Page 278: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/278.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
![Page 279: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/279.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
![Page 280: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/280.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
![Page 281: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/281.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
![Page 282: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/282.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
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© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
![Page 284: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/284.jpg)
© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
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© Activities for Learning, Inc., 2012
HexagonsConstructing the large star
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© Activities for Learning, Inc., 2012
The Clock112
23
4567
8910
11
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© Activities for Learning, Inc., 2012
The Clock112
23
4567
8910
11
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© Activities for Learning, Inc., 2012
The Clock112
23
4567
8910
11
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© Activities for Learning, Inc., 2012
The Clock112
23
4567
8910
11
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© Activities for Learning, Inc., 2012
The Clock112
23
4567
8910
11
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© Activities for Learning, Inc., 2012
The Clock
12 12
3
4567
8
9
1011
11223
4567
8910
11
![Page 292: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/292.jpg)
© Activities for Learning, Inc., 2012
Right Triangle Design
![Page 293: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/293.jpg)
© Activities for Learning, Inc., 2012
Right Triangle Design
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© Activities for Learning, Inc., 2012
Right Triangle Design
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© Activities for Learning, Inc., 2012
Right Triangle Design
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© Activities for Learning, Inc., 2012
Right Triangle Design
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© Activities for Learning, Inc., 2012
Right Triangle Design
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© Activities for Learning, Inc., 2012
Right Triangle Design
![Page 299: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/299.jpg)
© Activities for Learning, Inc., 2012
Right Triangle Design
![Page 300: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/300.jpg)
© Activities for Learning, Inc., 2012
Right Triangle Design
![Page 301: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/301.jpg)
© Activities for Learning, Inc., 2012
Right Triangle Design
![Page 302: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/302.jpg)
© Activities for Learning, Inc., 2012
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© Activities for Learning, Inc., 2012
Tangrams
![Page 304: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/304.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 305: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/305.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 306: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/306.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 307: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/307.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 308: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/308.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 309: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/309.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 310: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/310.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Are the 3 green figures are equal in area?
![Page 311: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/311.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 312: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/312.jpg)
© Activities for Learning, Inc., 2012
Tangrams
The 3 green figures ARE equal in area.
![Page 313: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/313.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 314: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/314.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 315: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/315.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 316: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/316.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 317: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/317.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 318: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/318.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 319: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/319.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 320: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/320.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 321: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/321.jpg)
© Activities for Learning, Inc., 2012
Tangrams
Constructing a tangram arrangement.
![Page 322: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/322.jpg)
© Activities for Learning, Inc., 2012
Tangrams
![Page 323: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/323.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
Start at the left side of the paper.
![Page 324: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/324.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
Start at the left side of the paper.
![Page 325: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/325.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
Reflect the image vertically across the line.
![Page 326: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/326.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
Reflect the image vertically.
![Page 327: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/327.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 328: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/328.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 329: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/329.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 330: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/330.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 331: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/331.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 332: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/332.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 333: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/333.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
Reflect the image horizontally.
![Page 334: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/334.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
Reflect the image horizontally.
![Page 335: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/335.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
The blue rotated 180° is the yellow.
![Page 336: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/336.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
Reflect the image vertically.
![Page 337: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/337.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 338: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/338.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 339: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/339.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 340: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/340.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 341: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/341.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 342: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/342.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 343: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/343.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 344: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/344.jpg)
© Activities for Learning, Inc., 2012
Tangram Design Symmetry
![Page 345: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/345.jpg)
© Activities for Learning, Inc., 2012
Two horizontal reflections is the original.
Tangram Design Symmetry
![Page 346: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/346.jpg)
© Activities for Learning, Inc., 2012
• Such constructions require thinking ahead.
Tangram Design Symmetry
![Page 347: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/347.jpg)
© Activities for Learning, Inc., 2012
• Such constructions require thinking ahead.
• Each step must be justified; no guessing.
Tangram Design Symmetry
![Page 348: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/348.jpg)
© Activities for Learning, Inc., 2012
• Such constructions require thinking ahead.
• Each step must be justified; no guessing.
• Symmetry is in everyday life.
Tangram Design Symmetry
![Page 349: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/349.jpg)
© Activities for Learning, Inc., 2012
• Such constructions require thinking ahead.
• Each step must be justified; no guessing.
• Symmetry is in everyday life.
• Symmetry is often on tests.
Tangram Design Symmetry
![Page 350: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/350.jpg)
© Activities for Learning, Inc., 2012
![Page 351: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/351.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
First construct a right triangle.
![Page 352: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/352.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 353: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/353.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 354: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/354.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 355: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/355.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 356: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/356.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 357: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/357.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 358: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/358.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 359: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/359.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 360: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/360.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
Area of blue squares = yellow square.
![Page 361: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/361.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
Area of blue squares = yellow square.
![Page 362: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/362.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
Draw a right triangle.
![Page 363: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/363.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 364: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/364.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 365: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/365.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
![Page 366: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/366.jpg)
© Activities for Learning, Inc., 2012
Pythagorean Theorem
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Pythagorean Theorem
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Pythagorean Theorem
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Pythagorean Theorem
Turn the t-square upside down.
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Pythagorean Theorem
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Pythagorean Theorem
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Pythagorean Theorem
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Pythagorean Theorem
Do not move the t-square.
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© Activities for Learning, Inc., 2012
Pythagorean Theorem
Do not move the t-square.
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Pythagorean Theorem
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Pythagorean Theorem
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Pythagorean Theorem
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Pythagorean Theorem
Area of blue squares = yellow square.
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Triangle Area
A
CB
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Triangle Area
Draw the altitude.
A
CB
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Triangle Area
Area is half of enclosing rectangle.
CB
A
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Triangle Area
Another altitude.
CB
A
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Triangle Area
Find the area.
CB
A
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Triangle Area
Another altitude.
A
CB
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© Activities for Learning, Inc., 2012
Triangle Area
Find the area.
A
CB
![Page 386: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/386.jpg)
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Triangle Area
Altitudes intersect at the orthocenter.
A
CB
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Triangle Area
3 areas slightly different. Why?
A
CB
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Geometric Approach
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Geometric Approach
• Basis of CAD (computer aided design).
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Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.
![Page 391: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/391.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.• Incorporates measuring.
![Page 392: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/392.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.• Incorporates measuring.• Allows independent work.
![Page 393: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/393.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• Basis of CAD (computer aided design).
• Integrates many concepts.• Incorporates measuring.• Allows independent work.• Excellent preparation for
high school mathematics.
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Geometric Approach
Goals
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Geometric Approach
• To use elementary math.
Goals
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© Activities for Learning, Inc., 2012
Geometric Approach
• To use elementary math.• To learn to read math texts.
Goals
![Page 397: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/397.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• To use elementary math.• To learn to read math texts.• To prepare for more advanced
mathematics.
Goals
![Page 398: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/398.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• To use elementary math.• To learn to read math texts.• To prepare for more advanced
mathematics.• To discover mathematics in
the everyday world.
Goals
![Page 399: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/399.jpg)
© Activities for Learning, Inc., 2012
Geometric Approach
• 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.
Goals
![Page 400: Personalized Learning Bridges Middle School Math with a Geometric Approach](https://reader033.vdocument.in/reader033/viewer/2022061112/545688eaaf795950098b5138/html5/thumbnails/400.jpg)
© Activities for Learning, Inc., 2012
Personalized LearningBridges Middle-School Math
with a Geometric Approach – Part 2Presented by
Tracy Mittleider, MSEd and Kathleen LawlerBased on work of Joan A. Cotter, Ph.D.
Aplus+ ConferenceOctober 24, 2012