CCSS High School: Geometry (Geometric M. & Dimension)

Tim Brzezinski, Emily Reed, Jul 13, 2017

[b]This GeoGebra Book contains lots of discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of geometry concepts both inside and outside of the mathematics classroom. [color=#1551b5]This GeoGebra Book also contains lots of contributions from the following individuals: Anthony C.M.OR ([url]https://www.geogebra.org/orchiming[/url])[url][/url] Steve Phelps ([url]https://www.geogebra.org/stevephelps[/url]) Dr. Ted Coe ([url]https://www.geogebra.org/tedcoe[/url]) Without their amazing talent and creativity, this resource would not have been possible. [/b][/color]

Table of Contents

  1. HSG.GMD.A.1
    1. TRUE MEANING of π
    2. Circumference = ? (Animation)
    3. Animation 66
    4. Circumference = ? (Animation II)
    5. Animation 70
    6. Animation 65
    7. Parallelogram: Area
    8. Animation 202
    9. Triangle Area Action! (V1)
    10. Triangle Area Action!!! (V2)
    11. Animation 175
    12. Circle Area (by Peeling)
    13. Circle Area (By Peeling!)
    14. Area of a Circle - without words (Animation 38)
    15. Area of a Circle (III)
    16. Area of a Circle (by Peeling)
    17. Area of a Circle II
    18. Volume of a Rectangular Prism
    19. Figure 6.7 Cavalieri's principle
    20. Cavalieri's Principle (祖暅原理)
    21. Washer Action!!! (1)
    22. Animation 169
    23. Trisecting the Cube into 3 Pyramids
    24. Volume of Pyramids
    25. Volume of Pyramids - Chinese Proof
    26. SolveMyMaths Action 3A!
    27. SolveMyMaths Action 3B!
    28. Animation 203
    29. SolveMyMaths Action 4!
    30. Animation 204
    31. 4 Triangles Action!!!
    32. Animation 179
  2. HSG.GMD.A.2 & A.3
    1. Volume of Spheres
    2. Volume of Spheres with Proof
    3. A sphere in a cylinder.
    4. Surface Area of Spheres
    5. Volumes and Surface Areas of Similar Cuboids
    6. oblique and right pyramid - Cavalieri
    7. Right Triangular Prism!
    8. Adjustable Triangular Prism
    9. Right Circular Cylinder!
    10. Sphere Peeling: Volume
    11. Net of a Cone
    12. Curved Surface Area of Cones (Combined Version)
  3. HSG.GMD.B.4
    1. Sections of Rectangular Prisms (Cuboids)
    2. Sections of Triangular Prisms
    3. Sections of Cylinders
    4. Sections of Rectangular Pyramids
    5. Sections of Triangular Pyramids
    6. Sections of Cones
    7. Sections of Spheres
    8. Exploring Sections of Cubes
    9. 11 Nets of the Cube
    10. Cube Geometry: Shortest Path Between Points - A Net
    11. Cube Dissection Problem
    12. Rotating a Triangle Around a Coordinate Axis
    13. Box with Open Top
    14. Cross Section? (1)
  4. Links to Other CCSS High School: Geometry Standards
    1. Geometry Resources
  5. Additional - Links to CCSS High School: Functions Resources
    1. Functions Resources

1.

HSG.GMD.A.1

  • 1. TRUE MEANING of π
  • 2. Circumference = ? (Animation)
  • 3. Animation 66
  • 4. Circumference = ? (Animation II)
  • 5. Animation 70
  • 6. Animation 65
  • 7. Parallelogram: Area
  • 8. Animation 202
  • 9. Triangle Area Action! (V1)
  • 10. Triangle Area Action!!! (V2)
  • 11. Animation 175
  • 12. Circle Area (by Peeling)
  • 13. Circle Area (By Peeling!)
  • 14. Area of a Circle - without words (Animation 38)
  • 15. Area of a Circle (III)
  • 16. Area of a Circle (by Peeling)
  • 17. Area of a Circle II
  • 18. Volume of a Rectangular Prism
  • 19. Figure 6.7 Cavalieri's principle
  • 20. Cavalieri's Principle (祖暅原理)
  • 21. Washer Action!!! (1)
  • 22. Animation 169
  • 23. Trisecting the Cube into 3 Pyramids
  • 24. Volume of Pyramids
  • 25. Volume of Pyramids - Chinese Proof
  • 26. SolveMyMaths Action 3A!
  • 27. SolveMyMaths Action 3B!
  • 28. Animation 203
  • 29. SolveMyMaths Action 4!
  • 30. Animation 204
  • 31. 4 Triangles Action!!!
  • 32. Animation 179

1.1.

TRUE MEANING of π

Note: LARGE WHITE POINT is MOVEABLE.
1.
How many diameters were we able to wrap perfectly around this circle? [br](Round your answer to the nearest 0.01.)
2.
Move the LARGE WHITE POINT a bit (to change the size of the circle). Does your answer to question (1) change at all?
3.
Does your response for (1) look familiar? Where you have you seen this number before?
Quick (Silent) Demo
– Tim Brzezinski

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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1.17.

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1.18.

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1.19.

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1.20.

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1.21.

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1.22.

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1.23.

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1.24.

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1.25.

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1.26.

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1.27.

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1.28.

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1.29.

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1.30.

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1.31.

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1.32.

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2.

HSG.GMD.A.2 & A.3

  • 1. Volume of Spheres
  • 2. Volume of Spheres with Proof
  • 3. A sphere in a cylinder.
  • 4. Surface Area of Spheres
  • 5. Volumes and Surface Areas of Similar Cuboids
  • 6. oblique and right pyramid - Cavalieri
  • 7. Right Triangular Prism!
  • 8. Adjustable Triangular Prism
  • 9. Right Circular Cylinder!
  • 10. Sphere Peeling: Volume
  • 11. Net of a Cone
  • 12. Curved Surface Area of Cones (Combined Version)

2.1.

Volume of Spheres

The figure shows a hemisphere of radius [i]r[/i] and a cylinder of base radius and height [i]r[/i] with an inverted cone of the same height and base radius removed. Drag the red point to see the cross-sections of the two solids at a height [i]h[/i].[br](a) Express [i]x[/i] and [i]y[/i] in terms of [i]r[/i] and [i]h[/i].[br](b) Are the cross-sections equal in area?[br](c) Hence show that the volume of the sphere of radius [i]r[/i] is 4/3 π [i]r[/i]³.
– Anthony OR 柯志明

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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3.

HSG.GMD.B.4

  • 1. Sections of Rectangular Prisms (Cuboids)
  • 2. Sections of Triangular Prisms
  • 3. Sections of Cylinders
  • 4. Sections of Rectangular Pyramids
  • 5. Sections of Triangular Pyramids
  • 6. Sections of Cones
  • 7. Sections of Spheres
  • 8. Exploring Sections of Cubes
  • 9. 11 Nets of the Cube
  • 10. Cube Geometry: Shortest Path Between Points - A Net
  • 11. Cube Dissection Problem
  • 12. Rotating a Triangle Around a Coordinate Axis
  • 13. Box with Open Top
  • 14. Cross Section? (1)

3.1.

Sections of Rectangular Prisms (Cuboids)

Drag the blue points to see the different sections of the rectangular prism (cuboid).
Anthony Or. GeoGebra Institute of Hong Kong
– Anthony OR 柯志明

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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3.13.

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3.14.

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4.

Links to Other CCSS High School: Geometry Standards

  • 1. Geometry Resources

4.1.

Geometry Resources

[list][*][b][url=https://www.geogebra.org/m/z8nvD94T]Congruence (Volume 1)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/munhXmzx]Congruence (Volume 2)[/url][/b][/*][*][b][url=https://www.geogebra.org/m/dPqv8ACE]Similarity, Right Triangles, Trigonometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/C7dutQHh]Circles[/url][/b][/*][*][b][url=https://www.geogebra.org/m/K2YbdFk8]Coordinate and Analytic Geometry[/url][/b][/*][*][b][url=https://www.geogebra.org/m/xDNjSjEK]Area, Surface Area, Volume, 3D, Cross Section[/url] [/b][/*][*][b][url=https://www.geogebra.org/m/NjmEPs3t]Proof Challenges[/url]  [/b][/*][/list]
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
What phenomenon is dynamically being illustrated here? (Vertices are moveable.)
– Tim Brzezinski

5.

Additional - Links to CCSS High School: Functions Resources

  • 1. Functions Resources

5.1.

Functions Resources

[list][*][b][url=https://www.geogebra.org/m/k6Dvu9f3]Interpreting Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/uTddJKRC]Building Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/GMvvpwrm]Linear, Quadratic, and Exponential Functions[/url][/b][/*][*][b][url=https://www.geogebra.org/m/aWuJMDas]Trigonometric Functions[/url][/b][/*][/list]
Half-life function: Quick Exploration. (Large point & slider moveable.)
What does it mean for a function to be odd? (Points moveable.)
– GeoGebra Team, Tim Brzezinski

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