Geometry measurement and modeling

Tim Brzezinski, Rose Neal, Nov 18, 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. Animation 66
    2. Animation 65
    3. Parallelogram: Area
    4. Animation 202
    5. Triangle Area Action! (V1)
    6. Triangle Area Action!!! (V2)
    7. Animation 175
    8. Circle Area (by Peeling)
    9. Circle Area (By Peeling!)
    10. Area of a Circle - without words (Animation 38)
    11. Area of a Circle (III)
    12. Area of a Circle (by Peeling)
    13. Area of a Circle II
    14. Volume of a Rectangular Prism
    15. Figure 6.7 Cavalieri's principle
    16. Cavalieri's Principle
    17. Mailbox? Backpack? (Composite Solid)
    18. Washer Action!!! (1)
    19. Animation 169
    20. Trisecting the Cube into 3 Pyramids
    21. Volume of Pyramids
    22. Volume of Pyramids - Chinese Proof
    23. SolveMyMaths Action 3A!
    24. SolveMyMaths Action 3B!
    25. Animation 203
    26. SolveMyMaths Action 4!
    27. Animation 204
    28. 4 Triangles Action!!!
    29. Animation 179
  2. HSG.GMD.A.2 & A.3
    1. Unwrapping a Cylinder
    2. Unwrapping a Cylinder: REVAMPED!
    3. Volume of Spheres
    4. Volume of Spheres with Proof
    5. A sphere in a cylinder.
    6. Surface Area of Spheres
    7. Volumes and Surface Areas of Similar Cuboids
    8. Square Pyramid: Underlying Anatomy
    9. oblique and right pyramid - Cavalieri
    10. Right Triangular Prism!
    11. Adjustable Triangular Prism
    12. Sphere Peeling: Volume
    13. Net of a Cone
    14. 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. Animation 66
  • 2. Animation 65
  • 3. Parallelogram: Area
  • 4. Animation 202
  • 5. Triangle Area Action! (V1)
  • 6. Triangle Area Action!!! (V2)
  • 7. Animation 175
  • 8. Circle Area (by Peeling)
  • 9. Circle Area (By Peeling!)
  • 10. Area of a Circle - without words (Animation 38)
  • 11. Area of a Circle (III)
  • 12. Area of a Circle (by Peeling)
  • 13. Area of a Circle II
  • 14. Volume of a Rectangular Prism
  • 15. Figure 6.7 Cavalieri's principle
  • 16. Cavalieri's Principle
  • 17. Mailbox? Backpack? (Composite Solid)
  • 18. Washer Action!!! (1)
  • 19. Animation 169
  • 20. Trisecting the Cube into 3 Pyramids
  • 21. Volume of Pyramids
  • 22. Volume of Pyramids - Chinese Proof
  • 23. SolveMyMaths Action 3A!
  • 24. SolveMyMaths Action 3B!
  • 25. Animation 203
  • 26. SolveMyMaths Action 4!
  • 27. Animation 204
  • 28. 4 Triangles Action!!!
  • 29. Animation 179

1.1.

Animation 66

What geometric principles are being dynamically illustrated in the applet below?
– Tim Brzezinski

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1.27.

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1.29.

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2.

HSG.GMD.A.2 & A.3

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

2.1.

Unwrapping a Cylinder

– Tim Brzezinski

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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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3.12.

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3.13.

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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

Information