Geometry (Geometric M. & Dimension)

Tim Brzezinski, Deirdre Longo, 6/6/2018

[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]

Tabla de Contenidos

  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. Segment Area: Quick Investigation
    19. Volume of a Rectangular Prism
    20. Figure 6.7 Cavalieri's principle
    21. Cavalieri's Principle
    22. Mailbox? Backpack? (Composite Solid)
    23. Washer Action!!! (1)
    24. Animation 169
    25. Trisecting the Cube into 3 Pyramids
    26. Volume of Pyramids
    27. Volume of Pyramids - Chinese Proof
    28. SolveMyMaths Action 3A!
    29. SolveMyMaths Action 3B!
    30. Animation 203
    31. SolveMyMaths Action 4!
    32. Animation 204
    33. 4 Triangles Action!!!
    34. 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. Build Your Own Right Triangular Prism (V2)!
    11. Build Your Own Right Triangular Prism!
    12. Right Triangular Prism!
    13. Adjustable Triangular Prism
    14. Sphere Peeling: Volume
    15. Net of a Cone
    16. 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. Segment Area: Quick Investigation
  • 19. Volume of a Rectangular Prism
  • 20. Figure 6.7 Cavalieri's principle
  • 21. Cavalieri's Principle
  • 22. Mailbox? Backpack? (Composite Solid)
  • 23. Washer Action!!! (1)
  • 24. Animation 169
  • 25. Trisecting the Cube into 3 Pyramids
  • 26. Volume of Pyramids
  • 27. Volume of Pyramids - Chinese Proof
  • 28. SolveMyMaths Action 3A!
  • 29. SolveMyMaths Action 3B!
  • 30. Animation 203
  • 31. SolveMyMaths Action 4!
  • 32. Animation 204
  • 33. 4 Triangles Action!!!
  • 34. 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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1.33.

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1.34.

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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. Build Your Own Right Triangular Prism (V2)!
  • 11. Build Your Own Right Triangular Prism!
  • 12. Right Triangular Prism!
  • 13. Adjustable Triangular Prism
  • 14. Sphere Peeling: Volume
  • 15. Net of a Cone
  • 16. 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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3.10.

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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

Información