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

Tim Brzezinski, Emily Reed, Jul 13, 2017

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. This GeoGebra Book also contains lots of contributions from the following individuals: Anthony C.M.OR (https://www.geogebra.org/orchiming) Steve Phelps (https://www.geogebra.org/stevephelps) Dr. Ted Coe (https://www.geogebra.org/tedcoe) Without their amazing talent and creativity, this resource would not have been possible.

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
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)
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)
Links to Other CCSS High School: Geometry Standards
1. Geometry Resources
Additional - Links to CCSS High School: Functions Resources
1. Functions Resources

Information

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? (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

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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 r and a cylinder of base radius and height r 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 h. (a) Express x and y in terms of r and h. (b) Are the cross-sections equal in area? (c) Hence show that the volume of the sphere of radius r is 4/3 π r³.