GGBI Sample Book

Kellie Evans, Jun 20, 2024

Table of Contents

  1. 2D Geometry
    1. Area of a Circle: Revamped!
    2. Circle Area (By Peeling!)
  2. Pythagorean theorem MISC
    1. Pythagorean theorem visual for basic proof
    2. Law of Sines
    3. Angle Sum Formulas for Cosine and Sine
  3. Graphs from the Unit Circle and Regular Polygons
    1. Trig Functions from Unit Circle
    2. Copy of The Unit Equilateral Triangle and Arbitrary Triangle
  4. Straightedge and Compass Constructions
    1. Fake or Fact?
  5. Probability and Statistics
    1. Correlation Coefficient and Line of Best Fit
    2. Correlation Exploration
    3. Box and Whisker Plots: A New Way to Visualize Data
    4. Simulate rolling fair 6-sided die
  6. 3D Geometry
    1. Unwrapping a Cylinder: REVAMPED!

1.

2D Geometry

  • 1. Area of a Circle: Revamped!
  • 2. Circle Area (By Peeling!)

1.1.

Area of a Circle: Revamped!

Interact with the app below for a few minutes. Then answer the questions that follow.
What do you notice? What do you see? What do you wonder?
How can we use what we see here to try to find the area of a circle?
– Tim Brzezinski

1.2.

–

2.

Pythagorean theorem MISC

  • 1. Pythagorean theorem visual for basic proof
  • 2. Law of Sines
  • 3. Angle Sum Formulas for Cosine and Sine

2.1.

Pythagorean theorem visual for basic proof

– Kellie Evans

2.2.

–

2.3.

–

3.

Graphs from the Unit Circle and Regular Polygons

  • 1. Trig Functions from Unit Circle
  • 2. Copy of The Unit Equilateral Triangle and Arbitrary Triangle

3.1.

Trig Functions from Unit Circle

– Kellie Evans

3.2.

–

4.

Straightedge and Compass Constructions

  • 1. Fake or Fact?

4.1.

Fake or Fact?

Watch the video (or scroll to the end).
[b]What do you think? Is the video FAKE or FACT?[br][br]Use any strategy to decide.[/b]
– Kellie Evans

5.

Probability and Statistics

  • 1. Correlation Coefficient and Line of Best Fit
  • 2. Correlation Exploration
  • 3. Box and Whisker Plots: A New Way to Visualize Data
  • 4. Simulate rolling fair 6-sided die

5.1.

Correlation Coefficient and Line of Best Fit

[size=200]Move the points below and see how the correlation coefficient changes.[/size]
[size=200]Can you move the points above so the correlation coefficient is as close as possible to 0? How about -1?[br][/size]
[size=85][size=150][size=200]Move points A and B below to make the line "best fit" the data. Compare to the actual line of best fit.[/size][/size][/size]
– Kellie Evans

5.2.

–

5.3.

–

5.4.

–

6.

3D Geometry

  • 1. Unwrapping a Cylinder: REVAMPED!

6.1.

Unwrapping a Cylinder: REVAMPED!

A [b][color=#0000ff]HUGE THANK YOU[/color][/b] and [b][color=#0000ff]CREDIT ACKNOWLEDGEMENT[/color][/b] to both [url=https://www.geogebra.org/bernat_geogebra]Bernat[/url] and [url=https://www.geogebra.org/stevephelps]Steve Phelps[/url], who calculated the surface equations for the [b][color=#ff00ff]curved parts of the cylinder's lateral area[/color][/b] (during the unwrapping process). [br][br]This enhanced version (of [url=https://www.geogebra.org/m/nY92fgyN]this original version[/url]) would not have been possible without their insight. [br][br][b][color=#1e84cc]To explore this resource in GeoGebra Augmented Reality, see the directions below this applet. [/color][/b]
TO EXPLORE IN AUGMENTED REALITY:
1) Open up GeoGebra 3D app on your device. [br][br]2) Go to the MENU (horizontal bars) in the upper left corner. Select OPEN. [br] In the Search GeoGebra Resources input box, type [b]rCxXxFhE[/b][br] (Note this is the resource ID = last 8 digits of the URL for this resource.)[br][br]3) In the resource that uploads, zoom in/out if needed.[br] The [b]r[/b] slider adjusts the radius of the cylinder.[br] The [b]h [/b]slider adjusts the height of the cylinder.[br] Drag the slider named [b]i[/b] to wrap/unwrap.
– Tim Brzezinski

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