Math 229

John Golden

GeoGebra sketches for a course for preservice high school teachers.

Table of Contents

  1. Polynomials
    1. Standard vs Vertex Forms
    2. Projectile Motion with Targets
    3. Path of Projectile
    4. Vertex Investigation
    5. Projectile Motion in x & y direction
    6. Cubic Forms
    7. Polynomial & Rational Factors
    8. Polynomial & Rational Factors
    9. Rational Function Game
    10. Algebra Tiles Templates
    11. Number of handshakes seen as a triangular number
    12. Quadratic Puzzle
  2. Trigonometry
    1. Unit Circle for Sine and Cosine
    2. Graphs of Trig Functions
    3. Ferris Wheel
    4. Shifted Sine
    5. Gear 1
    6. Ganson 1
    7. Ganson 2
    8. Basic Circle Functions
    9. Trigonometric Sum Identities
    10. unit circle reduced angles
    11. Trigonometry Reference
    12. Similar Triangles
    13. Cosine and sine addition formulas
    14. Tangent of a Sum: Discovery
    15. Sine & Cosine of a Sum: Discovery
  3. Geometry
    1. Visualizing Pythagorean Identities
    2. Circle Vocabulary
    3. Circle Lengths
    4. Circle Segment Relationships (Secant, Tangent, and Chord)
    5. Circle Theorems
    6. Handy Intro to Motions
    7. Flip Flop
    8. Motion Control
    9. Motion Introduction
    10. Langley’s Adventitious Angles (world's hardest easy geometry problem)
    11. Double Glide Reflection Tessellation
    12. Straightedge and Compass
    13. Circle Construction
    14. Catriona Angle Puzzle
  4. Statistics
    1. 500 Approximately Normal Data Values
    2. Normal distribution
    3. Sampling Distribution

1.

Polynomials

  • 1. Standard vs Vertex Forms
  • 2. Projectile Motion with Targets
  • 3. Path of Projectile
  • 4. Vertex Investigation
  • 5. Projectile Motion in x & y direction
  • 6. Cubic Forms
  • 7. Polynomial & Rational Factors
  • 8. Polynomial & Rational Factors
  • 9. Rational Function Game
  • 10. Algebra Tiles Templates
  • 11. Number of handshakes seen as a triangular number
  • 12. Quadratic Puzzle

1.1.

Standard vs Vertex Forms

This sketch allows students to experiment with the parameters in standard and vertex forms of quadratic functions. After gaining some experience with those forms, there is a game to play.[br][br]Clicking target practice makes the graphs go away. Set the parameters to try and match the purple parabola. With which form do you have the most confidence?[br][br]When you're ready, try the game! Here's that applet: [url=https://www.geogebra.org/m/VwAjXFNE]https://www.geogebra.org/m/VwAjXFNE[/url]
– John Golden

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1.10.

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1.11.

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1.12.

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2.

Trigonometry

  • 1. Unit Circle for Sine and Cosine
  • 2. Graphs of Trig Functions
  • 3. Ferris Wheel
  • 4. Shifted Sine
  • 5. Gear 1
  • 6. Ganson 1
  • 7. Ganson 2
  • 8. Basic Circle Functions
  • 9. Trigonometric Sum Identities
  • 10. unit circle reduced angles
  • 11. Trigonometry Reference
  • 12. Similar Triangles
  • 13. Cosine and sine addition formulas
  • 14. Tangent of a Sum: Discovery
  • 15. Sine & Cosine of a Sum: Discovery

2.1.

Unit Circle for Sine and Cosine

This sketch tries to show the relationship between the measurements of a point on the unit circle and the definition of the sine and cosine functions.
Posted at [url]mathhombre.blogspot.com[/url].
– John Golden

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2.10.

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2.11.

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2.13.

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2.14.

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2.15.

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3.

Geometry

  • 1. Visualizing Pythagorean Identities
  • 2. Circle Vocabulary
  • 3. Circle Lengths
  • 4. Circle Segment Relationships (Secant, Tangent, and Chord)
  • 5. Circle Theorems
  • 6. Handy Intro to Motions
  • 7. Flip Flop
  • 8. Motion Control
  • 9. Motion Introduction
  • 10. Langley’s Adventitious Angles (world's hardest easy geometry problem)
  • 11. Double Glide Reflection Tessellation
  • 12. Straightedge and Compass
  • 13. Circle Construction
  • 14. Catriona Angle Puzzle

3.1.

Visualizing Pythagorean Identities

You’ve seen this image before, but with only a single triangle – the purple triangle. You know on the unit circle, the x-coordinate corresponds with the cosine of the angle, and the y-coordinate corresponds with the sine of the angle. From that simple purple triangle, you can see that we have (using the Pythagorean Theorem): [math]\sin ^{2}\alpha +\cos^2\alpha=1[/math] But you’ve never seen that BLUE triangle or that RED triangle. It turns out the lengths of the legs of the other triangles actually are those other trigonometric functions. You’re going to discover that, and start finding some neat trigonometric identities (like that Pythagorean Identity) visually.

1.) Why can I conclude that all four triangles are similar? What is the mathematical justification for that conclusion? 2.) Find the side lengths for all of the triangles. 3.) Use the Pythagorean Theorem on all five triangles to come up with at least four equations. You don’t need to simplify/expand.
– HaileyMF

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3.6.

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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.

Statistics

  • 1. 500 Approximately Normal Data Values
  • 2. Normal distribution
  • 3. Sampling Distribution

4.1.

500 Approximately Normal Data Values

The figure below show different representations of 500 data values that are approximately Normal with a[br]mean of 50 and a standard deviation of 10.
– Steve Phelps

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Information