GeoGebra Workshop Exemplar Book

Brian Gervase, Feb 2, 2016

This book has been designed to accompany an introduction to GeoGebra workshop.

Table of Contents

  1. Discovering Geometry
    1. Parallel Lines Intersected by a Transversal
    2. Angles and Parallel Lines Discovery #1
    3. rhombus
    4. Circle Theorems - angles on the same arc
    5. Cyclic Quadrilateral 3
    6. Exterior Angles of Polygons
    7. triangle inequality
    8. Area of Circles
    9. Pappus Hexagon Theorem
    10. Axes of Symmetry
  2. Primary Arithmetic
    1. nlhukhlTwo-digit whole numbers
    2. Factorization - Visual illustration of divisor pairs
    3. Fraction Division1:　a ÷ b (Partitive)
    4. Multiplying 3 Factors
    5. Percent of a Number
  3. Dynamic Algebra
    1. Graph the Line
    2. Tangent-zoom
    3. How to draw Bezier curves
    4. Vektor 3D
    5. Radians in Unit Circle
    6. complex power visualization
    7. Multiple Angle Sine Solutions
    8. 3 circle motion
    9. Ellipse - string
    10. Riemann Sums - Rectangular Approximation (LRAM, RRAM, MRAM)
    11. Rational Function Game
    12. Velocity Acceleration Vectors on Parametric Curve
  4. Statistics Alive
    1. AQR Section 16: Five Number Summary Exploration
    2. AQR Section 17: Mean but Sensitive
    3. AQR Section 16: Matching a Pie Chart to a Dot Plot
    4. Binomial Distribution with Normal and Poisson Approximation
    5. Spinner
    6. Coin Flip Simulation
    7. Dice Roll Simulation
  5. Amazing Models
    1. How Far Can You See?
    2. Parallel Parking optimization (US customary units)
    3. Simple Earth / Sun Model
    4. Rubber Pencil Illusion
    5. Inclined Plane with Two Masses and a Pulley
    6. Curve of Pursuit
    7. fractal fern
    8. Planetary Motion
    9. Playing Card Dealer
    10. The Cycloid Curve
    11. Involute
    12. parabola hyperbola lens
    13. Displacement and Velocity
  6. Plain Old Fun!
    1. Kaleidoscope
    2. String Art Based on Bézier Curves
    3. Mandelbrot Visualization
    4. Turning Wheel
    5. Laser Triangle
    6. Golden Spiral
    7. draftmans ellipse
    8. Perspective Diagonals
  7. Student Samples
    1. Golf Course 3
    2. Law of Sines Proof
    3. unit circle 3
    4. Ellipse Lab

1.

Discovering Geometry

  • 1. Parallel Lines Intersected by a Transversal
  • 2. Angles and Parallel Lines Discovery #1
  • 3. rhombus
  • 4. Circle Theorems - angles on the same arc
  • 5. Cyclic Quadrilateral 3
  • 6. Exterior Angles of Polygons
  • 7. triangle inequality
  • 8. Area of Circles
  • 9. Pappus Hexagon Theorem
  • 10. Axes of Symmetry

1.1.

Parallel Lines Intersected by a Transversal

[b]The lines a and b are parallel, cut by transversal c. Drag the blue points on c to move the transversal. [/b][br] 1. How does this affect the angles formed by the intersection of a and b with c? [br] 2. Which angles are always congruent? [br] 3. Which angles are always supplementary?
– Pat Patterson, Linda Bollman, rbwalker15

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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2.

Primary Arithmetic

  • 1. nlhukhlTwo-digit whole numbers
  • 2. Factorization - Visual illustration of divisor pairs
  • 3. Fraction Division1:　a ÷ b (Partitive)
  • 4. Multiplying 3 Factors
  • 5. Percent of a Number

2.1.

nlhukhlTwo-digit whole numbers

Visualizing the meaning of two-digit numbers.
(Try moving the black slider.)
– Roy Wright

2.2.

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2.3.

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2.4.

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2.5.

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3.

Dynamic Algebra

  • 1. Graph the Line
  • 2. Tangent-zoom
  • 3. How to draw Bezier curves
  • 4. Vektor 3D
  • 5. Radians in Unit Circle
  • 6. complex power visualization
  • 7. Multiple Angle Sine Solutions
  • 8. 3 circle motion
  • 9. Ellipse - string
  • 10. Riemann Sums - Rectangular Approximation (LRAM, RRAM, MRAM)
  • 11. Rational Function Game
  • 12. Velocity Acceleration Vectors on Parametric Curve

3.1.

Graph the Line

Drag points A and B so the line matches the equation.
– Steve Phelps

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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4.

Statistics Alive

  • 1. AQR Section 16: Five Number Summary Exploration
  • 2. AQR Section 17: Mean but Sensitive
  • 3. AQR Section 16: Matching a Pie Chart to a Dot Plot
  • 4. Binomial Distribution with Normal and Poisson Approximation
  • 5. Spinner
  • 6. Coin Flip Simulation
  • 7. Dice Roll Simulation

4.1.

AQR Section 16: Five Number Summary Exploration

The worksheet below is designed to help you see how the "Five Number Summary" for a data set is related to the mean of the data set.[br]Drag the green points along the number line, and observe how the Five Number Summary and Box Plot change. Observe how the mean change. Observe which of these statistics seems to change most easily.
– Steve Phelps

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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5.

Amazing Models

  • 1. How Far Can You See?
  • 2. Parallel Parking optimization (US customary units)
  • 3. Simple Earth / Sun Model
  • 4. Rubber Pencil Illusion
  • 5. Inclined Plane with Two Masses and a Pulley
  • 6. Curve of Pursuit
  • 7. fractal fern
  • 8. Planetary Motion
  • 9. Playing Card Dealer
  • 10. The Cycloid Curve
  • 11. Involute
  • 12. parabola hyperbola lens
  • 13. Displacement and Velocity

5.1.

How Far Can You See?

The diagram below shows how the height of an object (the red dot) affects how much of the Earth can be seen from the object. The red dot (which could represent a satellite, for example) can be moved to change its height.
What equation describes the relationship between height and visible arc length here?
– Roy Wright

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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6.

Plain Old Fun!

  • 1. Kaleidoscope
  • 2. String Art Based on Bézier Curves
  • 3. Mandelbrot Visualization
  • 4. Turning Wheel
  • 5. Laser Triangle
  • 6. Golden Spiral
  • 7. draftmans ellipse
  • 8. Perspective Diagonals

6.1.

Kaleidoscope

Drag the large blue point.[br][br]You can also change the options to change the sort of pattern
– Michael Borcherds

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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7.

Student Samples

  • 1. Golf Course 3
  • 2. Law of Sines Proof
  • 3. unit circle 3
  • 4. Ellipse Lab

7.1.

Golf Course 3
– Karishma Johnson

7.2.

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7.3.

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7.4.

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