Workshop samples

Arthur Lee

This is a selection of tasks for general use in training workshop and demonstration. Find more resources in [list][*]The GeoGebra Institute of Hong Kong [url]http://www.geogebra.org.hk[/url] [*]gMath project at [url]http://www.geogebra.hk[/url] or [url]https://www.gmath.hk[/url]. [/list] Other GeoGebraBooks in my collection: [list][*][url=https://ggbm.at/D4pCGA6D]Primary Maths Contest[/url] [*][url=https://ggbm.at/R6Mga5uK]Circle Geometry[/url] [*][url=https://ggbm.at/vPpuXQjy]Similarity[/url] [*][url=https://ggbm.at/MXNBQqun]Shapes 3D[/url] [*][url=https://ggbm.at/FecdkeK4]Art and Design[/url] [*][url=https://www.geogebra.org/m/geZ4hED6]Trigonometry[/url] [/list] Some of my favourite authors and GeoGebraBooks: [list][*][url=https://www.geogebra.org/u/orchiming]Anthony Or[/url] [*][url=https://www.geogebra.org/u/alexchik]Alex Chik[/url] [*][url=https://www.geogebra.org/u/tbrzezinski]Tim Brzezinski[/url] [*][url=https://www.geogebra.org/u/pegasusroe]羅驥韡[/url] [*][url=https://www.geogebra.org/u/themadmathematician]Jonas Hall[/url] [*][url=https://ggbm.at/DmXMD4wP]STEM and GeoGebra[/url] [/list]

Table of Contents

  1. Simple Manipulation
    1. Reflection in a Square
    2. Pentagon on Square Grid
    3. PMC 2006-07 Q16a
    4. a triangle ABC cut into 2
    5. another triangle ABC cut into 2
    6. Ratio
    7. Parthenon
    8. 4 points and a square
    9. 3 points and a triangle
    10. perimeter of crescent
    11. mosaic puzzle
    12. Perimeter and Area 2
    13. What's My Rule #5?
  2. Geometry
    1. circles
    2. Annulus
    3. find two congruent triangles
    4. Find 2 similar triangles
    5. make 2 similar triangles (2)
    6. Spotlight
    7. exploring tangent-chord angle
    8. Circumcircle of a triangle (Soft Construction)
    9. task: make center
    10. Four Semi-circles
    11. regular polygons at a point
    12. Two hinging Pentagons
    13. find the angles
    14. isosceles hunt 1
  3. 3D
    1. questions about a cube
    2. cube in dodecahedron
    3. Rotational Symmetry of Dodecahedron
    4. Octahedron and Boat
    5. cutting a sphere
    6. three tetrahedrons
    7. Making a cone
    8. lighthouse
  4. Advanced Topics
    1. graphing an antiderivative function
    2. zoom tangent
    3. Confidence Interval
    4. Complex Addition and Multiplication
    5. Equiangular Spiral
    6. Mandelbrot Set
    7. A single equation for a smiley face
  5. Algebra
    1. Quadratic and Linear Graphs
    2. Compare Quadratic Graphs
    3. Parabolas
    4. Graphing Linear Equations in 2 Unknowns
    5. Diagonal from Area and Perimeter
    6. Compound Interest with Input Boxes
    7. Compound Interest
    8. Solving Exponential Equation
    9. guessing relation
    10. number machine
  6. Teaching
    1. Rectangle and a Square
    2. Percentages: Selling Problems (Java Version)
    3. slope of segment
    4. Constructing Quadrilaterals by Four Sides (2014)
    5. distance-time / division by fractions
    6. Difference of Two Squares 平方差 (2)
    7. Difference of Two Squares 平方差 (1)
    8. Trigonometric Ratios: Sine 三角比：正弦
    9. Solving Triangles (SSA case) 解任意三角形(SSA情況)
    10. AQR Section 17: Dot Plot and Box-and-Whisker Plot
    11. Travel Graph (Two Bodies) 行程圖 (雙物體)
    12. Measure Diagonal
    13. Battleship
    14. Percentage Change (length of horizontal bars)
    15. angles in a triangle (up and down)
    16. From simple to compound interest
    17. successive percentage changes
    18. Compare Prism Nets
    19. estimate fraction in a set
    20. percentage for comparison
    21. percentage ruler (2 groups)
  7. Patterns
    1. combining spirals
    2. Napoleon Tiling
    3. Dot Pattern 3
    4. TeTreehedron
    5. dot pattern 2
    6. dot pattern 1
    7. Factorization - Visual illustration of divisor pairs
    8. Curve Stitching: making a parabola from straight lines.
    9. Cairo Tiling 1
    10. Cairo Tiling 2
    11. making pentagonal tiles
    12. Square and Triangle Pattern
    13. doubling and halving a triangle
    14. polygon ring double
    15. unit circle pattern 1
    16. polygon patterns from rotation
  8. others
    1. making strange shapes from a circle and quadrilateral
    2. Playing Card Dealer
    3. epidemic simulation 40
    4. creating symmetry
    5. Pattern of Quadrilaterals
    6. stitching in a cube
    7. Cylinder Illusion

1.

Simple Manipulation

explore with dragging

  • 1. Reflection in a Square
  • 2. Pentagon on Square Grid
  • 3. PMC 2006-07 Q16a
  • 4. a triangle ABC cut into 2
  • 5. another triangle ABC cut into 2
  • 6. Ratio
  • 7. Parthenon
  • 8. 4 points and a square
  • 9. 3 points and a triangle
  • 10. perimeter of crescent
  • 11. mosaic puzzle
  • 12. Perimeter and Area 2
  • 13. What's My Rule #5?

1.1.

Reflection in a Square

Point E is reflected in the sides of the square. Drag E to see the change in the images.[br]What properties do you notice in the quadrilateral formed by the red points?[br]By dragging E to different positions, what kind of quadrilaterals can be made.
If we start with other shapes (instead of a square) for generating the mirror images, what different results will we have?[br]In what other ways would you extend this problem?
– Arthur Lee

1.2.

–

1.3.

–

1.4.

–

1.5.

–

1.6.

–

1.7.

–

1.8.

–

1.9.

–

1.10.

–

1.11.

–

1.12.

–

1.13.

–

2.

Geometry

  • 1. circles
  • 2. Annulus
  • 3. find two congruent triangles
  • 4. Find 2 similar triangles
  • 5. make 2 similar triangles (2)
  • 6. Spotlight
  • 7. exploring tangent-chord angle
  • 8. Circumcircle of a triangle (Soft Construction)
  • 9. task: make center
  • 10. Four Semi-circles
  • 11. regular polygons at a point
  • 12. Two hinging Pentagons
  • 13. find the angles
  • 14. isosceles hunt 1

2.1.

circles

a single construction that may generate different geometry textbook problems
circles
– Arthur Lee

2.2.

–

2.3.

–

2.4.

–

2.5.

–

2.6.

–

2.7.

–

2.8.

–

2.9.

–

2.10.

–

2.11.

–

2.12.

–

2.13.

–

2.14.

–

3.

3D

  • 1. questions about a cube
  • 2. cube in dodecahedron
  • 3. Rotational Symmetry of Dodecahedron
  • 4. Octahedron and Boat
  • 5. cutting a sphere
  • 6. three tetrahedrons
  • 7. Making a cone
  • 8. lighthouse

3.1.

questions about a cube

What different triangles can be formed?[br]What different polyhedrons can be formed?
questions about a cube
– Arthur Lee

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

3.8.

–

4.

Advanced Topics

  • 1. graphing an antiderivative function
  • 2. zoom tangent
  • 3. Confidence Interval
  • 4. Complex Addition and Multiplication
  • 5. Equiangular Spiral
  • 6. Mandelbrot Set
  • 7. A single equation for a smiley face

4.1.

graphing an antiderivative function

graphing an antiderivative function[br]see the construction at http://youtu.be/LospYWEhnDg
graphing antiderivative function
– Arthur Lee

4.2.

–

4.3.

–

4.4.

–

4.5.

–

4.6.

–

4.7.

–

5.

Algebra

  • 1. Quadratic and Linear Graphs
  • 2. Compare Quadratic Graphs
  • 3. Parabolas
  • 4. Graphing Linear Equations in 2 Unknowns
  • 5. Diagonal from Area and Perimeter
  • 6. Compound Interest with Input Boxes
  • 7. Compound Interest
  • 8. Solving Exponential Equation
  • 9. guessing relation
  • 10. number machine

5.1.

Quadratic and Linear Graphs

compare quadratic and linear graphs
Quadratic and Linear Graphs
– Arthur Lee

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

5.7.

–

5.8.

–

5.9.

–

5.10.

–

6.

Teaching

  • 1. Rectangle and a Square
  • 2. Percentages: Selling Problems (Java Version)
  • 3. slope of segment
  • 4. Constructing Quadrilaterals by Four Sides (2014)
  • 5. distance-time / division by fractions
  • 6. Difference of Two Squares 平方差 (2)
  • 7. Difference of Two Squares 平方差 (1)
  • 8. Trigonometric Ratios: Sine 三角比：正弦
  • 9. Solving Triangles (SSA case) 解任意三角形(SSA情況)
  • 10. AQR Section 17: Dot Plot and Box-and-Whisker Plot
  • 11. Travel Graph (Two Bodies) 行程圖 (雙物體)
  • 12. Measure Diagonal
  • 13. Battleship
  • 14. Percentage Change (length of horizontal bars)
  • 15. angles in a triangle (up and down)
  • 16. From simple to compound interest
  • 17. successive percentage changes
  • 18. Compare Prism Nets
  • 19. estimate fraction in a set
  • 20. percentage for comparison
  • 21. percentage ruler (2 groups)

6.1.

Rectangle and a Square

Drag the green dot to vary the rectangle. [br]Drag the red dot to find out which is bigger.
Which is bigger, the rectangle or the square?
Introduce the identity, difference of two squares, through a problem about comparing areas. See the making of this file in YouTube -> [url=http://youtu.be/v809gcQTfD4 ]http://youtu.be/v809gcQTfD4 [/url]
– Arthur Lee

6.2.

–

6.3.

–

6.4.

–

6.5.

–

6.6.

–

6.7.

–

6.8.

–

6.9.

–

6.10.

–

6.11.

–

6.12.

–

6.13.

–

6.14.

–

6.15.

–

6.16.

–

6.17.

–

6.18.

–

6.19.

–

6.20.

–

6.21.

–

7.

Patterns

  • 1. combining spirals
  • 2. Napoleon Tiling
  • 3. Dot Pattern 3
  • 4. TeTreehedron
  • 5. dot pattern 2
  • 6. dot pattern 1
  • 7. Factorization - Visual illustration of divisor pairs
  • 8. Curve Stitching: making a parabola from straight lines.
  • 9. Cairo Tiling 1
  • 10. Cairo Tiling 2
  • 11. making pentagonal tiles
  • 12. Square and Triangle Pattern
  • 13. doubling and halving a triangle
  • 14. polygon ring double
  • 15. unit circle pattern 1
  • 16. polygon patterns from rotation

7.1.

combining spirals

combining spirals from dilation and rotation of triangles
combining spirals
– Arthur Lee, GeoGebra Institute of Hong Kong

7.2.

–

7.3.

–

7.4.

–

7.5.

–

7.6.

–

7.7.

–

7.8.

–

7.9.

–

7.10.

–

7.11.

–

7.12.

–

7.13.

–

7.14.

–

7.15.

–

7.16.

–

8.

others

  • 1. making strange shapes from a circle and quadrilateral
  • 2. Playing Card Dealer
  • 3. epidemic simulation 40
  • 4. creating symmetry
  • 5. Pattern of Quadrilaterals
  • 6. stitching in a cube
  • 7. Cylinder Illusion

8.1.

making strange shapes from a circle and quadrilateral

Have some fun with the section formula (point of division). Use the slider to switch between a square and circle.
Click 'control' to display the original shapes. Drag the vertices to experiment with different starting quadrilateral.
[b]'[color=#ff0000]Pixar in a Box[/color]'[/b] has similar materials about modelling and 'weighted averages' -> [url=https://www.khanacademy.org/partner-content/pixar/environment-modeling-2]see the page on Environment Modeling[/url][br]https://www.khanacademy.org/partner-content/pixar/environment-modeling-2
These slides show more examples based on this applet.
How to make this file:
– Arthur Lee

8.2.

–

8.3.

–

8.4.

–

8.5.

–

8.6.

–

8.7.

–

Information