Workshop samples
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

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Workshop samples

Arthur Lee

This is a selection of tasks for general use in training workshop and demonstration. Find more resources in

The GeoGebra Institute of Hong Kong http://www.geogebra.org.hk
gMath project at http://www.geogebra.hk or https://www.gmath.hk.

Other GeoGebraBooks in my collection:

Primary Maths Contest
Circle Geometry
Similarity
Shapes 3D
Art and Design
Trigonometry

Some of my favourite authors and GeoGebraBooks:

Anthony Or
Alex Chik
Tim Brzezinski
羅驥韡
Jonas Hall
STEM and GeoGebra

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?
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
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
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
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
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)
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
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

Information

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?

Reflection in a Square

Point E is reflected in the sides of the square. Drag E to see the change in the images. What properties do you notice in the quadrilateral formed by the red points? 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? In what other ways would you extend this problem?

– Arthur Lee

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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

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2.10.

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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? What different polyhedrons can be formed?

questions about a cube

– Arthur Lee

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3.3.

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3.5.

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3.6.

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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 see the construction at http://youtu.be/LospYWEhnDg

graphing antiderivative function

– Arthur Lee

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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

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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. 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 -> http://youtu.be/v809gcQTfD4

– Arthur Lee

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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

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7.11.

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7.13.

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7.14.

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7.15.

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7.16.

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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.

'Pixar in a Box' has similar materials about modelling and 'weighted averages' -> see the page on Environment Modeling 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

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Workshop samples

Table of Contents

Information

Simple Manipulation

Reflection in a Square

Geometry

circles

circles

3D

questions about a cube

questions about a cube

Advanced Topics

graphing an antiderivative function

Algebra

Quadratic and Linear Graphs

Quadratic and Linear Graphs

Teaching

Rectangle and a Square