Triangle Inequality

Move sliders a, b and c and observe what happens.

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1. What are the conditions when a triangle is formed?
2. Explain why the three inequalities in the applet must be true for a triangle to exist.

Introducing the concept of function

This activity can be used to introduce the concept of function. Click here to view post on teaching function using this activity.

Activity

Move C along GC.
1. Are there ways of predicting the values of the changing quantities if you know the lenght of GC? You may want to make a table of values for GC vs the changing quantity.
2. Write a formula for determining the values of the changing quantities if GC is known.

(If you want to view the grid, click the View button in the menu then check 'show grid'.)

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Animation and Epicycloid

Note: This is the output of the one the Math and Multimedia GeoGebra Tutorials. To view the step-by-step instructions in creating the epicycloid worksheet below click here.


Click the Play button located on the lower left of the GeoGebra window to rotate the circle with center (2,0).




















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The path traced by the red point is called the epicycloid.

Activity for constructing quadrilateral with equal areas

This is one of the activities on problem solving involving quadrilaterals posted at Keeping Mathematics Simple. Click here to read the post.

Task
Move F. Describe the path it traces.
Explain or prove that the quadrilaterals formed have equal areas.
Write a procedure for constructing quadrilaterals with equal area using compass and straight edge.





















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Bubbles

Click the Play button located at the lower-left of the window to animate.






















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Approximating the area of a circle

Note: This is the output of the one the Math and Multimedia GeoGebra Tutorials. To view the step-by-step instructions in creating the worksheet below click here.

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Adjust sliders r and n at the right hand slide of the GeoGebra applet window.





















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1.) What do you observe about the relationship between the area of the circle as n increases?
2.) Vary the values of n and r and observe what happens. Based on your observations, what conjecture can you make?

Geometric representation of the sum of two radicals

This activity is part of the lesson on adding radicals posted at Mathematics for Teaching.

How to construct the figure:

Use the regular polygon tool. Click on two points (endpoints of the diagonal of 2 by 1 unit square in the grid). From then on just click on the diagonals each time to generate the squares.

To type the radical, use the text tool, click anywhere on the grid, check latex in the dialogue window and type \sqrt{5} and you're done.

To change the color, right click on the figure, click color, choose and you're done.

When you are ready click on the file menu and choose new. This will give you a brand new grid to practice constructing the figure.





















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The Rolling Circle

Drag the center of a circle to determine the radius, then drag the slider to roll the circle.




















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1.) What do you observe?
2.) What conjecture can you make based on the relationship of the diameter and the circumference of the circle?

Constructing regular polygons

This is an introductory task for teaching squares and square roots. Click here to view the full sequence of the lesson.

Activity

The pentagon was constructed by clicking the regular polygon tool and then clicking on the grid twice. In the dialogue window, type the number 5 for the number of sides. In the dialogue window you will see information about the polygon.

Your task:
Construct a few more regular polygons using the tool.
Why is it that GeoGebra only needed to know two points and the number of sides to contruct the polygon?






















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Animation, Roses and Radian

Click the Play button located at the lower-left corner of the GeoGebra applet and watch the applet for a while.

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1.)Pause the animation and refresh your browser. Click the Play button again. Click stop when Point C and point B' coincide. ?

2.) How many degrees has B' rotated the first time point B' and C coincide? Refresh the browser and repeat if necessary.

3.)How many petals are formed during the entire rotation of point B' along the circumference of the circle?

4.) Refresh your web browser and complete the petal. Count the number of rotations. What is the relationship between the the number of rotations and the number of petals. Make interpretation about this relationship.