Square of a Binomial

Move the slider and observe the relationships between the algebraic and geometric representation of the rectangles.





















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You can save the GeoGebra file using the File menu.

Four Leaf Petal

Move point B along the circumference of the circle. What do you observe? What shape is formed. Note: Click here to view step-by-step construction. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) The length of the segment AF is always equal to the area of the inscribed rectangle. Guillermo Bautista, Created with GeoGebra

The Square Problem

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Note: You can save the ggb file using the File menu.

Sum of the Coordinates

Move Points P and Q.




















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What do you observe about the points with respect to the origin?

Circumcircle and Incircle of a Triangle

This GeoGebra worksheet below shows that in a triangle, you can always create an incircle (a circle inside the triangle tangent to the tree sides) and a circumcircle (circle passing through the three vertices).

Drag the vertices of the triangle and observe what happens.



You can download the ggb file here and the tutorial how to construct it here.

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.

Graphing Piecewise Function

This is the output file of step-by-step GeoGebra Tutorial 32 - Graphing Piecewise Functions from Mathematics and Multimedia.

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Constructing a Square

This is the output of GeoGebra Tutorial 3 - Constructing a Square from the GeoGebra Step-by-Step Tutorial Series of Mathematics and Multimedia. The GeoGebra ggb file can be downloaded here.

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Move points A and B. What do you observe?

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Can you think of other ways of constructing a square without using the Regular Polygon tool, or the following the tutorial?

Graphs and Sliders

Move the small circles on sliders m and b. What do you observe?




















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1. How do the values of m and b affect the appearance of the graph?
2. Suppose, we can increase the value of m and b as much as we can, is it possible to plot a vertical graph?
3. Explain why your observations in 1 are such.

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia

Equilateral Triangle

Drag the vertices of the equilateral triangle below.

1. What do you observe?
2. Can you think of other ways of creating an equilateral triangle?

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia

Quadrilaterals and Midpoints

1. Use the Move tool (leftmost tool) to move the vertices of the quadrilateral. What do you observe?
2. Use the Distance tool to find the distance between the points and move the points. Do your observations hold true?
3. What conjecture can you make based on your observations?
4. Select the Angle tool (right button) and click the interior of the polygon. Does your conjecture still hold?
5.  Challenge: Prove your conjecture.

Notes:

1. Click here to download the ggb file.
2. Click here to read the step-by-step tutorial.
3. Click here to go to the Mathematics and Multimedia GeoGebra Tutorial Series.
4. Click here to go to Mathematics and Multimedia