# GeogebraFan Shop

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#### Unit Circle & Periodic Functions (Geogebra)

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This is a Geogebra program for teaching students the unit circle. The program has been designed using Geogebra 5.0 (download version). This resource is valuable for use when teaching trigonometry, radians and the graphs of sine, cosine and tangent. The program can also be used to show students how frequency and phase relate back to the unit circle and periodic functions. The program allows you to quickly enter specific angles of rotation for use when teaching students exact ratios. The program will even draw the sine, cosine and tangent graphs as the point rotates around the unit circle. This is a visually engaging teaching tool that will help students to better comprehend how the unit circle connects with periodic functions.

#### Integration & Area Under A Curve (Geogebra)

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This is a Geogebra program for use as a visual aid when teaching how integration can be used to determine the area under a curve and the area between two curves. This program has been designed using Geogebra 5.0 (download version). The program allows you to specify two separate functions and show the definite and indefinite integral for each function. The program can also subtract the second function from the first function to determine the area enclosed by the two functions. The teacher can also show students how the area under a curve can be approximated using the rectangle rule and trapezoidal rule for a given number of shapes. The program will represent this approximation both graphically and numerically. This is a visually engaging resource that will quickly and professionally present solutions to area by integration type questions.

#### Generating Square Waves Using Harmonics (Geogebra)

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This is a Geogebra program for use as a visual aid in teaching the concept of harmonics in the context of generating a square wave from sinusoidal waves. This program has been designed using Geogebra 5.0 (download version). The program will visually demonstrate how the addition of sine waves of specific amplitudes and frequencies can be added together to produce a periodic square wave signal. The specific amplitudes and frequencies on the harmonics are also displayed in a table. This resource will visually engaged your students and give them an intuitive understanding of how a signal can be broken down into the various harmonic constituents.

#### Functions & Limits (Geogebra)

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This is a geogebra program for use as a visual aid when teaching students about limits as a prelude to differential calculus. This program has been designed using Geogebra 5.0 (download version). You simply enter the numerator and denominator expressions of a function and specify and x limit. The program will then graph the function and display a point that represents the function value as the x values approach the specified limit. If the function is unable to be evaluated at the limit, the program will advise that the function is undefined and will show this as a hole in the graph. The program can also present a table of values as the function approaches the limit as well as any asymptote lines that exist in the function.

#### GPS Great Circle Distance (Geogebra)

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This is a Geogebra program designed as a visual aid for teaching great circle lines between two GPS positions. This program has been designed using Geogebra 5.0 (download version). The resource will assist teachers to accurately represent GPS positions on a 2D surface. Using a 3D simluation of the Earth’s surface, the program will show the two positions, draw the great circle line between the two positions and calculate the great circle distance. It should be noted that the Earth has been simulated as a perfect sphere so there will be a very small error when compared with the actual distance. The fact that the Earth is not completely spherical can be a good talking point in class discussions. There is also some pre-programmed city locations for quick access. This resource will help to visually engage your students and improve their geometric comprehension of the great circle line between GPS locations within an easy to use simulated 3D environment.

#### Binomial & Normal Probability Distribution (Geogebra)

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This is a Geogebra program for use a visual aid in the teaching of binomial and normal probability distributions. The program has been designed using Geogebra 5.0 (download version). This resource will display the binomial probability distribution for a given number of trials and probability of a successful outcome. The operator can determine the probability of an outcome, which will be displayed both numerically and graphically. Also, with the use of the animation feature teachers can demonstrate how the binomial distribution changes with a change in the number of trials or a change in the probability of a successful outcome. The program will also allow you to superimpose a normal distribution on top the binomial distribution. This is very useful in showing students how a normal distribution can be used to approximate a binomial distribution. Students will be able to clearly visualize whether or not the normal distribution is a good approximation, as a result on the extent to which the binomial data is skewed. You can also specified lower and upper X-scores or Z-scores to determine probability of a range of outcomes and the program will display this result both numerically and graphically. This allows the teacher to be very efficient in explaining answers to these types of questions. Students will appreciate the visual engagement of the program and you as the teacher will appreciate the time saved in being able to quickly and clearly present solutions.

#### GPS Coordinates (Geogebra)

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This is a Geogebra program for use as a visual aid in the teaching of coodinates for the Global Positioning System (GPS). This program has been designed for use with Geogebra 5.0 (download version). This resource assists the teacher in clearly showing students how latitude and longitude angles are able to define any position on a 3D simulation of the Earth’s surface. Simply enter a specific GPS position (in degrees, minutes, seconds) and the program will show this location on the Earth. The program also shows a 2D represention of the position in vertical and horizontal planes, which can also be dynamically adjusted. The Earth will also spin so students can clearly identify the position from different perspectives or you can manually rotate the Earth to any perspective. This is a resource that will visually engage your students, improve their comprehension and save you significant effort from trying to represent three dimensions on a two dimensional surface.

#### Venn Diagram (Geogebra)

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This is a Geogebra program that is ideal for showing students how to construct and populate Venn diagrams. This program has been designed for use with Geogebra 5.0 (download version). By projecting your screen onto a whiteboard, you can easily teach students how to represent scenarios using the Venn diagram without the hassle of redrawing the diagram each time. The program represents diagrams with either two or three circles and allows you to adjust the circle size and separation. Furthermore, it can shade regions both inside and outside of the circles to represent different logic operations. If you are tired of having to redraw your Venn diagram lines over and over, then you will love this time saving app.