## Calculus

Marc Renault, supported by Shippensburg University made  a complete library of applets for Calculus I that are suitable for in-class demonstrations and/or student exploration. He created these applets using GeoGebra software for creating dynamic visualizations of mathematical ideas.

My favorite applet I have used successfully in the  classroom was the chain rule applet.  It is a dynamic way to demonstrate the chain rule using an x-wheel, a u-wheel, and a y-wheel. You can change the speed of the x-wheel, and you can connect the wheels with belts and change their radii. This model is a great exploration of  the chain rule and enhances an intuitive understanding of where the formula comes from. The best part is crossing the belts in the applet!

The Intuitive Notion of the Chain Rule

Marc Renault has a library of calculus applets created with Geogebra on his website:

GeoGebra Calculus Applets

Other Calculus Applets

This applet demonstrates the epsilon-delta definition of the limit. (In particular, we are exploring whether lim f(x)=L as x approaches c)

Epsilon Delta Definition of the Limit

## Transformations

Eric Scott (Beacon High School in Manhattan, New York)

shared two Geogebra files he created on teaching transformations in Algebra 2.

Students see  the effects of a, b, h, and k on a function i.e. g(x) = a*f[b(x-h)]+k where f(x) is the parent function.    Eric reported that students enjoyed   doing transformations with Spongebob.
Eric used this video tutorial to import an image (Spongebob) into the program:

## Guides by GeoGebra Docu Team

Here are  excellent GeoGebra  step by step guides shared at the conference to help us create our own GeoGebra programs/applets.  Click on the appropriate link.

THE GEOGEBRA QUICKSTART SERIES  includes 3-D graphing, spreadsheets, statistics.

How to use CAS commands

Solving a system of equations

How to manipulate equations

The CAS tools

How to combine CAS and graphics view

Tips and Tricks for CAS Input

Here are books by the GeoGebra Docu Team:

https://www.geogebra.org/geogebra+docu+team

## GeoGebra-Getting Started

GeoGebra is a user friendly website to use.  This is what the page looks like when it opens.

## Start GeoGebra

GeoGebra was created by a student to earn his PhD.  The agreement made with the professor was to make all GeoGebra creations available to the public for easy access.  The first button allows to research GeoGebra programs according to topic.  The second button allows to start the program, and the third button gives an option to download GeoGebra onto a desktop, notebook or mobile device.
For the Anja Greer conference I have attended, we were asked to download GeoGebra onto our computers beforehand.  The online version of GeoGebra is not the same as the downloaded version.  I found participants preferred to work with the online version of GeoGebra.  The two programs are alike but do not work exactly the same for everything.
We also created an account with GeoGebra so that we can save materials we found on the site.  It was very easy to search for materials on line.  Click the “materials” button,  and then the search key (magnifying glass).  Type in any topic in the search bar, and all of the GeoGebra programs created for that topic will appear.  As in any search, it is important to check out the programs of interest.
The moderators of the GeoGebra  courses mentioned that the best way to learn how to create GeoGebra programs was to find the ones we like, and discover how the program was created by looking at the commands used.
We used these two guides to get started with GeoGebra: