Creating Classroom Resources
This book is a collection of ideas, examples, and steps I've taken over the years to create applets for my students to use. It is meant for someone who is a novice to intermediate user of Geogebra to have some examples for how to approach useful tools when building in Geogebra.
Table of Contents
- Introductions
- Why Geogebra?
- Building your materials
- Variables, Sliders, and Input Boxes
- Outline the Activity
- Learning Generating New Problems
- Examples
- Secants to Tangents
- Interior angles of a Circle
- Shifting the Absolute Value Function
- Unit Circle Exact Values
- Making Time
- Area Between Functions
- Arc Length and Sector Area Practice
- Discovering Taylor Polynomials
- empty Input Box for answering
- Euler Approximation
Why Geogebra?
I started using Geogebra (and Desmos and Cabri Geometry and calculators) because as often as possible I want students creating their own understanding. Geogebra allows for students to manipulate and long-term create their own constructions to better understand and explore mathematical concepts.[br][br]Below is an activity that I created to help students better understand the Mean Value Theorem. [br][br]Controls that the students have are the sky blue points on the x-axis, the slider (and text box) to control the height of the rectangle, and the function itself. TRY THEM OUT.[br][br]Information that I added for clarity are the function, the Area, and the Height. I used variables and LaTeX both built in in Geogebra.
Variables, Sliders, and Input Boxes
Variables
Everything in Geogebra is a variable. The lists, the functions, the coordinates. Most things can be referenced and connected to other operations in a file. Below is an example of how a simple variable value can be referenced from a point on the screen.[br][br]In the example below, you can drag Point A and it will control point B. In the Algebra window, you can change the equation f(x) as well as see how B is defined. I think of it has function notation said out loud. x(A) in my mind is [b]the x value of Point A.[/b]
Sliders
Sometimes you want to control a value using a slider instead of a point. It can limit the inputs, it can keep the controls in a place where can see time if you change an equation. Sliders can also control the steps of a construction. Below you can see how a number works, how an angle works (you need to use the angle for any angle or rotation) and integer when you don't want to use decimals in your values.
Input boxes
Sometimes, you'd like the applet to be a little cleaner without the algebra window being shared. A textbox would still allow for the control of variables and equations. Also, you can use a textbox as a way to check understanding with a "you got it" pop up. (Reverse engineer to see how to conditionally format any object--not just text)
Secants to Tangents
Complete a table of values for the following functions
Change the value of a to get a new coordinate for B. Find a=2, 1.5, 1.3, 1.1 for each of the following functions and make a table of values.[br][br]f(x)=sin(x)[br]f(x)=[math]0.5x^2[/math][br]f(x)=[math]\sqrt{x}[/math][br]f(x)=[math]\sqrt{2-x^2}[/math][br][br]For each function, what does the slope appear to approach as a approaches 1?