Make Math Move with Sliders and Animation in Geogebra

It is incredible that within the first few hours of posting the Geogebra Basics post, hundreds had already checked it out via Twitter, Facebook, and the BrokenAirplane RSS feed. There are so many people who are interested in learning more about using Geogebra in their classrooms and I hope you are getting the hang of the basics and perhaps tried a few things of your own.
The next two features, are one of the most requested and often used features for Geogebra because they promote interactivity and understanding. Once you get the hang of it, your students will never look at an equation the same.

This is one of my favorite features in Geogebra. Graphs/Functions show changes over a range of numbers, but what happens when you change the equation? These relationships are the core of the equations but students often miss it as they try to plot the graph.

Step 1: Open Geogebra (steps 1-3 in the basics post).
Step 2: Look at the bottom of the Geogebra window. On your left you will see the word "Input" and next to it is a text box to type in equations, variables, and more.

Step 3: Lets create some coefficients that we can play with. In the Input Bar, type in m=0 and hit "Enter" on your keyboard. It is important that you follow these instructions literally, so do not use an uppercase M (although you could use any letter in the future but for the example follow carefully)

After hitting "enter" you will notice under "Free Objects" a new object m which is set equal to zero.

Step 4: Create one more free object by typing "b=0" into the input bar and hit "enter".
Step 5: Next to the free objects "m" and "b" you will see a clear bubble. It is actually an ON/OFF switch for the slider. Click on the bubble for both of them and you should see a slider appear in the graphing window.

Step 6: Back in the input bar, type in "y=m*x+b" and hit enter. Note: The asterisk between the m and x is the multiplication symbol. You must type it this way as you will get an error if you try to just use "mx".
Step 7: It may have seemed like nothing happened, but in fact you just graphed y=mx+b, the equation of a line. The reason you can't see it is because you have your slope (m) set to zero and it is covered up by the x-axis.

So lets see that line and the power of sliders. If you look at the "m" slider, it says m=0. Click and drag the ball on the slider back and forth. Watch as the line changes its slope and imagine your students going "Ahhhhhhh" as you explain and show slope changing. The visual demonstration gives the student the mental connection they need to understand.

You can adjust the "b" slider as well and see the y-intercept change. Although it is called the "y-intercept" students still seem to get confused until you show them that its value determines where the line hits the axis and adjust it to show them how it can change.

As students begin to see these relationships, they can begin to apply their knowledge to new situations and visualize the graphs in their heads before they have to plot them by hand. Imagine a classroom where students and not calculators see the relationships between variables and coefficients.

If you really want a fun demonstration, create three new sliders "a", "b", and "c" (step 3). Then enter in the equation y=(a*x^2)+b*x+c (the "^" symbol comes from holding shift and pushing the number "6") and you can show your students the relationship of the variables and coefficients in a quadratic. Seeing these numbers change,  become positive and negative, and zero really makes it all the clearer that math can represent real things like data and physics.

Changing the range of these sliders can be really useful and you can do this by right clicking on the slider ball and choosing object properties. Changing the interval will choose the range of numbers over which the slider will show. There are many other settings you can change in this menu like color and thickness, and much more. Be sure to try changing the size or color of your lines as well to make them easier to see from far away if you are showing this to a large group.

It can be very useful to have your students see the sliders move through all of the numbers over and over. This frees you up to walk around the room but also shows an animation of math moving which can be very beautiful and help promote understanding with trigonometric and polar functions.

To activate animation of a particular slider, right click the ball of the slider you wish to animate, and select "Animation On". By default it will cycle through all of the positive numbers and then go through the negative numbers over and over. You can change this in the slider's "object properties" menu and under the "slider" menu and "Animation" setting change the speed of the animation. The three options for an animation are: Oscillating, which is the default back and forth cycling through all of the numbers; and Increasing or Decreasing which will only once go through the positive or negative numbers. It might be necessary to slow down the speed so narration and explanation are possible.

Play around with those, and I do mean play. This is software that really encourages fun in math and I hope that these features will help your students to see that. In the next post, we take a more global look and see how to share Geogebra files with your students and the World! Also, there are an enormous amount of resources out there that I want to share with you from educators already making great stuff with Geogebra. See you next time.

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