Blog Archives

Getting Started with GeoGebra – Tutorials, Examples and More

At Twitter Math Camp 2012, I gave a session about getting started with GeoGebra. Here are the resources from my session, including eight tutorials and links to pages with lots of other tutorials

TABLE OF CONTENTS

  1. Why Should you use GeoGebra?
  2. How do you use GeoGebra in your classroom?
  3. Why use GeoGebra instead of Geometer’s Sketchpad or another math visualization program?
  4. Where do I get GeoGebra?
  5. How can I learn how to use the program? <– TUTORIALS!
  6. How can I find ridiculously cool applets that are way above my skill level?

______________________________________

Why should you use GeoGebra?

The idea of learning a new technology and incorporating it into your teaching can sometimes very overwhelming. And you should never just use technology for technology’s sake, as some administrators seem to espouse. You have to have a real reason to use it. GeoGebra can improve math instruction in a million ways. The dynamic nature of the program gives you the ability to explain and explore concepts that simple pen and paper (or marker and whiteboard) can’t! I find myself using the program at least weekly, sometimes more.

______________________________________

How do you use GeoGebra in your classroom?

AS A DYNAMIC DEMONSTRATOR: To help students understand a tricky concept during direct instruction.
How can you get students to understand that the perpendicular bisectors of a triangle ALWAYS meet at one point? Construct a triangle with perpendicular bisectors in GeoGebra and move the vertices of the triangle around and let them observe that those lines always meet up at a point. (PS, sorry I didn’t upload these – this post took forever as it is and there are lots of examples of applets in the tutorials section below)

DYNAMIC WORKSHEET: To give students a chance to explore a concept at their own pace in small groups or individually.
One activity I do every year is let students “discover” derivative rules using a derivative tracer. They enter a function into a GeoGebra applet, which then traces out its derivative. With that, students try to guess what the equation of the derivative is. Once they collect a bunch of examples or correct derivative equations, they look for patterns to come up with a rule.

STUDENT EXPLORATIONS: To give students a powerful tool with which to complete their own investigations.
I have had students convert pictures to integrals, fit functions to data of really crazy things that they wanted to study, and calculate the volume of real world solids of revolution. Getting them comfortable with program with more guided activities earlier in the year gives them the skills to be able to do amazing things with it on their own later in the year.

CREATING WORKSHEETS/ASSESSMENTS: A tool for you to make your worksheets and assessments very professional looking.
You can copy and paste anything from GeoGebra into a Word Document, giving you the ability to put very good looking graphs and diagrams in your teaching materials.

______________________________________

Why use GeoGebra instead of Geometer’s Sketchpad or another math visualization program?

Well, first, it’s free. I mean, that should really be enough, but I’ll keep going. Because it’s free, you can install it on as many computers as you need (so students can use the program at home and at school). And you don’t actually need to install it – you can run GeoGebra right from a web browser, or host web applets that just require a student to have a browser with Java installed (i.e. 99% of people who own a computer and keep it even remotely up to date). Basically, no matter how annoying the tech department at your school is, GeoGebra is pretty easy to get going.

Additionally, because the program is free, it is developing quickly, and resources are easy to share and easy to come by. The community around GeoGebra is strong and constantly growing – check out GeoGebraTube, a ridiculously large repository of GeoGebra applets.

______________________________________

Where do I get GeoGebra?

Download it here. Click on “Webstart” to download the installer. You can also start a web applet here (in “Applet Start”) and download an offline installer for students without internet access.

______________________________________

How can I learn how to use the program?

Luckily, the program is incredibly intuitive. The best way to learn is to open up the program and experiment! But some people hate that and need a bit more of a push to get going (I had to teach my mom how to text with her new phone, so I think she is one of those people). That’s totally okay – my recommendation is to work through some tutorials that can show you how powerful you can be with the program. I wrote 8 tutorials that progress from GeoGebra basics to some cool intermediate to advanced things that will go a long way in creating your own applets.

GeoGebra Tutorials (written by me):

1. Basic Construction, Geometry Focus
(program basics, menus, windows, basic geometry tools)
(tutorial, finished product)

2. Basic Construction, Algebra Focus
(algebraic input, changing the display, copying into another program)
(tutorialfinished product)

3. How to Make Sliders to Animate a Concept
(dealing with variables, making your illustrations dynamic, animation)
(tutorialfinished product)

4. How to Make Tracers
(showing how things change and tracing the results)
(tutorialfinished product)

5. Inserting a Picture and Making a Checkbox to Show/Hide It
(putting a picture in and fixing it, checkboxes to show/hide objects)
(tutorialfinished product)

6. Using the Spreadsheet to Manipulate Data and Modeling
(inputting and visualizing data, fitting functions to sets of data)
(tutorialfinished product)

7. Uploading to GeoGebra Tube
(uploading your creations to the web to make sharable web applets)
(tutorialfinished product<– With GeoGebra 4.0, this is even easier! There is a menu item in File–>Export–>Dynamic Worksheet as Webpage (.html), and then you can directly upload to GeoGebra Tube.

8. GeoGebra and Google Forms
(using Google Forms to make a way to collect student responses)
(tutorialfinished product)

Other tutorials I have found:

______________________________________

How can I find ridiculously cool applets that are way above my skill level?

If you aren’t all that interesting in making your own, you can still find tons and tons of great applets. Like this applet that helps derive the equation for the area of a circle…

Head to GeoGebra Tube, an official searchable database of GeoGebra applets for just about any topic imaginable. Feel free to be inspired by the amazing work that some people do with the program!!

__________________________________________________

Best of luck using this program to help make your math teaching more dynamic!

Calculus Final Project Spotlight: 3D Solid Modeling

**The next few posts are going to be spotlights of final projects that students did that I thought were cool or interesting and then a few reflections on doing final projects in general. I could picture doing a lot of my student’s projects as a whole class!**

If I had one more week in my non-AP Calculus class, we would study volumes of revolution. That’s probably the biggest weakness of my course right now, and I am trying to figure out a way to include that next year. A junior who is in my regular class and is taking AP next year was a bit lost when coming up with an idea, so he asked me for a topic that we do in AP but did not do in our class so he could be a bit prepared. I suggested volumes of revolution and after a lot more nudging and guidance and idea planting than I did for other students, we decided that a good project for him would be to recreate an interactive 3D model of a solid of revolution using GeoGebra and Winplot. (actually it works with solids of known cross section too).

Here’s how it works…

1. Upload a picture into GeoGebra (he chose a huge vase from the art room). Fit functions to the edges of the object on the part that will be revolved.

2. Recreate the same exact functions in Winplot (which has much better 3D capabilities than GeoGebra does).

3. Use Winplot’s revolving capabilities to revolve the surface around an axis (any axis!). And then, voila, you have a 3D model of your object that you can use the arrows on the keyboard to rotate in any direction. It actually ends up being really impressive – my student told me that he left the model up on his computer and every time he would turn it on he would rotate his vase a bit.

After I saw the success of this project, I suggested the same one to a few students in my AP class (who were required to do a much more low key, shorter version of a final project because of time restraints). They decided to recreate a bunch of sports equipment using the program, which I thought was a really cool idea! Their rotate-able objects:


NEXT YEAR: I made an instruction sheet for those AP kids because they had less time, but I’m glad I did because this was a really cool project and is something that I can see myself doing with a whole class next year. Here it is below. If you haven’t tried making any 3D models (not necessarily real objects) with Winplot, definitely try it out – it’s super cool!