Category Archives: Moodle – GeoGebra Classrooms

The links to all of my courses and other information that is both Moodle and Geogebra related.

Pre Post for GeoGebra North American 2013

I am going to concentrate on three problems for my two presentations.  Two of the problems are based on orienteering and finding our location using Geogebra with the files below.  The third will be constructing a model in Geogebra that fits the situation of finding the distance between two towers with compass headings and the distance between the to measurements.

These problem work best if you make a video yourself and have students guess where you are based on a location that is familiar to them.  Also your students have a connection to you.  Feel free to use mine, but your students will respond better to their own teacher driving around in the country filming themselves:) 

  • first file you will need is the sectional maps of southwest Nebraska for my first orienteering problem done on the bus route.
  • Better Size picture for Geogebra
    Better Size picture for Geogebra

Orienteering sectional image

 

 

 

 

 

 

 

 

 

The second file needed is the Cheyenne Sectional for western Nebraska when I filmed by Chimney Rock.

Chimney-Rock-Orienteering

 

 

 

 

 

For the third problem you need to watch the video and then use GeoGebra to create a model of the situation.   Again this works best if you take your students out into the country and do it with them.  Place them in teams and make it a competition.  Who’s model will come closest to a measurement from google earth?  Have them write down a guess while you are out in the country.  Who is the best guesser?  Estimation on all problems gives students ownership of the outcome.  Very motivating.

The red and blue line segments are exactly one mile.  We took headings at each endpoint and created two problems.  With these measurements it is possible to find the distance between the two thumb tacks.
The red and blue line segments are exactly one mile. We took headings at each endpoint and created two problems. With these measurements it is possible to find the distance between the two thumb tacks.

 

 

 

 

 

 

 

Arapahoe Public School seniors calculating the distance between two towers.
Arapahoe Public School seniors calculating the distance between two towers.

 

Geogebra Beta 5.0 and Riemann Spheres

I know that Geogebra 3D is not ready, but I couldn’t resist downloading to try it out in a class I am taking here at the University of Nebraska Lincoln.  We are talking about Riemann spheres and stereographic projections with the complex plain.  Cool stuff, but the book was no help in visualizing this so I knew it would be worth the risk to download.  This program will be amazing when it is released officially.  The only thing I wish it had was a simple way to intersect two three dimensional objects.  I am sure it is possible, but have yet to see how it is done.

In the image above I show the set Z of all points of projection for a line that does not pass through the origin on the complex plane.  In the program as you pull point A out to infinity, it is possible to watch the intersection circle Z get smaller as it approaches the pole of the sphere at point N.  Sorry to not clean up my description mathematically, but just to excited and thought I needed to share the amazing fact that this problem which was hard to visualize was like putty in my hands with this program.  Great job Markus and the Geogebra Team!!! Can’t wait for the official release.

Here is a copy of my write up for that problem.  Have not had much time to clean it up, but Geogebra makes for a nice presentation Schaben Riemann Spheres Stereographic Projection