From circles to ellipses?

Many people seem to think of circles as simple things and ellipses as "oh, that's math and I was no good at it...".

Here is a bit of a perspective on that created in GeoGebra.

If you know nothing of ellipses beyond "oval", start by just using the control buttons at the top. If you are comfortable with ellipses, but a bit of a skeptic, experiment with the sliders as well. If you really want to know what is happening, download the complete file here.

Regardless of where you stand, GeoGebra does give a great dynamic approach to mathematics.

Math is Fun

Although I could fill pages with comments on the 2016 US presidential campaigns, I choose this time to stick with my GeoGebra efforts.  Here is a file I wish I could have used when I was in the classroom. Using basic geometric concepts out of any high school geometry class (circles, rotations, segments, midpoints) it targets a graphing question which would be extremely hard, if not impossible, to introduce without dynamic geometry. Anyone can experience it, even "math-haters".

This file (find it here) took around an hour to create, but has the benefit of reuse.  It only needs to be created once. By posting it as a public file, anyone anywhere with access to the web can use it.

I hope people do use it, and come to appreciate how, properly used,  programs such as Geogebra can transform and revitalize the classroom. 

Remember: math is a game. Go out and have some fun!

 

From 2 Circles: A Little Magic

Things that would be next to impossible with the old "chalk talk" become quite teachable using GeoGebra. That is not to say that files like this can be made by young students: rather, their teachers can use files like to help students discover math!!
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With precalculus students I would aim to give them specific circles, and ask them how they can use those circles to pinpoint an equation for the ellipse.

With 8th grade students I would use a file such as this to embed in their brains some basic geometry and basic geometric vocabulary. I might even give them a graph paper with two circles drawn, a compass, protractor, and straightedge, and ask them to recreate this process by hand.

Same file, same subject, totally different strategies. GeoGebra, creativity, and time: the key ingredients..

A Post Without Many Words

Find original here.