Coffee to Theorems

I just used a mathlet I found online: “Triangles By Side” (source: Math Hombre) in a lesson for geometry. (uploaded here: http://scottfarrar.googlepages.com/geom2009 The worksheet http://scottfarrar.googlepages.com/TriangleCategories.pdf ) It worked very well.

A few notes:
0. This was our second day on triangles so I had not used the vocab for each category. I purposely left it to the end of class then we all labeled each category as a class. Students worked in pairs, 1 computer per pair.
1. Students were a little confused about starting with the scalene. There’s not much to “observe” there. I think the best one to start with is the isosceles.
2. Its kind of a shame that the 3,4,5 and 6,8,10 are the only right triangles possible. Next time I would bump the sliders up to 13 so that students could make a 5,12,13. (obviously we haven’t covered pythagorean, but students were able to find the triangles easily enough)
3. I actually didn’t have the 2nd mathlet up there when my students did it. They used the first one for both activities.
Pros: integer lengths for c are easy to list. Students had no trouble figuring out what to do.
Cons: students don’t automatically consider fractional side lengths for side c.
This can be a pro, however!! A kid says if a=4 and b=6, c can be 3, 4, 5, 6, 7, 8, 9. Then they are ripe for me to ask “can c be 2 and a half?” They can flip back and forth from c=2 and c=3 to guess at what c=2.5 looks like. Then I ask “can c=2.1? 2.01? 2.001?” It was great to have students interrupt me half-annoyed and say “As long as its more than 2, its ok“

The one I just made (the 2nd one for 10-30) might be “too helpful” for day 2 of triangles. This is probably better as a review or lecture demonstration. http://scottfarrar.googlepages.com/triangleineq.html

So I think I might change my worksheet back to using the first mathlet, or a modifed version of the first. I’d limit the way they interact with side c first. Then I can give them more freedom to explore rational side lengths.

I welcome feedback and suggestions!

http://scottfarrar.googlepages.com/circumcenter_lomaprieta.html

So I put together this mathlet in anticipation of doing Triangle Centers. I love it, and I hate it. On one side, I’m very satisfied with how it turned out implementation-wise. On the other side, I’m not satisfied with what the lesson is. This is not a 50 minute activity. So they find Loma Prieta. Big whoop! There’s not really a *problem* to solve.

Could I muddy up the data? Could I muddy the data? Or should I go and try to get actual USGS data in terms of when the first shockwaves were felt and where. With all the differing topography in the Bay Area, I’m sure the shockwaves were not perfectly circular. And yet, if we took a lot of data we could probably do the calculations/constructions needed in order to find a good estimate for Loma Prieta.

Whats frustrating is that this lesson is not ready, and I’m not sure if I’ll have time to get it all the way there by the time this comes up in the year.

I did this with my students about a week ago: http://scottfarrar.googlepages.com/geom2009

Previous Knowledge: students have copied and bisected angles and segments before “IRL” using compasses and straightedges.

It went very well for a “first time” on computers this year. The versions of the files I initially used did not limit their tools, but I have now changed the mathlets: you are limited to Euclidean constructions via compass, straightedge and points/intersections.

The fourth mathlet is too hard. The first three took most of my students about 20-40 minutes to get through. So I definitely need a fourth problem that is relatively simple, yet exposes them to something new in Geogebra.

“Free exploration time” works for some students, but if they are that interested, they can do it at home on their own computers. I’d rather have an engaging mathlet.

f(t): How to Bounce a Ball Part 1 – The Problem

A student-led lesson (Geometry)