Everyone gets the chance to see all the triangles (no need to divide and conquer), calculate all the ratios and get a really nice table. Changing the triangle to see what is an invariant (the ratio!) is as simple as dragging a point and then re-calculating ratios. Everyone who was paying any attention easily worked through this lesson and made some good observations. It took a lot more to fully understand trigonometry (I can't tell you how many "aha!" moments there were where students finally realized that all this crazy vocabulary really just means those ratios that we started with), and then still more to grasp inverses. However, I liked this introductory lesson and loved the addition of GeoGebra to achieve the necessary precision.

That said, I will never eliminate paper and pencil activities from our explorations. We started similar triangles with protractors and rulers- filling posters with triangles (some which were similar, others which weren't) and we continued on to special right triangles using Mathy McMatherson's awesome worksheets (first two links). The technology made sense for us because students understood triangles and similarity, what we were focused on was a new type of ratio that required exact measurements.

The rest of my trig unit was okay, but still needs work. However, at this point it looks like I won't be teaching any triangle trig next year so I hope someone else will use this intro and build a better unit off of it.

Trig Intro

Thank you Tina! I've been doing the centimeter grid paper thing with similar precision frustrations. This is an excellent use of the dynamic geometry software.

ReplyDeleteGlad to help! The applet I ended up using with my class (since we couldn't get on GeoGebraTube for whatever reason) also included an image of a triangle with hypotenuse, opposite and adjacent labeled. Some students found that so helpful they wanted to keep the laptops when they were done with the applet. I'm not sure if that's a good thing, but if you want a copy of the file I used let me know.

DeleteThank you for the applet! I made a different discovery activity that is a little more scaffolded to support my students using your applet.

ReplyDeletehttp://crazymathteacherlady.wordpress.com/2014/02/10/day-100-discovering-trigonometry/