Trig Intro: An Applet!

I made my second GeoGebra Applet and this time I included a slider.  I'm so fancy, I know.  But, for trigonometry the technology really is a huge help.  Last year I had students draw triangles, measure sides, compute the ratios and make observations.  The problem was, all the ratios are supposed to be between 0 and 1 which leaves them with very little room for error if we want to get nice patterns.  Needless to say, last year's lesson left most students bewildered and me frustrated that we spent a lot of time to get results that weren't useable.  This year, GeoGebra draws the angles precisely and computes the distance down to the hundredths place.

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