I now have to teach trigonometric ratios in geometry, in addition to college prep math. I have apps on the iPad but I'm wondering about some hands on activities that would get students moving around. I like giving them an excuse to move around and get some oxygen into their brains.
I found this great blog by Dan Percy that provides a wonderful activity to introduce trigonometric ratios in the classroom. He opens with a picture of a crane outside his window and has students guess its height. He shows how you cannot use the Pythagorean Theorem to find the height because you only know its distance along the ground. He goes on to provide a worksheet with a variety of triangles of 20 to 70 degrees and students have to measure the lengths and record them on a data sheet. Once the measurements are filled in, they find the ratios in both fraction and decimal form. The next step requires the use of geogebra to verify the data. The whole activity allows students to see that Sin 30 is the same regardless of the measurements. Check it out.
The Teaching Channel has a video that has a great idea for helping students learn where the opposite side is or the adjacent using several cut out triangles and a bit of water sprayed across the triangle. The teacher highlighted in this video uses a drum to beat out SOH - CAH - TOA while she says it and has the students say it along with her. She noted that later in the year students will beat the rhythm of SOH - CAH - TOA on their desk.
I like the idea of using the triangles but I'm wondering about writing the words opposite or adjacent on the triangles and then holding the triangles above a heat source to make the words "magically appear" so it catches their attention.
Over at CPalms, there is another lovely activity that has students comparing triangles with the same angles. Its a worksheet that has them measure the lengths of the triangles and then calculate various ratios without knowing they are trigonometric ratios at first. The trigonometric ratios are introduced in the second part of this activity and comparing the data with the earlier calculations. Its a nice way to introduce the procedure without using the language quite yet. I like this one because it comes with accommodation version that separates the triangles better. This activity also comes with an applications page so students can apply the ratios to a page.
So three nice introductory activities for trigonometric ratios.