Monday, September 23, 2013

Reference Triangles

I had this idea to use string, masking tape, and dry erase markers so the students could explore reference triangles for the first time. I had a bunch of embroidery thread left over, so I gathered supplies:

I had my kids rip off a piece of masking tape and poke a hole through it to thread the string through then tape it to the desk. We discussed spacing issues and such, and they drew circles (eventually they were happy with them after a few erasings).

Then they drew the xy-plane with the origin at the center of the circle. (OCD note: do you SEEEEEE the pen with the cap off! It's drying out, people. CAP THE PEN!)

Then I had them get out their scientific calculators that I had them buy, and we explored sin(20), sin(380), sin(-340) and they noticed things. We then did (on the calculator) sin(160) and sin(-200). They discussed why the values were the same. Then they started moving the string around the circle.

We talked about how it didn't matter how you got there, you still got the same reference triangle (which I kept defining and bringing up) .... no notes yet. We talked about x, y, and r. We explored when the sine/cosine may be negative. I had them draw some more using their fingers and string and dropping of the perpendicular as references for their pens:

We explored when the sine value would get bigger and why.

THEN we went to notes:

I think they liked the novelty of drawing on the desks. Hopefully, the tactile aspect of creating the reference triangles will stick in their heads.


  1. That seems like an awesome way to explain the lesson without jumping straight into the textbook. They can come to the conclusions rather than having someone/something just tell them. Great idea.

    And yes, drawing on desk is pretty sweet. I'm instantly jealous. ;)

  2. Thanks, April. It was pretty low tech and cheap and easy to set up, so I think I would do it again.

  3. What?! You can draw on tables like that? And it just erases?? Where have I been?

  4. Yup ... dry erase ... off with ease ... except for red. What is it about red? That Expo liquidy stuff helps, though.

  5. Anonymous3:22 PM

    This seems like it would be a great way to also introduce the unit circle in higher levels of trig. It would give them a concrete example of how to calculate the different measurements, rather than trying to memorize that god-awful long list of measurements on the unit circle. Great job!

  6. I mentioned this post on my blog this week. Thanks

  7. I love this! I could even modify it for my geometry classroom.