Thursday, April 18, 2013

Unit Circle Philosophy

This year, we decided to expand the number of trig topics we teach in Algebra 2 to include the unit circle, the graphs of sine/cosine, and modeling of periodic motion. These are topics I haven't taught in quite a while, so I am getting to take a fresh look.

Here's how I started out:

1.  Review pre-requisite skills:  Angle measures, trig ratios, special triangles.
2.  Develop the idea of a reference angle.
3.  Given a special angle, draw a triangle in the appropriate quadrant, identify its reference angle, label its sides, and find the values for sine, cosine, and tangent.
4.  Replace old special triangles with new ones where hypotenuse = 1.

5.  Cut out special triangles where the hypotenuse equals one unit. Label their sides and glue them onto a unit circle.

6.  Label the points on the circle. Use the circle to evaluate sine, cosine, and tangent for all the special angles. Look for patterns.
7.  Extend the pattern to the axis angles. Use the circle to evaluate sine, cosine, and tangent for 0, 90, 180, 270.

At this point, I feel like my students have a pretty good conceptual understanding of the unit circle. What now? This is where I am stuck.

I generally don't believe in telling students to just memorize something, but I also cringe when I see a calculus student reach for their calculator when they encounter something like sin pi/2 or tan 3pi/4. 

Don't students need to be able to recall these values later on without a circle or a table in front of them?

What is the best way to tell them to remember these?

I did some searching and I decided on a mnemonic device. 

I am sort of ashamed to be using it.

So far, it is working.

My next post will be the procedure I decided to use, but I am wondering if anyone has any thoughts on memorization and the unit circle? How do you approach this in your classroom?

Monday, April 15, 2013

Sending My Friends to NCTM

First of all, I feel like I only blinked and there went three months. I subscribe to the "blog when you feel like it" philosophy, but I still find myself feeling guilty for such a long absence. 

To break my silence, I thought I would share something fun.

My two math teacher colleagues are going to NCTM this week. I am not. I am very sad about this, but I  am sure that I will get over it this summer, as I asked to be sent to #TMC13 instead. Yay!

I made my friends an activity book, to help pass the time during their very long drive from Small Town, KS to Denver.

They can earn 50 points for solving puzzles like this:

They can earn points for taking pictures of yellow cars, license plates, gas station/restaurant combos, and more.

There are games and drawing assignments:

A few activities are for my own entertainment:

And a few activities are designed to help me live vicariously through their experiences:

And finally, I am not above putting them up to stalker-ish behavior.

Have fun, friends! Learn a lot. I will miss you!