My favorite math lesson

So I guess it's time to start fulfilling my "New Year's Resolution." We'll see how long it lasts. :) Basically, I want to post a weekly blog about something that is happening in my classroom. If you are a new reader, please understand that this blog was previously my location for describing my missionary experiences in West Africa and then a place to post ramblings as I transitioned back into American culture.
Enjoy :)

The Sine Function
Here is my favorite math lesson to teach and I get to cover it at VM next week! It's over the sine function and how it is created from the unit circle values. I love hands-on activities, and I had that "Aha" moment when I completed the activity the first time.
(Note: This was adopted from an NCTM article that appeared many years ago. They used cooked spaghetti. Perhaps someone has the original article and can share the link with everyone!)

Supplies: Bulletin board paper (a large piece) and pull-n-peel licorice

My preparation beforehand:
Take a large piece of bulletin board paper and draw a large set of axes. Then make a circle with the radius equal to the length of one-pull-n-peel licorice strand. Create a unit circle marking the standard points. (I usually have my students fill in the point values and the radian measurement.)

Introduce lesson by asking them how we graph functions
1. Explain sine, cosine etc are functions. Ask them why we can’t call it a function on the circle.
2. Explain to the students how the circle was made.
3. Complete the following in groups.

Pull-n-peel Trigonometry

1. For the marked points, label the angles on the circle. (Use radians)
2. Place the string along the circle with one end at 0 radians and transfer the radian marks from the circle to the string.
3. Stretch the string along the line and transfer the marks on the string to the line. The end of the string that was at 0 radians on the circle must be placed at the beginning of the line. Label all the new points with the radian measures.
4. Use the pull-n-peel (pnp) to form a right triangle on the circle. (Pretend we are using pnp instead of drawing all the triangles.)
5. Move the piece of pnp that is the vertical leg of the triangle to the line and place it perpendicular to the line at the appropriate radian measure.
6. Now make a dot on the paper at the top of the piece of pnp to show the length of the vertical leg of the right triangle.
7. Do this for all the points.
a. Remember to think about values on the axes as well as what the triangles would look like in the 3rd and 4th quadrant.
b. Also, think about all the triangles and whether you need to construct them all.
8. Show Miss Pettit what your new graph looks like. Then connect all the points.


Questions:

1. What does the graph look like? Why?



2. What would the graph look like if you used the horizontal legs of the triangle instead of the vertical ones? How do you know?



3. What concept did you use to create the scale on the x-axis?



4. What would happen if we wanted to continue the graph. What value would be at 5π/2?
At -π/2? How do you know?



5. Explain why you really only needed to make 3-6 triangles instead of 14-17.



6. Explain how the sine function is created. Be specific. It is important that you know this.