Wednesday, September 19, 2007

Unit Circle Trigonometry - Follow the White Rabbit

Last class period, my PreCalculus (juniors) and Trigonometry (seniors) built up an understanding of the unit circle through discovery. The basic idea of the activity was, according to one student,
"if you choose one angle, and graph it in each quadrant, then the sin, cos, and tan values are the same in each quadrant, ignoring the plus and minus".

My students were able to work through it with minimal prompting. Through dialogue, students were able to encounter reference angles & triangles and learn the patterns of the unit circle. This and the next pdf are now available on

Today, students completed an arts and crafts activity (they had previously drawn the multiples of 30&45 degree angles on paper plates) by placing the points on the unit circle (all 16 of the 'main' ones).


Students were given the "Follow the White Rabbit" activity. There was a secret message encoded in the Trig and Inverse Trig problems [ "IF I AM A KID, DOES THAT MEAN THAT TRIG IS FOR ME?"]. A few years ago, a student made a poster that morphed the Trix rabbit into a logo for our classroom, "Trig is for Kids", and so I had a scavenger hunt based upon this idea. It was a mixture of Trix, Alice, and Trig.

Here's the progression in the hunt:
  1. Students use trig to decode the message
  2. Students use clues on bottom of worksheet to find an online quiz
  3. Students enter the secret message in the online quiz
  4. Students are given a locker number and combination (to an empty locker)
  5. Students go to the locker, open it, find the Trig Rabbit Poster and a piece of paper with a web address.
  6. Students come back to class, go to the webpage and are given instructions to download a video.
The "prize" at the end is a video of a commercial that a previous student made. In the commercial, I dress up as a bunny. "Silly rabbit, Trig is for kids". It was my first year teaching, and in retrospect, a silly first impression to make on some staff.

Even my most apathetic students were excited and said that they enjoyed the class period. Also, two of my most proficient math students were paired up and, although they finished the trig ratios with little trouble, were some of the last to figure out the rest of the non-math clues.

Students practiced the content, problem solved, and made connections. I want to play more with my students (enhancing mathematics through the play) and this was a great day for both.

Saturday, September 8, 2007

Linear Relationship Open-ended Questions

I'm working on asking more conceptual, open-ended questions in order to challenge students, encourage critical thinking, utilize the "Rule of 4", and prepare students for AP Calculus level of rigor. The questions below represent my first serious attempt. Visit for the full pdf.

---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- ----------
  1. Give an example of a linear relationship in graphical, numeric, and analytic (equation) forms. Use the same linear relationship for all three representations.
  2. What is the relationship between the slope formula and the point-slope form of a line? (How can you derive one from the other?)
  3. How can you identify two perpendicular lines if they are both in General Form? (What is special about the numbers A, B, and/or C between the two equations)
  4. Why is the “intercept form” given its name? (What makes it different from the slope-intercept form?). Also, give an example of a linear relationship in intercept form and graph the line.
  5. Will 2 pair of parallel lines that are perpendicular to each other always form a square on their interior? If so, state how you know and if not, provide a counter example.
    1. If : L1 || L2 and L3 || L4 , L1 _|_ L3 and L4 , L2 _|_ L3 and L4
    2. Then: Does the interior of these lines always form a square?
  6. Given the four lines described in question 5, if you multiplied the slopes of the 4 lines together, what would be the product?
  7. Do the following four points form a parallelogram? How do you know if it does or does not. Points: (−4,0), (2,4), (−2,−3), (4,1)
  8. The table below gives the price, the supply, and the demand, for a certain video game.
    1. Graph the points representing price & supply and the points representing price & demand.
    2. Estimate the price at which the supply of video games will equal the demand. Also estimate the quantity that is supplied/demanded at this price.
    3. What happens to the supply and to the demand when the price of the video game is higher than the price you found in part b? .... lower than the price of b?

linear functions review (skills)

A full pdf with solutions is located at Students solve linear function problems (slopes, equations, intercepts, etc.) to fill in parts of the sudoku board. The final solution requires solving the sudoku puzzle.

Students seemed to be motivated to work the problems. Not a lot of high-level thinking, but lots of practice problems.