[activity] Stick and String

Mysteries of Trigonometry, Jerzy Kocik

"trigonometry is the theory of a stick with a chord attached"

Wrote Jersy Kocik in his book, The Mysteries of Trigonometry (2005), along with a brilliant activity for teaching trig ratios, the stick and string.

Here is a handout and some files that support this activity.

I submitted this activity for a Rosenthal Prize, and here is my response to their implementation question,

Imagine that another teacher were trying to implement your activity in their classroom. If they had to start from scratch, what materials would they need? How much time would it take to prepare? What would be the cost (at market value) of all materials involved?*

This activity will likely take two 60-min periods or one 90-min block. It may take up to 2 hours to plan the first time around, but is relatively straightforward after that. Plan for groups of three. Each group should have a stick, string, protractor, 8.5x11 paper, scissors and markers. Ideally the sticks are as straight as possible, have no markings and are a range of sizes. If you can manage to have each individual build their own stick&string it might be worthwhile. One way to do that would be to ask each student to bring their own unmarked stick about 20 inches long and a string that is a bit longer. Whether you tell kids to bring materials or not, you’ll need your own supply. I find that shorter than 12 inches is crowded to mark (and less accurate) and longer than 40 inches is cumbersome to work with. I bought various lengths of (½”) dowels from home depot with a mean length of around 24 inches.

For a class of 30 with ten groups of three plan to buy:

- 4x72” dowel rods at $2.57 each and cut them at the store into 16”-40” lengths ($10-15 per class).
- A ball of twine or any inelastic string will do ($3-5).
- A class set of protractors ($10).
- A class set of markers ($20).
- A class set of scissors ($10).
- A ream of 8.5x11 paper ($3).

This activity would cost about $(50 + 12c) where c is the number of classes if you had none of these materials. I personally like doing it with branches because they feel like wands, and that cuts the cost to about $50 for the first time and less than $10 for each subsequent time. The class will benefit to have at least one computer to compile the data and graph the result, but it is not required.