|Chutes and Ladders - a game for ages 4 and up|
Tangents and Cotangents - a game for ages 16 and up
It wasn't long before I had decided upon a few rules, and come up with a game we could play in precalculus, which I decided to call "Tangents and Cotangents". I thought the name was a nerdy way of describing Chutes and ladders, because the graph of cotangents is always decreasing like chutes, and the graphs of tangents are always increasing like ladders.
I brought the game to school, and described the following rules to the students:
- Students (in teams) would answer estimation questions like sin(25) or tan(258). (NO CALCULATORS ALLOWED!) Each trig function was worth a different amount of points. If the students estimated within 10% of the correct value, they moved forward that many spaces. If not, the other teams would be able to steal the points if they had estimated correctly -- so everyone was interested in every question. The points were defined as follows:
- sine = 1pt
- cosine = 2pt
- tangent = 3pt
- secant = 4pt
- cotangent = 5pt
- cosecant = 6pt
- If the team guessed the value within 10%, but had the opposite sign, they went backwards that many spaces. While this might seem like an annoying penalty, eventually one of the teams caught on that it could be used their advantage to land on the coveted 28 square, and it wasn't long before teams were "purposely" getting the sign wrong to their advantage. I didn't mind, because it made them think about and practice the signs of the values too -- part of my objective for the day.
- Once per game, I allowed the teams to choose what point value they wanted to play for -- typically they were chosen at random like normally in the game. This added an element of strategy for the students who would wait to the opportune time to try to hit a big ladder. I think I would change this rule next time to reward REALLY close guesses (say, within 1%) with an additional free choice.
- Occasionally we would play a question that was available for all four teams. Any team that guessed within range was awarded the points (forward or backwards as necessary)