# Polynomial Guess

MOTIVATING COMPLEXITY             THROUGH PUZZLES

I found a really nice number guessing game several years ago, and I’ve used variations of this puzzle several times over the last few years in my Algebra class. Kids can’t help but want to know the answer to a logic riddle like this, and this year it occurred to me that I might be able to leverage this “want to know the puzzle answer” to motivate some more focus on understanding quadratics or higher degree polynomials.

The idea is that you choose a “secret” number, and give clues one at a time until students can narrow down the possibilities to a single answer.  I decided to try the same idea with more complicated expressions, so I created a couple of quadratics puzzles, and a polynomial version. I had these posted on the Sweet Math wall, and would add clues roughly one each day. I ran a simple number version, alongside the more advanced ones to allow entry for middle schoolers, and extension for high schoolers. I definitely noticed kids lingering at the clues as I added them. Some kids even asked me what time of day I would be adding another one. In an unexpected turn, it was a history teacher who submitted the correct guess for the first number puzzle. In your face Algebra students!

Although I haven’t done this yet, I like the idea of creating examples for sequences, and I think I’ll try this next year. Is the glory of being the first to guess correctly important enough to take the chance of guessing when there might be two possibilities for the common ratio of a geometric sequence? Do you team up with another student when you’ve narrowed it down to two possibilities so one of you is guaranteed to be victorious?

Here are a few of the puzzles I made in case you’d like to try them out. Please do let me know if you find them useful or if you think that I should sequence the clues differently or if you have other ideas for how to make them better.

Number Guess 1

Number Guess 2

Polynomial Guess