Adventures with Mathematics

When I was at the Math-In-Action Conference at GVSU a few weeks ago, I attended a session that highlighted some of the activities in the Adventures with Mathematics books published by MCTM. It was a really helpful session for obtaining some ideas of how to put “play” back into math -- even at the high school level! We looked at six games that provide a fun and challenging way to help students practice and/or review important concepts. Normally I am not one to purchase education materials given how much can be found for free via the Internet, but before the day was done I went to buy the two Adventures in Mathematics books that are aligned to the courses that I currently teach (Geometry and Algebra 1). Here’s the link if you would like to check them out: https://www.mictm.org/resources/publications/176

Here is a brief account of the six sessions that were highlighted in the Adventures with Mathematics session:

1. Polynomial Race Game: This game involves spinners, dice, and a game board. Based on the spins, a polynomial is established. The dice roll shows how many spaces to move on the game board, and where you land indicates what you need to do to your polynomial (add, subtract, multiply, or divide). There is also a “free” space where you can choose which operation you would like to use. Since the goal of the game is to end with a polynomial of highest degree, students hopefully pick up the strategy that multiplying is the best choice. I like that the polynomials and operations are selected randomly. One thing I would make sure I require is that all players in the game perform all operations so that they can check each other’s work.
2. Linear or Quadratic Battleship: This game is quite like the classic game of battleship. Each player picks a line or parabola (must be specified at the start of the round) to plot on their game board. Then the opponents take turns guessing certain coordinates to see if they get a hit or a miss. To win, the player must be able to write the opponent’s equation for the graph. I think students would have to have a pretty solid understanding of quadratics in order to play quadratic battleship (i.e. what must happen in the equation to make the parabola more narrow?) It would also help to tell the opponent at the beginning of the round what the axis of symmetry is. Linear battleship would be a great game for my Algebra 1B (struggling) students, as they only need to find two points to develop the equation.
3. Proof Puzzle: This is a great activity for making proof writing a bit more interesting. Students are given paper cutouts of statements and justifications, and they have to put them all in the appropriate column and order. I’ve seen this activity before, but what I really liked was how it was introduced. As a warm-up, students can practice putting various frames of a comic in order. This would be a fun way of showing students why sometimes order really matters in a proof, and other times two statements can be reversed without affecting its validity.
4. Taboo: In this game, there is a stack of cards with math vocabulary words. Whoever’s turn it is has to describe the word to his or her teammates without using the “taboo” words listed below it. Trust me, it was a challenge even for a bunch of math teachers! I like that is really gets at whether students understand the meaning of the terms rather than just reciting a definition.
5. Logarithm Game: I’m excited to use this one, because our logarithm unit is coming up in Algebra 1! Cards have a logarithmic or exponential equation or expression using the variables a, b, and c. Three different colored dice are rolled to assign those variables a value. Students have two minutes to rewrite the equation or expression in as many equivalent forms as possible. When finished, the student that has the most unique representations wins!
6. Guess My Function: For this game you need a game board with all different types of functions. One student picks a function without revealing it to the other players. Other students ask questions that enable them to start using the process of elimination to determine which is the correct function. (Examples: Is it a polynomial of degree 4?) This really requires students to have a good overall knowledge of the function families and various vocabulary terms associated with each.