Context and examples
When teaching mathematics to a new class in high school, I often open up with some mathematical games that can be played cooperatively and with minimal requirements (good old chalk and blackboard). On the one hand, this helps break the ice with the class (so to speak) and I get to quickly learn their names, and on the other hand, by trying different games I get to partially gauge their understanding of certain fundamental topics (such as parity, symmetry, prime numbers, ...) and their technical skills (multiplication table, visualisation skills, posing and solving simple equations, ...).
The games I use are simple enough in premise that even when there is a language barrier (such as welcoming classes for recently arrived refugees), kids will be able to quickly grasp the idea and participate.
Game of multiples and divisors
One good example is the Juniper-Green game, or simply the game of multiples and divisors: you set an upper bound (say 30), and then
- 1st student chooses a number between 1 to 30.
- 2nd student chooses either a multiple or divisor (still within 1 to 30) of the 1st student's number.
- 3rd student chooses similarly based on the 2nd student's number, so on and so forth.
- As they choose these numbers I write them on the blackboard with their name next to it. This is important because no number can be used twice.
- The last player who can still choose a valid number wins. The game is fun because they not only brush up on their multiples/divisors but after a few runs they also discover the tactical role of prime numbers in this game.
Color of a square on the chessboard
Another example is drawing a chessboard on the blackboard but only coloring the first row, rest being a blank grid. Then asking the students to guess the color of a random square I choose. At first they show their visual skills by instantly finding paths connecting to the that square from a known square and then using the alternating color rule.
- So if e5 is the target, one student tells me: I start from b1 which is a light square, then move to c1-dark, c2-light, d2-dark, d3-light, e3-dark, e4-light and e5 must therefore be dark.
Others find more efficient ways of rerouting to the target square and guess the color (e.g., moving diagonally). Then I would tell them, what if the board was much larger, not 8 by 8, but 100 by 100? Surely, it would take a long time to find the color of a random square with these path-finding methods and assuming we don't make mistakes along the way. What if there was a mathematical rule that would associate the coordinates of a square to its color?
As soon as I would say it and also substitute the file letters a-to-h with numbers 1-to-8 (like rows), they would discuss in small groups and within minutes hands would be raised! They've got it: if the sum of the coordinates of a square is an even number the square is dark, if the sum is odd the square is light. Suddenly, they discover on their own the power of mathematically modelling a problem: their predictions are no longer bound by how far they can visualize or how deep a sequence can be memorized.
- Do you know of other similarly spirited mathematical games (or more logic oriented) that can readily be played in classrooms? Ideally, accessible to most high school students.
Admittedly, this is a rather open question meaning that all proposals are welcome, whether they be games/puzzles you've used or seen used before, your own personal ideas for designing a new game, or simply examples you've read about before which may be fitting here. The latter brings me to the next question:
- Equally of interest would be puzzle themed book (or other resources) recommendations with similar mathematical games that would be particularly suited for teaching.