I wrote before about teaching math using inductive thinking. Here’s an example of a math game called The Game of 100 that builds on inductive thinking.
Remember, with inductive thinking, we (the teachers) set up patterns for students to discover. We don’t explicitly explain everything, but, instead, we empower students to think. We set the stage for them to uncover strategies and build their own understanding.
Game of 100: The Steps
The Game of 100 is an ancient game of mathematical strategy that requires no supplies, although I’d recommend paper and pencil.
- Both players add to a shared total.
- The shared total starts at 0.
- On their turn, a player may add from 1 to 10 to the shared total.
- The first player to reach 100 first.
Sample Game
- Total starts at 0.
- P1: Adds 10, total is 10.
- P2: Adds 7, total is 17.
- P1: Adds 8, total is 25.
- [time passes], total is at 75.
- P1: Adds 10, total is 85.
- P2: Adds 6, total is 91 👀
- P1: Adds 9, total is 100, Player wins!
While initially, students may rush through, adding 10 each time, they’ll quickly discover that they need to approach 100 carefully. Rush in, and you give your opponent the win, as Player 2 did in our sample. Play through a few times, and students will discover a special number that, if you reach it, guarantees you’ll be the one who gets to 100 first.
Find The Strategy
I recommend that students write down their totals as they go so they can analyze the game afterwards. Looking at our sample game, could my students adjust Player 2’s final move (noted with 👀) in order to set up a win rather than a loss? This purposeful analysis is key! We must push students towards deeper thinking.
Once they realize that there is a special number in the 80s that guarantees victory, students will begin to identify more patterns. Is there, then, a number in the 70s that will also guarantee victory? (Yes, eventually students will realize that the first player who goes can pick a number on their first turn that will set up their win!).
Naturally, anyone who can beat the teacher wins a prize! I’ve heard teachers who require two wins against them. This gives you a chance to judge whether your students really understand the strategy. It also allows you to try your hardest on that second time around!
Adjust
Then, since the game is so simple, you can test students’ inductive thinking by changing the rules a bit.
- Reach 71 by adding between 1-7.
- Reach 21 by adding between 1-3.
- Reach zero by starting at 25 and subtracting from 1 to 4.
Students should adjust their strategy to fit the new rules. What special number guarantees a win now?