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 Steps

The Game of 100 is an ancient game of mathematical strategy that requires no supplies, although Iโd 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 ๐
- P1: Adds 9, total is 100, Player wins!

While initially, students may rush through, adding 10 each time, theyโll 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 youโll 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 ๐) 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?**