To Accumulate a Rate — Integrate!

Teaching High School Mathematics

Geometric Probability – Just more practice with calculating area, or something more?

I’m planning on playing a game in class with my students today. I’ll give them each a penny when they come into the room. Without letting them look, I will let them toss a their penny into the box. If they win I’ll give them two pennies. Every student will record how many wins and losses. Once the whole class is done we’ll talk about the likelihood of winning for a player and for the game owner. Then I will let them see the inside and have them take measurements and figure out the different areas.
Question for students: Can you figure out the probability without playing the game?

Then I will have students make their own boards using geometric shapes that will convince someone to think they can win but that odds are still in the game owners favor.

As an extension students can include winning different amounts of money depending on where you land so a player is more enticed to play.