Funny Money
How it works
Imagine you want to make exactly 94 cents using pennies (1 cent), nickels (5 cents), dimes (10 cents), and quarters (25 cents) so that you use as few total coins as possible. How would you do it? How many coins would you use?
What if nickels are worth 6 cents instead of 5 cents? Would you use the same number of coins? More coins? Fewer coins? What about for other amounts of money?
What if you could design your own coin values with the goal of minimizing the total number of coins you have to use to make different amounts of money. What values would you choose?
In this activity, students start by making different amounts of money with the standard coin values. Next, they try making the same amounts of money but with a 6-cent nickel, and then with a 4-cent nickel and an 11-cent dime. They also play a game where each player chooses a different value for their nickels, and then each round everyone has to try to make the same random amount of money using only pennies and nickels, and whoever uses the fewest coins wins.
Why we like this activity
- It’s fun! Students enjoy exploring how to make money with unusual coins.
- It helps students to develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Using logic and finding and using strategies to figure out how to make different amounts of money using as few coins as possible.
Using logic and making and testing predictions when trying to choose the value for your nickel that gives you the best chance to win the game.
- It has a low floor and a high ceiling: It's possible to start making different amounts of money by trial and error, but finding the minimum number of coins you need requires more strategizing, especially when the coins don't have the standard values!