Math Game Monday: Dollar Nim

“Dollar Nim” is free on this website for one week only. It’s an excerpt from Math You Can Play Combo: Number Games for Young Learners, available as an ebook at my bookstore (Thank you for cutting out the middleman!) and in ebook or paperback through many online retailers. Read more about my playful math books here.

Many parents remember struggling to learn math. We hope to provide a better experience for our children.

And one of the best ways for children to enjoy learning is through hands-on play.

This game encourages children to think strategically as they add coin values.

Dollar Nim

Math Concepts: subtraction within one hundred, value of coins, thinking ahead.

Players: best for two.

Equipment: none.

How to Play

This is a mental math game, designed to be played in the car. Start by imagining a pile of money equal to $1, or 100 cents.

On your turn, “remove” any coin you like — quarter, dime, nickel, or penny. Say which coin you are taking and the new value of the pile.

The player who claims the last coin wins the game.

Variations

Allow half-dollar coins, if you wish, but no dollar coins—unless you are trying to demonstrate what mathematicians mean by a “trivial” problem.

Hundred Chart Nim: If your children have trouble doing the subtraction mentally, you may use a penny or other small token to keep track of your value on a printed hundred chart. Whoever wins gets to keep the penny.

Making Change: Play with real coins. Each player starts with one quarter, two dimes, three nickels, and four pennies. Or pick different coins, as long as everyone starts with the same collection. On your turn, discard one of your coins to a pile on the table. If there are any smaller coins in the pile, you may take back change up to one cent less than the value of the coin you put in. The last player who has money wins the game.

Alien Money: Imagine an alien civilization. What sorts of coins would they use? Perhaps the creatures have three fingers on each hand, so their coins are all multiples of three. Or maybe the alien society loves math so much that they put mathematicians on their coins instead of political leaders, and their coins are based on prime numbers. What is the value of an alien dollar? How would your aliens play Dollar Nim?

History

One of the oldest and most flexible strategy games in the world, Nim began with players taking one or more stones away from one or more piles. It’s usually played as a misère game, which means that the player who takes the last stone loses.

Nadine Block invented Dollar Nim on the way home from a camping trip, thus earning her official title: Mother of Twins and Creator of Math Games on Long Car Rides. I read about the game on her husband Patrick Vennebush’s blog, Math Jokes 4 Mathy Folks, named after his fun book, which Block helped edit.

Making Change is based on James Ernest’s game Fight, now renamed Pennywise. I found it at John Golden’s Math Hombre blog.

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