Math Game Monday: What’s My Rule?

“What’s My Rule?” is free on this website for one week only. It’s an excerpt from Prealgebra & Geometry: Math Games for Middle School, 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 challenges upper-elementary and middle school students to reason about number properties.

What’s My Rule?

Math Concepts: Venn diagrams, factors and multiples, divisibility, prime numbers, and other number properties.

Players: two or more.

Equipment: pencil and paper, or whiteboard and markers. Calculator optional.

How to Play

Choose one player to lead the game. The leader draws one or more large circles. With two or more circles, make them intersect in a Venn diagram. For each circle drawn, the leader must have a number-property rule in mind.

Each rule must be general enough to cover a reasonable range of guesses. For example, “numbers divisible by three” is a good rule because there are many common numbers that fit and also plenty that don’t belong. But a rule like “multiples of 117” would rain shame on the leader’s head and may result in banishment.

The other players take turns saying numbers. The leader writes each number in the appropriate circle of the Venn diagram. Numbers that fit more than one rule go in the region where those circles overlap. If the number doesn’t fit any of the mystery rules, write it in the outer margin.

After the number is written down, the player who named it may try to guess the rule for one circle. If the guess is correct, the leader writes that rule next to the circle.

If a rule proves too difficult for players to guess, the leader may add number clues in that circle.

If numbers fit both of the rules, put them in the area where the circles intersect. Can you identify the two properties for this diagram?


House Rule: Do you want to discourage wild guesses? Make a rule that the circle must contain at least three numbers before you allow players to guess its rule.

Words to Know

Venn diagrams use overlapping shapes to create a visual representation of the relationships between different sets. Mathematician Georg Cantor defined a set as “a Many that allows itself to be thought of as a One.”

While circles are the most commonly seen, a Venn diagram with four or more sets needs a more complex shape. For example, the Math Pickle website — a delicious source of mathematical activity ideas — has a five-set logo made from oblong pickle shapes.

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