This game challenges upper-elementary and middle school students to reason about number properties.
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.
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.
Variations
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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This game is an excerpt from Prealgebra & Geometry: Math Games for Middle School. Discover more of my books, printable activities, and cool mathy merchandise at Denise Gaskins’ Playful Math Store.
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“Math Game Monday: What’s My Rule?” copyright © 2026 by Denise Gaskins.
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I’ve used a different Rule game with my students and wanted to share a suggestion for keeping the thinking going for the whole class even after a student thinks they know the rule.
Rather than them telling you what they think the rule is, the student who thinks they know the rule says “rule”. That’s your cue for YOU to give that student a number, and they apply their rule to tell you where to write that number. If they are correct, they probably have the right rule, but they need to keep watching and listening to see if their rule applies to the numbers are placed after theirs.
Wait until several students say ‘rule’ and place the number you give them correctly before having students describe the rule.
I like that option! I’ve done the “test the students by giving them a number” part before, but hadn’t thought of making them wait until several students figure out the rule. Great way to keep students thinking.
I wonder, how would it work if you let the student who says “rule” start writing in the numbers other students guess (with you checking, of course), and the next student who gets it takes their place? Student involvement is nice, but it would probably be too awkward in practice. Turning what should be a quick review game into a production.