Math Game Monday: Distributive Dice

“Distributive Dice” is free on this website for one week only. It’s an excerpt from Multiplication & Fractions: Math Games for Tough Topics, 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 helps children practice math facts and understand the area model of multiplication. And it’s great for building multi-step mental math skills.

Distributive Dice

Math Concepts: addition, subtraction, multiplication, distributive property, rectangular area, multistep mental math.

Players: two to four.

Equipment: graph paper (1 cm squares for two players, or 1/4 inch squares for more) or the Galactic Conquest game board, three six-sided dice, colored markers.

Set Up

The free 44-page PDF Multiplication & Fraction Printables file features two decks of mathematical model playing cards, plus hundred charts and all the game boards for the Math You Can Play: Multiplication & Fractions book.

Get Your Printables File ❱

Print your preferred style of graph paper or the Galactic Conquest game board.

Each player will need a colored marker to shade in the game board squares, and the colors must be different enough to be easily distinguished.

How to Play

Players share a single sheet of graph paper or game board. Each player colors a large starting dot on one corner of the grid, as far apart from the others as possible.

On your turn, roll all three dice.

Choose two of the numbers to add or subtract, and that answer will form one side of your rectangle. The third die gives the other side.

Draw the rectangle on the graph paper so that it shares at least one corner with your current territory and does not overlap squares already claimed by any player. Inside the rectangle, write the area of your newly conquered space.

The game ends when a player cannot draw any rectangle to match the dice. Players add up the areas of all their rectangles, and whoever has conquered the most territory wins.

Distributive Dice game in progress. Red’s turn, and the dice have been rolling low — but this time, Red has two big numbers to play with. Would you move to gain the most territory, or try to block Purple’s ability to grow?


Damult Dice: (Any number of players.) No graph paper needed. On your turn roll three dice: choose two to add, multiply by the third, and then add that many points to your score. If you have enough dice and enough space to keep them separate, players can all roll at the same time. The first player to reach 300 points wins the game — or if two players pass 300 points in the same turn, then the highest score wins.

Double Damult: Roll six dice. Use any combination of addition, subtraction, multiplication, and division to calculate your score — but you have to use each operation at least once.

Masquerade: (For two players.) Roll three dice but keep the numbers hidden. Add two, multiply by the third, and then tell your opponent the score. The other player gets three guesses to try to win the number of points on your dice. For each correct guess, reveal that die, and the other player scores that many points. If two dice are the same, only show one per guess. Play five rounds, and the highest score wins.


Dan Finkel invented the Damult Dice games and shared them on his Math for Love blog. John Golden modified the game, and I tweaked that to make my Distributive Dice version.

Golden played the game with a fifth-grade class, and the students created several more variations, including Masquerade. Read more of their ideas in “Multiplying Game Possibilities” at Math Hombre blog.

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