The Product Game


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The Product Game is a fun game that exercises students’ skill with factors and multiples. It can be played on paper or on the Internet. It has been one of the most popular games in the math fair developed by Patricia Helmuth, but can also be used in class or individually by students.

Electronic version
Paper version (use 2 paper clips)

Object of the Game

To get four squares in a row—vertically, horizontally, or diagonally.

How to Play

  1. To begin the game, Player 1 moves a marker to a number in the factor list of numbers 1-9 along the bottom of the game screen.
  2. Player 2 then moves the other marker to any number in the factor list (including the number marked by Player 1). It’s okay to have both markers on the same factor. The product of the two marked numbers is determined, and that product is claimed for Player 2.
  3. Player 1 moves either marker to another number, and the new product is claimed for Player 1.
  4. Players take turns moving a marker, and each product is claimed, depending on which player made the product. However, if a product is already claimed, the player does not get a square for that turn.
  5. Play continues until one player wins, or until all squares have been claimed.

Here are some Lessons related to the Product Game.

Questions for Students

  • Why did you pick <#> as your first product to play? Is there a better product you could have placed on the board?
  • How many moves are your playing offensively vs. defensively? Can you make a move that is both?
  • What factor(s) is(are) your favorite, and why?
  • What factors give the most play options? Why do you think so?
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