Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on

Pin it!
Google Plus

Product Game

3-5, 6-8
Number and Operations
Math Content:
Number and Operations

The Product Game is a fun, interactive game that exercises your skill with factors and multiples.

This interactive is optimized for your desktop and tablet. 

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 (green square) 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 (green square) to any number in the factor list (including the number marked by Player 1). The product of the two marked numbers is determined, and that product is colored red for Player 2.
  3. Player 1 moves either marker to another number, and the new product is colored blue for Player 1.
  4. Players take turns moving a marker, and each product is marked red or blue, depending on which player made the product. However, if a product is already colored, the player does not get a square for that turn.
  5. Play continues until one player wins, or until all squares have been colored.


This Product Game Investigation was adapted with permission and guidance from Prime Time: Factors and Multiples, Connected Mathematics Project, G. Lappan, J. Fey, W Fitzgerald, S. Friel and E. Phillips, Dale Seymour Publications (1996), pp. 17‑25.

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?