ALEX Learning Activity

Factors...Multiples...Game On!

A Learning Activity is a strategy a teacher chooses to actively engage students in learning a concept or skill using a digital tool/resource.

  This learning activity provided by:  
Author: Kimberly Dockery
  General Activity Information  
Activity ID: 2699
Factors...Multiples...Game On!
Digital Tool/Resource:
Illuminations: Product Game
Web Address – URL:

The Illuminations tool, Product Game, is an excellent resource for students to gain a deeper understanding of factors and multiples. This tool challenges students to make offensive and defensive moves to obtain four products in a row by selecting factors ranging from one to nine. The challenge comes when one of the factors must be from your opponent’s last move. Students can either play against the computer or with a partner in their class.

GCF Venn Diagrams

Product Game Reflection

  Associated Standards and Objectives  
Content Standard(s):
Digital Literacy and Computer Science
DLIT (2018)
Grade: 6
6) Identify steps in developing solutions to complex problems using computational thinking.

MA2019 (2019)
Grade: 6
7. Use the distributive property to express the sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor.
Learning Objectives:

Students will:

  • find common factors of two given whole numbers.
  • explain offense and defense steps to win the Product Game.
  • demonstrate the difference between factors and multiples.
  • identify the steps in their offensive and defensive moves during gameplay to demonstrate computational thinking.
  Strategies, Preparations and Variations  

Prior to completing this activity, students need to understand the difference between multiples and factors. A multiple of a number is the product of that number and any nonzero whole number. A factor is a whole number that divides another whole number with a remainder of zero. Any number is always divisible by all its factors.

Pass out the GCF Venn Diagrams. There are ten different combinations. You have the flexibility to have students complete one or all of the Venn Diagrams. Some are more challenging than others to accommodate student’s different ability levels. Students will then list all the factors of the two numbers and complete the Venn Diagram by placing common factors in the middle. Understanding common factors between two numbers is an important step to be successful in the Product Game. Then students will discover the GCF by identifying the largest number in the middle. 

Have students access the Product Game and play a few rounds. One student will move one marker to make their first move. The resulting multiple will be identified on the gameboard. The next player can only move one of the two markers to create another multiple as their move on the gameboard. The object is for each player to get four moves in a row either horizontally, vertically, or diagonally. Students can either play against the computer or with a partner. Finally have students complete the Product Game Reflection. This will require them to think about how the game works and connect how to make strategic moves to win the game.

Assessment Strategies:

3-2-1: Have students list 3 new things they learned, 2 questions they still have, and 1 connection they made while playing the Product Game.

Teacher observation of students while using the digital tool Product Game.

Review students' responses to the Venn Diagram and/or Product Game reflection to assess student understanding.


Advanced Preparation:

Each student or pair of students will need an electronic device.

Ensure Internet access is available.

Make copies of the GCF Venn Diagrams.

Make copies of the Product Game Reflection.

Variation Tips (optional):

  • The GCF Venn Diagrams could be set up around the classroom as stations to allow students the opportunity to move.
  • Have students play after they complete the reflection task thinking about strategic moves.
  • Change the settings within the game to include more factors. This can be done with the customize button on the left of the game board.
Notes or Recommendations (optional):

If multiple days are available, create a class tournament using the Product Game. Depending on the class size, use single or double elimination.

  Keywords and Search Tags  
Keywords and Search Tags: Factor, Factors, Game, Interactive, Multiple, Multiples