Factors and their multiples are so important to students’ work with fractions and number theory. These concepts come under the National Council of Teachers of Mathematics (NCTM) Number and Operations Standard for the middle grades. The resources here are all hands-on, if only virtually. Important to their success is the classroom talk that the resources generate.

**The Factor Game**

This is more than a game; it is a full lesson plan, complete with handouts, including the game board, and questions for discussion. Students practice finding factors and then analyze the winning strategies. It’s this analysis that leads them to talk about prime, composite, abundant, deficient, and perfect numbers. The plan is downloadable and printable. (See the online version below.)

**The Factor Game (i-Math Investigations)**

This is the same game but online and interactive. One advantage here is that a single student can play against the computer. What is missing, however, is the winning strategy analysis, so rich in discussion. If you decide to use this version, you can simply borrow the discussion questions from the pdf version above.

**Coloring Multiples in Pascal’s Triangle**

Good practice in finding multiples of small factors! Students roll a number cube, then color in the multiples of that number in Pascal’s triangle. As they click on all the multiples of the number rolled, they also practice multiplication and observe the surprising patterns that form in the triangle.

**Factor Tree (grades 6-8)**

The activity starts with building a factor tree, but then moves to finding common factors and reviewing those old friends: GCF (greatest common factor) and LCM (least common multiple). The student must first find the prime factors for a pair of numbers. After two factor trees are built, the student drags the prime factors from each tree to a Venn diagram, showing the common factors of the two numbers in an overlapping area. Finally, the student enters the greatest common factor and the least common multiple, which can be checked immediately. This activity is interactive, visual, and good review!

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**Middle School Portal 2**publications. You can also email us at msp@msteacher.org. Post updated 11/16/2011.