Venn diagrams are one of many tools used in logic and reasoning. Their use is especially helpful in learning foundational notions of definition and set theory. One of the five Process Standards promoted by NCTM, Reasoning and Proof requires middle school students to sharpen such skills as they learn to develop mathematical argument.

**Venn Diagram Shape Sorter**

A good activity for introducing the concepts of definition and set! Students move various shapes, available in two sizes and three colors, into a circle. By seeing which figures are accepted into the circle, they determine the rule guiding the circleâ€™s selection. In a more complicated example, a Venn diagram of two intersecting circles is used, requiring that two rules be stated.

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

Students first find the prime factors for two numbers. These are displayed in tree diagrams from which the student drags the factors to the appropriate areas of a Venn diagram. The Venn diagram offers a useful visual display showing unique factors and common factors for the original pair of numbers. Using the display, the learner must find the pair’s least common multiple (LCM) and greatest common factor (GCF).

**Venn Diagrams**

This virtual manipulative with an interactive three-circle Venn diagram can be used to model set operations for union, intersection, and subset. For each statement, the student highlights the region that is the solution, then clicks a button to find out if the solution is correct.

**Who Played the Raptors?**

In this online activity, students analyze predictions made by sportswriters about which basketball teams will win to determine which teams are playing each other. The solution illustrates and explains three different ways to successfully organize information, including using a Venn diagram.

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