Mean is so much more than just adding up all the values in a data set and dividing by the number of values. There are two useful interpretations for us to learn and teach when it comes to thinking about mean. The first interpretation is to think of mean as equal sharing, or “leveling off” – what would all the values in a data set be if they were divided up equally or leveled off. A second interpretation is to think of mean as a central balance point. This activity helps build a conceptual understanding of the first interpretation – equal sharing/leveling off. (For an activity exploring the central balance point interpretation of mean, check out Make It Balance.)

In this lesson, students develop their conceptual understanding of mean as equal sharing using visual representations of data sets and moving around number tiles. Students use virtual manipulatives and develop multiple strategies to both find the mean and find the missing value of a data set that results in a desired mean.

The full lesson plan, guides teachers on how to help students use the interactive workspace on the Mathigon Polypad to explore this visual representations of finding the mean of a data set and includes suggestions for a closing discussion as well as supports and extensions.