Mean as balance point and fair-share: The goal of this lesson was for students to understand the mean as a balance point and fair-share. To begin this lesson, we first asked each student what their interpretation of the mean is with the intention of creating a discussion. To see that students had a conceptual understanding of the mean, after they all explained their interpretation, they were then asked to compute the mean for a random set of data. Our main activity consisted of finding data as a group, we asked how may people they have in their immediate family. This data is collected through a quick survey of our group members, with a total of six pieces of data for our collection. You are able to adjust the number of people in certain families in order to get a “nice” mean if you wanted to. Through manipulatives, the students can explore the different ideas of balance point and fair-share. For example, we used Unifix cubes in order to demonstrate the different representations of the mean. After we showed examples of the fair share, we asked the students to do the same thing by exploring with the manipulatives. We asked them questions in order to get them thinking about how the fair share is represented. We did the same with the balance point as well, we showed examples and then let the students gain a greater understanding through their exploration with the cubes. The format of our lesson is included below:
My rating of this activity would be a 5, where 1 is low and 5 is high. This activity was able to determine the difference between fair share and balance point. The students were able to see how the balance point is shown on a graph, but also how you can find the mean by the concept of a balance point on a graph. When introducing fair share, the students were also able to see how combining all of the data points with the cubes and then redistributing them into equal points gives a representation of the mean. Overall, this activity allows the students to gain a greater conceptual understanding through experimentation as well as observing the examples to illustrate the differences. Relating to the CCSSM Probably and Statistics Standards for grades 6-8, this lesson allows for a student to understand a measure of center and summarize a data set in relation to it’s context. When referring to the GAISE report, these students align with this report’s recommendations because truly understanding the data and the mean, with a deeper understanding of how the mean can represented, is the first step of moving a Level A student to a Level B student.