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This lesson will help students understand the concepts of range, median, mode, and mean through the use of graphs drawn from models.
Many students can calculate the range, median, mode, and mean of a set of numbers. But if asked what that looks like, students have difficulty expressing these concepts. This lesson will help students understand the concepts of range, median, mode, and mean through the use of graphs drawn from models. Students will use manipulatives to represent data that they have collected within groups. By using models, students can compare the differences between mode, median, and mean. Students should understand that the mean, median, and mode are just different ways of calculating what the middle is in a set of data. The range will be represented visually as students arrange their models from smallest to greatest. As students show a representation of the mean, the teacher can lead a discussion on the meaning of what the remainder represents. Depending on the students background knowledge, the teacher can either have the students disregard the remainder or model how the remainder can be represented in fraction or decimal form.
2. Become mathematical problem solvers.
4. Communicate mathematically.
5. Make mathematical connections.
6. Represent mathematical situations.
Invitation to Learn
Display a set of objects such as various sizes of crayons on the overhead. Ask the students if they can tell what the average length is in the set of crayons. Who can draw a picture on the board of what an average looks like? When do we use averages?
Have the students measure each member in their family and record the results. Use the information in a daily activity where students calculate the mean, mode, median, and range for the heights. Ask the students if they can tell by the data the age of the family members as it applies to range.
Lappan, G., Fey, J., Fitzgerald, W. Friel, S. & Phillips, E. (1996). Data about us. Connected Mathematics Project, Palo Alto, CA.
The mode, median, and mean are kinds of averages that are a part of representations and statistics used to analyze data. Students need to understand each of these measures and how they are applied and calculated. This article examines two ways in which the concept of mean can be demonstrated.
Hitch, C. & Armstrong, G. (1994). Daily activities for data analysis. Arithmetic Teacher. 41(1) 242-245.
Children develop mathematical concepts by seeing them in a variety of settings. For students to understand statistics and graphs, they need exposure to the process of collecting, organizing, and describing data. This article describes useful activities that help students understand and display data.