Calculating Mean: A measure of central tendency

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Objective

SWBAT find the mean of a given data set and recognize it as a measure of center.

Big Idea

Mean: The Center of Data Universe

Curriculum Reinforcer

10 minutes

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

Engagement

10 minutes

Today students will learn about Mean (Average). They will complete a learning task during instruction called “Fair Share.” This activity needs the following materials: Counter chips, and a mat with 5 characters at the bottom.

 

Activity: Each character at the bottom of the mat will receive a certain number of counter chips. Then, I will have my students redistribute the counter chips evenly among the characters to show how each character gets their fair share. This activity is to demonstrate the meaning of finding mean (gathering all the chips together – adding. Then, distributing them among the people – dividing). To ensure that they understand mean thoroughly, I will be sure to provide my students with an example where when the counter chips are distributed, they won’t be able to be distributed evenly and therefore will have a fractional answer. I will use the following amounts for each character.

  1. 5, 3, 6, 2, 4
  2. 5, 7, 4, 3, 6
  3. 2, 5, 3, 7, 4

 

A video of how I conduct this activity is attached to this section of this lesson.

Instructon & Teacher Modeling

10 minutes

Using the activity from the opening , I will ensure to demonstrate to students how finding the mean is a measurement of the center of a data set by placing all of the numbers on a number line and showing the students where the mean is in relationship to all of the numbers in the data set.

I will also be sure to demonstrate how to find the mean of a data set using the standard procedure which is to add all the numbers presented in the data set and then divide by the quantity of numbers in the data set. While showing students how to use the standard algorithm, I will ensure that I relate the steps of the standard algorithm to the activity from the opening exercise where students gave the characters, their "fair share."

Try It Out

5 minutes

During the guided practice, I will have the students find the mean of the following data sets using the standard algorithm:

 

  1. 6, 7, 5, 2, 5, 7, 6, 5
  2. 10, 15, 13, 12, 16, 13, 13

 

After the students complete these two exercises, we will then discuss any trouble the students ran into while finding the mean of each of these data sets.

 

Something to anticipate is difficulty with the division portion of the steps to finding the mean. Students seem to always run into issues when it comes to division.

Independent Exploration

20 minutes

To explore the concept of mean, the students will complete the worksheets attached to this section. 

There are a variety of worksheets available in this section to accommodate the several achievement levels that are present in most classrooms.

  1. You will find a worksheet that requires students to use the, "fair share" method to solving problems that involve the mean... There is a front and a back to this worksheet that are attached as separate documents. This worksheet comes from a reproducible workbook from, Houghton Mifflin Harcourt Publishing Company entitled, Core Standards for Math.
  2. You will also find a worksheet that puts the concept of finding the mean in a problem-solving context.
  3. the last worksheet that is available in this section is a worksheet that provides an enrichment opportunity for my higher achieving students. It requires more higher order thinking in order to find the solutions. This worksheet also requires a collaboration between students after they have finished their calculations. For this reason, I will ensure that the students have approximately 15 minutes to work on the problems in the worksheet and 5 to 10 minutes to collaborate with a partner that I will assign to them.
    • For low achieving students, they will be required to complete the first worksheet. If they complete that worksheet in the allotted time frame then, they can move on to the second worksheet, going as far as possible. Any problems that they are not able to solve in the given time, will have to be completed for homework.
    • For average students, they will be required to complete both the first worksheet as well as the second worksheet.
    • The higher achieving students will be required to complete the first and the third worksheet.

 

Closing Summary

15 minutes

To close out this lesson, I will select several students to present one of the problems that they completed on any of the three worksheets. 

  • Lower achieving students will be chosen to present a problem on the first worksheet.
  • Average students will be chosen to present a problem on the second worksheet.
  • Higher Achieving students will be chosen to present a problem on the third worksheet.

Students are to explain the process that they utilized to arrive to their solution while using precise mathematical language.

The observing students will be ready to ask questions, critique, and comment based upon what is presented.

 

TOTD: Students will answer the question, what does it mean to find the mean?.