Lesson 3

The Meaning of the Mean

Est. Class Sessions: 2–3
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Mathematical Standards

4.MD.A
Solve problems involving measurement and conversion of measurements. (4.MD.A.2)
4.MD.B
Represent and interpret data. (4.MD.B.4)
4.AO.A
Use the four operations with whole numbers to solve problems. (4.OA.A.3)

Standards for Mathematical Practice

MP2.
Reason quantitatively.
MP3.
Construct viable arguments and critique the reasoning of others.
MP4.
Model with mathematics.
MP5.
Use appropriate tools strategically.
MP6.
Attend to precision.

Students use adding machine tape to model the process of finding the mean of a set of data through measurement. They then learn to find the mean on a calculator by summing the data and dividing by the number of data points. Students also explore line plots as a way to organize data to find the median.

Content in this Lesson

  • Investigating the concept of averages as a representative value for a data set.
  • Finding the median of a data set [E5].
  • Finding the mean of a data set using manipulatives and numerical procedures [E6].
  • Making predictions and generalizations using averages [E8].
  • Measuring to the nearest centimeter [E9].
  • Using line plots to find the median of a data set.
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Materials for Students

Daily Practice and Problems Lesson Homework Assessment

Student Books

 Student Guide
Student Activity Book

Teacher Resources

 Teacher Guide - digital

Supplies for Student Groups

roll of adding machine tape
meterstick
scissors
tape
calculator
ruler
crayon
80 connecting cubes or 120 square-inch tiles

Materials for the Teacher

Display of Two-Column Data Table (Teacher Guide) Page 113 or chart paper for class data table
Unit 5 Assessment Record

Materials Preparation

Paper Strips. To decrease time students need to measure and cut the tape, tear strips of adding machine tape that are about 60 cm long. Groups can then cut the strips the lengths of students' head circumferences.

TIMS Tip

Since string stretches, measurements with string may not be reliable. For this reason, adding machine tape is preferable, if available.

Assessment in this Lesson

Assessment Expectation Assessed

The Meaning of the Mean
Check-In: Questions 13–15
Student Guide
Page 183
E5.
Find the median of a data set.
E6.
Find the mean of a data set using manipulatives and numerical procedures.

Cookie Factory with
Feedback Box
Teacher Guide - digital
E5.
Find the median of a data set.
E6.
Find the mean of a data set using manipulatives and numerical procedures.
E8.
Make predictions and generalizations using medians and means.

Practice Finding Means
Self-Check with menu
Student Activity Book
Page 153
E6.
Find the mean of a data set using manipulatives and numerical procedures.

Vocabulary in this Lesson