Mean

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Objective

SWBAT: • Define and identify the mode, mean, median, and range of a data set. • Create values in a data set that will have a particular mean. • Compare data sets and make observations.

Big Idea

What does the mean mean? Students work with blocks to understand that the mean is a number that evens out a distribution.

Do Now

6 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to analyze a line graph in order to answer questions. Each edition of Scholastic Action  typically includes a graph on its back page.

I ask for students to share their thinking.  I am interested to hear about the strategies students used to determine the answer to question 3.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Review

5 minutes

I have students work in partners to complete this review from the previous lesson.  The most common mistakes I see are that students confuse the median, mean, and mode.  I want to make sure students understand what each term means and how to find it.

Mean

7 minutes

Notes:

  • Before this lesson, I use the exit tickets from the previous lesson to Create Homogeneous groups of 3-4 students. 
  • Each group will need a set of cubes to work with.
  • Each group also gets a Group Work Rubric.
  • I create and Post a Key.
  • Before this lesson, I use the household data from the previous lesson and I fill out the “Analyzing Our Data” for each of my classes.

Students move into groups and I pass out materials.  I have volunteers read through the notes about mean.  Together, we work on Data Set A.  I model what I mean by “leveling” the stacks of blocks that represent the number of people living in a household.  I want students to understand that we are just evening out the distribution of blocks between the different numbers of people.  I make sure that when groups level out their blocks they still have 5 stacks of blocks, since there are 5 people in the data set.  

Group Work

22 minutes

Students work in their groups while I walk around to monitor student progress and behavior.  Students are engaging in MP2: Reason abstractly and quantitatively and MP6: Attend to precision.  When groups finish “More Mean Practice” they raise their hand and check in with me.  If they are on track I send them to check their work with the key.  If they are struggling, I may ask them to revisit a problem or a may ask them questions:

  • What is the definition of the mode/median/range/mean?
  • How do you find it?
  • What is a strategy you can use to find the mean?
  • How can you create a data set that has the same mean? 
  • How can you prove that your data set has the same mean?

When students finish “Comparing Means” I check in with them again.  If they are on track, they will work on “Analyzing Our Data”.  If groups complete all of this work, they can work on the challenge problems.

Closure and Ticket to Go

10 minutes

I ask groups to share out what they calculated for the mean of our class’ data.  I have students turn to the closure questions.  I have students participate in a Think Write Pair Share.  I ask students to share their ideas with the class.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others and MP4: Model with mathematics.  I want students to realize that a mean can be a decimal if the sum of the data values is not divisible by the number of values in a data set.  I also want students to connect their knowledge of mean or average to the do now.  If the average concert ticket in 2012 was $69, they calculated that value by adding up the different costs of the concert tickets and then divided by the number of values. 

I pass out the Ticket to Go and the Homework.