Playing with Measures of Central Tendency

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Objective

SWBAT: • Calculate the mode, mean, and median of a data set. • Make a prediction of how a new value will affect the mean, median, and mode. • Explain how a new value in a data set will affect the mean, median, and mode.

Big Idea

What will happen to the mode, median, and mean of data set when you add a new value? Students work to make predictions and understand how new data will affect measures of central tendency.

Do Now

8 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. Scholastic News  has a 5th-6th grade edition that 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.  I ask students what we should get when we add up all parts of a circle graph.  I want students to understand that the entire circle graph represents 100%.  I also want students to realize that this circle graph is not accurate because the sum of all of the pieces is 99%.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Review

8 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. Another common mistake is that students divide the new sum by 5 rather than 6.

Problem two gets to the big idea of this lesson.  It is important that before calculating the changes, students make predictions.  I ask students to share out their findings for problem 1 and 2.  I ask students:

  • Why did the mode and the median stay the same?
  • Why did the mean change?

I want students to understand that the mode stayed the same, since $3 is still the value that occurs most often.  The median stayed the same, since $3 is still in the middle.  The mean increased because we added a game that was more money.  Our new sum was $30, and we divide it by 6 since there are now 6 games.  Some students may not see this pattern yet, and that is okay.  I want students to start to recognize and anticipate how changes will affect the mode, median, and mean of a data set during their group work.

Buying Games

22 minutes

Notes:

  • Before this lesson, I use the exit tickets from the previous lesson to Create Homogeneous groups of 3-4 students. 
  • I copy sheets A-E and place them in the back of the room.
  • Each group also gets a Group Work Rubric.
  • I create and Post a Key.

Students move into groups and I pass out materials.  We work together to calculate the mean, median, and mode of the six games.  I have a volunteer read the directions for the groups.  I make sure that students understand that with each new problem, they are starting with the original set of six games and making a change.

Students work in their groups while I walk around to monitor student progress and behavior.  Students are engaging in MP2: Reason abstractly and quantitatively, MP6: Attend to precision, and MP8: Look for and express regularity in repeated reasoning.

If students are struggling, I may ask them one or more of the following questions:

  • How do you calculate the mode/median/mean?
  • What do you think will happen with this new piece of information?  Why?
  • How did your prediction compare with the new mode, median, mean?  Why is this?

If students are on track and need some extension I may ask them one or more of the following questions?

  • What will happen if you add another game that is more than the original mean? Prove it.
  •  What will happen if you add another game that is less than the original mean? Prove it.
  •  What will happen if you add another game that is the same price as the original mean? Prove it.

When students finish a page, I quickly check in with them.  If they are on track, I let them use the key to check their work and move on.  If groups complete all of this work, they can work on the challenge problems.

Closure and Ticket to Go

12 minutes

I ask students to share what patterns they noticed when they added a new game to the original six games.  Students participate in a Think Pair Share.  I want students to be able to anticipate how a new piece of information will affect the mode, median, and mean of a data set.   Students are participating in MP3: Construct viable arguments and critique the reasoning of others and MP8: Look for and express regularity in repeated reasoning.

If I have time I ask students, “What if we add one game to the original set and the new game causes the mean to change from $7 to $8.  How much did the new game cost?”  Students participate in a Think Pair Share.   I am interested to see the strategies students use.  Students should be able to understand that the new game must be more than the original mean of $7.  Some students may guess and check.  Other students may work backwards and realize that the sum of the 7 games must equal $56, since 56 divided by 7 equals $8.

I pass out the Ticket to Go and the Homework.