Andrea Palmer PROSPECT HILL ACADEMY CHARTER SCHOOL, SOMERVILLE, MA
6th Grade Math : Unit #9 - Statistics : Lesson #15

Box Plots and Interquartile Range

Objective: SWBAT: • Identify and label the minimum, maximum, lower quartile, upper quartile, and median of a data set and box plot. • Define and identify interquartile range. • Analyze and compare box plots.
Standards:
Subject(s): Math
60 minutes
1 Do Now - 7 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 DynaMath  typically includes a graphs in each edition.

I ask for students to share their thinking.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

2 Problem - 5 minutes

I introduce the problem to students.  I want students to apply what they already know about box plots from the previous lesson.  Students participate in a Think Write Pair Share.  I walk around and monitor student progress as they work.

I call on students to share out their ideas.  I push students to support their idea with data from the set.  I want students to notice that although Thaisha and Thaima have the same median about of money earned, their data sets are not identical.   I also want students to notice that the size of the box is different for each box plot.  If this comes up, I ask students what they think this tells us about the data sets.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others and MP2: Reason abstractly and quantitatively

3 Measures of Center vs. Measures of Variability - 8 minutes

I call on students to read and fill in the definitions for the measures of center.  I explain the difference between measures of center and measures of variability.  I introduce the concept of interquartile range.  We work together to calculate each measure for Thaisha and Thaima’s box plots.  I want students to see that the box in Thaima’s box plot is longer, which means that the middle 50% of her earnings are spread between $84 and $94.  Thaisha’s box is shorter, and her middle 50% of her earnings are spread between $85 and $90.  

How can you tell which IQR is higher?
Discourse and Questioning

After we went through and calculated all of the measures for Thaisha and Thaima, I asked, “How can you tell which IQR is higher?”  Students participated in a Think Pair Share.  Students shared that they could tell that the IQR for Thaima was higher since the rectangle was longer. 

My next question was, “What does that tell us?”  A student shared that it meant that the middle 50% of Thaima’s earnings had a wider range than the middle 50% of Thaisha’s earnings.  At this point in the lesson, some students were still unable to explain this fact.  I continued to ask this question throughout the lesson to ensure that students could not only define and calculate the IQR but that they also understood what it told us about the data set.

4 Creating a Box Plot - 7 minutes

We work together to use the data set to create a box plot.  A common mistake is for students to immediately start to find the median of the data set without reordering the values from least to greatest.  I start to make this mistake and ask students if they agree or disagree with my action and why. 

For the last two questions, students participate in a Think Write Pair Share.   I want students to be able to explain that the IQR shows the range of the middle 50% of the data.  Even though the range of the entire team is 9 inches, the range for the middle  ½ of the players on the team is 3 inches.

5 Practice - 13 minutes

Notes:

  • Before this lesson, I use the tickets to go from the previous lessons to Create Homogeneous Groups of 3-4 students.
  • I also use the ticket to go data to determine which practice page each group should start on.
  • I create and Post a Key around the room.
  • I copy a Group Work Rubric for each group.

I review expectations and students move into groups.  I tell groups which practice page to start on. Different groups will work through the practice pages at a different pace.  My goal is that I have grouped students so that they are working at a similar level for these practice problems.  Students are engaging in MP1: Make sense of problems and persevere, MP2: Reason abstractly and quantitatively, and MP3: Construct viable arguments and critique the reasoning of others. 

As students work, I walk around and monitor student progress and behavior.  If a group of students complete a page, I quickly scan their work.  If they are on track, I send them to check their work with the key.  If students are struggling, I may ask them one of the following questions:

  • What is the question asking?
  • What does this point represent?
  • What is does this part of the box plot tell us?  How do you know? 
  • What is a quartile? 

If students complete the questions they can work on the challenge problems.

6 Closure and Ticket to Go - 10 minutes

I ask students to flip to the closure problem.  I ask students how the weekly hours compares between Sarah and DeShawn.  I explain that they need to write 5 observations by analyzing the box plots.  I also want them to think about the two other questions about IQR.

Students participate in a Think Pair Share.  Students are engaging in MP2: Reason abstractly and quantitatively and MP3: Construct a viable argument and critique the reasoning of others

I call on students to share out their observations.  I push students to use accurate language and to use the box plot to support their observation.  I want students to recognize that the IQR for DeShawn’s weekly hours is smaller than the IQR for Sarah’s hours.  This means that the middle ½ of Shawn’s weekly hours have a range of 4 hours.  Sarah’s IQR is larger because the middle ½ of her weekly hours have a range of 8 hours.  I want students to see that Sarah’s data is symmetric and DeShawn’s data is skewed.  Students are engaging in MP6: Attend to precision

I pass out the Ticket to Go and the Homework.

How many weeks are included in Sarah's data set?
Discourse and Questioning

During the closure, I also asked, “How many weeks are included in Sarah’s data set?”  I called on students to share their observations.  I wanted to make sure that students understood that just by looking at a box plot they cannot tell the number of values in the data set.  This can be confusing to students when they are just learning about box plots, since you can determine the values in a data set from most other types of graphs.