Box Plots and Interquartile Range

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.

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. 

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.  

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.

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.

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.