# Engaging students: Box and whisker plots

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This submission comes from my former student Jesse Faltys. Her topic: how to engage students when teaching box and whisker plots.

A. ApplicationsHow could you as a teacher create an activity or project that involves your topic?

Students can take a roster of a professional basketball team and create a box and whiskers plot by using the players’ stats of height and weight.  As the teacher, you can provide these numbers to them. The weight should be left in pounds, but change the height measurement to inches.  The students could be placed in groups of 3 or 4 and given different team rosters.  First, have the student calculate the minimum, maximum, lower quartile, upper quartile, and median for their roster for both the weight and height. Then, have the students place the plots on large sheets of paper and present to the class.  As the students compare their plots, they can begin to see what effects the range of data has on the construction of each box and whisker plot. Depending on the knowledge of the students you might want them to all working on the same team.  As the teacher, you can remove one player’s stats from each group effectively changing the box and whiskers plots and having the students analyzing the data’s effect on the plot constructed from the same roster.

I actually used this in a lesson during my Step II class in a middle school classroom. I used information from the Illuminations website at http://illuminations.nctm.org/LessonDetail.aspx?ID=L737.

B. Curriculum – How can this topic be used in your students’ future courses in mathematics or science?

Any science course with a lab will require you to complete a formal lab write-up.  The data collected from your experiment will need to be represented in an organized manner.  The features of a box-and-whiskers plot will allow you to gather all your information and make observations off the data that your group and the class as a whole collected.  This information can be combined into one plot or the individual lab groups can be compared for any inconsistencies. A box-and-whisker plot can be useful for handling many data values. It shows only certain statistics rather than all the data. Five-number summary is another name for the visual representations of the box-and-whisker plot. The five-number summary consists of the median, the quartiles, and the smallest and greatest values in the distribution. Immediate visuals of a box-and-whisker plot are the center, the spread, and the overall range of distribution. This documentation will allow the student to make a formal analysis while putting together their formal lab write-up.

E. TechnologyHow can technology be used to effectively engage students with this topic?

1. Khan Academy provides a video titled “Reading Box-and-Whisker Plots” which shows an example of a collection of data on the age of trees. The instructor on the video goes through the representations of the different parts of the structure of the box and whiskers plot.  For our listening learners, this reiterates to the student what the plot is summarizing. http://www.khanacademy.org/math/probability/descriptive-statistics/Box-and-whisker%20plots/v/reading-box-and-whisker-plots

2. Math Warehouse allows you to enter the data you are using and it will calculate the plot for you.  After having the students work on their own plots, you can have them check their work for themselves.  This will allow for immediate confirmation if the student is creating the graph correctly with the data provided.  Also, this is allowing the visual learners to see what happens to the length of the box or whiskers when changes are made to the minimum, maximum or median. http://www.mathwarehouse.com/charts/box-and-whisker-plot-maker.php#boxwhiskergraph

3. The Brainingcamp is another website that allows for interaction between the different parts of the plot and the student.  This website allows for the students to see a group of data and the matching box-and-whiskers plot.  The student can then explore by manually changing different values and instantly seeing a change in the graph.  This involvement can stimulate questions to direct the student to complete understanding of the subject.  As a hands on learner, it allows the students to manipulate the plot immediately in different “what if” situations. http://www.brainingcamp.com/resources/math/box-plots/interactive.php

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