# Paper Airplanes for Measures of Central Tendencies

I got this amazing idea from Bruno Reddy, @MrReddyMaths.  Go and read his post here. I love his discussion about mean and deciding who should win!  When I saw his post I knew it would be fun.  I planned on using the data to calculate mean, median, and mode.  However, I did not realize how much mileage I would get out of this one activity!  I pretty much teach the entire data chapter using just the data from this one activity.

I have my students watch the “How to Make a Paper Airplane” video and give them the template.  I do not give them any instructions and do not allow them to help each other.  Following directions is always a skill I am trying to teach 6th graders.

After we make the airplanes, we get to fly them!  Of course, I make it a competition. And of course, I video it!

Everyone gets a partner, to help with measuring, and three attempts at the best flight!  Student’s whose planes fly backward get to record NEGATIVE flights.  All three flights are recorded and then entered into a Google Form.  For homework that night, they had to find the mean of their three flights.

Line Plots and Scale:

I have students make a line plot out of all three entries.  This year, I only had 21 students, so this is 63 entries.  This is a great time to talk about scale.   I have them record their distances in inches, but then they quickly realize that it is a much better idea to make the line plot using feet.  We find the mean, median, and mode of our data using our line plot.

Range:

Range is one of my favorites here, especially with the inclusion of the negative flights.  This year, our flights ranged from about -300″ to 600″.  Predictably, almost all students told me that the range was 300″.  Students love plugging values into formulas incorrectly.  To help correct this misunderstanding, I had my -300″ flight student and my 600″ flight student come to the front of the room.  I stood at the starting point (the edge of the blacktop for us, also known as 0) and had them stand where their respective planes had landed.  Students immediately not only saw that 300″ was way off, but they saw why.  This was a wonderful opportunity to show them that 600 – (-300) was indeed 900″, not 300″.  My analogy to help deepen understanding was, “You leave from Charlotte to fly to New York, but you have a layover in Atlanta first”!  Nothing is ever better than visual learning and real life examples.

Box Plots:

The next day we learned about box plots.  I project the line plot of our flight data and as a class we make it into a box plot.  They loved seeing that a box plot can helpfully catagorize  their data.  Outliers are visual here, as well as where 50% of their flights landed.  Next year I am going to take a picture of their airplanes laying on the blacktop to back this statistic up visually.

I also had the students create a box plot of their mean flight data.  They wrote their mean flight length (in feet) on a sheet of 8×11.5 paper.  Then, they organized themselves into a human box and whiskers plot.  The students who were the lower and upper extremes, Q1, Q3, and median all held index cards with the name on them.  We also decided who was in our interquartile range.

Histograms:

The line plot looks very much like a bar graph.  After a very brief explanation about histograms, we turn our line graph into a histogram.  The students love seeing their data grouped and of course ask why we didn’t do this in the FIRST place instead of making the tedious line plot.  It’s all for the sake of learning.  (Insert evil teacher smile.)