Paper Airplanes for Measures of Central Tendencies

IMG_6886I 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.

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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.

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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.

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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.)

Google Doc Data:

I shared the data with the students and we then all made bar graphs and histograms on Google Spreadsheets.  The students like the histograms better as it condensed the data into groups.  They also learned how to sort the data and find the mean using a formula.  Again, they love finding the mean using spreadsheet formulas, find it less “mean” than calculating it by hand, and call me a “mean” teacher for not showing them this in the first place!  Practice makes perfect.

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18 thoughts on “Paper Airplanes for Measures of Central Tendencies

  1. I’m going to be using this idea during my data analysis unit in a few few weeks. I like how you introduced the range and how students began to realize that it can include negative numbers. This can be tricky for some. My class will be doing a similar activity once the snow has melted. Thanks for sharing.

  2. Super fun lesson here, Julie. Thanks for sharing. Can I ask about Google Forms? If there’s anything it didn’t do for this lesson that you wish it would do, what would that be?

    • Hi Dan, thanks for visiting.

      There is one thing that would help me out with Google Forms. When students enter data into the form, I cannot request a specific format for their input (as in “numbers only”). Instead, I include directions in the question. The directions in this form say, “ONLY enter the numbers, do not enter in, inc, inches…” However, some students still add the word in, inches, in., inc, and the ” symbol. Spreadsheets cannot calculate words so I have to go back and edit these entries before we can work with the data. Thank goodness for Find, Replace, but it still takes a while.

      The only other thing I have is when you edit a form to add a question, it puts that question in the last column in the corresponding spreadsheet, instead of where the question is in the questionnaire. Or, if you rearrange your questionnaire, the corresponding spreadsheet does not rearrange. This is important when I want my students to create scatterplots in Google Spreadsheets, because unlike Excel, the columns must be adjacent to each other. I can move the columns around once the data is entered, but that is an additional step I must do after the last student fills out the form, but before the students can work with the data. We often collect data and then begin working immediately so this sometimes creates a lag.

  3. Pingback: My All Time Favorite Middle School Math Lessons | I Speak Math

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