# Body Graphing

Here’s another wonderful activity I learned at the Dana Hall Math Conference.  I’ve written about more activities I learned there HERE and HERE.

Set up a Cartesian plane with x and y-axes wherever you have outdoor space at your school.  You can use chalk if you have a blacktop, or string, or cash register receipt rolls.  Label the axes, and label the scale on each one.  Ask students to choose a spot on the x-axis, (and make sure that some choose negative numbers).  Take a portable whiteboard with you (or you could prepare some paper ahead of time), and write a function of x (e.g. y=2x+3).  Ask students to “act out” their x-coordinate on the plane.

My students got the hang of this quickly, but they also appreciated the challenge.  You can make this a mental math practice by giving targeted, or more complicated equations.  Or you can give them paper or whiteboards on which to calculate.  It worked well to illustrate functions – whenever one student was not “in line” with the others, it was obvious that something was wrong, and there was rich discussion about how to fix the problems.  It also showed in a memorable way where linear functions got their name (That was my exit ticket question for the day).

I had really good success with this, and the kids very much appreciate getting to go outside.  I recently did some professional development with an expert on brain development, who suggested that kinesthetic activities like this really cement concepts in kids’ memory as well.  An outside location was important because we could effectively illustrate how quickly some functions grow (compared to others) by allowing real distance for exponential functions.

I came up with an extension on the fly that seemed like a good idea, but didn’t work out so well.  I’ll share it in case someone has a thought about how to make it work better.  I asked one kid to come up with a function, and bring the other kids to x,y coordinates that fit their function.  Then I asked other students to try to identify the function.  It seemed like it should have been rich, but it fell sort of flat.  Please share any idea that might improve this.

There are definitely other variations on this lesson floating around, including this example, specifically geared toward slope-intercept form.

In a related post, Michael Pershan writes a nice post about functions HERE.  I especially love the yarn.  There is something wonderful about the aesthetic sensibility; about how that slightly sad piece of yarn is elevated by giving it “function” status.  While we’re on yarn, check out the yarn work from Minneapolis artist, Hot Tea.  I’m not sure how yet, but I’m confident that these artworks will have a classroom use at some point.

## 3 thoughts on “Body Graphing”

1. Barry Lewis

I love the kinesthetic dimension here, especially the ways that it can amplify the clicking sounds that happen when students use calculation to verify their estimates. “It looks like I’m standing on (3, 4). I wonder if I’m right?” Yes. By all means. Please bring us another round of “I wonder.”
A possible change-up to your extension: working in groups of 4, have two students claim spots on the plane NOT on either axis. Then, have two other students stand on the x- and y-intercepts (of that line). Ask them to estimate their locations. Ask them to verify. Also, I wonder what could be done with four kids taking up random locations and a fifth staking out the point of intersection. This could be wild with several teams working at once o the same Cartesian lawn!
Along your same lovely lines of outdoor adventure math, here’s PumphreyMath’s Sidewalk Chalk .

1. Nat Post author

Hi Barry,

Thanks for the suggestions. I’ll definitely try the student linear teams in some way next time I do this, and I’ll keep you posted as to how it goes. The sidewalk chalk sounds great both to get us outside, moving around, and doing giant math, but also makes our work public in a way that celebrates both our understandings and our mistakes. Thanks for your thoughts!
-Nat