line of best fit — On teaching

I bought a 1-lb bag of rubber bands for my Barbie Bungee activity today.

We should have done Barbie Bungee earlier in the year while learning linear equations and lines of best fit, but better late than never. My collection of Barbies could use some refurbishing work — they get used so much each year for this activity and for our lesson on proportions.

OBJECTIVE: Create a bungee line for Barbie to allow her the most thrilling, yet SAFE, fall from a height of 3 meters.

I randomly assigned students to groups of three. Each group got their own Barbie and 7 new same-size rubber bands. My instructions:

Measure Barbie's height. Record this as rubber band length of 0.
Connect 2 rubber bands with a slip knot.
Wrap one of the two rubber bands tightly around Barbie's ankles.
Drop Barbie, holding the rubber band level with the meter stick.
Record Barbie's fall using the lowest point her head reaches in centimeters. This number is your rubber band length of 1. (The rubber band around her ankle is not counted in the length of the line.)
Add another rubber band, drop Barbie, and record. Do this for a total of six rubber band lengths.

Measuring: They quickly went to work. (We're lucky to have good weather here pretty much year-round because I need some students to be outside whenever we do projects like this — they need to spread out to do the work.)

Graphing: The groups graphed rubber band lengths vs. distance of fall. Then they drew in the line of best fit. From this line, students predicted the number of rubber bands for Barbie's bungee line that would be thrilling enough for her 3-meter jump without cracking her head open!

Once groups made their prediction — written on their papers and on the board — they may not change it. I had taped a small ruler to that rod to mark the 3-meter height. I can't have students on the ladder, so that's me getting ready to drop a Barbie. (The numbers on the left were their initial guesses before doing anything else.)

This was a blast!! I had two kids lying on the ground with meter sticks to watch and measure Barbie's initial plunge; they were our judges. We clearly had a winning jump when one group's Barbie came within 2 cm of the floor. They asked if they could get a second chance, so all 10 dolls had another jump after adjusting the number of rubber bands on the bungee line.

What I heard around the room

I noticed the centimeters went up by 10 on average.
Her height is the y-intercept.
Nine rubber bands is approximately 100 cm, so we need...
Stop stretching the rubber bands, you're gonna ruin our estimate!
Each meter stick is 98 cm. (His two teammates did not say anything when they heard this!)
I have to re-do our graph. I stuck it too close to the top, and the line of best fit has nowhere to go.
You're not supposed to connect the dots!
This was so much fun!
Oh, I didn't realize how stretchy the rubber bands got. (To which another student said, "Hello, it's rubber."
Ken is heavier [than Barbie]. We forgot this.
Hair centimeters! She was that close!

Notes

Barbies are Barbies. My kids are used to handling the dolls, a few of them have no clothes on (I got many of them on eBay). But I start every lesson with my usual warning that if I see anything remotely suggestive or derogatory done to the dolls, the student would be sent to the office and not be able to return to my class until I spoke with his/her parent. There has never been a problem in the last 8 years. The same applies to the rubber bands.

Handout