I hate to say I told you so, to Kathleen Porter-Magee regarding her CCMS+Bungee Barbie = Epic Fail blog post, so instead, I'll say NA NA NA BOO BOO! This was the most fun I've probably had in any math class EVER! For my students too! My other classes can't wait to try it out for themselves. And guess what... we actually LEARNED a few things!
A little background, for those who have not been following my blog long: the article above insinuates that the Bungee Barbie lab boils down to throwing barbies around the room, and that students don't really get a good grasp of linear equations from the experiment. I have concretely and soundly proved this WRONG. Or my students did anyway.
Over the past few weeks, my accelerated class has been learning how to calculate slope using "rise over run", making steps on their coordinate grids, following the online analogy of "Joan the Chameleon" to graph lines using slope intercept form. We then took the concrete visual/kinesthetic approach to a more mathematical, algebraic understanding, playing with x-intercepts and y-intercepts, solving equations for both variables, and making input/output tables to demonstrate linear patterns in the numbers.
Upon introducing the Barbie problem this past Monday, I gave them a simple ratio tool from my own trial, stating that I tried 2 rubber bands, and Barbie fell around 48 centimeters. They were asked to predict intuitively or mathematically how many rubber bands they would need to drop a doll to a height of 530 cm (That is the distance from the top rail of our balcony to the floor below). Predictions brought forth various comments on weight of the dolls, elasticity of the rubber bands over time, and ability to accurately measure the drop height. They also named their dolls (the headless Ken doll, now called "Leonardo", as well as "Tape" and "Ian" for Barbies) and to practice the slip knot method for 2 bands, as well as the drop motion to be used.
On Tuesday and Wednesday, students practiced and perfected drop measurements; many decided to redo data that did not seem accurate, or to adjust the number of rubber band inputs to meet the height constraints of our 2.5 meter - high upstairs ceiling. I suggested trying odd numbers of rubber bands, instead of the even numbers given in the spreadsheet, as 10 and 12-bands made all the dolls hit the floor. We determined that our rubber bands were bigger than were probably used in the initial design of the experiment. Groups then averaged their data, plotted their coordinates, and drew best-fit lines.
The REALLY cool part of the project came on Thursday, when groups were able to calculate the equation for their best fit lines. There were moments of real joy and understanding when they realized that the y-intercept of the equation, the value of x=0 (no rubber bands), was the height of the Barbie herself! This prompted many students whose best-fit lines didn't seem quite right, to go back and measure their actual doll, in order to write a more accurate equation.
Other break-throughs came when I asked students what their "3 boxes rise / 4 boxes run" slope actually meant. I queried, "are you counting by 1's on either your x-axis or your y-axis?" Student response: "ummm, no?"... my response: "then what do 3 boxes actually represent from your experiment?".... pause.... thinking... "Oh! That's the height of the drop!".... my response... "and so what did you count by?"... student response: "We counted by 20's... AH! So the rise of my slope is SIXTY!!!" ... I prompt the same question for the x-axis... pause for thinking... "AH HA! That is for 2 rubber bands! We skipped every other line!" (queue heavenly music of bliss as actual learning takes place)
It didn't take much more prodding for students to interpret their slope as a unit rate, shrinking their 60 cm/4 rubber bands to roughly 15 cm per band. Then they could set up their slope intercept equation, and actually get a visual, kinesthetic, tactile interpretation of y=mx+b with "m" as their drop rate, and "b" as the Barbie height. Solving for the equation of 530=15x+30 was an absolute cinch. They had that down for over a week.
But now it MEANT something.
Leading into the actual drop test on Friday, with all Barbies poised on the cliff... and the final drop challenge proved a little more complicated. Groups found out quickly when their Barbie hit the floor, or only dropped to the ceiling of the floor below, that their experimental bands had stretched out. About half of the groups had taken into account the variables of aging/usage of the rubber bands, as well as the weight of the doll and the slight added pull of gravity from the greater height. Theirs were the drop heights of 18, 36, 40, and 48 cm's from the floor. The top two groups actually tied, with heads dropping to a dare-devil 15 cm's from the ground. No one had a clear photo, and even after two trials, I couldn't venture to declare a winner. So both groups will get silly bragging rights certificates on Monday.
We then returned to the classroom where students were given reflection time; to think about why their dolls exceeded or failed to reach an appropriate drop height. Were their predictions correct? How did their experimental accuracy help or hurt their data analysis process? What tips might they use in the future to minimize error?
I was greatly pleased to see that several students chose to take their packets home, to continue reflecting over the weekend, rather than rushing through answers to get it turned in today. How many would have done the same thing, had it been a boring old pencil and paper test? Fewer, I'm sure. One thing I do know for sure... they will never forget the day that Barbie plummeted off the balcony. And I wouldn't be surprised if they remember some of the math behind it too.