Estimated Time
1 day
Prerequisites
- Familiarity with scatter plots and lines of best fit.
- Knowing how to obtain the equation of a line from its slope and y-intercept.
Materials Needed
- Each team will need a toy doll, a supply of rubber bands, a measuring tape (or meter stick), and some sticky dots or masking tape to mark each bungee jump.
- Each student will need a copy of the activity pages and a sheet of graph paper.
- A graphing calculator or access to the online applet will be needed by each team if they elect to do the linear regression step 6.
Ohio Standards Alignment
Topics
Scatter plots, linear functions, slope-intercept equation of a line, representation
Overview
Students determine the length of a bungee cord made of rubber bands that will allow a toy doll to fall as close as possible to the ground without hitting it. Teams of students collect data using cords of varying lengths up to 6 or 8 rubber bands. Then they graph these data, determine a trend line and its equation, and extrapolate to the desired distance the doll is to fall. Activity sheets, a solution to the problem, and links to the NCTM site that inspired the problem are included.
Learning Objectives:
- Collect data, construct a scatterplot, and determine a line of best fit.
- Develop an equation of this line and solve the equation to predict the maximum number of rubber bands that will allow the doll to safely jump from a given height.
The "Hook"
Present a short scenario about bungee jumping, and ask the students if the length of the bungee cord and a person's size matter when they are bungee jumping.
Critical Question
Would you want to lie about your height or weight before you make a jump?
Tell the class that they will work in teams to make bungee cords for a toy doll.
Critical Question
How many rubber bands looped together will give this toy doll the most thrilling, but safe fall from a height of 10 meters?
The Investigation
Teams of students will drop a toy doll using bungee cords made from linked rubber bands and use the data to predict how far the doll will fall as a function of the number of rubber bands in the cord.
First, the students measure how far the doll falls using various bungee cords made from just a few rubber bands. Then they make a sctterplot of these data and determine a line of best fit. (This may be done visually or by using linear regression methods.) Students use the resulting linear function to predict how far the doll will fall using a bungee cord made of 100 rubber bands, and they solve for the number of rubber bands needed to cause the doll to drop 10 meters.
You may use the included student activity pages.
Alternatively, you may use the activity packet from the Barbie Bungee website.
Teaching Tips
- Rubber bands should all be the same size. Since rubber bands lose some of their elasticity after being stretched, it is a good idea to start with a fresh package of rubber bands.
- Keep in mind that the rubber band that is tied to the doll's feet will be shorter than the others.
- If it will not cause too much disruption, you can let the teams make longer bungee cords and drop their dolls from a second story window or the top of the bleachers. They should attempt to predict the length of a bungee cord that will give the doll a thrill by letting its hair brush the ground without hitting its head.
- If graphing calculators are available, the students may elect to use the regression menu to determine the line of best fit for their data.
- If time permits, the experiment can be repeated with a heavier or lighter toy to determine the effect of the jumper's weight on the length of the optimal bungee cord.
- One possible solution to the problem can be found here.
Citation
From the teaching files of David Kullman.