Barbie Bungee

Standards Addressed:

8-3.7 Identify the slope of a linear equation from a graph, equation, and/or table.

8-6.1 Generalize the relationship between two sets of data by using scatterplots and

lines of best fit.

8-6.2 Organize data in matrices or scatterplots as appropriate.

EA-4.3 Carry out a procedure to write an equation of a line passing through two given

points.

EA-4.4Use a procedure to write an equation of a trend line from a given scatterplot.

EA-4.5 Analyze a scatterplot to make predictions.

Materials:

Barbie dolls

Rubber bands (all the same size)

Ruler

Meter stick

Pencil

Graph paper

Graphing calculators (optional)

Directions:

  1. Read the following to your students:

Barbie is an adventure seeker to the max. She loves the thrill of death defying activities. She believes the adrenaline rush makes her hair more lustrous and her waistline thinner; so she will pay big bucks to the company which gives her the most thrilling ride. In the back of her mind though, she wants to be sure that she’s really safe.

You are the owners of a new outdoor adventure company offering bungee jumps to the public. Barbie is your first customer. It is your task to design the most thrilling ride by attempting to land Barbie as close to the ground as possible letting her head hit the ground. Therefore, it is very important that you collect and analyze your data carefully so that you can give Barbie the ride of her life.

  1. Put students in groups of 2 to 4. Distribute to each group a Barbie doll, ruler, meter stick and rubber bands.
  2. Each group will need to secure the meter stick to a wall with tape. Be sure that it is vertical, and that the zero is at the top.
  3. Stretch Barbie out completely with her hands at her sides. Measure Barbie’s height. Record this amount next to the zero rubber bands in the table.
  4. Connect two rubber bands with a slipknot. Then wrap one end around Barbie’s ankles. Be sure the rubber band is on tight enough not to fall off when she is being dropped.
  5. Hold the end of the rubber band tightly at the end of the meter stick, and let Barbie drop from the head-down position. Measure the LOWEST point her head reaches to the nearest centimeter. Record the drop in the table. You will probably have to drop Barbie two or three times to get an accurate lowest reading. It helps to have another person watch too.
  6. Now it is time to start adding more rubber bands. Once again use a slipknot to connect a second rubber band to the bungee line. (Remember the rubber band around her ankle does not count in the length of the line.)
  7. Drop Barbie with two rubber bands attached to her ankles. Hold the rubber band tight at the top of the meter stick, and let her drop from the head-down position. She should bounce a bit more than she did with just one rubber band. The amount of the bounce will get markedly larger as you add rubber bands.
  8. Continue adding rubber bands and recording the lowest point Barbie’s head reaches in the table. Record up to 10 rubber bands.
  9. Pass out graph paper. Before plotting the data in the table, discuss where the independent and dependent variables go on graphs. Also discuss which data represents the independent variable- the number of rubber bands or the lowest point Barbie’s head reaches.
  10. After labeling all parts of the graph (title and labels), plot the data.
  11. Draw the line of best fit for the data on the graph.
  12. Select two points from the line of fit, write their coordinates, and determine the slope of the line. Discuss what the slope means in relation to the graph.
  13. Write the equation of the line of fit in slope-intercept form. What does y represent? What does x represent?
  14. Use your equation to determine how many rubber bands would be needed to drop Barbie from a ledge that is about (height selected by the teacher) centimeters tall. Before you begin your calculations consider the safety issue vs. the thrill issue. If you put the number of rubber bands found from using your equations, Barbie’s head will reach the floor, she will crack her skull, and die. You will then be sued for negligence and will lose your business and owe her family millions of dollars that you don’t have. On the other hand, if you shorten the bungee line too much, the ride may not be thrilling enough, and Barbie will pay her big bucks to your competitor. You will lose your clients and your business will suffer. So, make your decision on how many rubber bands to use, then attach that many bands to Barbie’s line using slipknots as explained earlier.
  15. Grading Scale:

If Barbie came within this many centimeters from the ground, / then your grade is…
0-20 / 100
21-40 / 95
41-60 / 90
61-80 / 85
81-100 / 80

and so on.