### Keywords:

## Topic:

### Estimated Time Required:

### Target Grade (Ages):

### Diversity Indicators:

## Tab Wrapper

### Goals:

### Prerequisites:

*Uncertainty*: Variation in data appears naturally from repeated measures because measures and collection of data are inherently uncertain.*Functional relationships (between two variables or quantities)*: A function describes how one thing depends upon another.*Patterns*: Patterns is a process of change that repeats in predictable ways.

- Collect data using a rubber band bungee cord and a Barbie doll
- Use the data collected to construct a scatterplot and generate a line of best fit
- Predict how many rubber bands are needed for Barbie to safely jump from a given distance.

### Background:

Students will work in groups to simulate a bungee jump using a toy doll or action figure such as a Barbie^{®} or GI Joe^{®} doll and rubber bands. Students will formulate a conjecture, design a method to determine how many rubber bands are needed to have Barbie bungee a given distance, and use the data to develop the concepts of estimation, slope, and line of best fit.

Things for students to think about:

- How many rubber bands are needed for Barbie to safely jump from a height of 400 cm? [Answers will vary, but students should use the line of best fit and the regression equation to determine an answer.]
- What is the minimum height from which Barbie should jump if 25 rubber bands are used? [Answers will vary, but students should use the line of best fit and the regression equation to determine an answer.]
- How do you think the type and width of the rubber band might affect the results? For example, do you think age of the rubber bands would affect the results - that is, what would happen if you used older rubber bands? [Answer: Rubber bands lose their elasticity with age or when exposed to extreme temperatures. Students would probably choose not to jump from a bridge fi the bungee cord were old and brittle.]
- If some weight were added to Barbie, would you need to use more or fewer rubber bands to achieve the same results? Conjecture a relationship between the amount of weight added and the change in the number of rubber bands needed.

### Materials:

__Student Materials__

- Bungee Barbie Activity Packet
- Bungee Barbie Spreadsheet
- Doll
- Big ball of rubber bands
- Measuring tape
- Cash register tape
- TI 84+ calculator

__Teacher materials__

- Bungee Barbie Project Rubric
- Calculating a Spring Constant Extension Activity
- Laptop
- Projector
- Model set

### Procedure:

Get students' interest by asking, "Do you think the length of the cord and the size of the person matters when bungee jumping? Would it be smart to lie about your height or weight?" Allow students to offer suggestions as to why an accurate estimate of height and weight would be important to conduct a safe bungee jump.

You may also wish to show a short video about bungee jumping. Some bungee videos are available on the following web sites. (Note that the third video shows the tribal ritual of land diving, a precursor to bungee jumping, and may not be appropriate for all classrooms.)

__Bungee TV__(www.bungee.com)__Bungee Jump Preview__(www.extremeworld.com)__Land Diving Ritual__(www.nationalgeographic.com) (Beware... mature audiences only! Graphic traditional tribal ritual)

After a brief introduction, set up the lesson by telling students that they will be creating a bungee jump for a Barbie^{®} doll. Their objective is to give Barbie the greatest thrill while still ensuring that she is safe. This means that she should come as close as possible to the ground without hitting the floor.

Explain that students will conduct an experiment, collect data, and then use the data to predict the maximum number of rubber bands that should be used to give Barbie a safe jump from a height of 400 cm. (At the end of the lesson, students should test their conjectures by dropping Barbie from this height. If you school does not have a location that will allow such a drop, then you may wish to adjust the height for this prediction.)

Distribute the Bungee Barbie Activity Packet to each student. In addition, give each group of 3-4 students a Barbie doll, 15-20 rubber bands, a large piece of paper, some tape, and a measuring tool. Be sure that all rubber bands are the same size and thickness. Differences in rubber band elasticity will affect the results.

Before students begin the activity, demonstrate how to create the double-loop that attaches to Barbie's feet. Also show how a slip knot can be used to add additional rubber bands. Then, allow students enough time to complete the experiment and record the results in the data table, provided in the activity packet, for Question 2.

After all groups have completed the table, ask them to check their data. They should look for numerical irregularities. If any numbers in their table do not seem to fit, they may need to re-do the experiment for the number of rubber bands where the data appears abnormal. (Common student errors include measuring incorrectly and adding too many or too few rubber bands. As students conduct the experiment the first time, circulate and attempt to spot these errors as they occur. It will save time if students fix the errors during the initial experiment instead of having to re-do the experiment later.)

Note that the number of rubber bands in the first column increases by 2. This is so students consider the idea of slope during the experiment. If the number of rubber bands increases by 1, then students are not required to think about what the slope means. When increased by 2, however, students have to realize that the slope of the line actually represents "centimeters per rubber band" instead of "centimeters per two rubber bands."

To create a graph of the data, you may wish to have students use the Illuminations __Line of Best Fit__ activity, or allow them to enter the data in the Bungee Barbie Spreadsheet.

At the end of the lesson, take students to a location where Barbie can be dropped from a significant height. Possibilities include a balcony, the top row of bleachers, or even standing on a ladder in an area with a high ceiling. Allow students to test their conjecture about the maximum number of centimeters that can be used for a jump of 400 centimeters.

Please see the Calculating a Spring Constant of a Rubber Band activity.

The attached Bungee Barbie Project Rubric can be used to evaluate student work. You may wish to share this rubric with students prior to completing the lesson, so that they are aware of the criteria on which their performance will be measured.

**Student Questions**

- How many rubber bands are needed for Barbie to safely jump from a height of 400 cm? [Answers will vary, but students should use the line of best fit and the regression equation to determine an answer.]
- What is the minimum height from which Barbie should jump if 25 rubber bands are used? [Answers will vary, but students should use the line of best fit and the regression equation to determine an answer.]
- How do you think the type and width of the rubber band might affect the results? Do you think age of the rubber bands would affect the results--that is, what would happen if you used older rubber bands? [Answer: Rubber bands lose their elasticity with age or when exposed to extreme temperatures. Students would probably choose not to jump from a bridge fi the bungee cord were old and brittle.]
- If some weight were added to Barbie, would you need to use more or fewer rubber bands to achieve the same results? Conjecture a relationship between the amount of weight added and the change in the number of rubber bands needed.

You may also wish to show a short video about bungee jumping. Some bungee videos are available on the following web sites. (Note that the third video shows the tribal ritual of land diving, a precursor to bungee jumping, and may not be appropriate for all classrooms.)

This lesson prepared by Samuel E. Zordak, NCTM Illuminations

- Modified by Tiffany Lucey
- Louise Baratta UBD lesson
- Physics Extension as explained by J Tracey