Illuminations: Barbie Bungee

# Barbie Bungee

 The consideration of cord length is very important in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbie® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.

### Learning Objectives

 Students will: 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.

### Materials

 Rubber bands (all the same size and type) Yardsticks or measuring tapes Masking tape Barbie® dolls (or similar) Barbie Bungee Activity Sheet

### Questions for Students

 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? [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.

### Assessment Options

1. As a journal response, have students answer the Key Questions above. Then, require students to present their solutions to the class and demonstrate that their answers are correct. For instance, if a student says that Barbie can jump safely from a height of 400 cm with 12 rubber bands, then they should demonstrate that Barbie will not hit the ground when 12 rubber bands are used.
2. The following 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.

 Barbie Bungee Project – Grading Criteria Rubric Score ANALYSIS The project is complete and turned in on‑time. The project demonstrates an understanding of the mathematical concepts. APPLICATION The procedures checklist is complete. All group members work efficiently during the class period. REPRESENTATION The data table is accurate. The scatter plot includes a title, labels, scales, and data points. The sketch of the line of best fit is reasonable. The equation of the line of best fit is accurate, based on the data. EXPLANATION The relationship between the variables is clearly stated. The slope and y‑intercept are explained in context. JUSTIFICATION The predictions are made and their reliability is discussed. The predictions are compared to the original conjecture.

### Extensions

 Using dolls of different sizes and weights, note the effect on the results. Will more or fewer rubber bands be needed for a jump of the same height? Consider the effects of gravity, and have students consider the speed at which Barbie falls during her jump. What is her speed one second after the jump starts? What is her speed at the bottom of the jump?

### Teacher Reflection

 Were students able to explain the meaning of the slope and y‑intercept within the context of this problem? If not, what other activities would help? Was students’ level of enthusiasm/involvement high or low? Explain why. How did the students demonstrate understanding of the materials presented? What, if any, issues arose with classroom management? How did you correct them? If you use this lesson in the future, what could you do to prevent these problems?

### NCTM Standards and Expectations

 Algebra 6-8Use graphs to analyze the nature of changes in quantities in linear relationships. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope. Algebra 9-12Use symbolic algebra to represent and explain mathematical relationships. Approximate and interpret rates of change from graphical and numerical data. Data Analysis & Probability 6-8Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit. Data Analysis & Probability 9-12Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.
 This lesson prepared by Samuel E. Zordak.

1 period

### NCTM Resources

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