Select, create, and use appropriate graphical
representations of data, including histograms, box plots, and scatter plots.
Make conjectures about possible relationships
between two characteristics of a sample on the basis of scatter plots of the data and approximate lines of fit.
Identify trends in bivariate data and find
functions that model the data or transform the data so that they can be modeled.
Learning
Objectives
Students
will:
Collect data using a rubber band bungee cord
and a Barbie doll.
Use the data collected to construct a scatter
plot 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
Instructional
Plan
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.
(Technology)
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):
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 Barbie Bungee 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, 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 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. The teacher may need
to assist the students with measurements. (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.)
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."
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.
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 if 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
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.
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
oThe project is complete and turned in on‑time.
oThe project demonstrates an understanding of the mathematical concepts.
APPLICATION
oThe procedures checklist is complete.
oAll group members work efficiently during the class period.
REPRESENTATION
oThe data table is accurate.
oThe scatter plot includes a title, labels, scales, and data points.
oThe sketch of the line of best fit is reasonable.
oThe equation of the line of best fit is accurate, based on the data.
EXPLANATION
oThe relationship between the variables is clearly stated.
oThe slope and y‑intercept
are explained in context.
JUSTIFICATION
oThe predictions are made and their reliability is discussed.
oThe 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?
