lesson provides a great introduction to the use of box-and-whisker
plots and statistical analysis, but students should have some
familiarity with measures of center including mean, median, and range.
In addition, this hands-on lesson is great for engaging students, but
be aware that a fair amount of advanced preparation is required to make this lesson successful. Prior to the lesson, you will need to:
- Fill each of the four plastic container about halfway with water. The water
needs to be deep enough so that the aluminum foil boats made by
students will eventually sink when filled with bears. The plastic
containers must be at least 8" wide, 8" long, and 4" deep, although
larger containers work better. (Throughout this lesson, these
water-filled containers will be referred to as "lakes." A few suggestions are: Lake Huron, Lake Ontario, Lake Michigan, Lake Erie, or Lake Superior.)
- Arrange the lakes throughout the room so that students have ample space to work. It is best to place only one lake on a table.
- Next to each lake, place about 100 bears. (Note that other
objects can be used if plastic bears are not available. Unifix cubes or
any small plastic items that are uniform in weight and size will work,
but the approximate weight of each item should be 3‑5 grams.)
- Have an ample supply of clean-up materials, including a sieve
(to scoop the bears out of the water), towels to dry the bears, and
paper towels to mop up any spills made while students are working.
Distribute one piece of 6" × 6" aluminum foil to each student.
Explain to students that they will use the foil to create a
"boat" by folding it in any manner they choose. Warn them not to rip,
tear, or make a hole in the foil. If they do, their boat will sink.
Tell them that after constructing their boat, it will be floated in a
lake and filled with bears. Their goal is to keep the bears afloat
(dry); they do not want the boat to sink. Tell them that they will test
their boat by placing it in the lake and loading it with bears until it
sinks. Show students the lakes and bears around the room.
Divide the class so that there is approximately the same number
of students at each lake. One at a time, students should place their
boats on the lake and carefully load the boat with bears. A sample boat
loaded with bears is shown in the picture below. The students' goal is
to get as many bears as possible into their boats. They will quickly
learn to balance the load and place the bears carefully. You may be
asked, "May I start again?" and it is acceptable to permit that once.
Each student should record the number of bears that their boat was able to hold. The capacity
of the boat is the number of bears in the boat just before the boat
sinks. For example, if the 28th bear placed in a boat caused it to
sink, then the capacity of that boat was 27.
Record the capacity of each student’s boat. Sort the capacities
and place them in a table. It is not unusual to have capacities that
range from lows of 9 or 10 to highs greater than 60. The following is a
typical sample for a group of 13 students:
From the data collected, work with the class to identify the five‑point summary, which includes the minimum, first quartile (Q1), median, third quartile (Q3), and maximum. For the set of data shown above:
- Minimum: 10
- First Quartile: 19
- Median: 34
- Third Quartile: 42
- Maximum: 61
Construct a large box-and-whisker plot of the data set on your whiteboard. Students should use the Mean and Median Tool
to create the box-and-whisker plot. If your class has fewer than
15 students, you can do this as a whole class activity. If your class
has more than 15 students, divide them into two or more groups, and
allow each group to enter their data into this tool to create a
box-and-whisker plot. (Later in the lesson, students will be given an
opportunity to create a second boat and compare their data from the
first and second attempts. Consequently, the groups should remain
intact throughout the lesson.)
If you have divided your class into two or more groups so that they
could use the Mean and Median Tool, select one group to use as an
example, and draw a large box-and-whisker plot of their data on a
whiteboard, chalkboard, or overhead projector. Place the actual boats
from the example group in order from best to worst under or near the
box-and-whisker plot, so that the students can associate each boat with
its placement in the graphical display. Have them note which boats are
near the five‑point data values. For the data set above, the Mean and
Median tool would generate the following box-and-whisker plot, which
could be projected on a screen or interactive whiteboard:
After the students look at the boats, their positions on the plot,
and their capacities, ask, "Now that you have seen this information, do
you think you can build a boat that will hold more bears?" Their
response, of course, will be an overwhelming, "Yes!"
Give each student another piece of foil. Students will closely
examine the boats with the greatest capacities before building their
Again one at a time, have students place their boat on a lake
and carefully load it. Repeat the steps above for collecting and
sorting the data, and drawing a second box-and-whisker plot above or
below the first one. (This can be accomplished easily using the Mean
and Median Tool, which allows for up to three box-and-whisker plots to
be constructed and compared.)
The results of the second distribution will be remarkable. A typical second try is shown below:
For this second set of data, the five-point summary is:
- Minimum: 38
- First Quartile: 44.5
- Median: 48
- Third Quartile: 52.5
- Maximum: 60
The Mean and Median tool will generate the following box-and-whisker plots for comparison:
Ask students to compare the box-and-whisker plots. What can these
representations tell them about the data, and how can they be used to
analyze the results of the first and second attempts?
The results shown above are typical, and students' second
attempts are generally far superior to their first attempts.
Consequently, the results from your class will have similar
characteristics, and students might make the following observations:
|First Attempt || || Second Attempt |
|median ||≤|| minimum|
|third quartile ||≤|| first quartile|
|maximum ||≈|| maximum|
- The moral for students is that if the first attempt had poor
results, then the use of new information and careful effort can lead to
significant improvement; but if the first attempt result was
exceptional, it is hard to meet that goal every time.
- The large capacity boats will generally look similar —
typically large square bottoms with carefully folded sides of medium
height. They will resemble the barges that can be found on large
rivers, such as the Ohio or Mississippi.
To conclude the lesson, ask students what they have learned.
You may be surprised at all that students will share. In addition to
mathematical observations, students may offer the following:
- The organization and analysis of the data helped us to "learn by our experiences."
- Students probably talked about the data and the attributes of
the boats with each other before building their second boat. This
reinforces that communication is important — both talking and
- Each representation of the data (table, box-and-whisker, and actual boats) gives us different perspectives and insights.
- There is probably a "perfect boat design," but the physical
environment, human error, and potential motion of the water may make it
difficult to build and fill the boat perfectly. This is a reminder that
theory and practice must mesh in the real world.