From the Pen of Dr. Shelly Saunders
Dear Mathletes,
I am an anthropologist from Canada who investigates
changes in human body size and shape over time. I have
been working on comparing the differences in heights of
people who lived during the 19th century and the present.
Unfortunately, I don’t always have complete skeletons of
the 19th century folks to work from. I do have many radius
bones that I dug in a pioneer graveyard.
Here is where I need your help (since my math is bit shaky
and I heard through the grapevine that you guys are the
best!): Is there a way to predict the height of a person by
just knowing the length of the radius bone? (In case you
don’t know the radius bone extends from your elbow to
your wrist. See picture on right.)
I hope you can help me.
Sincerely,
Shelly
Next, the teacher asks the class for suggestions about how they might help Dr. Saunders. Hopefully, the students
will suggest that if they do some measurements they might discover some patterns that may lead to some
predictions. The students, working in small groups, measure the radius bone and height of each student in the
group. (Each group gets a recording sheet like the one below and a measuring device.)
Names
Radius
in cm. or inches
Height in cm.
or inches
After each group completes its measurements, a spokesperson from each group reports their results to the
teacher who records them using an overhead projector. (The transparency is the same as their recording sheets.)
The teacher then asks the students if they see any patterns. After some discussion, the teacher suggests that the
students draw a graph using the a spreadsheet program program. It would look something like this:
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The teacher asks: What can you tell me about the graph? (It’s sort of linear.) Does it make sense to connect the
points with a straight line? Why? The best we can do is draw a line of "best fit."
We can then use this line to make predictions. For example, if someone had a radius bone that was 17 cm, what
would you guess his or her height to be? (Answers will vary. A student might come up and suggest where the
point with a radius value of 17 should be placed on the graph.) Is it possible for someone to have a 17 cm radius
bone and have a height of 170 cm? (Not very likely, but possible.) Why? What if Akeem Olajuwon (the
Houston Rocket basketball player) walked into the room? Could you predict the length of his radius bone?
(Olajuwon is 7’ 1” tall. The students will have to convert his height to centimeters.) How confident are you
about your prediction?
Next, the students are told that this computer program can determine a mathematical equation for this line of
"best fit." Can you figure out what the computer will come up with?
The teacher then helps them to come up with an equation that would fit this data by playing the game they are
familiar with: Guess my Rule. The hint is to first multiply the radius by 3.
A
1
B
Radiu s
C
Radiu s x 3
Heigh t
2
22.4
67.2
147
3
26.1
78.3
160
4
18.7
56.1
135
5
Then they should see that if they add about 80 to the "Radius x 3" column, they would get a close approximation
to the Height. (A good approximation for this relationship is Height = (Radius x 3) + 80. Once the group agrees
on a prediction for an equation, the computer program can be used to confirm their guess.
“Going further” questions
The class could explore other examples of mathematical relationships. For example, they can through
experimentation discover that he relationship between the Fahrenheit and Centigrade temperature scales are
related by the formula F = 9/5 C + 32. Students can approach this problem in the same way. They take
temperatures in both scales, draw a graph, and then determine an approximation for the relationship. Another
example, would be to determine the temperature outside based on how fast crickets chirp (See Crickets lesson.)