Is there a fun way to teach about slopes in math?

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Request for Question Clarification by mathtalk-ga on 12 Dec 2002 06:30 PST

Hi, jbach-ga:

It could be like the joke about the painless dentist, but I'll ask
anyway:  fun for who?  I'll assume fun for both teacher _and_
students, but at what level of curriculum?  high school? college?

Demonstrations are fun, and perhaps for the right size class a
"physics" application could be used to illustrate "slope".  On the
other hand I've used a microcomputer lab component in connection with
both high school and college courses, and I could relate "slope" to
some programming of graphics on the screen.

regards, mathtalk-ga

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Clarification of Question by jbach-ga on 12 Dec 2002 07:17 PST

The request is for my wife who is teaching 8th grade math to some
bewildered students.

Dear J Bach, 

Let me first of all thank you, probably also on behalf of the wives of
the world, who would like their husband to care for their success!

One of the best ways to relate mathematics to those who "hate" it,
would be to use examples from the reality. In the case of slopes, that
are widely used in the "real" world, that is no problem. Those who
would later turn to "unmethematical" professions in social science or
humanities, are likely to find again these old friends from
high-school, lurking.

So, there are many ways to teach these: 
(1) Showing the relationship between X and Y in matters of things
people really like. Ask them, for example, to ask 10 people, how many
hours of TV they see per week. Then, you can spread the information on
a slope lines with age development (small children view 4 hours in
average, teenagers 10 and adults 3, for example). Slopes are much used
in the issue of consumption, so this could be a good idea, as well as
other ideas:
- candy/snacks consumption
- how much is spent on clothing, make-up, etc. (10th or 11th grade)
- how many pages you've reached, in which time, in your math book (for
example, in September, you were in page 10, now you're on page 30).
- naturally, everything that has to do with sports, like advancement
of a certain team in a certain season (how many points, etc.)

(2) Doing "real" excursions, such as with a map, to a hill area near
the school, to measure the land and to understand "real" slopes.
Similar excursion might be done, in this weather, in a museum (from
ancient to modern art?), with pictures of the city skyline, etc. Ski
videos, trekking, etc. - might be also a good idea to demonstrate what
slopes are; as well as learning about the Egyptian Pyramids (see
http://math.truman.edu/~thammond/history/EgyptianPyramids.html)

(3) Learning about slopes from "real" cases in sciences. This might
require some background, that I don't know if the students posses. For
example,e NASA offer a lesson plan on slopes and space
<http://imagine.gsfc.nasa.gov/docs/teachers/lessons/slopes/ss_title.html>
In economics: 
http://illuminations.nctm.org/lessonplans/6-8/printing/ 

You may be able to use this book chapter, "slopes and more": 
http://whyslopes.com/etc/CalculusAndBeyond/foreword.html 
and http://www.whyslopes.com/freeAccess/appetizer1.html 

Another good site is http://math.rice.edu/~lanius/Algebra/stress.html
, that also provides many good links.

I hope that helped. What I did (except for using my memory and
imagination, I used to work in pedagogics myself), was to search for
"slopes" with the term "lesson plan", and I got many interesting
ideas. Please contact me, however, if you feel like you need further
clarifications. I'd be pleased to provide them, before you rate the
answer (and good luck with those students :=)