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Topic: teaching about scale

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Subject:   RE: scaling on coordinate plane
Author: Mathman
Date: Jun 15 2005
On Jun 15 2005, Bethany wrote:
> Guess I wasn't too clear in my first message.  I meant scaling in
> the terms labeling axes on a graph.  For instance, a problem I gave
> my students:

You work at a jewelry store and earn $200 per week
> as a base salary.  You earn 15% commission.  We then created a table
> of values for how much  you would earn if you sold $1000 worth of
> jewelry in a week, $2000, $5000, $10000.  We developed a linear
> function to represent the table and then graphed on paper.  

> biggest struggle in this (and other similar) exercises was getting
> them to think about how to best label the x and y axes.
> Hopefully this clears it up.

Sorry.  I don't see the problem.  The amount earned depends on the varying sales
amount.  So, the amount earned is the dependent variable, depending on the
amount of sales, the independent variable.  Traditionally the first is plotted
on the vertical axis, and the secondalong the horizontal. So, in terms of x and
y, the formula is

y = 200 + .15x

So I'd label the x-axis as "Sales", and the y-axis as "Earnings", or
"Income", or whatever.

If you mean the grid units, then that's another story, and one of those things
that becomes easier with experience, but is indeed difficult at first.  It is
purely arbitrary, and that's what makes it difficult to determine if the graph
show real relative relations.  The difficulty here is that you are interested in
starting not at the vertical axis, but some distance along the horizontal.  One
*workaround* is the "break" in the horizontal axis, usually a gap with a
zig-zag either side.  Also, choice of units is arbitrary [thousands of
dollars?], and can be seen only by examination of several samples again to show
advantages and disadvantages by class discussion.

About getting them to understand differences in approach, I could only suggest
accepting any and all at first, then having an all-round class discussion
about pros and cons of each.

Here, in choice of scale, is one source of the phrase, "Lies, damned lies, and
statistics."  A very difficult concept for the young and inexperienced.


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