The Model Shop is a collection of 54 problem sets
in which students work to find a mathematical model for a set of
data. There are many kinds of models, but in this book, we're concerned
about elementary functions: lines, parabolas, square roots, exponentials,
sinusoids, and power laws.
The data comes on a CD-ROM. You can use any data analysis
package to analyze it, but the most fun would be Fathom Dynamic
Data (TM) doftware from Key Curriculum Press.
The book begins with linear functions as an introduction
to Fathom and to modeling. Then we see a data set for each family
of elementary functions. Then things really get interesting.
After students have met all of the familes of functions
in the book, three sections follow: in the first, students get a
formula or its equivalent that they can use to make sense of the
data. In the second, they get no help in trying to decide what kind
of function it might be. In the third, they may get some help, but
the data analysis will require stepping a little outside the box
of the plain elementary function.
To do this, students need some help. The book contains
an extensive section about transforming functions by sliding and
stretching (i.e., trandlation and dilation), a section about using
residual plots to help in data analysis, and another on transforming
data to make them linear.