Linear Relationships in a Middle School Class

Every module begins with a tripodal base.

What the students are expected to learn.
What the students are expected to do.
Engaging the students' interest and keeping them interested. Modules should be open-ended.

Topics like determining the location of an earthquake are good topics because they do engage students' interest in a setting that illustrates and will help students learn important mathematics. This topic is also open-ended -- students can work with it at various levels. As a result it can be a comfortable topic for every student while challenging the best students.

What are students expected to learn?

Linear relationships from numerical, graphical, and formal perspectives.
Relationships like linear relationships can be used to deduce unknown facts.
Mathematically expressed relationships are models but not necessarily exact models of reality.
Basic skills for working with linear relationships.
If y depends linearly on x and z depends linearly on x then so does y - z.

What are students expected to do?

Work with linear relationships in all three forms -- numeric (tabular), graphical, and formal. Convert from one to the other.
Discover the fact that if y depends linearly on x and z depends linearly on x then so does y - z.
Deduce the location of earthquakes using maps and compasses along with what they've learned about linear relationships.
Explore on their own -- for example, the Encyclopedia Britainnica CD (1998) has a nice short explanation of P- and S-waves.
This basic situation is very open-ended. Students might ask, for example, whether the waves start on the earth's surface or far below the surface.

What do we need from the Virtual Earthquake?

Tabular data listing distance from earthquake to detectors and arrival times for P- and S-waves. Two sets of data might be useful -- a clean set and a real set.
Access to bare graphs like the bare graphs below. Note that we want the students to do the work that is done by the underlying programs at the current Virtual Earthquake websites.

Note that this map should be printable. Students will use compasses to add the circles showing the distance from detectors to the earthquake.

What don't we need from the Virtual Earthquake?

We don't need and don't want graphs like the one below. It is better for students to draw these graphs for themselves.

We don't need and don't want graphs like the one below (and the underlying program that produced it). It is better for students to draw graphs like this themselves using a compass.

On to a high school class studying quadratic equations.