GIS Lesson Demonstrating Local Maxima
Title: Modeling Local Maxima
Level: Mathematics, Multi-Disciplinary
Technology: ArcGIS Explorer (Elevation Profile Map Tool)
Scale: Local, National, Global
Target Audience: High School
Location: Salem, VA and USA and another place in the world
Time Required: 50 minutes
Description:
Students will find minimum and maximum elevations for a portion of Salem, VA, and then for
various places in the US. They will use these findings to postulate about why Salem’s maximum
elevation is not as big as Virginia’s, Colorado’s, and the whole USA. They will use this information to
better understand local maxima and by induction, to better understand local minima. This is a sticking
point for many of my students- Why is a value on a graph a “local” maximum when there is clearly a
higher point elsewhere on the graph? Students will also choose a place where they believe will have a
very high elevation and map its elevation.
Name_________________
Instructions and Worksheet:
Understanding Local Maxima Using Mapping Software
{Steps 1-6 will be completed together with teacher leading to show students how software works}
1. Go to http://edcommunity.esri.com/software/webmapping/ in your web browser and scroll
down to “Elevation Profile Map Tool” and click on the link.
2. You should see a map of the United States. Zoom in by double clicking on the location you want
(which is Virginia) and then keep zooming and moving the screen until you can see Salem as
below.
3. Find Salem High School (between Goodwin and Spartan Drive) and choose the squiggly line tool.
The zig zag the mouse from SHS to the other side of Little Brushy Mountain like so.
4. You will see an elevation graph pop onto the screen. Record the highest elevation on YOUR map
here: __________meters.
5. Move your mouse over the elevation so you can see where on the map the highest point is.
Record the nearest landmark here: __________________
6. What does this elevation mean? Is it the highest in all of Salem? All of Virginia? Or is it simply
the highest point you happened to drag your mouse across?
7. Now change to street view using the boxes in the upper right corner of the screen and zoom out
until you have all of Virginia clearly on your screen and this time, use the squiggly line tool to
zigzag across the state as before and record your highest point: __________meters and the
nearest town:_______________________.
8. Was your highest point higher or lower than the highest point you drew in Salem?
9. Would you expect the highest point in Louisiana to be higher or lower than Virginia?
10. What about Colorado?
11. We will now divide into 4 groups but for now, we will work on our computers individually.
Everyone in each group will record the highest elevation and a landmark in their assigned area.
Group A will do the state of Colorado, group B will do the state of Louisiana, Group C will do the
East Coast, and Group D will do the whole USA (you’ll have to zoom out).
 Highest point in your zigzag:

Nearest landmark:
12. After everyone has done the “zigzagging” across his or her area, you will get together and find
the highest “highest point” of all group members and record it.
 Highest point in your group:

Nearest landmark:
13. Now we will compare the four groups findings. Have one member from your group tell the class
your highest elevation. Was it what you expected?
14. What do you think a “local” maximum means? Does a local maximum necessarily mean it is the
maximum for the whole world? Could it be?
15. Decide as a group a place anywhere in the world that will have a higher elevation than
anywhere in the US and have one member zigzag across it. Where did you choose?
16. Did you get a higher elevation than any that we found?
17. Tomorrow, we will discuss what local minima and maxima mean for a graph and why it is
important to be able to find the minimum and maximum for portions of the graph.