Exercise 2: Introduction to coordinate systems and projections

Barbara and David Tewksbury, Hamilton College


This exercise gives students personal experience with data sets that have spatial reference "issues" so that they learn first hand both why it matters to be meticulous about projections and coordinate systems and how to work with coordinate systems, projections, and datum transformations in ArcMap. You might also be interested in our Full GIS course with links to all assignments.


Type and level of course
Entry level GIS course for geoscience students.

Geoscience background assumed in this assignment

GIS/remote sensing skills/background assumed in this assignment
Basic familiarity with ArcMap and ArcCatalog; how to create a hillshade of a DEM; how to create a basic map layout (although instructions for the latter two could easily be added to the instructions).

Software required for this assignment/activity:
ArcGIS 10.6 or higher with Spatial Analyst extension (required for hillshading, but that could be left out).

Time required for students to complete the assignment:
This set of homework and lab activities (3 homework assignments plus 2 hours of lab) takes one week of the course.


GIS/remote sensing techniques students learn in this assignment
Downloading and prepping data from a variety of sources; determining spatial reference information from metadata in ArcMap or from the data source; defining a projection; projecting a data set; choosing a datum transformation; trouble-shooting coordinate system and projection issues.

Other content/concepts goals for this activity

Higher order thinking skills goals for this activity
Applying knowledge about coordinate systems and projections to reason out the cause of unexpected results.

Description of the activity/assignment

This is Exercise 2 in a semester-long GIS for Geoscientists course. You can find the other exercises in this series on the course summary page or by typing Tewksbury GIS Exercise into the Cutting Edge search engine.

In this exercise, students download and prep their own data in a variety of formats from a variety of online sources. The data sets are fabulous, because they have coordinate system "issues". In the time since we wrote the original version of this exercise a number of years ago, the coordinate system issues of some of the data sets hav been fixed on the respective download sites. For those data sets, we continue to use the problematic versions in the exercise because they are so instructive, even though they are no longer available on the web. We have included those original data sets in the exercise materials that can be downloaded at the bottom of this page.

Students start by working with a simple shapefile of world continents (WGS84), an orthoquad downloaded from the NYS GIS clearing house (NAD27 UTMN 18N), and an old shapefile of NYS bedrock faults downloaded from the NYS Museum (which comes in without a defined coordinate system). Students create several data frames in ArcMap, adding all three files to each data frame but adding a different one first each time. The results are spectacularly baffling to the students and provide an opportunity to talk about what has happened, and why.

The DEM and collared orthoquad that the students download from the NYS GIS clearing house are in NAD27 UTM 18N. The Cornell University Geospatial Repository (CUGIR) site has DEMs for USGS quads, and they, too, are in NAD27 UTM18N. CUGIR also used to have uncollared topo tiles that could be mosaicked together for areal coverage. When they were available, they came in to ArcMap without a defined coordinate system. We still use this old data set because it provides a wonderful opportunity to have students make a logical (but, as it turns out, incorrect) assumption that these topo tiles must also be in NAD27 UTM 18N. After defining the projection that way for the topo tiles, students create a composite map of the GIS Clearing house orthoquad and the CUGIR DEM (both of which line up) and then add the CUGIR topo tiles (which are offset from the other two by a couple hundred meters). Students then go back to the CUGIR site and learn that they can check metadata there, and they discover that the coordinate system for the topo tiles is actually NAD83 UTM 18N. After defining the coordinate system correctly, all three sets of data align perfectly.

Students also explore the difference in coordinates for the corner of the Science Center at Hamilton in different datums.

The remainder of the exercise gives students experience with projecting data, including permanent datum transformations and projecting "on the fly".

Exercise 2a: This is a preparatory homework assignment that follows class coverage of projections and coordinate systems. Students answer a number of questions about coordinate systems, datums, ellipsoids, and projections based on class notes and reading in their textbook.

Exercise 2b: This is a preparatory homework assignment. Students download and prep their own data from the New York State GIS Clearing House, the Cornell Geospatial Repository, the New York State Museum, and the CGIAR SRTM site.

Exercise 2c: This is the main lab assignment described above.

Determining whether students have met the goals

Assessment is based on the answers to the questions in the exercises and on an ArcMap layout that each student creates that illustrates a main point that each has learned about coordinate systems and projections.
More information about assessment tools and techniques.

URLs and References

Most of the data is downloaded from online sources as part of the exercise, and download instructions are included in the exercises. Several data sets are also provided in the zipped folder of teaching materials below.

The exercise also requires a table of datum transformations, which can be downloaded from the ESRI web site at:


Download teaching materials and tips

  • Activity Description/Assignment:
    • Ex 2: Projections and Coordinate Systems 2019 (Zip Archive 63.3MB Jan9 20): This is a zipped folder of the exercises, homework, handouts, and a few data sets that are not currently available on line.
    • A set of Coordinate System Challenges: (Zip Archive 2.3MB Jan10 20) This is a zipped folder of 6 progressively more difficult assignments to give students practice in using coordinate system terminology and operations correctly and in solving coordinate system problems.

Exercise 2: Introduction to coordinate systems and projections -- Discussion  

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