understand how we use topographic maps to represent the three-dimensional world.
learn to interpret contour lines
Topographic maps 115B and 115 C
1 Start the class with the profile of a mountain on the board. Tell the class that cartographers have had the challenge of how to represent the three-dimensional world on two-dimensional pieces of paper. If you had to go for a hike, for example, in an area you didn’t know, you would want to know if you were going to encounter easy terrain, cliffs, valleys, mountains, ravines, or other geographical features. How much will the trail climb? Will it be an easy hike or a hard one?
Elevation is a measurement of how high a location is above sea level. Every place on earth can be compared by the number of metres it is above sea level, which is a constant.
2. Use the drawing on the board. Measure equal distances up the mountain, and mark them off at 50 metre intervals. To accurately represent elevations and show the rise and fall of terrain, cartographers create topographic maps. These use “contour lines” to show areas that are the same elevation. A contour line connects all of the areas at the same elevation.
3. Use the profile on the board again. Tell the students that we are going to translate the profile into how this mountain would look on a topographic map. Instead of looking at its profile, we will be looking down from the top. Draw dotted lines down from where the 50m interval lines intersect with the profile of the mountain. Attach the same elevations together, using contour lines, and creating the dimensions not shown on the profile. Show how two peaks would be represented, and a ridge. Show how a valley or depression would be represented.
4. Gather the students into groups of 3. Hand out one topographic map to each group. Ask groups to find the following:
- the intervals represented by each contour line - three different peaks - a ridge - a valley - a depression - a gradual rise in elevation - a steep slope - a basically flat area.
5. Now, each student chooses an area on Mount Logan. They lay a ruler along the line, and decide which 5cm straight line they will create a profile of. They must keep the ruler in the same place.
Now, they must combine their understanding of scale with their understanding of contour lines. On their sheet of paper, they make a horizontal line, 25 cm long. (1cm on the map will equal 5cm on their paper). This is the horizontal axis for their profile. They should indicate the cm and mm on this line.
Next, they draw a vertical line on each end of the horizontal. They calculate the rise in elevation along their 5cm chunk of Mt. Logan. What is the lowest elevation? What is the highest? At a scale of 1:250,000, how many cm will be needed to represent the elevation gain on the side axes? They should mark off the equivalent of every 200m on the side axes (at a scale of 1:250,000, .08 cm equals 200 m. As they have multiplied their scale by 5, 0.4 cm or 4mm will represent 200m). Either make this calculation together as a class, or circulate to ensure that students are setting up their profile correctly.
Keeping the ruler in place, they measure the distance to the first contour line, and mark that off on the horizontal of the profile. They measure to the intersection of the horizontal with the contour marking from the vertical axis. This is the first point on their profile. They mark each of the other contour lines their ruler crosses in similar fashion until they have represented all of the data from the map as points on the profile. To finish, they connect the dots on their profile to recreate the third dimension from the contour map.