# Facilitator/Educator Guide: Cartography: Projecting the Globe on a Rectangular Map

As useful as flat world maps are, they are not the most accurate representation of Earth. Help your students examine distortions introduced when projecting Earth on a flat map using a balloon, a bottle cap, a permanent marker, scissors, a piece of cardboard, and some push pins.

 Activity's uses: Demonstration or small group exploration Area(s) of science: Earth & Environmental Science Difficulty level: Prep time: < 10 minutes Activity time: 20-30 minutes Key terms: Earth, maps, globes, geography, map projections, cartography, latitude, longitude Downloads and Links: Facilitator / Educator Guide PDF. Student Guide web page or PDF. In order to print these activities you need a free Science Buddies account. Please sign in or create a free account.

### Background Information

The main characteristics of a map are:

• It portrays, as accurately as possible, spatial relationships.
• It is drawn to a scale (although this may vary across the map). The scale is a ratio of a distance on the map to the corresponding distance on the ground.
• It is a selected representation of reality. The design objectives determine what is emphasized and omitted.

Making a map might be relatively easy for a small area, such as a room, a house, or even a village; however, making a flat map of the spherical globe is a completely different challenge. Cartographers (map makers) have found various ways to create flat world maps. These are called projections, and every type of projection distorts reality in some way. For example, a Mercator projection represents the directions (north, east, south, and west) correctly, but distances and areas are distorted, greatly increasing toward the top (North Pole) and bottom (South Pole) of the map. Looking at the Mercator projection, you would mistakenly conclude Africa is smaller than North America or Australia is smaller than Greenland.

 Figure 1. A Mercator projection of the world. In this projection, lines of longitude are vertical lines and lines of latitude are horizontal lines. Note the size distortions, such as Africa appears smaller than North America and Australia appears smaller than Greenland.

Scientists use imaginary lines to divide Earth into sectors. Examples of these lines are the equator (imaginary circle around the center of Earth, equidistant from the North and the South Pole), lines of latitude (imaginary lines that circle the globe, parallel to (and including) the equator) and lines of longitude (imaginary lines running over the globe, perpendicular to the equator, connecting the North Pole to the South Pole).

 Figure 2. Diagram showing the equator and two other lines of latitude (dashed lines) and two lines of longitude (yellow lines).

Scientists measure how distorted a map is using Tissot's indicatrix. This is done by drawing same-sized, equally spaced circles all over the globe and then seeing how the circles become distorted in area, shape, and distance on the projection. In this activity, you will use a balloon to represent the globe, draw same-sized circles all over this globe (balloon), create a projection, and study the distortions.

### For Discussion

This science activity can serve as a starting point for a variety of science and geography discussions. Here are a few examples of questions that can be used to start a discussion:

• What information do people like to obtain from world maps? Think of why maps are used.
• Do flat world maps represent information about the globe, like the distance between two continents or the relative size of continents, accurately?
• Do flat world maps represent the direction to go from one place to the other, or the shape, or the size of an area accurately?
• What ways can you think of to create a flat surface from a spherical object?
• How do people refer to a specific place on Earth? Do they use names, coordinates, distances from a specific landmark?
• Would the GPS (Global Positioning System) be helpful to cartographers? Why or why not?

### Materials

• Butcher paper (enough to cover the working surface)
• Cardboard (about 20 x 25 cm or larger per demo or small group); use thick cardboard or two layers of regular cardboard per demo or small group so the push pins do not stick through.
• Scissors (1 pair)
• Ruler, metric (1)

Needed for each demo or small group at the time of the science activity:

• Surface covered with butcher paper (1)
• Balloon, 12 inch (1); provide some extra in case a balloon pops.
• Permanent marker, medium-thick or thick (1)
• Bottle cap, 2–3 cm diameter (1)
• Scissors (1 pair)
• Cardboard piece (1), 20 x 25 cm or larger; use thick cardboard or two layers of regular cardboard so the push pins do not stick through.
• Push pins (6); have some extra handy in case a stretched-out balloon rips and can be saved with extra pins.
 Figure 3. You need only a few simple household materials per demo or group to do this fun science activity.

### What to Do

#### Prepare Ahead (< 10 minutes)

1. For each area where you will perform a demo or where a small group will work, do the following:
1. Protect the work surface with butcher paper. Note: The permanent marker on the balloon may leave prints on any surface it touches.
2. Cut the cardboard into a piece that is approximately 20 x 25 centimeters (cm). Prepare two layers per demo or small group if the cardboard is thin so the push pins do not stick through.
 Figure 4. Materials as they will be presented to the students.

#### Science Activity (20-30 minutes)

1. Each classroom demo or small group should have the following items ready: covered work surface, piece (or pieces) of cardboard, balloon, bottle cap, permanent marker, scissors, and six push pins.
2. If this is not a demo, have students work in small groups of two or three.
3. Review some safety measures before the students start:
1. Students will pin the stretched-out balloon onto the cardboard. As further explained later, it is important that they place the pins slightly slanted outward (with the points aimed inward, toward the center of the balloon, and the colored ends of the pins aimed outward, away from the balloon) so the tension in the stretched balloon does not propel the pins out.
4. Have one student blow up the balloon about half-full (to a diameter of roughly 6 inches) and tie the end. The balloon represents the globe. The top of the balloon and the knot represent the North and South Poles, respectively.
5. The students have the option to write an "N" on the top and an "S" on the knot of their balloon to identify the North and South Pole.
6. Have one student draw the equator and four equally spaced lines of longitude (perpendicular to the equator) on the balloon with the permanent marker.
 Figure 5. Picture of a balloon representing the globe. The equator and four equally spaced lines of longitude are drawn on the balloon. Note that only one line of longitude is visible from this angle, but there is one line of longitude on the left (barely visible), one on the right, and one on the other side of the balloon.
1. Have students draw a total of 26 circles on the balloon with a permanent marker. Circles should be drawn by tracing around the bottle cap placed on the balloon.
1. Start with one circle centered on an intersection of the equator and a line of longitude. Repeat for the three other lines of longitude.
2. Add four more circles on the equator that are equally spaced between each pair of circles already there.
3. Add a circle on the North Pole (top of the balloon) and the South Pole (area with the knot).
4. Add eight circles in the northern hemisphere, about midway between the equator and the pole, with two circles between each pair of lines of longitude. Note that these circles are located on the same line of latitude.
5. Repeat step 7.d. for the southern hemisphere.
 Figure 6. Identical circles are drawn on the balloon by tracing around a bottle cap with a permanent marker. The first circles are centered on the intersection points of the equator and the four lines of longitude; then one additional circle on the equator between each pair of circles; followed by a circle around each pole; and finally, eight circles in each hemisphere. The two bottom right pictures show the final result (from different angles).
1. You might ask students to observe the following:
1. The circles on the equator are equally spaced from each other. The circles between the equator and each pole (which are on the same line of latitude as well) are also equally spaced from each other.
2. Starting with a circle on an intersection of the equator and one of the lines of longitude, the closest circles to this circle (that are not on the equator) are located to the northeast, northwest, southeast and southwest. These observations will be used in the analysis of the data.
2. Have a student deflate (not pop!) the balloon by using the scissors to snip a tiny hole in the balloon, close to the knot.
 Figure 7. Scissors are used to snip a tiny hole in the balloon close to the knot. This allows the balloon to slowly deflate.
1. Once the balloon is deflated, have a student cut the balloon open from the South Pole (the knot) to the North Pole following a line of longitude, but the student should stop a little before the very top of the balloon. Cutting over the very top of the balloon increases the risk of the balloon ripping when it is stretched out.
 Figure 8. To cut the balloon open from one pole to the other, start at the knot—following a line of longitude—and cut all the way to the top (the other pole), stopping a tiny bit before the very top, as shown in the picture on the bottom left.
1. Have the students work together to stretch out the balloon into a shape as close as possible to a flat rectangle. The goal for this projection is to keep the equator straight and to get the lines of longitude as straight as possible so it looks as close as possible to a Mercator projection. As they do so, you can ask the students to pay attention to how the circles change in form, size, and distance. You might ask students to think about why you would choose a rectangular shape to create a map and why you would like to have straight lines for the equator and for the lines of longitude.
 Figure 9. The balloon is stretched out into a rectangular, flat shape.
1. Have the students work together to pin the stretched-out balloon to the cardboard.
1. Please make sure you advise the students to put the pins in with the colored ends angled slightly outward, as shown in the next figure. Push pins that are pointing straight down or with the colored tips pointing inward might shoot out due to the tension in the balloon, causing a hazard.
2. Students should also be asked not to stretch the balloon too much. Harsh stretching creates a lot of stress on the pins and could possibly rip the balloon.
 Figure 10. Pins need to be put in with the colored ends angled slightly outward so the tension in the balloon does not propel them out.
1. Occasionally, the balloon will rip in the process. In this case, students should be asked to hold the ripped edge with their fingers while making observations. Sometimes, an extra push pin can hold the ripped part.
2. Students could be prompted to observe and communicate details about their projection.
1. Attention should be directed to the type and extent of distortions in different areas of the map. The main focus should be on size and distance. You can remind students that the following was true on their original globe:
1. All circles were the same size.
2. The circles on the equator were equidistant from each other; so were the circles between the equator and each pole.
3. The circles in the northern and southern hemispheres were drawn midway between the equator and each pole.
2. Students should observe if the circles are projected into circles (and not into ellipses or any other shape) all over, or only in particular areas of their map.
3. Students could investigate if direction is maintained in specific areas of their map. They do this by comparing a circle on the intersection of the equator and a line of longitude with the closest circles in the northern or southern hemisphere. Note that they observed the relative direction of these circles on the globe in step 8.b.

### Expected Results

Figure 11 displays the expected result.

 Figure 11. The image shows the projection created by stretching out a cut-open, deflated balloon into a flat, rectangular map.

• The size of the circles is no longer identical on the map, indicating relative size and distance are distorted. The circles on the equator are still mostly equal in size, indicating that features located on the same line of latitude can be compared in size. Compared to the sizes of the circles on the equator, enlargement gets more prominent as you move away from the equator, and is most extreme at the poles. This explains why Mercator projections provide misleading information when comparing size or distance of continents or countries. Note: This balloon map shows distortions on the edges that would not appear in Mercator projections.
• Most circles still look like circles, indicating that shape is maintained in most areas of the map. In some areas—mainly near the edges—the original circles look like ellipses, indicating that shape and direction are distorted in these areas. (Note: These shape and direction distortions do not appear in Mercator projections.)
• Directions of the features relative to each other are maintained over a large area around the center of this map. In a real Mercator projection, the lines of longitude are perfectly straight and direction is exactly maintained, making them particularly useful in navigation.

### For Further Exploration

This science activity can be expanded or modified in a number of ways. Here are a few options:

• As an alternative to drawing circles on the balloon, continents can be drawn on the balloon. The following hints can help make this activity a success:
• Let students identify the prime meridian on the globe (balloon) and locate the continents relative to the lines of longitude and the equator on the balloon.
• Advise students to draw the continents in an abstract way, using primitive shapes (rectangle, triangle, circle).
• Use different colors for different continents, or write the first letters of the continent within it.
• Use patterns (e.g. stripes) to differentiate land from water.
• A grapefruit or pomelo can be used to represent a globe. In this case, circles can be added using nail polish.
• To detach the peel from the flesh, cut the peel along a line of longitude.
• Peel the grapefruit without further breaking the skin by passing your fingers under the peel, all the way around. Some tears in the flesh will most likely be introduced while peeling the grapefruit, which is ok.
• You can then carefully open the peel along the one longitudinal cut you made and remove the fruit.
• Now push the peel down to create a flat map from the originally spherical peel. You will need to create extra cuts in the peel to get the peel to lay flat. This will create a different type of projection, closer to a Goode homolosine projection.
 Figure 12. A grapefruit can be used to introduce a different type of world projection. The distortions introduced in this projection are very different from the ones observed in the balloon activity.

### Credits

Sabine De Brabandere, PhD, Science Buddies
Sponsored by a generous grant from Chevron