THE GLOBAL GRAPEFRUIT

BY:  BY:  Valerie Stovall
      Indianapolis, 6/1990

Purpose:
To introduce the concept of distortion and to learn how different map projections are to be used.

Teaching level:  Grades 3 - 9

Geographic theme:  Location

Objectives:
At the conclusion of this lesson the students will be able to:
 1.  tell how maps differ from globes.
 2.  state some characteristics of 3 different types of map projections.
 3.  realize that distortions are inherent in various systems of map projections
 4.  understand that there are many types of map projections used for various purposes.

Materials:
-grapefruit or orange for each student                -knife
-pencils                                                            -modeling clay or Play-Doh
-toilet paper rolls                                              -wall map
-globes

Procedure:
1.  Discuss with the class that the Earth is round like a ball.  Any object with this shape is called a sphere.  Because the globe is a sphere, it can show the surface of the earth accurately.  Distances, directions, sizes, and shapes of land and water areas are accurate.  (Teacher may show examples of spheres.)
2.  Explain that cartographers had a difficult time trying to make a flat map depict a round globe.  To demonstrate how difficult it is to flatten a sphere's surface perfectly, tell students that they are to peel their own version of the globe.
3.  Depending on the grade level, the teacher may have to cut the grapefruit, starting at the stem end and making a cut halfway around the grapefruit to the opposite spot.  Student will then carefully work their fingers around and under the edges of the skin and peel carefully, keeping it in one piece if possible.
4.  After peeling, students turn the yellow side up and flatten it as best as they can.  Discuss what kinds of problems they may be having and observe the way the "world" looks now, compared to the way it did when it was still round.  It's difficult to flatten a curved surface without some pulling and pushing, or even cutting.
5.  Cartographers found this to be a problem too.  They had to stretch their maps and even cut them a little, therefore, leaving gaps in the map.  (Observe wall map of the world).  Introduce the word "projection".  Write the word on the board and have students find and read the definition from the dictionary. The word may be divided into syllables.
6.  Tell students that mapmakers discovered how to use mathematics to help them "stretch" the earth into a flat shape.  There are many types of projections used for different purposes.  Though one shape may be shown accurately, another may be distorted.  One type of projection is called the Eckert Projection (show picture).  Explain that an advantage of this projection is that it shows the sizes of most continents and oceans correctly, but the shapes of some land and water areas are distorted.  Have student observe this on the map.
7.  Another type of projection is the Interrupted Projection.  This is called interrupted because it stops and starts again.  This type shows the relative sizes of important land areas almost accurately, but as a result, the oceans and some land areas are split or broken up.  Have students observe the splits in the map of the Interrupted Projection.
8.  The Mercator Projection was developed by a cartographer named Gerhard Kremer more than 400 years ago.  He developed a projection that turned the spherical surface of the earth into a can shape or cylinder.  (show other examples of cylinders).  This projection is great for navigational use (sailors and pilots) because it shows true direction, but it distorts the land in the high latitudes.  Show a picture of a Mercator Projection and note the size of Greenland as compared to South America.  (It looks much larger, but it is actually less than a third the size of the United States).
9.  At this time, the students will make their own model of a Mercator Map.  Distribute clay and empty tissue rolls to each pair of students.  Working together, they will flatten out the clay and then roll it onto the tissue roll, making sure it wraps around the entire roll.  Then using a pencil, draw lines both vertically and horizontally on the clay.
10. Students will unroll the clay to view their own projections, comparing their grids to the rectangular grids on the Mercator Map, which is another characteristic of maps.

Evaluation:
Review the three types of map projections learned and their uses.  Assess completion of models.

Extensions/Adaptations:
This could be split into multiple lessons in consideration of time and the maturity level of students:
 Lesson 1:  Procedures 1 - 5, Peeling a grapefruit.
 Lesson 2:  Procedures 5 - 6, Eckert Projection
 Lesson 3:  Procedure 7, Interrupted Projections
 Lesson 4:  Procedure 8, Mercator Projection
 Lesson 5:  Model making
The above lessons 2, 3, and 4 could also be combined into one lesson, making a total of 3 lessons in this unit.