Choose the right map, and see what each projection distorts

Grade 9 Social Studies Worksheet - Challenge Me

Circle the best answer.

1. Read this first

   Use this

   Card E. Three world projections. Mercator (1569): shapes kept and compass lines straight, but lands far from the equator are stretched, so Greenland looks as big as Africa. Robinson (1963): a compromise, with shapes and sizes both a little off. Gall–Peters: an equal-area map, with sizes true but shapes stretched. Note: Africa covers about 30.3 million km²; Greenland covers about 2.17 million km² (2,166,086 km²). Africa stretches from about 37°N to 35°S; Greenland lies between about 60°N and 83°N. On a Mercator map, areas are stretched by about 1.0 times at 0°, 1.3 times at 30°, 4 times at 60° and 8.5 times at 70°, and the stretch keeps rising toward the poles.

2. 1.

   Noah sees that Mercator draws Greenland about as big as Africa, which is about 14 times larger. What does that imply about the stretch?

   • Both are stretched equally, so the 14 times is a measuring slip and not a feature of the projection
   • Gall–Peters stretches Greenland about 14 times, because it keeps sizes true and corrects Africa instead
   • Greenland is stretched about 14 times more than Africa, because it lies far from the equator
   • Africa is shrunk about 14 times, because Mercator keeps shapes and so it must reduce the largest lands

3. Use this

   Card E. Three world projections. Mercator (1569): shapes kept and compass lines straight, but lands far from the equator are stretched, so Greenland looks as big as Africa. Robinson (1963): a compromise, with shapes and sizes both a little off. Gall–Peters: an equal-area map, with sizes true but shapes stretched. Note: Africa covers about 30.3 million km²; Greenland covers about 2.17 million km² (2,166,086 km²). Africa stretches from about 37°N to 35°S; Greenland lies between about 60°N and 83°N. On a Mercator map, areas are stretched by about 1.0 times at 0°, 1.3 times at 30°, 4 times at 60° and 8.5 times at 70°, and the stretch keeps rising toward the poles. Card F (made up for practice). Three jobs. Job 1: a ship's navigator wants to steer by drawing a straight line at one compass bearing. Job 2: a climate office compares each continent's share of the world's land area. Job 3: a school wants a wall map that looks balanced overall, with no large error in shape or size.

4. 2.

   Luz picks projections for Job 1 (steering by a compass bearing) and Job 2 (comparing continents' shares of land). Which pair is right?

   • Mercator for both jobs, because it keeps shapes and so it must keep the sizes that Job 2 compares
   • Mercator for Job 1, because its compass lines are straight; Gall–Peters for Job 2, because its sizes are true
   • Gall–Peters for Job 1 and Mercator for Job 2, because the equal-area map is the one that keeps compass lines straight
   • Robinson for both jobs, because a compromise map is a safe choice when each job needs something exact
5. 3.

   Tala picks a map for Job 3, a balanced school wall map. Which choice fits, and why not Mercator?

   • Mercator, because it keeps shapes true, and a wall map should have no large shape error
   • Gall–Peters, because it has no large error in size or shape, so the wall map is balanced overall
   • No projection suits Job 3, because flat maps have some error and a balanced one cannot be drawn
   • Robinson, a compromise a little off in shape and size; Mercator makes Greenland look as big as Africa

6. Use this

   Card E. Three world projections. Mercator (1569): shapes kept and compass lines straight, but lands far from the equator are stretched, so Greenland looks as big as Africa. Robinson (1963): a compromise, with shapes and sizes both a little off. Gall–Peters: an equal-area map, with sizes true but shapes stretched. Note: Africa covers about 30.3 million km²; Greenland covers about 2.17 million km² (2,166,086 km²). Africa stretches from about 37°N to 35°S; Greenland lies between about 60°N and 83°N. On a Mercator map, areas are stretched by about 1.0 times at 0°, 1.3 times at 30°, 4 times at 60° and 8.5 times at 70°, and the stretch keeps rising toward the poles.

7. 4.

   Jun writes: "Gall–Peters is the true map because it keeps sizes." What is the best correction using Card E?

   • Mercator is the true map instead, because it keeps shapes and compass lines straight in the same way
   • Gall–Peters keeps shapes true too, because an equal-area map has to match the shapes of the lands
   • The note is right, because a map that keeps sizes is the right map for the jobs a geographer has
   • Gall–Peters keeps sizes true but stretches shapes, so it is true for one property, not for both

8. Use this

   Card E. Three world projections. Mercator (1569): shapes kept and compass lines straight, but lands far from the equator are stretched, so Greenland looks as big as Africa. Robinson (1963): a compromise, with shapes and sizes both a little off. Gall–Peters: an equal-area map, with sizes true but shapes stretched. Note: Africa covers about 30.3 million km²; Greenland covers about 2.17 million km² (2,166,086 km²). Africa stretches from about 37°N to 35°S; Greenland lies between about 60°N and 83°N. On a Mercator map, areas are stretched by about 1.0 times at 0°, 1.3 times at 30°, 4 times at 60° and 8.5 times at 70°, and the stretch keeps rising toward the poles. Card F (made up for practice). Three jobs. Job 1: a ship's navigator wants to steer by drawing a straight line at one compass bearing. Job 2: a climate office compares each continent's share of the world's land area. Job 3: a school wants a wall map that looks balanced overall, with no large error in shape or size.

9. 5.

   Pia says a climate office measured each continent's area on a Mercator map for Job 2. Which shares come out too small?

   • Equatorial continents like Africa, whose areas are stretched little while far-north lands are stretched a lot
   • The shares come out too small by the same factor, since the stretch applies to the whole map alike
   • No shares are wrong, because Mercator keeps shapes and so each continent keeps its true share of the area
   • Far-northern lands, because Mercator stretches lands far from the equator so their areas come out too small

10. Use this

    Card E. Three world projections. Mercator (1569): shapes kept and compass lines straight, but lands far from the equator are stretched, so Greenland looks as big as Africa. Robinson (1963): a compromise, with shapes and sizes both a little off. Gall–Peters: an equal-area map, with sizes true but shapes stretched. Note: Africa covers about 30.3 million km²; Greenland covers about 2.17 million km² (2,166,086 km²). Africa stretches from about 37°N to 35°S; Greenland lies between about 60°N and 83°N. On a Mercator map, areas are stretched by about 1.0 times at 0°, 1.3 times at 30°, 4 times at 60° and 8.5 times at 70°, and the stretch keeps rising toward the poles.

11. 6.

    Bo writes: "Greenland looks as big as Africa on Mercator, so Greenland is as big as Africa." What is the best correction using Card E?

    • No true comparison is possible, because the projection changes the sizes and the areas cannot be known
    • Mercator stretches lands far from the equator; Greenland is about one fourteenth of Africa in true area
    • Greenland is about 14 times Africa in true area, because Gall–Peters draws it larger than Mercator does
    • Mercator keeps shapes, so what it draws is true; Greenland and Africa must be nearly equal in area
12. 7.

    Milo estimates the least that Mercator stretches Greenland's area. Greenland's southern tip is near 60°N. What can be said?

    • At least 4 times: even its southern parts near 60°N are stretched 4 times, and the stretch rises north
    • About 2 times, the length stretch at 60°N, because areas are stretched by the same amount as lengths
    • About 8.5 times, because Greenland's middle is at 70°N and the middle gives its average stretch
    • Exactly 14 times, because that is the ratio that makes Greenland look as big as Africa on the map
13. 8.

    Zee says the Robinson projection "fixes" Mercator's problem. What does Card E support?

    • Robinson trades Mercator's size error for small errors in both shape and size, a compromise
    • Yes, Robinson keeps sizes true like Gall–Peters and shapes true like Mercator, so no error is left
    • No, Robinson is a Mercator map with the compass lines straightened out and so has the same size error
    • Yes, and for that reason Robinson is the right map for steering a ship by a compass bearing
14. 9.

    Kira draws Africa as 4.2 cm² on a Gall–Peters map. About how large should Greenland be on the same map?

    • About 4.2 cm², the same as Africa, because the two lands look equal in size on the world maps people know
    • About 0.3 cm², one fourteenth of Africa's, because an equal-area map keeps the true ratio of areas
    • About 3.9 cm², because Greenland is the part of Africa's 4.2 cm² that is left after taking away 0.3 cm²
    • About 0.5 cm², because dividing Africa's 4.2 cm² by Mercator's 8.5 area stretch at 70°N gives Greenland's size

15. Use this

    Card E. Three world projections. Mercator (1569): shapes kept and compass lines straight, but lands far from the equator are stretched, so Greenland looks as big as Africa. Robinson (1963): a compromise, with shapes and sizes both a little off. Gall–Peters: an equal-area map, with sizes true but shapes stretched. Note: Africa covers about 30.3 million km²; Greenland covers about 2.17 million km² (2,166,086 km²). Africa stretches from about 37°N to 35°S; Greenland lies between about 60°N and 83°N. On a Mercator map, areas are stretched by about 1.0 times at 0°, 1.3 times at 30°, 4 times at 60° and 8.5 times at 70°, and the stretch keeps rising toward the poles. Card F (made up for practice). Three jobs. Job 1: a ship's navigator wants to steer by drawing a straight line at one compass bearing. Job 2: a climate office compares each continent's share of the world's land area. Job 3: a school wants a wall map that looks balanced overall, with no large error in shape or size.

16. 10.

    Esme writes: "Africa and Greenland look equal, so for Job 2 either map would do." What is the best correction using Cards E and F?

    • Either map would do, because both keep the shapes of the continents and shares depend on shape
    • Mercator would do after dividing each area by 8.5, because the stretch is the same on each continent
    • Job 2 compares land shares, so it needs true sizes; Gall–Peters shows Africa 14 times Greenland
    • Robinson would do better, because it is a compromise and the office needs a balanced result