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?

   • Africa is shrunk about 14 times, because Mercator keeps shapes and so it must reduce the largest lands
   • 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
3. 2.

   Ari applies the 8.5 times stretch at 70°N to Greenland's 2.17 million km². Why does that not alone explain Africa's look?

   • It gives about 18 million km², short of Africa's 30; Greenland's far-north parts are stretched even more
   • It gives about 72 times larger, because 8.5 is a length stretch and the area stretch is its square
   • The table cannot be used, because Greenland spans many latitudes and a single stretch fits no part of it
   • It gives about 18 million km², which is Africa's size, so the table explains the look in full

4. 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.

5. 3.

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

   • Gall–Peters for Job 1 and Mercator for Job 2, because the equal-area map is the one that keeps compass lines straight
   • Mercator for both jobs, because it keeps shapes and so it must keep the sizes that Job 2 compares
   • Robinson for both jobs, because a compromise map is a safe choice when each job needs something exact
   • Mercator for Job 1, because its compass lines are straight; Gall–Peters for Job 2, because its sizes are true
6. 4.

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

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

7. 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.

8. 5.

   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 sizes true but stretches shapes, so it is true for one property, not for both
   • 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

9. 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.

10. 6.

    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

11. 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.

12. 7.

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

    • 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
    • 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
13. 8.

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

    • 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
    • About 0.3 cm², one fourteenth of Africa's, because an equal-area map keeps the true ratio of areas
    • About 4.2 cm², the same as Africa, because the two lands look equal in size on the world maps people know
14. 9.

    Ren writes: "Mercator is useless because it distorts size." What is the best correction using Card E?

    • The note is right, because any map that distorts size has no use, as it gives a false picture of the world
    • The note is wrong, because Mercator distorts nothing near the poles, where its shapes are kept true
    • It distorts size but keeps shapes and straight compass lines, so whether it is useful depends on the job
    • The note is wrong, because Mercator is an equal-area map and keeps sizes true in the same way as Gall–Peters

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?

    • 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
    • Either map would do, because both keep the shapes of the continents and shares depend on shape
    • Robinson would do better, because it is a compromise and the office needs a balanced result