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.

   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 72 times larger, because 8.5 is a length stretch and the area stretch is its square
   • It gives about 18 million km², which is Africa's size, so the table explains the look in full
   • 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, short of Africa's 30; Greenland's far-north parts are stretched even more

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

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

   • 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
   • Mercator, because it keeps shapes true, and a wall map should have no large shape error

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?

   • The note is right, because a map that keeps sizes is the right map for the jobs a geographer has
   • 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
   • 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?

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

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?

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

    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
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 0.3 cm², one fourteenth of Africa's, because an equal-area map keeps the true ratio of areas
    • 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 4.2 cm², the same as Africa, because the two lands look equal in size on the world maps people know
    • About 3.9 cm², because Greenland is the part of Africa's 4.2 cm² that is left after taking away 0.3 cm²
14. 9.

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

    • It distorts size but keeps shapes and straight compass lines, so whether it is useful depends on the job
    • 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 is an equal-area map and keeps sizes true in the same way as Gall–Peters
    • The note is wrong, because Mercator distorts nothing near the poles, where its shapes are kept true

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
    • Robinson would do better, because it is a compromise and the office needs a balanced result
    • Job 2 compares land shares, so it needs true sizes; Gall–Peters shows Africa 14 times Greenland