Why every flat map stretches something

Grade 6 Social Studies Worksheet - Challenge Me

Circle the best answer.

1. 1.

   At 60° N, a Mercator map draws land 2 times too wide and 2 times too tall. How many times too big does Pia see its area?

   • 1 time: the area is true
   • 8 times too big
   • 2 times too big
   • 4 times too big
2. 2.

   At about 70° N, Ren's Mercator map draws land about 3 times too wide and 3 times too tall. About how many times too big does its area look?

   • About 27 times too big
   • About 3 times too big
   • About 9 times too big
   • About 6 times too big
3. 3.

   At about 75° N, Tala's Mercator map draws land about 4 times too wide and 4 times too tall. About how many times too big does its area look?

   • About 16 times too big
   • About 8 times too big
   • About 4 times too big
   • About 64 times too big
4. 4.

   Ari's friend says a Mercator map is useless. Which response is right?

   • Disagree: it shows sizes correctly
   • Disagree: it keeps compass directions straight for sailors
   • Agree: it shrinks the lands near the poles
   • Agree: it is the one flat map that bends anything
5. 5.

   World map with straight, parallel longitude lines; latitude lines at 0°, 30°, 60° spaced wider and wider toward the poles. On Esme's Map P, latitude lines spread farther apart toward the poles, and longitude lines never meet. Which map is it, and what does it get wrong?

   • Mercator: land near the poles looks too big
   • Equal-area: land keeps its true shape
   • Mercator: land near the equator looks too big
   • Equal-area: land near the poles looks too big
6. 6.

   On Jun's Map Q, latitude lines crowd closer together toward the poles, and land near the poles looks short and wide. Which map is it, and what does it keep?

   • Equal-area: shapes true, sizes squashed
   • Mercator: nothing is stretched or squashed
   • Mercator: sizes true, shapes squashed
   • Equal-area: sizes true, shapes squashed
7. 7.

   Kira's Map R keeps every small shape right, and steady compass courses are straight lines on it. Which map is it, and what does it get wrong?

   • Mercator: sizes are wrong near the equator
   • Mercator: sizes are wrong near the poles
   • Globe: it keeps sizes and shapes true
   • Equal-area: sizes are wrong near the poles
8. 8.

   Luz's note says: "Mercator maps stretch land most near the equator." Which fix makes the note right?

   • Change "equator" to "poles"
   • Change "most" to "evenly"
   • Change "stretch" to "keep the true size of"
   • Change "land" to "oceans"
9. 9.

   Milo's note says: "2 times too wide and 2 times too tall means 2 times too big in area." Which fix makes it right?

   • Change it to 4 times, because 2 + 2 = 4
   • Change it to 4 times, because 2 × 2 = 4
   • Change it to 8 times, because 2 × 2 × 2 = 8
   • Leave it at 2 times; it is already right
10. 10.

    Noah's note says: "Equal-area maps keep both sizes and shapes true." Which fix makes the note right?

    • Sizes stay true, but shapes bend
    • Shapes stay true, but sizes bend
    • Neither stays true on any flat map
    • Both stay true, as the note says