Scale, distance and exact location

Grade 9 Social Studies Worksheet - Building Confidence

Circle the best answer.

1. Read this first

   Use this

   Card A. A town map (an example). Ratio scale 1:50,000. Bar scale marked 0, 1 and 2 km, with 2 cm for each 1 km. On the map the school is 4 cm from the lake and the river is 10 cm long. A main road is drawn as a line 1 mm wide; real main roads here are about 10 m wide.

2. 1.

   A reader says the school is 4 km from the lake because the map shows 4 cm. What went wrong, Ari asks?

   • At 1:50,000, 1 cm stands for 0.5 km, so 4 cm is 2 km, not 4
   • At 1:50,000, 1 cm stands for 5 km, so 4 cm is 20 km on the ground
   • The bar scale says 1 cm is 1 km, so 4 km is right and the ratio is wrong
   • Multiplying 4 cm by 50,000 gives 200,000 km, which is the true ground distance

3. Use this

   Card A. A town map (an example). Ratio scale 1:50,000. Bar scale marked 0, 1 and 2 km, with 2 cm for each 1 km. On the map the school is 4 cm from the lake and the river is 10 cm long. A main road is drawn as a line 1 mm wide; real main roads here are about 10 m wide. Card B. A country map of the same area (an example). Ratio scale 1:1,000,000. On it, the school and the lake are 0.2 cm apart.

4. 2.

   On the country map the school and the lake are 0.2 cm apart. Is that consistent with the town map, Esme asks?

   • No: the distance between two places should be 4 cm on any map
   • No: it should be 80 cm, since 1,000,000 divided by 50,000 is 20, times 4
   • Yes: 2 km is 200,000 cm, and 200,000 divided by 1,000,000 is 0.2 cm
   • Yes, but just because both maps cover the same ground and agree by chance

5. Use this

   Card A. A town map (an example). Ratio scale 1:50,000. Bar scale marked 0, 1 and 2 km, with 2 cm for each 1 km. On the map the school is 4 cm from the lake and the river is 10 cm long. A main road is drawn as a line 1 mm wide; real main roads here are about 10 m wide. Card C. A copy shop enlarges the town map to 150%, so every length on paper is 1.5 times longer. The printed ratio still says 1:50,000. The bar scale is enlarged along with the map.

6. 3.

   After the 150% copy, how far apart are the school and the lake on paper, and on the ground, Jun asks?

   • 4 cm on paper, since copying cannot change a map’s lengths
   • 9 cm on paper, since 4 × 1.5 × 1.5, once for each direction
   • 6 cm on paper, but now 3 km on the ground, since the map is bigger
   • 6 cm on paper, still 2 km on the ground
7. 4.

   After the copy, which printed scale is still correct, Kira asks?

   • The bar scale, since it was enlarged along with the map
   • The ratio 1:50,000, since a ratio is a fixed fact about the place
   • Both, since a copy keeps the printed information correct
   • Neither, since copying breaks the scales on a map
8. 5.

   What would the ratio scale be after the 150% copy, Luz asks?

   • About 1:33,000, since 1 cm now stands for 50,000 ÷ 1.5 cm
   • 1:100,000, since doubling the map length doubles the ratio
   • 1:50,000, since the printed ratio is unchanged by copying
   • 1:75,000, since 50,000 × 1.5 follows the bigger paper

9. Use this

   Card A. A town map (an example). Ratio scale 1:50,000. Bar scale marked 0, 1 and 2 km, with 2 cm for each 1 km. On the map the school is 4 cm from the lake and the river is 10 cm long. A main road is drawn as a line 1 mm wide; real main roads here are about 10 m wide.

10. 6.

    The main road is drawn 1 mm wide on the 1:50,000 map. Is the road 50 m wide on the ground, Milo asks?

    • No: roads are drawn wider than true scale to be seen; 1 mm here is 50 m
    • Yes: the bar scale shows that 1 mm stands for 50 m of road
    • No: roads are drawn narrower than true scale so they hide nothing
    • Yes: 1 mm at 1:50,000 is 50 m, so the line shows the real width
11. 7.

    The school is 4 cm from the lake on the map. What does that tell Pia about the walk from one to the other?

    • The walk is 4 km, because the route doubles each map distance
    • The straight-line distance is 2 km; a walk around the river could be longer
    • A map distance says nothing about a walk, so a map is no use
    • The walk is exactly 2 km, since a map distance is the walking distance
12. 8.

    Ren’s note says: “1:50,000 means 1 cm stands for 50,000 km.” Which fix is right?

    • Change it: 1 cm stands for 5,000 cm, which is 50 m
    • Change it: 1 cm stands for 50,000 cm, which is 500 m
    • Leave it: ratio scales are written in kilometers
    • Change it: 1 cm stands for 50,000 m, which is 50 km

13. Use this

    Card A. A town map (an example). Ratio scale 1:50,000. Bar scale marked 0, 1 and 2 km, with 2 cm for each 1 km. On the map the school is 4 cm from the lake and the river is 10 cm long. A main road is drawn as a line 1 mm wide; real main roads here are about 10 m wide. Card B. A country map of the same area (an example). Ratio scale 1:1,000,000. On it, the school and the lake are 0.2 cm apart.

14. 9.

    Tala writes: “Both maps put the school 2 km from the lake.” Do the cards support that?

    • No: the cm distances differ, 4 and 0.2, so the ground distances must differ
    • No: just a bar scale can give distances in km, and Card B has no bar
    • Yes: 4 cm at 1:50,000 and 0.2 cm at 1:1,000,000 both stand for 2 km
    • Yes, but just the town map is exact; the country map is an estimate
15. 10.

    A reader can measure to within 0.1 cm. Which map gives the school–lake distance more exactly, Zee asks?

    • The country map: the shorter paper distance leaves less to read wrongly
    • Neither: a 0.1 cm error is too small to matter on any map
    • Both: a 0.1 cm error is 0.1 cm on each map, so they are equal
    • The town map: 0.1 cm is 50 m there but 1 km on the country map