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
   • The bar scale says 1 cm is 1 km, so 4 km is right and the ratio is wrong
   • At 1:50,000, 1 cm stands for 5 km, so 4 cm is 20 km on the ground
   • 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.

   Which map shows the school and the lake in more detail, and why, Bo asks?

   • The country map, since it covers more ground and so has more to show
   • The town map: 1:50,000 is the larger scale, so features are drawn bigger
   • The country map: 1:1,000,000 has the bigger number, so it is the larger scale
   • Neither: both maps show the same school and lake, so detail is equal
5. 3.

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

   • Yes, but just because both maps cover the same ground and agree by chance
   • 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

6. 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.

7. 4.

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

   • 6 cm on paper, still 2 km on the ground
   • 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
8. 5.

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

   • 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
   • The bar scale, since it was enlarged along with the map
9. 6.

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

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

10. 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.

11. 7.

    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?

    • Yes: 1 mm at 1:50,000 is 50 m, so the line shows the real width
    • No: roads are drawn narrower than true scale so they hide nothing
    • 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

12. 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.

13. 8.

    Which statement fits a small-scale map such as the country map, Noah asks?

    • It covers a small area and shows a lot of detail
    • It has the smaller number in its ratio, such as 1:50,000
    • It covers a large area and shows a lot of detail
    • It covers a large area and shows little detail
14. 9.

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

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

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

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