Scale, distance and exact location
Grade 9 Social Studies Worksheet - Building Confidence
Circle the best answer.
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.
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
- Multiplying 4 cm by 50,000 gives 200,000 km, which is the true ground distance
- At 1:50,000, 1 cm stands for 5 km, so 4 cm is 20 km on the ground
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.
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
- 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
- No: it should be 80 cm, since 1,000,000 divided by 50,000 is 20, times 4
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.
After the 150% copy, how far apart are the school and the lake on paper, and on the ground, Jun asks?
- 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
- 4 cm on paper, since copying cannot change a map’s lengths
- 6 cm on paper, still 2 km on the ground
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
- Neither, since copying breaks the scales on a map
- The bar scale, since it was enlarged along with the map
- Both, since a copy keeps the printed information correct
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
- 1:75,000, since 50,000 × 1.5 follows the bigger paper
- 1:50,000, since the printed ratio is unchanged by copying
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.
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
- 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
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.
Which statement fits a small-scale map such as the country map, Noah asks?
- It has the smaller number in its ratio, such as 1:50,000
- It covers a large area and shows little detail
- It covers a large area and shows a lot of detail
- It covers a small area and shows a lot of detail
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.
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
- 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
- The straight-line distance is 2 km; a walk around the river could be longer
Ren’s note says: “1:50,000 means 1 cm stands for 50,000 km.” Which fix is right?
- Leave it: ratio scales are written in kilometers
- Change it: 1 cm stands for 50,000 m, which is 50 km
- Change it: 1 cm stands for 50,000 cm, which is 500 m
- Change it: 1 cm stands for 5,000 cm, which is 50 m
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.
Tala writes: “Both maps put the school 2 km from the lake.” Do the cards support that?
- 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
- No: the cm distances differ, 4 and 0.2, so the ground distances must differ
- Yes: 4 cm at 1:50,000 and 0.2 cm at 1:1,000,000 both stand for 2 km