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 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
- 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 0.5 km, so 4 cm is 2 km, not 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 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 map shows the school and the lake in more detail, and why, Bo asks?
- Neither: both maps show the same school and lake, so detail is equal
- The country map: 1:1,000,000 has the bigger number, so it is the larger scale
- The town map: 1:50,000 is the larger scale, so features are drawn bigger
- The country map, since it covers more ground and so has more to show
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?
- 4 cm on paper, since copying cannot change a map’s lengths
- 6 cm on paper, still 2 km on the ground
- 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
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
- The bar scale, since it was enlarged along with the map
- Neither, since copying breaks the scales on a map
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?
- 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
- No: roads are drawn wider than true scale to be seen; 1 mm here 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.
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 small area and shows a lot of detail
- It covers a large area and shows little detail
- It covers a large 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?
- A map distance says nothing about a walk, so a map is no use
- 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
- The walk is exactly 2 km, since a map distance is the walking distance
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 50,000 m, which is 50 km
- Change it: 1 cm stands for 5,000 cm, which is 50 m
- Leave it: ratio scales are written in kilometers
- Change it: 1 cm stands for 50,000 cm, which is 500 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
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
- The town map: 0.1 cm is 50 m there but 1 km on the country map
- Both: a 0.1 cm error is 0.1 cm on each map, so they are equal