Cover lesson · Geography · Year 7 · Beginner
LNF: Numeracy → Learning about geometry helps us understand shape, space and position, and learning about measurement helps us quantify in the real world → Measurement
Name: Class: Date:
Print: this sheet, one per pupil, and the stimulus sheet “Cwm Tawelan: a map for measuring distance”, one per pupil if possible, in colour if you can. It does not matter if the map prints bigger or smaller: pupils measure with the grid and the scale bar printed on the map, which change size together. No computers are needed. Pupils need a pen, a pencil, a ruler, a calculator and a strip of scrap paper with a straight edge, about 3 cm wide and at least as long as the scale bar.
Run: 4 min pupils read the stimulus in pairs · 5 min Step 2 · 5 min Step 3 · 8 min Step 4 · 10 min Step 5 · 10 min Step 6 · 7 min Step 7 · 4 min Step 8, alone · 2 min success criteria. Total 55 minutes.
Collect: this sheet. It is numeracy practice in measurement: Steps 3 to 5 show measuring real distances with a grid and a scale bar, Steps 2 and 6 show unit conversions and ratio scale calculations with working, and Step 7 shows time calculations from a distance and a speed. It prepares pupils for the map skills in GCSE Geography, where they measure straight-line and route distances on Ordnance Survey maps. All answers are on the worked example. Accept map measurements within 0.2 km for straight lines and 0.3 km for winding routes.
Your class is staying at the youth hostel in Cwm Tawelan. You are the route planners. You will measure how far apart places are, how long the roads and paths really are, and how long the walks will take.
Read the key and the box “3 ways to measure on this map”. Find the school and the waterfall. Check that you agree they are exactly 2 grid squares apart, so they are 2 km apart.
Use the units box on the stimulus. Fill in the gaps.
| (a) 3 km = ___ m | (b) 2.4 km = ___ m | (c) 850 m = ___ km | (d) 50 m = ___ km |
|---|---|---|---|
| (e) 250 cm = ___ m | (f) 25 000 cm = ___ m | (g) 100 000 cm = ___ km | (h) 1.5 km = ___ cm |
Each pair of places is in a line going east to west or north to south. Count the whole squares, then estimate the part of a square in tenths. Give each answer in km to 1 decimal place.
| From and to | Distance (km) |
|---|---|
| School to waterfall | |
| Youth hostel to viewpoint | |
| Car park to viewpoint | |
| Campsite to Fferm Hafod |
These places are on a slant, so counting squares is hard. Use the paper edge method: mark the 2 centres on the edge of your strip, then read the distance on the scale bar. Write a letter next to each mark, for example C for church, so you do not mix them up.
| From and to (straight line) | Distance (km) |
|---|---|
| Church to youth hostel | |
| Bridge to mast | |
| Car park to youth hostel | |
| Campsite to waterfall |
(a) Use a fresh edge of your strip. Measure each route section by section: mark the start, turn the strip at every bend, and mark the end. Then read the total on the scale bar. Copy the straight-line distances from Steps 3 and 4, then subtract to find the extra distance.
| Route | Route distance (km) | Straight-line distance (km) | Extra distance (km) |
|---|---|---|---|
| Road: car park to youth hostel, through Llanhelyg and over the bridge | |||
| Footpath: car park to viewpoint, over the footbridge (FB), past the church and through Coed Tawelan |
(b) Use the map to give 2 reasons why the road is longer than the straight line.
(c) Gareth laid his ruler straight from the car park to the youth hostel and said the walk up the road is 4.1 km. Why is his answer too short?
(a) These lengths were measured on full-size Ordnance Survey style maps of the valley, so they do not depend on how your sheet printed. Use the ratio scales box. Show your working in the table. Example: 2 cm on a 1:25 000 map is 2 × 250 = 500 m, which is 500 ÷ 1000 = 0.5 km.
| Map length | Real distance in m | Real distance in km |
|---|---|---|
| 1:25 000 map: school to waterfall, 8 cm | ||
| 1:25 000 map: youth hostel to viewpoint, 10 cm | ||
| 1:25 000 map: car park to school, 5 cm | ||
| 1:25 000 map: car park to viewpoint, 13.2 cm | ||
| 1:50 000 map: school to waterfall, 4 cm | ||
| 1:50 000 map: campsite to Fferm Hafod, 4.6 cm | ||
| 1:50 000 map: car park to youth hostel, 8.2 cm |
(b) Now go the other way. How long would each distance be on each map?
| Real distance | Length on a 1:25 000 map (cm) | Length on a 1:50 000 map (cm) |
|---|---|---|
| Llyn Tawelan, 1 km long | ||
| A path 750 m long | ||
| A walk 3.5 km long |
(c) Elin says: “On the 1:50 000 map the bridge is 3 cm from the mast. 3 × 50 000 = 150 000, and 150 000 ÷ 1000 = 150, so they are 150 m apart.” What has she done wrong? What is the correct distance? Does it match your Step 4 answer?
(d) The school to the waterfall is 8 cm on one map and 4 cm on the other. Explain why both maps show the same real distance.
(a) The youth hostel warden’s route card for a round walk is below. Use 4 km per hour, so each km takes 15 minutes. Show your working.
| Section | Distance (km) | Time (minutes) |
|---|---|---|
| 1. Ridge path: youth hostel to viewpoint | 2.5 | |
| 2. Footpath: viewpoint down to car park | 3.8 | |
| 3. Road: car park back up to youth hostel | 4.5 | |
| Total |
(b) Write the total time in hours and minutes.
(c) The group leaves the youth hostel at 09:30 and stops for 45 minutes for lunch. The coach leaves the youth hostel at 13:30. What time will they get back? Will they make the coach, and with how many minutes to spare?
(d) Do the warden’s distances for sections 2 and 3 agree with your Step 5 answers to within 0.2 km? If not, what might you have done differently?
Rhodri’s printer printed the map smaller. On his copy the school is 6 cm from the waterfall. He says: “4 cm is 1 km, so the school is 1.5 km from the waterfall.” Explain what is wrong, give the correct distance, and say why the grid squares and the scale bar still work on his copy.