Cover lesson · History · 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 “The drovers’ road from Tregaron to London”, one per pupil if possible (pupils measure on its map). Print at 100% (“actual size”), not “fit to page”. No computers are needed. Pupils need a pen, a pencil, a ruler marked in centimetres and millimetres, and a calculator.
Run: 5 min pupils read the stimulus and check the 10 cm line · 15 min Step 2, measuring the stages and using the scale · 6 min Step 3, kilometres to miles · 8 min Step 4, how many days · 8 min Step 5, how many hours a day · 12 min Step 6, the railway and a short written answer. Total 54 minutes. If a pupil’s check line on the map is not 10 cm (allow 2 mm either way), give them the back-up page at the end of the stimulus: it lists the map length of every stage, so they skip measuring and carry on from the “Real distance” column.
Collect: this sheet. It is numeracy practice in measurement: measuring lengths to the nearest millimetre, using a map scale, converting between kilometres and miles, and working with speed, distance and time, including rounding up and changing parts of an hour into minutes. The History context is the Welsh drovers (porthmyn) who walked cattle to London before the railways, and Step 6 asks pupils to use their numbers to explain why the trade ended. The map is simplified and some figures are invented; this is said on the stimulus.
For hundreds of years, Welsh drovers walked herds of cattle all the way from Wales to markets near London. How far did they walk, how many days did it take, and how long was each day on the road? You will measure a simplified map of one drovers’ road, use the scale to find the real distances, and then work out the days and hours. Finally, you will use your answers to explain why the railways ended long-distance droving.
Read the “Who were the drovers?” section and the “Useful facts for the maths” box. Then put your ruler on the check line under the map. It should measure exactly 10 cm. If it does not, tell your teacher.
The route is drawn as 8 straight stages, numbered 1 to 8 in red circles. Measure each stage from the centre of one town dot to the centre of the next, to the nearest millimetre (for example 2.3 cm). Then use the scale to find the real distance.
Scale: 1 cm on the map stands for 20 km. So real distance (km) = map length (cm) × 20.
Example: if a stage measured 2.3 cm, the real distance would be 2.3 × 20 = 46 km.
| Stage | From | To | Map length (cm) | Real distance (km) |
|---|---|---|---|---|
| 1 | Tregaron | Llandovery | ||
| 2 | Llandovery | Brecon | ||
| 3 | Brecon | Abergavenny | ||
| 4 | Abergavenny | Hereford | ||
| 5 | Hereford | Ross-on-Wye | ||
| 6 | Ross-on-Wye | Gloucester | ||
| 7 | Gloucester | Oxford | ||
| 8 | Oxford | Barnet | ||
| Total for the whole route | ||||
(a) Check your total in 2 ways: add up the real distances, then multiply your total map length by 20. Do you get the same answer?
(b) Which stage is the longest? How many times as long as stage 5 is it? (Round to 1 decimal place.)
(c) Tregaron, Llandovery, Brecon and Abergavenny are all in Wales. How far did the herd walk before it left Wales (stages 1 to 3)?
In the drovers’ time, people measured distances in miles. 8 km is about 5 miles, so to change kilometres to miles: divide by 8, then multiply by 5.
Example: 40 km ÷ 8 × 5 = 25 miles.
(a) Change your total distance for the whole route into miles. Show your working.
(b) Change stage 7 (Gloucester to Oxford) into miles.
The stimulus says a herd covered about 25 to 30 km a day. Number of days = total distance ÷ distance per day.
(a) How many days would the whole route take at 25 km a day? Write the calculator answer, then your answer in whole days.
(b) Explain why you must round up to the next whole day, even if the decimal is small.
(c) At 25 km a day, how far would the herd walk on its last day?
(d) How many days would the route take at 30 km a day? Round up.
A herd of cattle walked at about 3 km an hour. Time (hours) = distance ÷ speed. To change part of an hour into minutes, multiply the decimal part by 60.
Example: 2.5 hours = 2 hours and 0.5 × 60 = 30 minutes, so 2 hours 30 minutes.
| Distance walked in a day | Time in hours (calculator answer) | Time in hours and minutes |
|---|---|---|
| (a) 25 km | ||
| (b) 30 km | ||
| (c) The whole route (your total from Step 2) |
(d) Drovers also had to feed, water and rest the cattle and find a field for the night. What do your answers to (a) and (b) tell you about a drover’s working day?
In the second half of the 1800s, railways spread across Wales and England. The stimulus says a cattle train travelled at an average of about 30 km an hour (invented figure).
(a) How long would a cattle train take to cover your total distance? Give your answer in hours and minutes.
(b) How many times faster than the walking herd (3 km an hour) is the train?
(c) Why did the railways end long-distance droving? Write 3 or 4 sentences. Use at least 2 numbers from your answers and at least 1 fact from the “Who were the drovers?” section.