Information for Teachers
Peter M Evans
Nell Garfath-Cox
The World of Maths: Night Train
Note to teachers
This document was not created by Teachers TV but the author has allowed us to publish it here to be used for educational purposes

A WORLD OF MATHS
NIGHT TRAIN
INFORMATION FOR
TEACHERS
This programme contains twelve short and stylish sequences, all shot behind the scenes on the overnight sleeper train from London to Scotland.
Each sequence features a different aspect of mathematics for pupils to explore and investigate. The mathematical content is intentionally understated, although the material rewards repeated viewing and provides a rich source of mathematical imagery.
Each sequence poses a question to stimulate mathematical discussion rather than to elicit a correct answer to a computation.
‘How would you work out….’ is a more stimulating question than
‘How many..’ or ‘How much..’
The programme is intended to be used in sections, stopping and replaying the video to analyse the information we’ve given. It can be shown to pupils collectively on a whiteboard, where the pictures can be discussed and annotated, or worked on by pupils individually or in groups on PCs or laptops. The items are best used in programme order because some rely on information given or worked out in a previous clip.
These are the individual topics and their timings in case you want to
‘chapterise’ the programme into individual sections. Each heading here links to some background information about each sequence.
Introduction [00.00 to 00.53]
1. The journey [00.53 to 02.02]
2. Train size [02.02 to 03.15]
3. Passengers [03.14 to 03.54]
4. Staff ratio [03.54 to 04.40]
5. Ticket prices [04.40 to 05.50]
6. Food and drink [05.50 to 06.54]
7. The cabins [06.54 to 07.27]
8. Laundry [07.27 to 08.13]
9. Cleaning the trains [08.13 to 09.05]
10. Train speed [09.05 to 10.54]

11. Single track [10.54 to 12.21]
12. Patterns [12.21 to 13.01]
13. ..and finally [13.01 to 13.40]
Introduction
[00.00 to 00.53]
This section sets the mood of evening drawing in London, as a montage of images moves us toward London’s Euston Station and the imminent departure of the 21.15 Caledonian Sleeper train to
Fort William.
Then there is a menu of items coming up in the programme.
[There’s information about First ScotRail’s Caledonian Sleeper service at http://www.firstgroup.com/scotrail/content/caledoniansleeper/index
.php
]
1. The journey
[00.53 to 02.02]
This clip sets out the journey the train will make from London
Euston to Fort William, giving mileage and time checks for the various stops along the way.
We ask what total distance the train will travel and what time the journey will take, which pupils should be able to answer from the visual information given.
London Euston dep 2115
Watford Junction dep 2133
Crewe
Preston
Westerton dep 2345 dep 0044
(Train stops and splits at Edinburgh)
Dalmuir arr 0555 arr 0603
Helensburgh Upper arr 0626
Garelochhead
Arrochar & Tarbet
Ardlui
Crianlarich arr 0640 arr 0705 arr 0720 arr 0741
Upper Tyndrum arr 0753
Bridge of Orchy
Rannoch
Corrour
Tulloch arr 0811 arr 0840 arr 0856 arr 0915

Roy Bridge
Spean Bridge
Fort William arr 0927 arr 0934 arr 0952
Vacate cabins by 0954
This is the actual timetable for the journey, although there are some extra unpublished stops to service the train and to change drivers.
As we explain in item 9 - ‘Cleaning the trains’ - the train from
Euston stops at Edinburgh to split into sections which go on to Fort
William, Inverness and Aberdeen.
[Pupils will find it useful to have the timetables for these various sleeper services – see http://www.firstgroup.com/scotrail/gf/sleeper%20times.pdf
..and the railway route map at http://www.nationalrail.co.uk/system/galleries/download/print_map s/Nat_Rail_Passenger_Operators.pdf
]

2. Train size
[02.02 to 03.15]
This clip asks pupils to work out the total length and weight of the train.
The train’s sleeper services manager explains how the 16-carriage train is built up from different types of coaches, and we show the information boards that give the length and weight of each type of coach so pupils can work out an answer.
2 lounge cars
2 seating coaches
6 first class sleeper coaches
6 standard class sleeper coaches
Total 16 coaches
3. Passengers
[03.14 to 03.54]
This clip asks how pupils might work out the total number of passengers the train can carry.
It then gives information about the capacity of each carriage.
Combining this with the information from the previous clip help pupils arrive at an answer.
2 seating coaches – 31 passengers in each
6 first class sleeper coaches – 12 cabins – 1 person in each
6 standard class sleeper coaches – 12 cabins – 2 people in each
2 lounge cars – for use of sleeping passengers

4. Staff ratio
[03.54 to 04.40]
The train manager explains what staffing ratios they need to run the train properly.
We then ask pupils to work out how many staff they should have on the train if it were full.
Using the passenger numbers worked out from the previous clip should help towards an answer.
Some pupils might realise that the whole overnight journey is too long for one shift of staff to work, particularly the train drivers, plus they would end up far from home. Pupils might consider how this could be solved. Remember, for every northbound service there’s a corresponding service travelling south at the same time so staff might be able to switch over at some point to get back home.
5. Ticket prices
[04.40 to 05.50]
This clip reveals that the passengers on the train have paid many different prices for their tickets, and the train manager describes the range of ticketing options that are available.
We ask why the train company has so many different ticket prices.
This question is to encourage discussion about the factors that many companies, particularly in travel and tourism, know use to vary the price of their products according to some estimate of the changing demand for them.
Pupils could look at http://www.thetrainline.com
and explore the range of train tickets on offer for the same journey, such as the night sleeper service, and see how the price depends on how far in advance you make a booking. Similarly they could look at an airline website to see how their prices change from day to day.
It seems a general principle that booking earlier is cheaper, and prices usually rise as the time of travel approaches and seats become scarcer. On the other hand, prices sometimes fall as companies try to fill a part-empty plane or hotel with ‘last minute bargain offers’.
[Demand pricing is a complex art. This article gives some background: http://www.informationage.com/article/2007/january_2007/on_demand_experience ]

6. Food and drink
[05.50 to 06.54]
This clip is eventually about ‘nets’.
It starts by explaining how the train is stocked up with food and drink along the way, but ends by asking pupils what the ‘net’ would be of a paper coffee cups and of a folded cardboard breakfast box.
7. The cabins
[06.54 to 07.27]
This clip is about estimating dimensions.
It shows a passenger trying to sleep in one of the sleeper cabins, and asks how the size of the cabin bed might compare with a standard size bed, and how the size of the cabin might compare with a normal bedroom.
We reckon pupils should be able to estimate the height and shoulder width of the person in the video and relate that to the size of the cabin bed and thence the cabin. Again pupils should be able to estimate the dimensions of a normal bed and room, though KS3 pupils often have difficulty estimating units of measurement.
8. Laundry
[07.27 to 08.13]
This clip explains that the railway company has a laundry at each end of its sleeper routes – one at Inverness in Scotland and one at
Wembley in north London.
We ask how many clean sheets the train company might need each week.
This could be worked out from the number of potential sleeping passengers we established in the earlier item. Pupils might also realise that there is also the reverse sleeper service to consider when the train returns from Fort William and goes back south to
London.

9. Cleaning the trains
[08.13 to 09.05]
The night train from Euston has now reached Edinburgh. Here the long train is split into three sections, which will go on to Fort
William, Inverness and Aberdeen.
The train manager explains that all the coaches have to go to
Inverness at least every eight days to be cleaned.
We ask pupils to consider how the coaches might be organised so this will happen.
If the train is split into three lots of 5 coaches at Edinburgh (OK there’s one left over), on their return journey they will be recombined at Edinburgh for their journey back south to London.
There is no direct service between, say Aberdeen and Inverness, so the train must be organised so that each set of 5 coaches takes it in turn to go from London to Inverness. Note that each journey – north or south - takes one whole night, and that for every northbound service there is a corresponding overnight service travelling south at the same time. Pupils might come up with a scheme like this for each set of 5 carriages, working out that the company must have at least 6 sets of five carriages, with some spares, to run the service.
Day 3
Fort
William
Day 4
London
Euston
Day 2
Day 6 Edinburgh
Day 1
Inverness
Day 7
Aberdeen
Day 5

10. Train speed
[09.05 to 10.54]
After splitting at Edinburgh, the section of the train going to Fort
William climbs into the Scottish Highlands as dawn begins to break.
The line becomes a winding single track and the train stops at a series of small stations and halts.
The train manager explains that, while the train is capable of travelling at 100mph, this is nowhere near possible on the singletrack sections and would anyway make the whole journey too short for passengers to have a decent night’s sleep.
We ask pupils to work out the average speed for the journey and the various sections of it, which they can do using the time and distance information given in the first ‘journey’ sequence and elsewhere throughout the video.
11. Single track
[10.54 to 12.21]
This is another time and distance calculation.
The clip shows a speeded up section of the journey between
Rannoch and Tulloch in the west of Scotland, but gives the times and distance involved.
12. Patterns
[12.21 to 13.01]
This clip asks pupils what mathematics they can see in some patterns on the train.
13. ..and finally
[13.01 to 13.40]
The final sequence completes the journey into Fort William station.
Peter M Evans
Nell Garfath-Cox
July 2007