Friday, 20 October 2017

Quibans 71: I’d walk a million miles for one of your goals

Apparently (thanks to Scott for the heads-up), Scottish football fans sing “I’d walk a million miles for one of your goals”.  [Link]  

What questions could we ask and answer?  (My suggestions are below.)
How many times around Scotland would that be?
How many trips from Land’s End to John O’Groats?
How long would it take you?  (What is a reasonable number of miles to walk in a day?)

According to Wikipedia, the mainland coastline of Scotland is 6160 miles and the border with England is 96 miles.  This gives 6256 miles in total and 160 laps will be necessary to get over 1 million miles.
Land’s End to John O’Goats is 874 miles – so that’s 1145 journeys to get over a million miles.  (One journey being counted as one direction only.)

If you walk 30 miles a day then it will take over 91 years to do it.  What age would you need to be to start walking this sort of distance, though?

Monday, 18 September 2017

Quibans 70: Commuting by train

As part of an article about commuting an article from the Daily Telegraph includes an information box.

It gives numbers and what they stand for.  Match them up.

700 million

100 million

2.99 million



Journeys made by season ticket holders out of Waterloo station alone

Average amount of weekday morning trains at peak times that were overcrowded

Number of people commuting more than two hours per day in 2014, an increase of 72pc in 10 years

The number of journeys made by season ticket holders across the UK in 2014-15.

Number of people forced to stand every morning on peak trains into the capital - an increase of 19,000 in a year

Here is the box in full:


1) What percentage of journeys that were made in 2014-15 involve Waterloo station?

2) How many season ticket holders are there?

3) How many people commuted for more than two hours per day ten years previously?

4) What percentage of season ticket holders travelled longer than 2 hours?

5) By what percentage did the number of people forced to stand on trains into London rise by?

6) If that percentage increase continues, how long will it be before half a million people are standing?  Is this realistic?


1) 100/700 = 14.2857...%  Given that the two numbers are clearly not exact it would be appropriate to give the percentage as 14%.

2) This is difficult!  700 million journeys per day.  If a passenger takes more than one train does that count as more than one journey?  How many days per year will they travel?  48 working weeks x 5 days = 240 work-days per year, which will be at least 480 journeys (there and back) per person.  Some will take more than one train so let's call that 500 journeys per person on average.  700 million / 500 = 1.4 million commuters.

3) 2.99 million is 172% of the 10-years-ago value.  Back then it was 2.99 million / 1.72 = 1.74 million

4) 139000 out of 1.4 million = 9.9%.  Call it 10%

5)  In the previous year 120,000 people stood on their train and it rose by 19,000.  This is a 15.8% rise (16%)

6) We need 120 * 1.16^n > 500.  Then we need to subtract 1 from n.  Use a spreadsheet to see that n=10 is the first time 500 is breached.  So a further 9 years will be required.  This involves major extrapolation, so is unlikely to be accurate.

Sunday, 17 September 2017

Quibans 69: QR code of trees

From BBC News:

Chinese maze: Village makes giant tech code from trees

At first glance, it could be the courtly maze of an English country manor - albeit with some rather large gaps.

But a tech-savvy eye will instantly see the green design for what it is - a massive QR code.  These high-tech barcodes are hugely popular in China as a way to make cashless payments on a smartphone.

Xilinshui village, in the northern Hebei province, has created one from trees in a bid to raise its profile.  The design was made from 130,000 Chinese junipers, and can be scanned from above using a phone or tablet.

It is not clear how high above the trees you would have to be to scan it - or how you might get there - but visitors who successfully capture the code will be connected to the village's tourism account on WeChat, a Chinese social media site.

The vast design measures 227m (744ft) along each side, and the trees are between 80cm and 2.5m in height, the South China Morning Post reports.  Xilinshui was named "the most beautiful village in Hebei" in 2015, and received a 1.1 million yuan ($168,000; £124,00) development grant from the province.

Some possible questions:

1) What typo is there in the article?
2) You can see this as being made up of square pixels.  What is the side-length of each pixel?
3) How many juniper trees are there in each pixel?
4) What is the conversion factor between metres and feet?
5) Convert the heights of the trees to feet and inches.
6) What are the conversion factors between the currencies?
7) If they spent all of the development grant money on tress how much was each one?
8) How long might it have taken to plant all of the trees?

Some answers:

1) Typo: “($168,000; £124,00) development grant” – it looks as if a zero is missing from the sterling figure.
2) Side-length of each pixel: I count 37 pixels along each edge, but if the empty border is included then it is 39 by 39.  227 metres divided by 37 is 6.1m, whereas 227m divided by 39 is 5.8m.  Let’s say 6m.
3) Number of trees in a pixel: I counted part of it and then scaled up – I got about 650 tree-filled pixels.  This means there are, on average, 200 trees per pixel.
4) What is the conversion factor between metres and feet?  Remember there are 12 inches in a foot.  3.278 feet is 3 feet 3 inches.
5) 80cm is 2 feet 7 inches.  2.5m is 8 feet 2 inches.
6) Convert currencies: $1 = 6.55 yuan.  £1 = $1.35 £1 = 8.87 yuan.
7) Cost of a tree:  8.46 yuan.  About 95 pence.
8) How long to plant them:  If we assume one minute per tree (because they were very small when planted) and an 8 hour day, five days per week, then it would take one person 54 weeks to plant the trees.  Essentially it is a year.  If we have two people working on this then we can divide the time required.  If it takes longer than a minute to plant a tree (which is likely!) then we will need to multiply.

Thursday, 17 August 2017

Quibans 68: Human Chain

 from the Daily Telegraph:

Beachgoers form incredible human chain to save drowning family  

This is the incredible moment strangers on a beach formed a human chain to save a drowning family caught in a riptide in the Gulf of Mexico.
Dozens of beachgoers, including some who couldn’t swim, joined together and linked arms to help nine people, including two young children, swept away by the powerful offshore current.
Around 70-80 people were involved in the dramatic rescue effort on a busy Panama City Beach in Florida on July 8.
Jessica Simmons, a strong swimmer who jumped in to help, along with her husband, initially assumed there was a shark in the water before she realised people were drowning. 
“Some people started gathering people on the beach to form a human chain,” she said. 

How far out to sea were the family?  Give an upper bound and a lower bound.

Sunday, 11 June 2017

Quibans 67: General Election graphs

Here is a sprinkling of infographics and data about the election from a number of different sources (listed below).  These could all be used as a full lesson, or a few could be selected.  (NB: my brief answers follow the questions, so it may be sensible/necessary to copy the images to a file before displaying them.)

Voting by demographic:

It is obvious what most of the categories mean.  AB, C1, C2, DE might be unfamiliar.  They are a way to describe different groups based on their type of employment.  See here.

What are the good things about this infographic?
What are the problems?
What does it show us?

It shows the percentages as well as the party colours.
The numbers are not easy to read.  It is easier to pick out the blue proportion each time and to compare these across the different demographics because they are aligned to the left.  This is harder with the other colours.
It shows us that older people are more likely to vote Conservative.  (Lots of other things too.)

Question: What are these two diagrams?  What do they show?

Answer: The left is a map that shows the colour of each constituency after the 2017 election.  the right shows each constituency the same size and has them in roughly the right place relative to each other.  The left-hand one looks overwhelmingly blue, with the yellow/orange parts being bigger than the red.  The right-hand one clearly has rather a lot of red involved. This suggests that Labour supporters are overwhelmingly from cities (where the area is small compared to the population) whereas Conservative support comes from rural areas.

The next two graphs come from two different newspapers.
What is the same/different about them?  Any other comments?

(NB: check the axes!)

What do the columns mean?  What is the link between the number of seats and the share of the vote?

We might expect that a party that gets 42.45% of the vote would get 42.45% of the seats.  Why is this not the case?
Is that unfair?

This could be worked out using a spreadsheet:

Party Percentage Seats Seats shared using % How many extra seats?
Conservative 42.45 318 276 42
Labour 39.99 262 260 2
SNP 3.04 35 20 15
LibDem 7.37 12 48 -36
DUP 0.91 10 6 4
Sinn Fein 0.74 7 5 2
Plaid Cymru 0.51 4 3 1
Green 1.63 1 11 -10
Ind 0.45 1 3 -2
UUP 0.26 0 2 -2
SDLP 0.3 0 2 -2
UKIP 1.84 0 12 -12
Other 0.52 0 3 -3
  100.01 650    

The 4th column shows what 42.45% of 650 seats is.  The final column shows that the Conservatives got an additional 42 seats over and above that amount.  This is a result of the 'first-past-the-post' system we use in this country whereby each constituency is sorted out separately.  The Green Party got a few votes in many constituencies. Other countries (including elections for the Scottish Parliament) have voting systems that are more proportional than that.

What do these graphs tell us?  Are their titles accurate?


Answer:  They do seem to be accurate.

What is going on here?

Answer: This is difficult to interpret.  Are these the changes in the percentage values, or are they the percentage change in the percentages?  What else can you see in these?

Guardian, via:
Financial Times, via:

Quibans 66: Paris Climate Accord

Slightly different from usual, this is a full article from the Daily Telegraph.

The headline is:
Did the US get a bad deal under the Paris Climate Agreement?

The article is in a Word document (link here).

I emailed this to my class for them to work on.  Questions are provided in purple.  The main focus here is commenting on the graphs (one of which is possibly the most pointless graph I have seen!).

Wednesday, 24 May 2017

Quibans 65: Primary school breakfast club

From Schools Week:

Conservatives’ free breakfast pledge ‘costed at just ??p per meal’

The Conservatives have set aside just under ??p per pupil for its manifesto pledge to give all primary school pupils free breakfasts, in what food experts have labelled a “black hole” in the government’s manifesto calculations.
The party’s manifesto, launched last Thursday, scraps universal infant free school meals (UIFSM), which cost an estimated £600 million a year, in favour of free breakfasts for all primary pupils, which a press release today said will cost just £60 million a year.
But critics have calculated that if the country’s ?? million primary state school pupils were fed a free breakfast on this budget for ?? school days each year, each meal would have to cost no more than ??p.
Aisling Kirwan, the founding director of the Grub Club, a school-based social enterprise that provides cooking lessons for pupils in poorer areas, said that a nutritious meal costs 25p per pupil on average – which even then would only amount to porridge with milk.
A more filling portion, which would include bacon, two sausages, one egg and bread, would cost 85p per portion.
“Clearly there’s a huge disparity between the realistic costing and that put forward by the Tories,” she said.


Following on from the Quibans about Diane Abbott’s (Labour) issues with incorrect figures, the Conservative Party appear to have dropped the ball with some dodgy numbers of their own.

I suggest students read the story above and then try to determine what could be hiding behind the question marks.

How can they predict the number of children at primary schools? What about the number of days in the school year?

When they have made their predictions and calculations, you could give them the figures: 4.62 million pupils and 190 school days per year. Can they get a more accurate answer?

Here is the complete paragraph:

But critics have calculated that if the country’s 4.62 million primary state school pupils were fed a free breakfast on this budget for 190 school days each year, each meal would have to cost no more than 6.8p.

How much would it cost to provide porridge for everyone?

How much would it cost to provide a full-English breakfast for all?

If they do want to provide porridge for everyone, what fraction of children are they expecting to eat breakfast at school if it really will cost £60 million?


Quibans 71: I’d walk a million miles for one of your goals

Apparently (thanks to Scott for the heads-up), Scottish football fans sing “I’d walk a million miles for one of your goals”.  [ Link ]   ...