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?


Friday, 5 May 2017

Quibans 64: Diane Abbott

This Quibans is structured a little differently from usual.

You may have heard the radio interview that Diane Abbott (Labour Shadow Home Secretary) took part in on LBC radio. It starts with the journalist, Nick Ferrari, asking her about the plan she had just announced for a new Labour government to increase the number of police officers by 10,000 in the next parliament. I told the Core Maths class this and also said that when politicians announce new ideas they are always immediately asked how much it will cost and how they will pay for it.

I told the class that this interview didn’t go well. Here is the task:

Task: Write down all of the numbers that are used in the interview and afterwards write a report explaining why certain numbers are incorrect and which are plausible.

Here is the webpage:

Below are some of the things my class noted:

10,000 police officers cannot possible cost £300,000 because that would be £30 per police officer (per year!).

£80 million is also not enough because that is only £8000 per officer. There is the sound of papers being shuffled in the background, so she has obviously lost her pieces of paper and is searching for them while she speaks. If she was estimating how much it would be in the first year, for four-year roll-out of the plan then £80 million for 2,500 new police officers seems more possible.

Diane Abbott then said 25,000 new officers per year over four years (and Nick Ferrari didn’t pick up on it). That would be 100,000 new officers in total.

The 250,000 new police per year would end up being a million in total.

Finally, when she found her papers, Diane Abbott said the following:

  • Year 1 would be setting up and wouldn’t cost anything.
  • Year 2: £64.3 million (presumably for about 2,500 new police officers). This is £25,720 on average.
  • Year 3: £139.1 million (5,000 officers). £27,820 on average.
  • Year 4: £217 million (7,500 officers). £28,933 on average.
  • Year 5: £298 million (10,000 officers). £29,800 on average. [NB: I would prefer to round these numbers off.]

The students then Googled police salaries and decided that these were about £22,000 per year on average. The additional money in Year 2 might then be needed to pay for training, uniform, equipment, national insurance, etc. The new officers would get pay rises as they became more experienced, which could be why the numbers rise in subsequent years.

Finally, they noted that the final figure (£298 million) could be rounded to £300 million. At the start of the interview Diane Abbott said £300 thousand. Maybe she was distracted at the beginning because she was trying to hold a phone conversation while searching for her notes and said “thousand” instead of “million”.

Nick Ferrari seemed to be using some good Core Maths skills when he pointed out some of the problems while Diane Abbott was speaking!

Saturday, 29 April 2017

Quibans 63: Car crime

This article from the Cmabridge News could be used as an opportunity for students to comemnt on the way the data has been presented and on the conclusions that have been drawn.

The riskiest places to park your car around Cambridge, according to police stats
Vehicle crime hot spots around the city
Bottom of Form
The riskiest places to park your car in the Cambridge area have been revealed - and you may be surprised to find out where the safest spot is.
Cllr John Hipkin, who represents Castle ward on Cambridge City Council, said: “What these statistics reveal is that no part of the city or, indeed, county is immune from this sort of opportunistic crime.
“I would call upon residents to be extremely vigilant in not leaving articles of value visible in their unattended cars, especially at night.”
These were the worst hit policing areas in 2016:
1. Cambridge South
This was the worst area for vehicle crime with a total of 448 recorded incidents. The worst month was October with 57. With a population of 62,000, the area includes Cherry Hinton, Coleridge, Teversham, Romsey and edges of the southern part of the city centre.
2. Cambridge North
Second on the list with 374 vehicle crimes reported. November was the worst month at 49. The area has a population of about 60,000.
3. Huntingdon
A total of 370 vehicle crimes were reported here, with September the worst month at 44. The area has a population of almost 68,000.
4. Histon area
The Histon policing team covers a wide area and a population of almost 56,000. It suffered 315 vehicle crimes with the worst month August, with 40 reports.
5. St Neots
There were 243 vehicle crime reports with 36 in the worst month, July. It has a population of 45,000.
6. Cambourne
The policing district covers a wide area and 218 reports of vehicle crime were reported across the villages, with April the worst month with 42 reports. The policing area has a population of 50,000.
7. Sawston area
With a population of 42,000 this area had 177 vehicle crimes reported to police. The worst month was April with 24 incidents reported.
8. St Ives and Ramsey
This area suffered 168 incidents of car crime. With a population of 55,000, the worst months were October and August with 20 each.
9. Ely south
With a population of 36,600, a total of 96 car crimes were recorded. The worst month was June with 12 of the crimes reported.
10. Ely north
A total of 46 car crimes were reported here with thieves more prolific in February with 21 vehicles attacked. It has a population of 27,000.
11. Ely city centre
A total of 41 vehicle crimes were reported in the city centre. The worst month was April with 9. The population is 20,000.
12. Cambridge city centre
The city centre had the fewest vehicle crime reports at just 34. The worst months were December and November at five each. The population is about 7,000.

Comments (1):
This table might be useful:
  Crimes Population
1. Cambridge South 448 62000
2. Cambridge North 374 60000
3. Huntingdon 370 68000
4. Histon area 315 56000
5. St Neots 243 45000
6. Cambourne 218 50000
7. Sawston area 177 42000
8. St Ives and Ramsey 168 55000
9. Ely south 96 36600
10. Ely north 46 27000
11. Ely city centre 41 20000
12. Cambridge city centre 34 7000

Comments (2):
Making a spreadsheet to show the number of crimes per 1000 residents would seem to be reasonable and sensible.  If you do this the area that jumps out as being out of place is Cambridge City Centre.  Why might this be (cars might be damaged where they are parked for the day/evening, rather than just outside someone's home, and Cambridge will have lots of visitors)?

The pmcc is 0.89, indicating a strong correlation between the number of crimes and the population of the area.

Thursday, 20 April 2017

Quibans 62: TV Debate?

In the Guardian:

"that's an ambitious door target"!

The election is 7 weeks away.  Can Theresa May talk to 7 million people before then?

Here are some of the things my classes did:

If there are 4 people per household and she goes to 200 houses per day then she will talk to about 40,000 people over 49 days.  [Is 200 houses per day reasonable?]

Dividing 7 million by 49 gives 142,000 people per day to talk to.  This is 1.65 people per second.  (Long enough to say "hi", but not "vote for me"?  And there is no time for sleep, food, etc.)

Our school has 2000 students.  It seems plausible that you could get them all in a big hall and address them altogether.  It would be necessary to have 71 of those big meetings per day to talk to 7 million people.

142,857 people per day divided by 4 for a household, gives 35,740 houses per day.  A 5 min conversation with each would require 2796 hours in each day.  [We discussed rounding ...]


Sunday, 16 April 2017

Quibans 61: Easter Eggs

From the Daily Mail:
How much exercise will it take to burn off your Easter egg?

Even if you're dedicated to your fitness regime and healthy eating, you might be tempted to allow some leeway for an Easter treat. But before you crack open that chocolate egg, it might be worth noting just how much exercise you'd have to do to burn off all those extra calories.
There follows a table of values, provided below.  I have added to it the weight of the Easter Eggs (taken from elsewhere in the article).

If you can't see all of the data then you could use the image that follows, or copy and paste into Word or Excel (this works best from IE rather than Chrome).

DairyMilkXL 1,758 5.9hours 3hours 2hours 5.2hours 2.1hours 3.7hours 331
CadburyCaramel 1,683 5.6hours 2.9hours 1.9hours 4.9hours 2hours 3.5hours 331
Mars 1,623 5.4hours 2.8hours 1.8hours 4.8hours 1.9hours 3.4hours 331
Flake/Wispa 1,562 5.2hours 2.7hours 1.8hours 4.6hours 1.9hours 3.3hours 295
DoubleDecker 1,549 5.2hours 2.7hours 1.7hours 4.5hours 1.9hours 3.2hours
Oreo 1,528 5.1hours 2.6hours 1.7hours 4.5hours 1.8hours 3.2hours 278
Snickers 1,429 4.8hours 2.5hours 1.6hours 4.2hours 1.7hours 3hours 274
M&M's 1,385 4.6hours 2.4hours 1.6hours 4.1hours 1.6hours 2.9hours 268
Minstrels 1,357 4.5hours 2.3hours 1.5hours 4hours 1.6hours 2.8hours 262
Aero 1,259 4.2hours 2.2hours 1.4hours 3.7hours 1.5hours 2.6hours 235
Yorkie 1,033 3.5hours 1.8hours 1.1hours 3hours 1.2hours 2.2hours 192
ToffeeCrisp 1,004 3.4hours 1.7hours 1.1hours 3hours 1.2hours 2.1hours 176
MiniEggs 980 3.3hours 1.7hours 1.1hours 2.9hours 1.2hours 2hours 187
CremeEgg 922 3.1hours 1.6hours 1hour 2.7hours 1.1hours 1.9hours 186
KitKat 943 3.1hours 1.6hours 1.1hours 2.8hours 1.1hours 2hours 180
Milkybar 886 3hours 1.5hours 1hour 2.6hours 1.1hours 1.9hours 162
Matchmaker 872 2.9hours 1.5hours 1hour 2.5hours 1.1hours 1.8hours 162
Thorntons 806 2.7hours 1.4hours 54mins 2.4hours 1hour 1.7hours 149
Smarties 680 2.3hours 1.2hours 46mins 2hours 49mins 1.4hours 122

Things to do:
What is the conversion rate between the different types of exercise?
What type of correlation would you expect between the weight of the egg and the number of calories?  Work out the pmcc.  Comment on your answer.

The pmcc between the weight of the egg and the number of calories is 0.993
The correlation is extremely good.  Unsurprisingly, this tells us that heavier eggs (which presumably contain more chocolate) contain more calories!


Wednesday, 12 April 2017

Quibans 60: Two short Quibans - United Airlines / Carers

Here are two brief pieces of information from BBC articles that could be used to create short questions, or which could be explored in greater detail.

United Airlines incident: Why do airlines overbook?
Overbooking on flights happens all the time. Empty seats cost airlines money, so they offset the number of passengers who miss flights by selling too many tickets.Of the 613 million people who flew on major US carriers in 2015, 46,000 were involuntarily denied boarding, according to data from the Department of Transportation.

Question: Is that a lot of people?

Answer: It depends how you look at it.
In percentage terms, it is 0.008%
613 million people is about 10 times the population of the UK, whereas 46,000 is the population of a town.
613 million people is about a tenth of the population of the world.  46,000 is the population of 23 large secondary schools

Social care system 'beginning to collapse' as 900 carers quit every day
More than 900 adult social care workers a day quit their job in England last year, new figures reveal.  60% of those leaving a job left working in the adult social care sector altogether.  The average full-time frontline care worker earned £7.69 an hour, or £14,800 a year.

Question 1:  What percentage of the total workforce leaves that sector each year?

Question 2:  How much do you have to work to earn the stated figure?
Answer 1:  We need to estimate how many workers there are in total.  I predict that of the 65 million people in the country about one in 20 need some form of care.  Maybe each carer can look after 3 people?  That gives about 1 million carers. 
About 900 per day is 900 x 365 per year, which is approx. 300,000 who leave their job, and 180,000 (60% of them) leave the sector.  180,000 out of 1 million leave each year, so about 18% (approx 1/6) leave each year.
The article states:  Data gathered by the charity Skills for Care, shows that in 2015-16 there were more than 1.3 million people employed in the adult social care sector in England.

Answer 2: This is for 1925 hours of work.  I don’t know whether the newspaper has taken the hourly figure and multiplied by 38-hour weeks over 50 weeks in the year, or whether this is genuinely what most carers do.


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 ]   ...