Friday, 24 June 2016

Quibans 33: EU Referendum

My Yr 12 class arrived this morning asking whether we would be doing a Quibans based on the Referendum result.  Here is what we did.

They knew that the country had voted as follows:
Leave – 52%
Remain – 48%
They told me the turnout was 72%
I had looked up the total number of people who voted and wrote that up:  33,551,983.

The questions they decided on were:
  1. How many people voted Leave/Remain?
  2. What proportion of the population of the UK voted?
  3. How many eligible voters didn’t vote?

Instead of them giving me answers verbally, we set up a spreadsheet on the board and they came up in turn to do some typing.  This allowed us to talk about how to structure this sort of thing on Excel, and what they should type.  It also helped us explore the difference between typing the number 52 and treating it as a percentage (dividing by 100 when we used it) and typing 52%, which Excel treats as the decimal 0.52

After that I gave them figures for South Cambs (where my school is):
Leave – 39.8%
Remain – 60.2%
93,189 people voted.

They worked out the number who voted to remain/leave:

They pointed out that these can’t be exact because you can’t have 0.78 of a vote.  I then told them the actual figures (shown above). 

First they worked out the accurate percentages, and found that they had been correctly rounded to 1dp here.  This then led to the use of the upper and lower bounds to determine how many people might have voted each way.

Clearly, if the figures for South Cambs ended up being approximate because of rounding issues, then the national figures might also be approximate, so we worked out upper and lower bounds for those.

Finally, I gave them the numbers for Cambridge, where 57,799 voted and 73.8% said ‘remain’ and we worked out upper and lower bounds for that.

So: we did lots of good percentages work (including inverse percentage to calculate the total number of eligible voters), used spreadsheets, considered upper and lower bounds.  Lots of interesting things.

At the very end of the lesson one student was interested in whether the margin of victory was big or not.  Is 52% to 48% a 4% difference, or is it a 2% difference?  Or should you look at the raw figures (1.3 million is a big difference).

Here are some of the links we used:

Thursday, 2 June 2016

Quibans 32: Boring tunnels

From BBC News:
Swiss Gotthard rail tunnel - an engineering triumph

The world's longest - and deepest - rail tunnel opens in Switzerland on Wednesday [1 June 2016].

The Gotthard rail link has taken 20 years to build, and cost more than $12bn (£8.2bn). It will, the Swiss say, revolutionise Europe's freight transport.

The Alps are sometimes described as Europe's natural trade barriers. From Roman times, the routes across them have been mapped, and fought over.

But the plan was ambitious, costly to the Swiss taxpayers who had agreed to pay for it, and fraught with engineering challenges.

A massive 10m (30ft) diameter tunnel-boring machine could, on a good day, dig out 40m of tunnel a day - a world record.

But now the tunnel is ready, and Europe's leaders, including German Chancellor Angela Merkel, French President Francois Hollande and Italy's Prime Minister Matteo Renzi, are all arriving to take a look.

Twin tunnels running in both directions north-south should transport Europe's freight not only much more safely, but much faster. With no danger of collision, trains will race through the tunnel at speeds of up to 250km/h (155mph).

Where older alpine tunnels corkscrewed their way up through the mountains, the new railway line, from Zurich in the north all the way to Lugano in the south, is completely flat and straight.

What can we work out? (It might be useful to explain that there are two 10-metre diameter tunnels and that four boring machines were used – they met up in the middle.) This is one where the students could come up with their own questions. Here are mine:

  1. What exchange rate did they use?
  2. How much of the cost went on salaries? (What assumptions did you make?)
  3. How much did it cost per year?
  4. The Swiss people voted in a referendum to pay for the tunnel: look up how many people there are in Switzerland. How much did it cost them each, per year?
  5. How long is a football field?
  6. What volume of rock was cut on a good day?
  7. Give a lower bound for the length of time to drill the tunnel.
  8. How much freight does a single shipping container hold?
  9. How many times would the copper cable go along the tunnel?
  10. How much concrete is there in the Empire State Building?
  11. My favourite question: how thick is the concrete in the tunnel?

For question 11:
If we assume the tunnel was cut as a circle, diameter 10m and that there is an equal amount of concrete all around (presumably the base should be flat for the trains to run on, so this won't be perfect!) then we have this:

We could use trial and improvement to estimate the thickness of the concrete.
Or we could form and solve a quadratic equation.
Call the thickness of the concrete BC = t.
This gives AC = 5-t
The area of the red annulus is:

Multiply this by the length of the tunnel and this would equal (approximately) the volume of half of the concrete (because there are two tunnels).

Solving this (using the quadratic formula) gives about 1.3 metres.


Quibans 85: Crime and Police figures

From the Cambridge News: Violent crime in Cambridge has nearly doubled in a decade as police numbers drop 9 APR 2018 Bottom of For...