In May 2015 the United Kingdom went to the polls. A Conservative Government was elected. The UK uses the “first past the post” electoral system. The country is divided into 650 constituencies. The candidate with the most votes from each constituency is elected.

Most other countries in Europe use various forms of proportional representation. This means that the number of MP’s for each party would be proportional to the number of votes that were cast for them. (There are many different forms of PR, but in this exercise, to keep it simple we are going to work out the number of MPs by dividing the vote for each party by the total vote and then multiplying by 650, which is the total number of MP’s in the House of Commons. )

First fill in the missing numbers in this table. You will need a calculator. Remember that to round to two decimal places you need to look at the 3rd decimal place. If this is 5 or more round the 2nd decimal place up. If it is less than 5 then ignore it. eg 34.349239=34.35 to 2dp. 2.983432909=2.98 to 2 dp.

If you got the first exercise correct I want you to illustrate your results with two pie charts. Use this table to work out the degrees for each party. You can draw them in excel or with a protractor and pencil.

If you would rather do this exercise using a worksheet download here.

Hi Graham,

thanks for your site, which I have just discovered. I would like to use some of your excellent resources for my Functional Skills maths classes. I have noticed that there might be a small error in the Proportional Representation task (a very interesting task, by the way). Forgive me if I’m wrong but I think for UKIP, the % of total votes to 2 dp should be rounded up to 12.78. The site requires 12.77 to be inputted for a correct answer. If you have time, please could you check? Thank you very much again for all this helpful material.

Kind regards,

Robin Goldberg

Many thanks for pointing this out. It’s taken me rather a long time to get round to fixing it, but it is now fixed!

Graham