Mathematics and statistics lessons about elections

July 13, 2017

(This article was originally published at Learn and Teach Statistics and Operations Research, and syndicated at StatsBlogs.)

Study elections in mathematics because it is important

Too often mathematics is seen as pure and apolitical.  Maths teachers may keep away from concepts that seem messy and without right and wrong answers. However, teachers of mathematics and statistics have much to offer to increase democratic power in the upcoming NZ general elections (and all future elections really). The bizarre outcomes for elections around the world recently (2016/2017 Brexit, Trump) are evidence that we need a compassionate, rational, informed populace, who is engaged in the political process, to choose who will lead our country. Knowledge is power, and when people do not understand the political process, they are less likely to vote. We need to make sure that students understand how voting, the electoral system, and political polls work. Some of our students in Year 13 will be voting this election, and students’ parents can be influenced to vote.

There are some lessons provided on the Electoral Commission site.   Sadly all the teaching resources are positioned in the social studies learning area – with none in statistics and mathematics. Similarly in the Senior Secondary guides, all the results from a search on elections were in the social studies subject area.

Elections are mathematically and statistically interesting and relevant

In New Zealand, our MMP system throws up some very interesting mathematical processes for higher level explorations. Political polls will be constantly in the news, and provide up-to-date material for discussions about polls, sample sizes, sampling methods, sampling error etc.


It would be great to hear from anyone who uses these ideas. If you have developed them further, so much the better. Do share with us in the comments.

Suggestions for lessons

These suggestions for lessons are listed more or less in increasing levels of complexity. However I have been amazed at what Year 1 children can do. It seems to me that they are more willing to tackle difficult tasks than many older children. These lessons also embrace other curriculum areas such as technology, English and social studies.

Physical resources

Make a ballot box, make a voting paper. Talk about randomising the names on the paper. How big does the box need to be? How many ballot boxes are being made for the upcoming election? How much cardboard is needed?

Follow the polls

Make a time series graph of poll results. Each time there is a new result, plot it on the graph over the date, and note the sample size. At higher levels you might like to put confidence intervals on either side of the plotted value. A rule of thumb is 1/square root of the sample size. For example if the sample size is 700, the margin of error is 3.7%. So if the poll reported a party gaining 34% of the vote, the confidence interval would be from 33.3% to 37.7%.

You can get a good summary of political polls on Wikipedia.

From NZ maths  – On the Campaign Trail (CL 4)

Figure it Out, Number sense  Book 2 Level 4 – has an exercise about finding fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.

From NZ maths – Whose News (CL 4)

This is a guide to running an analysis on the level of representation of different geopgraphic areas in the news. The same lesson could be used for representation of different parties or different issues.

Graphical representations

The newspapers and online will be full of graphs and other graphical representations. Keep a collection and evaluate them for clarity and attractiveness.

How many people will be employed on election day?

This inquiry uses a mixture of internet search, mathematical modelling, estimation and calculation.

  • How many electorates are there?
  • How many polling booths per electorate?
  • How many people per booth?
  • How long are they employed for?

Fairness of booth provision

  • Is the location of polling booths fair?
  • What is the furthest distance a person might need to travel to a voting booth?
  • What do people in other countries do?

The mathematics of MMP

This link provides a thorough explanation of the system. A project could be for students to work out what it is saying and make a powerpoint presentation or short video explaining it more simply.

Overhang and scenario modelling

Overhang occurs when a party gets more electoral MPS elected than their proportion allows. Here is a fact sheet about overhang and findings of the electoral review. Students could create scenarios to evaluate the effect of overhang and find out what is the biggest overhang possible.

Small party provisions

How might the previous two election results have been different if there were not the 5% and coat-tailing rules?


Different ways of assigning areas to electorates get different results. The Wikipedia article on Gerrymandering has some great examples and diagrams on how it all happens, and the history behind the name.

Statistical analysis of age and other demographics

Statistics should be analysed in response to a problem, rather than just for the sake of it.
Suggested Scenario: A new political party is planning to appeal to young voters, under 30 years of age. They wish to find out which five electorates are the best to target. You may also wish to include turn-out statistics in your analysis.

Resource: Enrolment statistics by electorate – some graphs supplied, percentages for each electorate.

Statistical analysis of turn out

In the interests of better democracy, we wish to have a better voter turnout. Find out the five electorates with the best voter turnout and the worst, and come up with some ideas about why they are the best and the worst. Test out your theory/model by trying to predict the next five best and worst. Use what you find out to suggest how might we improve voter turnout.

Resource: Turn out statistics – by electorate or download the entire file

Happy teaching, and fingers crossed for September.

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