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Primary Magazine - Issue 30: Maths in the city

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 05 November 2010 by ncetm_administrator
Updated on 16 November 2010 by ncetm_administrator


Primary Magazine Issue 30Hong Kong photograph by E.Hoba used under the Creative Commons Attribution 2.0 Generic licence

Maths in the city  

Did you know that there are currently just 66 recognised cities in the United Kingdom? Traditionally this ‘city status’ was given to towns with cathedrals, but grants made since the start of the 20th century have been awarded on other criteria such as population size.

Now city status grants are often used to mark royal and other special occasions. The first ‘competition’ was won by Sunderland in 1992, to mark the 40th anniversary of the Queen’s reign. Since then, Armagh and St David’s won in 1994, followed by Brighton & Hove, Wolverhampton and Inverness in the year 2000, to mark the new millennium. In 2002, the Queen’s Golden Jubilee year was celebrated by awarding city status to Preston, Lisburn, Newry, Newport and Stirling. The latest competition was launched earlier this year, inviting towns to bid for city status to mark the Queen’s Diamond Jubilee in 2012.

When was your local city awarded city status? Encourage pupils to research award dates for several cities across the country, and create their own timeline on which to position them. Which of their cities gained their ‘official status’ first? Which century was the city awarded its title? How many years ago? Here are some dates to get you started.

So if there are no set criteria for awarding city status, what exactly is a city? Most definitions refer to a ‘large settlement’, or a ‘densely populated area’.

To most of us cities are busy, noisy, bustling places, packed with useful amenities and businesses, shops and restaurants…the perfect place for some mathematics!

The term ‘city’ often conjures up images of tall, imposing skyscrapers, casting shadows at ground level, limiting our view of what lies beyond. Use this image to help you solve the following ‘Skyscraper Puzzle’.

  • this diagram shows an aerial view of Blocktown, each of the 16 squares representing a skyscraper.
  • skyscrapers in Blocktown are 1, 2, 3 or 4 blocks in height. Each ‘street’ contains one skyscraper of each height.
  • imagine standing at the edge of Blocktown, looking in the direction of the arrow on the diagram. The number shows you how many skyscrapers you can see.
  • you cannot see a shorter skyscraper behind a taller one.
  • try to determine the height of each of the 16 skyscrapers in Blocktown and enter them onto the diagram.
  • a Word document and Adobe Acrobat pdf version of the diagram are available to download.

This puzzle was adapted from brainbashers.com. Is this the only solution? The puzzle can easily be simplified by making Blocktown smaller. Start with a 2 x 2 town, or 3 x 3, reducing the number of possibilities. Allow pupils the opportunity to build their skyscrapers from linking cubes to support their visualisation.

There are many mathematical possibilities linked to the context of ‘cities’, such as:

  • investigating large numbers by looking at population sizes (there are nearly 12 000 people per square mile in London!)
  • exploring routes and directions from city street maps and plans. Google Maps is perfect for ‘zooming in’ and helping pupils to link the map to the ‘real world’
  • the London Underground map is perfect for finding shortest routes between points. Can they get from A to B without going through C station?
  • looking at shapes and dimensions of buildings, linking to work on 3D shape, and making nets and models. Google Building Maker supports the representation of building designs on screen and has a useful image bank of well-known city buildings from around the world.
  • investigating the tallest buildings in the world. Which is the tallest? If St Stephen’s Tower (holding Big Ben) is 96 metres tall, how many could be stacked on top of each other to make the International Commerce Centre in Hong Kong? (Use some of these statistics from the portal to get you started. Issue 10 of the Primary Magazine gives some ideas for Data Handling activities.) Assuming an even distribution of floors within the height of each building, which building has the tallest individual floors?
  • finding out about transport in the city. Which is the most common mode of transport? Is this the same as where you live? Why not? Why is public transport used more in the city? How many people travel through the world’s cities each day?

‘Maths Trails’ are already available for many cities and their buildings across the country. Examples include those for Durham and Bristol, as well as the trail for The O2 in London. Contact your local authority mathematics team for details of ready-prepared maths trails in your area.

Try using photographs of sights around your local town or city to stimulate some mathematical discussion in the classroom. 

Clock face photograh by H Grobe used under the Creative Commons Attribution 3.0 Unported licence

  Clock face photograph by H Grobe

What time is it?

What if the clock was upside down?

What if the right-hand mark (currently seen as no. 3) became the top of the clock?

Could the clock be secured in a different orientation? Why? Why not?

Here are photos of some more examples to get you started. You could also make use of these pictures:

Let us know of any other ideas you have - we'd love to hear about them.

Image Credits
Page header - cities photograph Hong Kong by E.Hoba some rights reserved
Clock face photograph by H Grobe some rights reserved

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02 January 2011 22:25
prefer the origional lay out however this issue is valuable for specific topic work.
By PenelopeW
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