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What Distance?

Age 7 to 11 Challenge Level:

What Distance?

Here are the distances (as the crow flies) in km from London to various cities in the world:

Abu Dhabi 5480           Barcelona 1139               Cape Town 9680
Delhi 6718                   Edmonton 6805                Florence 1209          
Gothenburg 1039         Houston 7812                   Istanbul 2501
Jerusalem 3611             Karachi 6314                  Lauceston 17425

Challenge 1

If someone took you the first 1000km how much further would you have to go for each of the twelve journeys?

Now create some similar questions of your own.

Challenge 2

If you started at Copenhagen then went to London, which is about 1000 km away each time for all of the journeys shown above, how far would you have travelled in each case?

Why do this problem?

This simple challenge offers pupils the chance to find 1000 more or less than a given number.

Possible approach

You could show the map images with the associated numbers and invite children to suggest what the numbers mean.  (This may provoke a discussion about how miles related to kilometres!)  

Then set learners off on the challenges.  You could suggest that, rather than attempting all of the calculations, pairs could decide which they think would be the easiest to work out and which would be the hardest, and why. 

After a suitable period of time, you could invite pairs to join with another pair and compare their thoughts. If pairs do not agree on which is the easiest/hardest, challenge them to try to persuade the other pair that their 'ranking' is better.  This will require knowledge of a range of calculation methods and sound reasoning.

Key questions

How did you work this out?
If you wrote it down to work it out can you show me and talk me through it?

Possible extension

Here is a set of small cards which could be used for pupils working in pairs and creating there own games.
As a jpg 
here.jpg ; as a pdf here.pdf

Although unrelated to the main questions you might like to make use of these maps to discuss why the 'straight' lines of the 'as the crow flies' are drawn as various curves.

Possible support

Some pupils may need help with focusing on each particular little map and the names that may be unusual for them.