Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Cut it Out

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

What Distance?

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.