Problem Teachers' Notes Hint Solution

There are at least three different ways to solve this problem , and that's why it's a good class or group investigation. Whilst the answer is important, the meat of the question is in the discussion of the different methods of solving it.

The problem needs little introduction, however the method of working might need more.

Organise the children into groups of three or four and explain that once they have solved the problem they will be expected to explain their working to the rest of the group, so they will need to keep a record of what they do. They may choose to use large sheets of flip-chart paper to record as they work, or as an aid for their presentation to the others at the end.

When all the groups have come to a satisfactory conclusion, invite them to explain their working and look for similarities between them.

What do we know about division that might help us?

What methods of problem solving that we know might be useful?

Can they apply what they have learnt to a similar problem, where the answer is $3.375$? $4.5$? $4.1$?

Can they make up a similar question and solve it?

Some groups will have used trial and improvement but this is a rather unsatisfactory way of working as there are so many pairs of numbers under $50$ that have an answer of approximately $3$. You may however wish to encourage them to find any two numbers (not necessarily whole ones) in order to 'get into' the problem and appreciate the use of multiplication as a possible strategy.