Why do this problem?
would be a good start to, or could follow on from, work on finding percentages of quantities. In whichever context it is used, it will provide a good assessment opportunity for you to find out what your pupils understand well and what they have difficulties with.
These problems are probably best tackled as a group activity with children working in threes or fours. Give each group a set of these cards (.doc
of which contain one each of the scenarios and one of which is blank. Challenge each group to decide which situation they would prefer and say that you will want them to explain how they came to their decisions.
Having given them a suitable length of time to work on the problems, bring everyone together. You could take a vote on each one to start with and then ask one group to explain how they came to that conclusion. Invite other groups to contribute different ways of working out the solution as well so that a range of methods are discussed.
You could then ask each group to make up their own question in a similar style which they could write on the blank card. These could then be swapped. Of course the group which poses the problem must have also worked out the solution!
How will you compare these two scenarios?
Can you express this percentage in any other way?
What do you estimate this percentage to be?
Making up a similar problem (with its solution!), whose answer is not immediately obvious, will challenge many learners.
Calculators may be useful.