mini-problems

nb this download is a sample only . . . the full set is available from my website.

The mini-problems take only a few moments to read – but each one of them presents a small challenge to the solver, an invitation to take in a straightforward set of facts and then to find a way of getting to the desired answer, using only existing skills. The key thing for pupils to grasp is that they need to be creative, to use imagination and experiment, in order to find a way of getting to the answer. None of the problems requires maths skills or knowledge beyond the Key Stage 2 level. Of course, there are skills (in algebra, for example) which can be taught and which would make these problems easier but the aim here is to encourage pupils to make the best use of the skills they already have. The attitude that, when faced with new or difficult problems, the first line of attack should be to use one’s own imagination is an attitude to be encouraged in pupils; this way pupils gain in both confidence and enjoyment.

The problems cover a range of topic areas : number problems (inevitably the largest category), geometric & spatial problems, as well as problems on statistics, probability, logic, sets etc. The difficulty level of the problems is somewhat below the difficulty level of those in eg our ‘no problem’ books.
The printed format is perhaps unusual in that each problem is given within an A6 rectangle, so that there are four mini-problems on each A4 page; cut up into the four separate items (ready to pritt-stick into maths exercise books), these mini-problems make excellent shorter exercises in problem-solving, ideal for individual early finishers or to give to a whole class for class or home working.
By contrast, the answers are not short in format : whilst repeatedly making the point that there is no one correct way to solve any of the problems, suggested approaches are offered for the benefit of those who have been unable to get started on a particular problem or for those who might be interested in comparing an alternative approach with the one they have already found.