Strategies


 * Common Problem Solving Strategies**
 * 1) Guess (this includes guess and check, guess and improve)
 * 2) Act It Out (act it out and use equipment)
 * 3) Draw (this includes drawing pictures and diagrams)
 * 4) Make a List (this includes making a table)
 * 5) Think (this includes using skills you know already)

This stands for two strategies, **guess and check** and **guess and improve.** As problems get more difficult, other strategies become more important and more effective. However, sometimes when you are completely stuck, guessing and checking will provide a useful way to start and explore a problem. Hopefully that exploration will lead to a more efficient strategy and then to a solution.
 * 1 Guess**
 * Guess and check** is one of the simplest strategies. Anyone can guess an answer. If they can also check that the guess fits the conditions of the problem, then they have mastered guess and check. This is a strategy that would certainly work on the [Farmyard Problem|Farmyard] problem but it could take a lot of time and a lot of computation.
 * Guess and improve** is slightly more sophisticated than guess and check. The idea is that you use your first incorrect guess to make an improved next guess.

We put two strategies together here because they are closely related. These are **Act it Out and Use Equipment.** You can take the role of things in the problem. In the [Farmyard Problem|Farmyard] problem, you might take the role of the animals though it is unlikely that you would have 87 children in your class! But if there are not enough children you might be able to press gang the odd teddy or two.
 * 2 Act It Out**
 * Use Equipment** is a strategy related to Act it Out. Generally speaking, any object that can be used in some way to represent the situation tyou are trying to solve, is equipment. One of the difficulties with using equipment is keeping track of the solution. Actually the same thing is true for acting it out. The children need to be encouraged to keep track of their working as they manipulate the equipment. Sometimes you can draw but sometimes using equipment is better.

It is fairly clear that a picture has to be used in the strategy **Draw a Picture**. But the picture need not be too elaborate. It should only contain enough detail to solve the problem. Hence a rough circle with two marks is quite sufficient for chickens and a blob plus four marks will do for pigs. It’s hard to know where **Drawing a Picture** ends and **Drawing a Diagram** begins. You might think of a diagram as anything that you can draw which isn’t a picture. Venn diagrams and tree diagrams are particular types of diagrams that we use so often they have been given names in their own right.
 * 3 Draw**

Making **Organised Lists and Tables** are two aspects of working systematically. it is important to make your list in an organised way. This will help you explore the problem in a systematic way. There are a number of ways of using **Make a Table**. These range from tables of numbers to help solve problems like the Farmyard, to the sort of tables with ticks and crosses that are often used in logic problems. Tables can also be an efficient way of finding number patterns. When an **Organised List** is being used, it should be arranged in such a way that there is some natural order implicit in its construction. For example, shopping lists are generally not organised. They usually grow haphazardly as you think of each item. A little thought might make them organised. Putting all the meat together, all the vegetables together, and all the drinks together, could do this for you. Even more organisation could be forced by putting all the meat items in alphabetical order, and so on. Someone we know lists the items on her list in the order that they appear on her route through the supermarket. In many ways we are using this strategy category as a catch-all. This is partly because these strategies are not usually used on their own but in combination with other strategies.
 * 4 Make a list**
 * 5 Think**

The strategies that we want to mention here are **Being Systematic, Keeping Track, Looking For Patterns, Use Symmetry and Working Backwards and Use Known Skills.** It is very important to **keep track** of your work. We have seen several groups of children acting out a problem and having trouble at the end simply because they had not kept track of what they were doing. __So keeping track is particularly important__ with Act it Out and Using Equipment. But it is important in many other situations too. You have to know where you have been and where you are going or you will get hopelessly muddled. In many ways **looking for patterns** is what mathematics is all about. We want to know how things are connected and how things work and this is made easier if we can find patterns. Patterns make things easier because they tell us how a group of objects acts in the same way. Once we see a pattern we have much more control over what we are doing. Finally **working backwards** is a standard strategy. However, it’s a powerful tool when it can be used and is very useful when looking at games. It frequently turns out to be worth looking at what happens at the end of a game and then work backward to the beginning, in order to see what moves are best.
 * Being systematic** may mean making a table or an organised list but it can also mean keeping your working in some order so that it is easy to follow when you have to go back over it. It means that you should work logically as you go along and make sure you don’t miss any steps in an argument. And it also means following an idea for a while to see where it leads, rather than jumping about all over the place chasing lots of possible ideas.
 * Using symmetry** helps us to reduce the difficulty level of a problem. Playing Noughts and crosses, for instance, you will have realised that there are three and not nine ways to put the first symbol down. This immediately reduces the number of possibilities for the game and makes it easier to analyse. This sort of argument comes up all the time and should be grabbed with glee when you see it.

Then we come to **use known skills**. The trick here is to see which skills that you know can be applied to the problem in hand. An example of this is if you know the formula for finding area then you can use this to solve an area problem.

This strategy is related to the first step of problem solving when you say 'have I seen a problem like this before?' Being able to relate a word problem to some previously acquired skill is not easy but it is extremely important.