Anyone who has taught maths for any length of time will know how difficult it can be to teach pupils to solve maths problems out of context. Present pupils with a familiar setting or a sum that they've tackled before then they're usually fine, but turn it into an unfamiliar problem then it's a different matter. However, in the same ways that we teach strategies for other areas of maths, we can also teach strategies to solve maths problems.
When solving maths problems, students should be encouraged to follow a general problem solving procedure. This is summed up as follows:
1. Read the problem carefully. The first and most important step is to read the problem carefully to understand what you're asked to find out and what information you have been given. Underlining the important information is also useful so you have all the important numbers/facts to hand.
2. Choose a strategy and make a plan.
3. Carry out the plan and solve the problem.
4. Check the working out and make sure that your solution is actually answering the question.
There are a number of strategies that can be used to solve maths problems, as follows:
Create a diagram
Creating a diagram can help mathematicians to picture the problem and find the solution. To create a diagram, the problem must be read carefully and the information that has been given to them in the question drawn into the diagram. They can then work out the solution from the diagram that has been drawn.
Guess and check
The guess and check strategy can be helpful for many types of problems. When students use this strategy, they will make a reasonable guess, based on the information that they have been given and then check to see if their guess is correct The guesses should get closer and closer to the answer, until the correct answer is found.
Use a table or make a list
Using a table is a good way to sort out and organise the information that has been given in the question. The information that has been set out in the table will hopefully lead students to the correct solution.
Making a list is a strategy that will help students sort out the information that has been given in the problem. Once the students can see all of the possibilities for the solution, they can then attempt to solve the problem more easily.
This strategy requires students to use the information they have been given in the question to eliminate possible solutions to finally discover the correct solution.
Find a pattern
When students use this strategy they look for a pattern from the information that has been given. Once the pattern has been identified, the students can predict what will happen next and then continue the pattern to find the correct solution.
Working backwards is an excellent strategy to use when the final outcome of the problem has already been given. Students just need to work out what the events were that occurred previously.
Solve an easier version
Sometimes the problem is too difficult to solve in one step. When this happens the students will be able to make the problem more simple by dividing it into smaller and easiest steps, such as rewording the problem using smaller numbers.
These strategies are really useful in helping to solve maths problems. I have used them with the classes that I've worked with in KS2 to great effect. Giving children the experience of using these maths problem solving strategies will provide themv with a really useful toolkit for their maths arsenal as well as making them more confident when presented with a maths problem.