When solving a problem (as opposed to merely using a given formula), it is generally good to proceed along the following lines:
- First, you have to understand the problem.
- After understanding, make a plan.
- Carry out the plan.
- Look back on your work. How could it be better?
Understanding the Problem
Before you begin calculating, it is a good idea to spend some time trying to understand exactly what it is that is being asked. Here are some questions to ask yourself before you begin:
- What is being asked?
- Are there terms or definitions in the problems that I don't understand?
- What information will I need to solve this problem? Is it all present in the question?
- Can I restate the problem in my own words?
- What form will a correct answer take?
Make a Plan
There are often many reasonable approaches to solving a problem, and every student has a different apporach. Make a plan that will help you get to the answer. Some possible apporaches:
- Draw a picture.
- Solve an equation.
- Guess and check.
- Make a list and look for patterns.
- Solve a simpler problem and see if it sheds light on this one.
- Look at individual cases.
- Work backwards from the answer.
- Use a formula.
Carry out the Plan
This is usually much easier than understanding the problem or making the plan. Proceed forward with patience and care. If you find that your plan has failed or that you did not fully understand the problem before beginning, now is the time to start over and begin again. Don't be afraid to discard a failed plan; keep trying and you will solve it!
Review your Work
Problem solving is a skill that can only be aquired through extensive practice, and one of the things that ensures you continue to progress is actively paying attention to your own work. Did you make any careless mistakes? Was there anything that would have been easier if you'd understood it better? Review your work to make the next problem easier.
Note: these instructions were inspired by How to Solve It by George Pólya.