# Problem Solving

When solving a problem (as opposed to merely using a given formula), it is generally good to proceed along the following lines:

1. First, you have to understand the problem.
2. After understanding, make a plan.
3. Carry out the plan.
4. 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:

• 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!

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.

Note by Arron Kau
5 years, 6 months ago

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Good advice. But you must consider that answering questions in exam is much different from doing it this way because of the shortage of time. So can you provide any strategies for that.

- 4 years, 9 months ago

Well in the beginning it may be boring and frustrating, but if you practice these steps enough times, you surely can do all of these in a minute or two, while seeing the mathematics with a different angle and every angle, and writing the genuine solution, and having a feeling like you have invented the solution.

- 4 years, 9 months ago