Content

• Steps
• Part 1 of 3: Understanding the Problem
• Part 2 of 3: Planning a Solution
• Part 3 of 3: Solving the Problem
• Tips

While math problems can be solved in a variety of ways, there is a common visualization, approach, and solution method that allows you to solve even the most complex problems. This method also allows you to improve mathematical knowledge and skills. The article describes how to solve a number of mathematical problems.

Steps

Part 1 of 3: Understanding the Problem

1. 1 Determine what type of task is. Is this an arithmetic problem? Actions with fractions? Solving quadratic equations? Before proceeding with the solution, find out which area of ​​mathematics the problem belongs to. This is important because it will greatly simplify the search for a solution.
2. 2 Read the problem statement carefully. Even if the task seems simple, carefully study its condition.You should not start solving a problem only after a cursory acquaintance with its condition. If the task is difficult, you may need to re-read its statement several times to fully understand it. Do not spare the time for this and do not proceed with further actions until you know exactly what is given in the condition and what needs to be found.
3. 3 State the problem statement. For a better understanding of the problem, it is useful to state its condition in your own words. You can simply retell the condition, or write it down if it is inconvenient for you to speak out loud (for example, on an exam). Compare your own statement of the problem with its original condition, thereby finding out if you understood the task correctly.
4. 4 Draw the task graphically. If you think this will help, present the task graphically - it may make it easier to determine the next steps. It is not necessary to create a detailed diagram, it is enough to sketch the condition of the problem in general terms, indicating the numerical values. When creating a circuit, cope with the condition of the problem, when finished, compare the finished image with the condition again. Ask yourself the question: "Does my drawing represent the task correctly?" If so, you can start solving the problem. If the answer is no, re-read the condition again.
   • Plot a Venn diagram. This diagram depicts the relationship between the quantities appearing in the problem. The Venn diagram is especially useful for solving arithmetic problems.
   • Build a graph or diagram.
   • Place the values ​​given in the condition along a straight line.
   • Use simple geometric shapes to represent more complex objects.
5. 5 Examine the structure of the problem. After carefully reading the condition, you may remember similar problems that you solved earlier. You can build a table with the data entered into it to help you determine the nature of the task. Note the identified features of the problem - they will help you in solving it. It is even possible that you will remember similar tasks and get an answer right away.
6. 6 Examine the notes you made. Check your notes again, making sure you are not mistaken in numbers and other data. Don't start planning a solution until you are sure you have all the information you need and fully understand the problem. If you do not fully understand the problem, study similar examples in the textbook or on the Internet. Familiarization with similar problems solved by other people will help you understand what needs to be done to solve the problem that you are solving.

Part 2 of 3: Planning a Solution

1. 1 Find out what formulas you need to solve the problem. If the task is complex enough, several formulas may be required. Check out the necessary material in the tutorial for the solution.
2. 2 Write down what you might need to solve the problem. Make a sequential list of the steps you need to take to get an answer. This will help you organize your work properly and focus on solving the problem. A well-written plan will also help you to roughly estimate the answer in advance, before you solve the problem.
3. 3 Practice on an easier task. If there is a simpler problem similar to the one that needs to be solved, try your hand at it first. A preliminary analysis of a simple problem that uses the same techniques and formulas will make it easier to solve a more complex problem.
4. 4 Make an educated guess about what the answer should be. Before you start directly solving the problem, try to evaluate the answer. Determine the quantities and other factors influencing the assessment. Check your reasoning to see if you missed anything.

Part 3 of 3: Solving the Problem

1. 1 Stick to your plan. Follow the steps sequentially in the order in which you outlined them earlier. To avoid mistakes, double-check the result obtained at each stage.
2. 2 Compare your results with preliminary estimates. At the end of each stage, it is useful to compare its result with previous estimates; compare also the final answer with its preliminary estimate. Ask yourself the question: "Are my assumptions close to the results obtained?" If the answer is no, consider why. Verify your results by reviewing all the steps in the solution again.
3. 3 Try another solution scheme. If the plan you made didn't work, go back to the planning phase and develop a new plan. Do not be discouraged in case of an unsuccessful attempt, learning is not complete without mistakes - on the contrary, you will learn from your mistakes and will be able to avoid them in the future. Identify the mistakes you made and keep working. Don't get hung up on mistakes or get upset about them.
4. 4 Analyze the problem. When you get the correct answer, go back to the beginning and review the solution again. Analyzing the problem and solving it will help you the next time you face a similar problem. Also, you will better learn the methods and techniques used, which will definitely be useful to you in the future.

Tips

• If you have tried a variety of options without success and are unable to progress further with the problem, ask your teacher or tutor for help. He will identify the mistakes you made and help you fix them.
• Keep using charts and arithmetic. Review your class notes regularly. To make it easier to understand, write down the methods used in your own words and apply them as needed.