Although math problems can be faced and solved in multiple ways, there is a general approach, divided into several steps, which allows you to find a solution to even the most complex and difficult problems. Using this strategy you can benefit by improving your analysis and calculation skills and, in general, your mathematical skills. Continue reading this article to learn a general strategy to apply in solving any mathematical problem.
Steps
Part 1 of 3: Analyzing the Problem
Step 1. Identify the type of problem you are facing
Is it a geometry problem? Is the data hidden in the text? Is it a fraction? Do you have to solve a quadratic equation? Before making any move, you need to understand what category the problem you are facing falls into. Taking the time to identify the class of problem you are facing is a fundamental step to take the correct path that will lead you to the solution.
Step 2. Read the problem text very carefully
While it may seem easy at first glance, take the time to read the text very carefully. Don't make the mistake of neglecting this step to throw yourself headlong into trying to fix it. If it is a complex issue, you may need to reread it several times before fully understanding it. Take your time and don't go any further until you understand exactly what you are being asked to do.
Step 3. Rework the problem text
To help the mind analyze in depth the question that has been posed to you, it may be useful to re-elaborate it orally or in writing using your own words. You can do this simply orally or use a sheet of paper if the situation does not allow you to speak loudly to yourself, for example if you are in class and taking a test or test. Check carefully what you said or wrote and compare it with the original text of the problem to be sure that you have interpreted it correctly and accurately.
Step 4. Visually represent the question you need to solve
If you think it will be helpful in finding the solution to the type of problem you are facing, create a visual representation of what is being asked of you so you can determine what next steps you should take. The design does not have to be elaborated, it will simply have to shape all the data in your possession. As you create your graphical representation of the problem, strictly stick to the text and, once finished, check that what you have written is consistent with the data you have been provided. Ask yourself the following question: "Does my graphic scheme accurately and accurately represent the mathematical question I am facing?". If the answer is yes, then you can proceed to the next step. If not, it is a good idea to reread the text of the problem more carefully, to identify what you have missed.
- Draw a Venn diagram. It is a tool that serves to graphically represent the relationships existing between the elements that make up the problem to be solved. Using the Venn diagram is very useful when dealing with mathematical questions described in textual form.
- Draw the related chart.
- Arrange the elements of the question on a line.
- Use simple shapes to represent elements that describe the more complex aspects of the problem.
Step 5. Look for known patterns
Sometimes one is able to recognize known mathematical patterns simply by carefully reading the text of the problem. To facilitate this step, you can create a table. Make a note of any known mathematical patterns or patterns that you can locate within the problem. This new information will be a valuable aid in identifying the final solution or may even be the answer to the problem.
Step 6. Review the information you have
Check carefully what you have written so far to make sure that the numbers and other essential data are correct. Do not proceed with drafting the action plan until you are certain that you have all the necessary information and that you have fully understood the question that has been posed to you. If you don't understand what you're being asked to do, take the time to look up examples in your textbook or online. Looking for and analyzing the solutions adopted by people who have successfully solved the same problem as you may help you understand what you have been asked to provide.
Part 2 of 3: Develop a Plan
Step 1. Identify the mathematical formulas you need to solve the problem you are facing
If the question you are facing is particularly complex, you may need more formulas. Taking some time to review the theoretical concepts in the textbook you are following may be helpful in identifying the solution to the problem.
Step 2. Take note of what you need to get to the final answer to the question
Make a list of all the steps you need to take and all the items that are needed to solve the problem. The list you create will help you organize your work and stay focused on the final goal. You can also use it to get an idea of what the solution to the question will be before actually identifying it.
Step 3. Work on a simpler problem
If there is a question that is simpler than the one in front of you, but that appears to be similar, start by trying to solve it. Solving simple math questions, which however require you to use some of the same steps and formulas, is of great help when you are faced with much more complex problems.
Step 4. Make a reliable guess of what you foresee will be the final solution to your problem
Before proceeding to really solve the mathematical question under consideration, try to evaluate what the final solution can be. Try to identify numbers and other factors that can help you make your assessment. Review your hypothesis and the process you used to make it, to make sure you didn't miss a thing.
Part 3 of 3: Fix the Problem
Step 1. Follow the plan you created
Complete all the steps you wrote in the previous section, necessary to get to the final solution of the problem. Check carefully the correctness of each step to be sure that you have done a precise and accurate job.
Step 2. Compare the answer you have identified with the one you hypothesized
After completing each step, it may be useful to compare the data obtained with those assumed for each, as well as in the case of the final solution of the problem. Ask yourself the following question: "Do the solutions I have identified coincide or are they compatible with the hypotheses I have developed?". If the answer is no, identify the reason for this result. Check your calculations to make sure they are correct for each step you went through.
Step 3. Try a different action plan
If the first one you worked out didn't work, go back to the planning stage and create a new one. Should this scenario occur, don't be discouraged; when you are learning something new, making mistakes is normal, they are part of the natural learning process. Accept that you were wrong, learn from your mistakes and move on to the next stage of the work. Try not to waste precious energy on mulling over your mistakes or getting angry with yourself.
Step 4. Think about the problem
After you have come to the correct answer to the question that has been posed to you, carefully analyze the process by which you came to this conclusion. Take some time to think about how you solved it, so that you are ready and prepared when you face other similar problems. This step is also used to identify all the concepts you still have some uncertainty about and need to learn more by practicing..
