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How to Solve Math Problems

Last Updated: May 16, 2023 Fact Checked

This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 575,763 times.

Although math problems may be solved in different ways, there is a general method of visualizing, approaching and solving math problems that may help you to solve even the most difficult problem. Using these strategies can also help you to improve your math skills overall. Keep reading to learn about some of these math problem solving strategies.

Understanding the Problem

Step 1 Identify the type of problem.

  • Draw a Venn diagram. A Venn diagram shows the relationships among the numbers in your problem. Venn diagrams can be especially helpful with word problems.
  • Draw a graph or chart.
  • Arrange the components of the problem on a line.
  • Draw simple shapes to represent more complex features of the problem.

Step 5 Look for patterns.

Developing a Plan

Step 1 Figure out what formulas you will need to solve the problem.

Solving the Problem

Step 1 Follow your plan.

Expert Q&A

Daron Cam

  • Seek help from your teacher or a math tutor if you get stuck or if you have tried multiple strategies without success. Your teacher or a math tutor may be able to easily identify what is wrong and help you to understand how to correct it. Thanks Helpful 1 Not Helpful 1
  • Keep practicing sums and diagrams. Go through the concept your class notes regularly. Write down your understanding of the methods and utilize it. Thanks Helpful 1 Not Helpful 0

how to solving a math problem

You Might Also Like

Do Math Proofs

  • ↑ Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
  • ↑ http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies
  • ↑ http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
  • ↑ https://math.berkeley.edu/~gmelvin/polya.pdf

About This Article

Daron Cam

To solve a math problem, try rewriting the problem in your own words so it's easier to solve. You can also make a drawing of the problem to help you figure out what it's asking you to do. If you're still completely stuck, try solving a different problem that's similar but easier and then use the same steps to solve the harder problem. Even if you can't figure out how to solve it, try to make an educated guess instead of leaving the question blank. To learn how to come up with a solid plan to use to help you solve a math problem, scroll down! Did this summary help you? Yes No

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4 steps to solve even the toughest math problem and improve your math skills, mathematics is a field where one can take multiple approaches to get to the solution of a problem. this simplified step-by-step approach will help you unravel the solution to even the toughest math problem..

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4 steps to solve even the toughest math problem and improve your math skills

There are multiple ways to solve math problems; however, a simplified method that can help everyone to solve even the toughest problem is a three-step process.

The process is:

1. Visualize the problem 2. Approach to be followed for that problem 3. Lastly, solve the problem

This three-step process could probably help you to improve your overall math skills.

1. Read carefully, understand, and identify the type of problem

how to solving a math problem

Negative thoughts about word problems can be barriers to success.

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts like the student in the cartoon below. Read the positive thoughts and say them out loud.

A cartoon image of a girl with a confident expression holding some books is shown. There are 4 thought bubbles. They read,

When it comes to word problems, a positive attitude is a big step toward success.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-Solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.

Pete bought a shirt on sale for $[latex]18[/latex], which is one-half the original price. What was the original price of the shirt?

Solution: Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

  • In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

  • In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

  • Let [latex]p=[/latex] the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

The top line reads:

Step 6. Check the answer in the problem and make sure it makes sense.

  • We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.

Step 7. Answer the question with a complete sentence.

  • The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”

If this were a homework exercise, our work might look like this:

The top reads,

We list the steps we took to solve the previous example.

Problem-Solving Strategy

  • Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the internet.
  • Identify what you are looking for.
  • Name what you are looking for. Choose a variable to represent that quantity.
  • Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
  • Solve the equation using good algebra techniques.
  • Check the answer in the problem. Make sure it makes sense.
  • Answer the question with a complete sentence.

For a review of how to translate algebraic statements into words, watch the following video.

Let’s use this approach with another example.

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[/latex] apples to the picnic. How many bananas did he bring?

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?

  • Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
  • Question ID 142694, 142722, 142735, 142761. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
  • Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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How to Study Maths: 7 Tips for Solving Maths Problems

Mathematics  is a subject that every student has to study at one time or another. Some love it but if we’re being honest, most people hate studying maths. The importance of maths for students has never been more prominent. Most university courses include some level of maths while almost every profession uses maths in some form on a daily basis. The problem many students have is that they don’t know  how to study maths to get good results.

Maths is one of those subjects which you can easily spend hours studying but end up none the wiser. However much you have studied, if you can not solve the problem on day of the test, you are lost. Thankfully, there are some  techniques for studying maths  that you can do regardless of your level.

7 Tips for Maths Problem Solving

1. practice, practice & more practice.

It is impossible to study maths properly by just reading and listening. To study maths you have to roll up your sleeves and actually solve some problems.   The more you practice answering maths problems, the better . Each problem has its own characteristics and it’s important to have solved it in numerous ways before tackling the exam. There is no escaping this reality, to do well in a Maths exam you need to have solved a LOT of mathematical problems beforehand.

2. Review Errors

When you’re practising with these problems, it’s important to  work through the process for each solution . If you have made any mistakes, you should review them and understand where your problem-solving skills let you down. Understanding how you approached the problem and where you went wrong is a great way of becoming stronger and avoiding the same mistakes in the future.

3. Master the Key Concepts

Do not try to memorise the processes.  This is counter-productive. It is much better and rewarding in the long-run to focus on understanding the process and logic that is involved. This will help you understand how you should approach such problems in the future.

Remember that Maths is a  sequential subject  so it’s important to have a firm understanding of the key concepts that underpin a mathematical topic before moving on to work on other, more complex solutions which are based on understanding the basics.

4. Understand your Doubts

Sometimes you can get stuck trying to solve part of a maths problem and find it difficult to move on to the next stage.  It’s common for many students to skip this question and continue on to the next. You should avoid doing this and instead spend time trying to understand the process of solving the problem. Once you have grasped an understanding of the initial problem, you can use this as a stepping stone to progress to the remainder of the question.

Remember: Maths requires time and patience to master.

It is a good idea to study with a friend who you can consult with and bounce ideas off when trying to solve complex problems.

5. Create a Distraction Free Study Environment

Mathematics is a subject that requires more  concentration  than any other. A proper study environment and a  distraction free area  could be the determining factor when solving complex equations or problems in geometry, algebra or trigonometry!

Studying with music can help create a relaxing atmosphere and stimulate the flow of information. Having suitable background music can foster an environment of maximum concentration.

6. Create a growing Mathematical Dictionary

Mathematics has specific terminology with a lot of  vocabulary . We suggest you create notes, flash cards or cheat sheets with all the concepts, terminology and definitions you need to know. You should include their meanings, some key points and even some sample answers so you can consult them at any time and recap.

7. Apply Maths to Real World Problems

As much as possible, try to apply real-world problems when approaching maths. Maths can be very abstract sometimes so looking for a practical application can help change your perspective and assimilate ideas differently.

Probability, for example, can be used in everyday life to predict the outcome of something happening and determine whether you want to take a risk such as if you should buy a lottery ticket or gamble.

Don’t forget that it’s also important  to have confidence in yourself  and face the exam knowing that you have prepared properly!

Article credit:  https://www.goconqr.com/en/examtime/blog/how-to-study-maths/

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What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

  • The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
  • The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
  • The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
  • The calculus section will carry out differentiation as well as definite and indefinite integration.
  • The matrices section contains commands for the arithmetic manipulation of matrices.
  • The graphs section contains commands for plotting equations and inequalities.
  • The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

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A Guide to Problem Solving

When confronted with a problem, in which the solution is not clear, you need to be a skilled problem-solver to know how to proceed. When you look at STEP problems for the first time, it may seem like this problem-solving skill is out of your reach, but like any skill, you can improve your problem-solving with practice. How do I become a better problem-solver? First and foremost, the best way to become better at problem-solving is to try solving lots of problems! If you are preparing for STEP, it makes sense that some of these problems should be STEP questions, but to start off with it's worth spending time looking at problems from other sources. This collection of NRICH problems  is designed for younger students, but it's very worthwhile having a go at a few to practise the problem-solving technique in a context where the mathematics should be straightforward to you. Then as you become a more confident problem-solver you can try more past STEP questions. One student who worked with NRICH said: "From personal experience, I was disastrous at STEP to start with. Yet as I persisted with it for a long time it eventually started to click - 'it' referring to being able to solve problems much more easily. This happens because your brain starts to recognise that problems fall into various categories and you subconsciously remember successes and pitfalls of previous 'similar' problems." A Problem-solving Heuristic for STEP Below you will find some questions you can ask yourself while you are solving a problem. The questions are divided into four phases, based loosely on those found in George Pólya's 1945 book "How to Solve It". Understanding the problem

  • What area of mathematics is this?
  • What exactly am I being asked to do?
  • What do I know?
  • What do I need to find out?
  • What am I uncertain about?
  • Can I put the problem into my own words?

Devising a plan

  • Work out the first few steps before leaping in!
  • Have I seen something like it before?
  • Is there a diagram I could draw to help?
  • Is there another way of representing?
  • Would it be useful to try some suitable numbers first?
  • Is there some notation that will help?

Carrying out the plan STUCK!

  • Try special cases or a simpler problem
  • Work backwards
  • Guess and check
  • Be systematic
  • Work towards subgoals
  • Imagine your way through the problem
  • Has the plan failed? Know when it's time to abandon the plan and move on.

Looking back

  • Have I answered the question?
  • Sanity check for sense and consistency
  • Check the problem has been fully solved
  • Read through the solution and check the flow of the logic.

Throughout the problem solving process it's important to keep an eye on how you're feeling and making sure you're in control:

  • Am I getting stressed?
  • Is my plan working?
  • Am I spending too long on this?
  • Could I move on to something else and come back to this later?
  • Am I focussing on the problem?
  • Is my work becoming chaotic, do I need to slow down, go back and tidy up?
  • Do I need to STOP, PEN DOWN, THINK?

Finally, don't forget that STEP questions are designed to take at least 30-45 minutes to solve, and to start with they will take you longer than that. As a last resort, read the solution, but not until you have spent a long time just thinking about the problem, making notes, trying things out and looking at resources that can help you. If you do end up reading the solution, then come back to the same problem a few days or weeks later to have another go at it.


The 10 Must-Know Math Problem Solving Techniques for Every Student

  • February 2, 2023

Math is a subject that has been feared by many for generations. From simple arithmetic to complex equations, math can seem like a never-ending series of obstacles. However, solving math problems can become much easier and less intimidating with the right techniques. 

Math Problem Solving Techniques:

Math-Problem-Solving Techniques

These 10 math problem solving techniques are designed to help you overcome any math problem, no matter how difficult it may seem.

  • Math Problem Solving Techniques: Read and Understand the Problem
  • Math Problem Solving Techniques: Create a Plan
  • Math Problem Solving Techniques: Use Visual Aids
  • Math Problem Solving Techniques: Practice Estimation
  • Math Problem Solving Techniques: Check Your Work
  • Math Problem Solving Techniques: Use the Order of Operations
  • Math Problem Solving Techniques: Keep It Simple
  • Math Problem Solving Techniques: Learn by Doing
  • Math Problem Solving Techniques: Seek Help When Needed
  • Math Problem Solving Techniques: Keep a Positive Attitude

1. Read and Understand the Problem

Read and Understand the Problem

The first step in solving any math problem is understanding what the problem is asking. Read the problem carefully and ensure you know the question before solving it. If there is anything you need help understanding, feel free to ask your teacher or tutor for clarification.

You May Also Like: Math Quiz: A Day at School with Spider-Man

2. Create a Plan

how to solving a math problem

Once you understand the problem, the next step is to create a plan. This could mean creating a simple arithmetic formula, drawing a diagram, or listing the steps you need to take to solve the problem. Having a plan before you start solving the problem will help you stay organized and focused.

3. Use Visual Aids

how to solving a math problem

Visual aids can be incredibly helpful when solving math problems. Diagrams, graphs, and charts can help you understand complex issues and see relationships between variables. If you need help understanding a problem, try drawing a diagram or chart to help you see the problem in a new way.

4. Practice Estimation

how to solving a math problem

Estimation is a useful technique for solving math problems, especially when dealing large numbers. By estimating the answer, you can quickly see if your answer is in the right range and adjust accordingly.

5. Check Your Work

Check Your Work

It’s always a good idea to check your work after solving a problem. It will help you catch any mistakes you may have made and ensure that you have the correct answer. Checking your work is especially important when solving complex problems or working with decimals and fractions.

6. Use the Order of Operations

how to solving a math problem

The order of operations is a set of rules that dictate how they should perform mathematical functions. By following the order of operations, you can ensure that your answer is correct and avoid making mistakes.

7. Keep It Simple

Keep It Simple

When solving a math problem, it’s easy to get bogged down in complex calculations and formulas. However, keeping things simple often leads to a quicker and more accurate solution. Try to simplify the problem as much as possible and only use the necessary calculations.

8. Learn by Doing

how to solving a math problem

The best way to improve your math skills is to practice, practice, practice. You will become more familiar with the techniques and formulas you need to know by solving math problems regularly. The more you practice, the better you will get at solving math problems.

9. Seek Help When Needed

Seek Help When Needed

If you’re struggling with a particular math problem, don’t hesitate to seek help. Whether it’s from a teacher, tutor, or online resources, getting help can make all the difference.

10. Keep a Positive Attitude

Keep a Positive Attitude

Finally, keeping a positive attitude when solving math problems is important. Math can be challenging, but approaching it with a positive attitude can make all the difference. Believe in yourself and your abilities, and don’t give up. With the right techniques and a positive attitude, you can solve any math problem.

In conclusion, solving math problems doesn’t have to be a struggle. By following these 10 techniques, you can make math easier and more manageable. Whether a student or a professional, these tips will help you overcome any math problem and improve your math skills. So the next time you’re faced with a difficult math problem, remember these techniques. With these techniques, you’ll be able to solve any math problem with ease.

Anyway, don’t miss your chance to showcase your knowledge and skills in Mathematics by participating in the Kangaroo Math Competition 2023 , registration is now open!

Registration can be done through our website 👉 CONTESTHUB

Q: What is the first step in solving a math problem? A: The first step in solving a math problem is to read and understand the problem.

Q: What is Estimation in math? A: Estimation in math approximates a value or solution to a problem.

Q: What is the best way to improve my math skills? A: The best way to improve your math skills is to practice, practice, practice. You will become more familiar with the techniques and formulas you need to know by solving math problems regularly.

how to solving a math problem

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how to solving a math problem


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