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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 577,841 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
- 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.
Developing a Plan
Solving the Problem
- 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
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- ↑ 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
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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How to Solve Algebra Problems Step-By-Step
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Solving Algebra word problems is useful in helping you to solve earthly problems. While the 5 steps of Algebra problem solving are listed below, the following will help you learn how to first identify the problem.
- Identify the problem.
- Identify what you know.
- Make a plan.
- Carry out the plan.
- Verify that the answer makes sense.
Identify the Problem
Back away from the calculator ; use your brain first. Your mind analyzes, plans, and guides in the labyrinthine quest for the solution. Think of the calculator as merely a tool that makes the journey easier. After all, you wouldn’t want a surgeon to crack your ribs and perform a heart transplant without first identifying the source of your chest pains.
The steps of identifying the problem are:
- Express the problem question or statement.
- Identify the unit of the final answer.
Express the Problem Question or Statement
In Algebra word problems, the problem is expressed as either a question or a statement.
- How many trees will John have to plant?
- How many televisions will Sara have to sell to earn $50,000?
- Find the number of trees John will have to plant.
- Solve for the number of televisions Sara will have to sell to earn $50,000.
Identify the Unit of the Final Answer
What will the answer look like? Now that you understand the word problem’s purpose, determine the answer’s unit. For example, will the answer be in miles, feet, ounces, pesos, dollars, the number of trees, or a number of televisions?
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- How do you solve algebraic expressions?
- To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.
- What are the basics of algebra?
- The basics of algebra are the commutative, associative, and distributive laws.
- What are the 3 rules of algebra?
- The basic rules of algebra are the commutative, associative, and distributive laws.
- What is the golden rule of algebra?
- The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.
- What are the 5 basic laws of algebra?
- The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.
- Middle School Math Solutions – Equation Calculator Welcome to our new "Getting Started" math solutions series. Over the next few weeks, we'll be showing how Symbolab... Read More
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This is work in progress, so please keep checking.
Linear equations are the easiest ones to solve. Don't try any other equations before you master these with our tutorials and interactive linear equation solvers.
Graphing functions is very similar graphing equations. Here you will learn proper functional notation as well as graphing functions that are more complex that the ones found in Graphing equations tutorials.
Are absolute values absolutely incomprehensible? Take a quick look at our step-by-step tutorials with interactive absolute value problem solvers.
Math roots worse than root canals? Not with our tutorials and interactive solvers. You will learn how to add, subtract multiply and divide roots as well as rationalize denominators.
Are you unsure about exponent rules, polynomial operations and similar topics? These tutorials will teach you the basic rules and operations, and our polynomial solvers will generate infintely many step-by-step solutions to a variety of problems
Quadratic equations are a little bit trickier than linear ones. If you are unsure about linear equations go over linear equations tutorials first. If you think you can handle them, use our quadratic equations tutorials and interactive solvers to learn about quadratic formula and other ways of solving second order equations.
Are complex numbers too complex to learn? No, they are not if you use our complex number solvers and interactive tutorials. You will learn about why we need them, what an imaginary unit is, and a lot of other interesting things.
Have problems with factoring? Which rule to apply when? Take a look at these handy interactive tutorials on different factoring methods.
Are fractions giving you a headache? Learn how to reduce fractions and simplify a variety of rational expressions using our tutorials that include interactive fraction solvers.
Need a bit of a brush up on arithmetics? Review the basics of arithmetics calculations and learn about representation of integers and real numbers using our interactive solvers.
Graphing equations with our interactive graphers is easy! Not only do they let you graph equations, but with our tutorials you also learn about characteristic shapes and points of of common equations.
Is exponential function exponentially harder to learn than other functions? Not so with our interactive solvers, graphers and tutorials!
If you already know how to graph equations, inequalities are easy-peasy. Lots of shading involved! Use our interactive graphers and tutorials to learn this important topic
This set of tutorials will explain how to solve and graph a system of two linear equations in a variety of ways
There is nothing very radical about radical equations! That is, if you know what a radical is. If not, go through our Roots and Radicals tutorial first. Then come back and use our interactive radical equations solvers and tutorials to learn how to solve this type of equations.
This set of tutorials explains how to simplify a variety of expressions, such as fractions and radicals.
Good news: Solving linear inequalities inequalities is very similar to solving linear equations. Bad news: there is this pesky little inequality sign (< or >) that can change directions based on what you do with your inequality. Read our tutorials and use the absolute value solver to learn more.
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Strategies for Solving Math Word Problems
Math word problems can be tricky and often challenging to solve. Employing the SQRQCQ method can make solving math word problems easier and less intimidating.
The SQRQCQ method is particularly useful for children with learning disabilities and can be used effectively in special education programs. SQRQCQ is an abbreviation for Survey, Question, Read, Question, Compute, and Question.
Step 1 – SURVEY the Math Problem
The first step to solving a math word problem is to read the problem in its entirety to understand what you are being asked to solve. After you read it, you can decide the most relevant aspects of the problem that need to be solved and what aspects are not relevant to solving the problem. The idea here is to get a general understanding.
Step 2 – QUESTION
Once you have an idea of what you’re attempting to solve, you need to determine what formulas, steps, or equations should be utilized in order to find the correct answer. It is impossible to find an answer if you can’t determine what needs to be solved. Basically, what are the questions being asked by the problem?
Step 3 – REREAD
Now that you’ve determined what needs to be solved, reread the problem and pay close attention to specific details. Determine which aspects of the problem are interrelated. Identify all relevant facts and information needed to solve the problem. As you do, write them down.
Step 4 – QUESTION
Now that you’re familiar with specific details and how different facts and information within the problem are interrelated, determine what formulas or equations must be used to set up and solve the problem. Be sure to write down what steps or operations you will use for easy reference.
Step 5 – COMPUTE
Use the formulas and/or equations identified in the previous step to complete the calculations. Be sure to follow the steps you outlined while setting up an equation or using a formula. As you complete each step, check it off your list.
Step 6 – QUESTION
Once you’ve completed the calculations, review the final answer and make sure it is correct and accurate. If it does not appear logical, review the steps you took to find the answer and look for calculation or set-up errors. Recalculate the numbers or make other changes until you get an answer that makes sense.
How does SQRQCQ help students with learning disabilities?
Math word problems tend to be especially challenging for Learning Disabled (LD) students. LD students often lack “Concept Imagery”, or the ability to visualize the whole problem by creating a complete mental image. They often jump right into calculations and computations without understanding what the problem is asking or what they’re looking for.
LD students may also struggle to understand the words or wording within math word problems correctly. The inability to correctly interpret and understand wording greatly impacts their math reasoning skills and often leads them to making the wrong calculations and arriving incorrect conclusions.
Remembering and manipulating information and details in their working memory is another challenge some LD students face as they try to see the whole picture. Slow processing of information, followed by frustration and anxiety, will often lead LD students to try and get through math word problems as quickly as possible – which is why they often jump straight into computations in their attempt to make it to the finish line as quickly as possible.
SQRQCQ is a metacognitive guide that provides LD students with a logical order for solving math word problems. It provides just enough direction to guide them through the reasoning process without overwhelming them. SQRQCQ is also a mnemonic that is easy for students to remember and which they can fall back on when completing homework or taking tests.
Read also: – A Guide for Studying Math
- Discover Your Learning Style – Comprehensive Guide on Different Learning Styles
- 15 Learning Theories in Education (A Complete Summary)
- Inquiry Based Learning: The Definitive Guide
- Developing a Student-centered Classroom
- Distance Learning: The Ultimate Guide to Online Learning
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