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• Solve equations and inequalities
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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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Free Wolfram|Alpha Math Resources

Free help with your math—check your answers, quiz yourself, explore topics and more.

Wolfram|Alpha Website

Use the Wolfram|Alpha website for free to check answers, plot equations, balance chemical equations, visualize results, review interesting facts on a subject area and more.

Math Input on the Wolfram|Alpha Website

Use textbook notation to enter your math input and see it displayed in 2D. We've provided popular templates for you to use, as better visualization and quick editing mean faster results.

Wolfram|Alpha Mobile Apps

Use Wolfram|Alpha how and where you want with our natively designed apps. From additional features to specially designed keyboards, we’ve made it easy to use Wolfram|Alpha on the go.

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Use our convenient calculator pages to input your queries into Wolfram|Alpha. Read more information on topic areas and explore example queries.

Wolfram|Alpha Math Topic Coverage

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Add more to your toolbox with Wolfram|Alpha Pro! Get step-by-step solution help, generate printable worksheets and more! Discounts are available for students and educators— go Pro now »

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Input your math even faster with photo input. Enter your math problems using photo-based input to get you quickly to results and step-by-step solutions.

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Wolfram|Alpha Pro subscribers get integrated step-by-step solutions and can create unlimited printable worksheets for study sessions and quizzes.

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Easy inputs with our form-based interfaces get you straight to answers. Our Web App collections cover a wide variety of math topics, including algebra, calculus and more.

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This tool combines the power of mathematical computation engine that excels at solving mathematical formulas with the power of artificial intelligence large language models to parse and generate natural language answers. This creates a math problem solver that's more accurate than ChatGPT, more flexible than a math calculator, and provides answers faster than a human tutor.

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Problem Solver Subjects

Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

• Math Word Problems
• Pre-Algebra
• Geometry Graphing
• Trigonometry
• Precalculus
• Finite Math
• Linear Algebra

Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

Basic Math Solutions

Below are examples of basic math problems that can be solved.

• Long Arithmetic
• Rational Numbers
• Operations with Fractions
• Ratios, Proportions, Percents
• Measurement, Area, and Volume
• Factors, Fractions, and Exponents
• Unit Conversions
• Data Measurement and Statistics
• Points and Line Segments

Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

Below are examples of Pre-Algebra math problems that can be solved.

• Variables, Expressions, and Integers
• Simplifying and Evaluating Expressions
• Solving Equations
• Multi-Step Equations and Inequalities
• Ratios, Proportions, and Percents
• Linear Equations and Inequalities

Algebra Solutions

Below are examples of Algebra math problems that can be solved.

• Algebra Concepts and Expressions
• Points, Lines, and Line Segments
• Simplifying Polynomials
• Factoring Polynomials
• Linear Equations
• Absolute Value Expressions and Equations
• Radical Expressions and Equations
• Systems of Equations
• Quadratic Equations
• Inequalities
• Complex Numbers and Vector Analysis
• Logarithmic Expressions and Equations
• Exponential Expressions and Equations
• Conic Sections
• Vector Spaces
• 3d Coordinate System
• Eigenvalues and Eigenvectors
• Linear Transformations
• Number Sets
• Analytic Geometry

Trigonometry Solutions

Below are examples of Trigonometry math problems that can be solved.

• Algebra Concepts and Expressions Review
• Right Triangle Trigonometry
• Radian Measure and Circular Functions
• Graphing Trigonometric Functions
• Simplifying Trigonometric Expressions
• Verifying Trigonometric Identities
• Solving Trigonometric Equations
• Complex Numbers
• Analytic Geometry in Polar Coordinates
• Exponential and Logarithmic Functions
• Vector Arithmetic

Precalculus Solutions

Below are examples of Precalculus math problems that can be solved.

• Operations on Functions
• Rational Expressions and Equations
• Polynomial and Rational Functions
• Analytic Trigonometry
• Sequences and Series
• Analytic Geometry in Rectangular Coordinates
• Limits and an Introduction to Calculus

Calculus Solutions

Below are examples of Calculus math problems that can be solved.

• Evaluating Limits
• Derivatives
• Applications of Differentiation
• Applications of Integration
• Techniques of Integration
• Parametric Equations and Polar Coordinates
• Differential Equations

Statistics Solutions

Below are examples of Statistics problems that can be solved.

• Algebra Review
• Average Descriptive Statistics
• Dispersion Statistics
• Probability
• Probability Distributions
• Frequency Distribution
• Normal Distributions
• t-Distributions
• Hypothesis Testing
• Estimation and Sample Size
• Correlation and Regression

Finite Math Solutions

Below are examples of Finite Math problems that can be solved.

• Polynomials and Expressions
• Equations and Inequalities
• Linear Functions and Points
• Systems of Linear Equations
• Mathematics of Finance
• Statistical Distributions

Linear Algebra Solutions

Below are examples of Linear Algebra math problems that can be solved.

• Introduction to Matrices
• Linear Independence and Combinations

Chemistry Solutions

Below are examples of Chemistry problems that can be solved.

• Unit Conversion
• Atomic Structure
• Molecules and Compounds
• Chemical Equations and Reactions
• Behavior of Gases
• Solutions and Concentrations

Physics Solutions

Below are examples of Physics math problems that can be solved.

• Static Equilibrium
• Dynamic Equilibrium
• Kinematics Equations
• Electricity
• Thermodymanics

Geometry Graphing Solutions

Below are examples of Geometry and graphing math problems that can be solved.

• Step By Step Graphing
• Linear Equations and Functions
• Polar Equations

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Best 5 Websites For Solving Math Problems

Florencia basavilbaso.

• Best Apps And Tools , Non-Traditional Students , Writing Tips

Content Writer At Gradehacker

Find the top 5 websites to solve math problems in our video too!

Mathematics can be challenging for many, with complex equations and mind-bending concepts that require time, patience, and skill to master.

Fortunately, in the age of technology, we have plenty of websites to solve math problems and make the subject more accessible and exciting.

At Gradehacker, we dedicate ourselves to providing the best resources to non-traditional adult students and improving their college experience. 

Here are the best 5 websites to solve the math concepts you need to learn!

1. Symbolab

first on our list of websites to solve math is Symbolab. 

Whether you’re a beginner or an advanced student, this math skills resource has you covered with its detailed step-by-step solutions, interactive graphics, and helpful examples.

You can also put equations or problems and get math answers with detailed steps, graphics, and examples , making it a game-changer when it comes to finding solutions to math problems.

As a mathematical resource for students’ grades, it covers a wide range of topics, such as:

• Trigonometry

And in addition to it, the website offers a note-taking section, allowing users to write down key details for future reference.

Symbolab’s availability in both free and premium options ensures that students of all backgrounds can benefit from its remarkable features and unleash their full mathematical potential.

Symbolab Subscription and Cost

Symbolab has both price-free and premium options.

Free Plan: You have access immediately to practice problems, custom settings, and save notes. 

Pro Plan: Here, besides having the benefits of the free subscription, you’ll also be available to:

• Full access to solution steps
• Web & Mobile subscription
• Assessments
• Detailed progress report

The platform offers three different payment options:

• Monthly: $7.99
• Semi-Annual: $29.99
• Annual: $34.99

Symbolab is also available on Google Play and App Store

Mathway is another of the best websites to solve math problems that can help you with your class activities.

It stands as a reliable and accessible online tool for a range of math topics like:

• Trigonometric functions
• Descriptive statistics

One key feature that sets Mathway apart is its ability to provide step-by-step solutions to math problems.

It simplifies solving math problems by breaking down the solution process when entering an equation or problem, serving as a valuable companion for students , educators, and individuals seeking instant support.

With its step-by-step explanation and advanced graphing capabilities, this math solution app helps users obtain correct answers and understand each step, concept, and reasoning.

Mathway Subscription and Cost

Mathway subscription consists of its “Step-by-Step Access,” allowing users to see each step of the solution without advertisements.

This is the only current subscription plan that costs:

• $9.99 with a monthly subscription
• $39.99 with a yearly subscription

This smart calculator is available on Google Play and Apple Store

Cymath offers college students a powerful tool for solving math questions easily and precisely.

With its very simple interface and advanced capabilities, this website simplifies the process of tackling any complex math question you may have, making it a great resource for learners at all levels.

Unlike other math solver websites, it only covers algebra and calculus functions, but it’s a very intuitive tool that provides instant feedback and suggestions , ensuring users can correct errors or misconceptions along the way.

Cymath Subscription and Price

You can use this app for free, or you can pay $5 a month for:

• Shows how a step is done
• Shows why a step is taken
• Learn from reference material

Cymath has a mobile app available for iOS and Android .

4. QuickMath

QuickMath allows you to solve equations and simplify fractions by just typing your problem.  

After that, QuickMath will generate a step-by-step solution. It also includes a graphing tool that can be used to visualize solutions. 

One of the advantages of QuickMath is that it also provides instant feedback to students, allowing them to identify any mistakes they have made quickly . This can be especially useful for students struggling with math and needing extra support.

QuickMath is also accessible from anywhere with an internet connection , making it a useful tool for students studying remotely or outside the classroom. 

This math solver app will help you with:

• Solving complex math equations
• Factor polynomials
• Simplify expressions
• Graph equations and inequalities

And it also has features like:

• Advanced solvers: Partial fractions, matrices, factors, etc.
• All solvers: Arithmetics, fractions, etc.

QuickMath Subscription Plan and Costs

To see what steps to take, they offer a subscription plan that costs:

• $9.99 a month
• $19.99 every six months
• $29.99 a year

You can find it available on Google Play and Apple Store .

5. Microsoft Math Solver

Microsoft Math Solver is a powerful and versatile mobile application that serves as your personal math assistant on the go.

This app combines the convenience of a calculator with advanced problem-solving capabilities to help users easily tackle a wide range of mathematical equations and problems.

One of the standout features of Microsoft Math Solver is its ability to solve math problems using various methods and approaches. Users can simply snap a photo of a handwritten or printed math problem, and the app will analyze and provide step-by-step solutions.

This feature saves time and promotes a deeper understanding of the problem-solving process.

 This math problem solver covers:

• Pre-algebra
• Algebra calculator
• Trigonometric equations

This app is absolutely free, and you can find it on Google Play and Apple Store .

Tips For Solving Math Problems

Having websites to solve math problems can be an effective solution when you are taking care of math homework, but there are other practices you can adopt that will help you improve your math skills without the internet needed.

We know that this subject can be challenging for many students, but it can also be enjoyable and rewarding with the right approach. Here are six tips for solving math problems:

1. Understand The Problem:

Before attempting to solve a math problem, take the time to read it carefully and make sure you understand what you are being asked to do. 

Look for important keywords, such as “find,” “calculate,” or “solve,” and make note of any important information or data that is provided.

2. Draw a diagram:

Sometimes, it can be helpful to draw a diagram or graph to visualize the problem and make it easier to understand . 

This can be especially useful for geometry problems or problems involving complex data sets.

3. Work from left to right:

When performing calculations, always work from left to right and be sure to follow the order of operations Parentheses, Exponents, Multiplication and Division (PEMDAS). 

This will help you avoid errors and ensure that you arrive at the correct answer.

4. Show your work:

When solving a math problem, be sure to show your work step-by-step. 

This not only helps you keep track of your progress, but it also allows you to identify any mistakes you may have made and correct them before moving on.

5. Check your answer:

After solving a math problem, double-check your answer to ensure it is correct .

If possible, try using a different method to arrive at the same answer to confirm that your solution is accurate.

This step helps you catch any potential errors or miscalculations that may have occurred during the problem-solving process , especially when dealing with complex equations like quadratic equations.

6. Practice, practice, practice:

The more you practice solving math problems, the easier it will become. 

Set aside time each day to work on these problems, and don’t be afraid to ask for help if you need it. Remember, with perseverance and dedication, anyone can become proficient in math problem-solving!

Solving Math Problems Like a Pro

The world of mathematics is now more accessible and exciting thanks to effective websites to solve math calculations.

Whether you’re a student struggling with homework, a professional needing quick solutions or improving your abilities, these websites provide the necessary tools and resources.

From the comprehensive step-by-step solutions offered by Symbolab to the fast and efficient calculations of Mathway and the versatile capabilities of Microsoft Math Office, each website brings its unique features to the table.

But if you are looking for one-on-one guidance with your complex math problems, here at Gradehacker, we have years of experience helping students like you with their homework assignments and even entire STEM classes .

You can also check more tips to enhance your learning experience:

7 Best Websites to Find Free College Textbooks in 2023

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How to Become a Minimalist Student: A Lifestyle That Improves The Study

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How to Take Notes Like a Pro 

Best Sites For Scholarly Sources | Websites To Find The Best Academic Sources

Florencia Basavilbaso is a content creator passioned for writing, music, films, and the arts. At Gradehacker, she helps to improve non-traditional students life’s by finding and providing the most useful information, so they can always progress. You can find her on LinkedIn .

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• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
• Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
• Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
• Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
• Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
• Linear Algebra Matrices Vectors
• Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
• Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
• Physics Mechanics
• Chemistry Chemical Reactions Chemical Properties
• Finance Simple Interest Compound Interest Present Value Future Value
• Economics Point of Diminishing Return
• Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time Volume
• Pre Algebra
• One-Step Addition
• One-Step Subtraction
• One-Step Multiplication
• One-Step Division
• One-Step Decimals
• Two-Step Integers
• Two-Step Add/Subtract
• Two-Step Multiply/Divide
• Two-Step Fractions
• Two-Step Decimals
• Multi-Step Integers
• Multi-Step with Parentheses
• Multi-Step Rational
• Multi-Step Fractions
• Multi-Step Decimals
• Solve by Factoring
• Completing the Square
• Quadratic Formula
• Biquadratic
• Logarithmic
• Exponential
• Rational Roots
• Floor/Ceiling
• Equation Given Roots
• Newton Raphson
• Substitution
• Elimination
• Cramer's Rule
• Gaussian Elimination
• System of Inequalities
• Perfect Squares
• Difference of Squares
• Difference of Cubes
• Sum of Cubes
• Polynomials
• Distributive Property
• FOIL method
• Perfect Cubes
• Binomial Expansion
• Negative Rule
• Product Rule
• Quotient Rule
• Expand Power Rule
• Fraction Exponent
• Exponent Rules
• Exponential Form
• Logarithmic Form
• Absolute Value
• Rational Number
• Powers of i
• Complex Form
• Partial Fractions
• Is Polynomial
• Leading Coefficient
• Leading Term
• Standard Form
• Complete the Square
• Synthetic Division
• Linear Factors
• Rationalize Denominator
• Rationalize Numerator
• Identify Type
• Convergence
• Interval Notation
• Pi (Product) Notation
• Boolean Algebra
• Truth Table
• Mutual Exclusive
• Cardinality
• Caretesian Product
• Age Problems
• Distance Problems
• Cost Problems
• Investment Problems
• Number Problems
• Percent Problems
• Addition/Subtraction
• Multiplication/Division
• Dice Problems
• Coin Problems
• Card Problems
• Pre Calculus
• Linear Algebra
• Trigonometry
• Conversions

Most Used Actions

Number line.

• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

word-problems-calculator

• Middle School Math Solutions – Simultaneous Equations Calculator Solving simultaneous equations is one small algebra step further on from simple equations. Symbolab math solutions...

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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills.  students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

• Draw a model
• Use different approaches
• Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

• The context
• What the key information is
• How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

Similarly, you could draw a model to represent the objects in the problem:

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

• Understand the problem
• Devise a plan
• Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

How Third Space Learning improves problem-solving 

Resources .

Third Space Learning offers a free resource library is filled with hundreds of high-quality resources. A team of experienced math experts carefully created each resource to develop students mental arithmetic, problem solving and critical thinking. 

Explore the range of problem solving resources for 2nd to 8th grade students. 

One-on-one tutoring 

Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE : 8 Common Core math examples

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies of problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

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Easy Finger Math Tricks to Help Kids Solve Problems

While using your fingers isn't the fastest way to recall a multiplication fact while doing a problem, finger math tricks can help kids figure out how to answer the problem at hand — and as they work on their math, they will eventually learn all the facts by repetition.

Note that before your child can understand other finger tricks, they must be able to count by 2s, 5s, and 10s and multiply by 2s, 3s, and 4s.

Quick Finger Math Tricks for Threes and Fours

The tricks for multiplying by threes and fours are really a matter of counting out the answer on your fingers. As your children count out the answer repeatedly, they'll memorize it and then be able to move on to larger numbers.

Multiplying by Three

Did you realize that all of your fingers have three segments? Therefore, you can figure out anything from 3 x 1 to 3 x 10 by counting the segments on each finger. To start:

• Hold up the number of fingers you're going to multiply by 3. For example, if the problem is 3 x 4 — hold up four fingers.
• Count each segment on each finger you're holding up, and you should come up with 12 — which is the correct answer.

Multiplying by Four

Multiplying by four is the same as multiplying by two — twice. To start:

• Hold up the number of fingers to correspond with the number you are multiplying by four. For example, if you are multiplying 4 x 6 — hold up six fingers.
• Count each finger by two, moving from left to right. Then count each finger again, continuing to count by twos, until you've counted every finger twice.

Helpful Hack To keep track of the fingers you've counted twice, sometimes it's easier to put your finger down as you count the first time, and back up as you count the second time.

Finger Math Tricks for Multiplying by 6, 7, 8, and 9

While numbers one through five are easy for most kids to remember, six and up often pose a problem. This handy trick will make it a little easier to work those problems out.

Multiplying 6, 7, 8, and 9 by Hand

To begin, assign each finger a number. For example, your thumbs represent 6, your index fingers each represent 7, etc. This will remain the same throughout the finger math hack.

Your left hand will represent the first number that you are multiplying and your right hand will represent the second number you are multiplying. In this example, we are multiplying 7 x 8. 

To Determine the Part of Your Answer:

• On your left hand, put down the finger that represents the number you are multiplying as well as any fingers whose number value is less than this figure. In this example, you are multiplying 7 x 8, so the left hand will represent 7. You will drop your index finger (number 7) and your thumb (number 6).
• Similarly, the right hand will represent eight, so you will drop down your middle finger (number 8), your index finger (number 7), and your thumb (number 6).
• Now, just multiply the fingers that are still pointed upwards. In this case, you will have three fingers on your left hand and two on your right, so you will multiply 3 x 2 to get 6. This is the first part of your answer!

To Determine the Second Part of Your Answer:

• Keeping your fingers in the same positions, count how many fingers are folded down. In the 7 x 8 example, you should have five fingers folded. 
• You will count each of these in quantities of ten. So, 10, 20, 30, 40, 50.
• 50 is your answer.

To Determine Your Final Answer:

• Add your two numbers together. In this example, you would add 6 + 50, which gives you 56!

Another Finger Math Trick Just for Nine

There is a trick that works separately, just for multiplying by the number nine.

• To start, hold up all ten fingers, with your palms facing you.
• Assign each finger a number, starting with your left-hand thumb and ending with your right-hand thumb. The left-hand thumb will be one, the left-hand index finger will be two, and so on until you reach the number 10 for your right-hand thumb.
• To tackle a problem, put down the corresponding finger of the number you're multiplying by nine. For example, if you are multiplying 9 x 8, you'd put down the eighth finger (which will be on your right hand).
• Count all the fingers to the left of the finger you have folded down. This will give you 7. This is the first digit of your answer.
• Count all the fingers to the right of the finger you have folded down. This will give you 2. This is the second digit of your answer.
• Put the numbers together! Your answer is 72.

Finger Multiplication Tricks Can Make Math Easy and Fun

While the hope is that your kids will eventually memorize their multiplication charts , using some quick hand tricks for multiplication and letting them count things out on their fingers is not a bad way to learn. It keeps frustration at bay since the answer is always a fingertip away, and the repetition of having to figure it out will help cement those facts into their brains.

• April 18, 2024

Watch this dog that can solve math problems with her paw

Luna, a mini cockapoo, has a unique talent for solving math problems with help from her owner.

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3 Ways to Strengthen Math Instruction

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Students’ math scores have plummeted, national assessments show , and educators are working hard to turn math outcomes around.

But it’s a challenge, made harder by factors like math anxiety , students’ feelings of deep ambivalence about how math is taught, and learning gaps that were exacerbated by the pandemic’s disruption of schools.

This week, three educators offered solutions on how districts can turn around poor math scores in a conversation moderated by Peter DeWitt, an opinion blogger for Education Week.

Here are three takeaways from the discussion. For more, watch the recording on demand .

1. Intervention is key

Research shows that early math skills are a key predictor of later academic success.

“Children who know more do better, and math is cumulative—so if you don’t grasp some of the earlier concepts, math gets increasingly harder,” said Nancy Jordan, a professor of education at the University of Delaware.

For example, many students struggle with the concept of fractions, she said. Her research has found that by 6th grade, some students still don’t really understand what a fraction is, which makes it harder for them to master more advanced concepts, like adding or subtracting fractions with unlike denominators.

At that point, though, teachers don’t always have the time in class to re-teach those basic or fundamental concepts, she said, which is why targeted intervention is so important.

Still, Jordan’s research revealed that in some middle schools, intervention time is not a priority: “If there’s an assembly, or if there is a special event or whatever, it takes place during intervention time,” she said. “Or ... the children might sit on computers, and they’re not getting any really explicit instruction.”

2. ‘Gamify’ math class

Students today need new modes of instruction that meet them where they are, said Gerilyn Williams, a math teacher at Pinelands Regional Junior High School in Little Egg Harbor Township, N.J.

“Most of them learn through things like TikTok or YouTube videos,” she said. “They like to play games, they like to interact. So how can I bring those same attributes into my lesson?”

Part of her solution is gamifying instruction. Williams avoids worksheets. Instead, she provides opportunities for students to practice skills that incorporate elements of game design.

That includes digital tools, which provide students with the instant feedback they crave, she said.

But not all the games are digital. Williams’ students sometimes play “trashketball,” a game in which they work in teams to answer math questions. If they get the question right, they can crumble the piece of paper and throw it into a trash can from across the room.

“The kids love this,” she said.

Williams also incorporates game-based vocabulary into her instruction, drawing on terms from video games.

For example, “instead of calling them quizzes and tests, I call them boss battles,” she said. “It’s less frightening. It reduces that math anxiety, and it makes them more engaging.

“We normalize things like failure, because when they play video games, think about what they’re doing,” Williams continued. “They fail—they try again and again and again and again until they achieve success.”

3. Strengthen teacher expertise

To turn around math outcomes, districts need to invest in teacher professional development and curriculum support, said Chaunté Garrett, the CEO of ELLE Education, which partners with schools and districts to support student learning.

“You’re not going to be able to replace the value of a well-supported and well-equipped mathematics teacher,” she said. “We also want to make sure that that teacher has a math curriculum that’s grounded in the standards and conceptually based.”

Students will develop more critical thinking skills and better understand math concepts if teachers are able to relate instruction to real life, Garrett said—so that “kids have relationships that they can pull on, and math has some type of meaning and context to them outside of just numbers and procedures.”

It’s important for math curriculum to be both culturally responsive and relevant, she added. And teachers might need training on how to offer opportunities for students to analyze and solve real-world problems.

“So often, [in math problems], we want to go back to soccer and basketball and all of those things that we lived through, and it’s not that [current students] don’t enjoy those, but our students live social media—they literally live it,” Garrett said. “Those are the things that have to live out in classrooms right now, and if we’re not doing those things, we are doing a disservice.”

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More From Forbes

Alan alda on fame, curiosity, ufos and more.

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PASADENA, CA - CIRCA 1980: Alan Alda circa 1980 in Pasdena, California. (Photo by Barbara ... [+] Rosen/IMAGES/Getty Images)

In the first part of this interview series with Alan Alda, we covered the actor’s fascination with Nobel Laureate Richard Feynman, including the Broadway play Alda made about the physicist in 2001, Q.E.D. Here, in Part 2, we discuss curiosity and play word association with topics including UFO’s, fame and fear. Following are edited excerpts from a longer Zoom conversation.

Jim Clash: You seem like a curious person, Alan, something Richard Feynman embodied.

Alan Alda: It’s funny, but I’ve been asked by science teachers how they can get their kids more curious. It’s an interesting question. One way of looking at it is either you’re born curious or you’re not. Another way is that everybody has some modicum of curiosity already built in. It’s similar with empathy. Does everybody have it? Is there a range? In any case, can you build curiosity?

I think you can. One way, maybe not the most effective, is to let your own curiosity show, and, as much as possible, draw someone else’s out by doing that. They might be curious already. But a little encouragement might bring more out. “I wonder why it gets dark like that during an eclipse?” Get the other person to join you in your curious question.

Clash: One of the reasons I built my career in participatory adventure journalism is a guy named George Plimpton, now deceased, who you played in the movie, “Paper Lion.” Clearly, Plimpton was a curious person.

In the paper-strewn writing studio at his summer home, American writer and journalist George ... [+] Plimpton (1927 - 2003) works at his desk, Wainscott, New York, January 1985. (Photo by Susan Wood/Getty Images)

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Alda: I thought he invented a really fun way to report on things through his own personal experiences. Actually, it’s related to how I feel about good communicating. The more personal you can make it without losing the meaning, the importance of it, the better.

Clash: Let’s play a little word association. Fear, what are you afraid of, and how do you handle it?

Alda: Fear for me is getting hit in the nose [laughs]. That’s the first thing that comes to mind. If I had more time, I might think of something else. The best way to handle it? Watch what I say to people.

Clash: Fame?

Alda: Fame is a hard thing to get used to. I saw my father become famous. It was something he had to cope with. I’ve known people who thought fame would solve all of their problems. Then they find out they have even more problems to work with.

It takes time to figure out how to deal with people. You have to expect that they are thinking a lot of things when talking to you, that they’re not really talking to you but to your famous persona. Hawkeye Pierce in M*A*S*H - it’s a part I played. I never really talked about that character when I played it. I still don’t talk about it much. I wanted it to come out in the doing of it.

Clash: Edward Teller, father of the Hydrogen Bomb?

Alda: I had a lot of opinions about him early on, but I can’t remember exactly what they were. They weren’t flattering.

(Original Caption) 5/11/1950-Minnville, OR: A picture of a flying saucer photographed by farmer Paul ... [+] Trent shown flying over his farm.

Clash: UFO’s?

Alda: I kind of wish that the phrase UFO - unidentified flying object - was taken a little more seriously. There are things that have not been identified - events, objects, etc. But that doesn’t mean they’re people from another planet. It just means we haven’t identified them. Of course, there are UFOs; we don’t know what they are. The idea that there are creatures in them that come from some other part of the galaxy is low down on my list of possibilities.

Clash: This may be an odd question, but I’ve always thought that you have a friendly but sarcastic grin on your face much of the time, with your eyes and mouth. It’s endearing. Has anyone ever told you that?

Alda: I would think that my wife would be the first to tell me. But I haven’t heard that, no [laughs]. But thank you, I guess.

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