websites that solve math problems

• Solve equations and inequalities
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• Graph equations and inequalities
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• Arithmetics
• Determinant
• Percentages
• Scientific Notation
• Inequalities

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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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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Number Line

The Algebra Calculator is a versatile online tool designed to simplify algebraic problem-solving for users of all levels. Here's how to make the most of it:

• Begin by typing your algebraic expression into the above input field, or scanning the problem with your camera.
• After entering the equation, click the 'Go' button to generate instant solutions.
• The calculator provides detailed step-by-step solutions, aiding in understanding the underlying concepts.
• -x+3\gt 2x+1
• (x+5)(x-5)\gt 0
• 10^{1-x}=10^4
• \sqrt{3+x}=-2
• 6+11x+6x^2+x^3=0
• factor\:x^{2}-5x+6
• simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}
• x+2y=2x-5,\:x-y=3
• 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.

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• Middle School Math Solutions – Inequalities Calculator Next up in our Getting Started maths solutions series is help with another middle school algebra topic - solving...

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15 Best Math Learning Websites

reviewed by Jessica Kaminski

Created on Jun 04, 2024

Updated on June 4, 2024

There are so many Internet resources and platforms that provide information on different subjects. But what are the best websites to learn math? Short answer: it depends on what you’re looking for. From online math learning programs to tutoring services, you have a lot of options. 

In this article, we outlined 15 websites that help with math for students of all ages and needs.

What are some good math websites?

Here are some good math websites that cater to learners’ unique needs:

• Khan Academy
• CliffsNotes
• Prodigy Math
• MathPlayground
• SplashLearn
• Math is Fun
• Wolfram Alpha
• Art of Problem Solving  

Note : Some students need personal feedback to build a solid math foundation, while others only need math games for daily practice. When looking for math study websites, prioritize accurate, regularly updated, and user-friendly sites for the best user experience.

What are the best websites to learn math?

The best websites to learn math are tutoring platforms like Brighterly, free math sites like Khan Academy, and exam preparation websites like Cliff Notes, depending on the learner’s goals. 

Now let’s check them out in more detail!

1. Brighterly: The Best Math Learning Website

Brighterly is one of the best math sites for students between 1st and 12th grades. Imagine personal feedback, interactive slides, and fun games all in one place.

Here is how it works: you book a free demo and then sign up for a bundle of 6, 16, or 25 online classes. Then, through 1:1 lessons, Brighterly’s expert tutors explain all sorts of math topics in an interactive way. This helps children build a connection with their tutor, while truly understanding math.

Parents appreciate the personalized and modern approach of the platform — reviews mention friendly tutors, engaging lesson material, and improvement in students’ math grades . 

Brighterly Pros:

• Personalized lesson plans and feedback
• 1:1 lessons to ensure each student gets 100% of the tutor’s attention
• Free first lesson to match students with the best tutors

Brighterly Cons:

• Only for students from 1st to 12th grade

Improve your child’s math skill today with Brighterly

Let them be at the top of their class.

2. Khan Academy: Math Learning Website from Pre-K to College

One of the most popular free math learning websites, Khan Academy, is on a mission to make free education accessible. This goes for math as well. Once you sign up, you can access videos, quizzes, and exercises covering all things math, from addition to calculus.

As a member, you’ll also get access to the learning dashboard to track progress. This way, you’ll see which areas your child is good at, and which areas need more attention. 

While the website has a lot of great, free content, it lacks live lessons, so you wouldn’t have personalized feedback as you would in tutoring platforms. 

Khan Academy Pros:

• Math lessons for various levels, from kindergarten to college
• Learning dashboard to track progress

Khan Academy Cons:

• No live classes, so no personalized feedback

3. IXL Math: Math Learning Website for Early Learners

IXL Math holds your child’s hand from pre-K and brings them all the way to advanced topics like calculus. 

It has over 4,500 math activities, along with interactive questions, games, and quizzes. All of them are tailored for children of different grades, but you wouldn’t have immediate feedback from tutors, which helps learn from mistakes.

Membership prices start at $9.95.

IXL Math Pros:

• Has resources for parents
• Learners can study at their own pace

IXL Math Cons:

• It’s not free
• There are no live lessons, so no personalized feedback

4. CliffsNotes: Math Learning Website for Exam Prep

CliffsNotes helps students prepare for exams. 

Besides its famous textbooks, it has a website to help with math, as well as other subjects.

You can use its study guides to revise math subjects like algebra , statistics, and trigonometry. Once you feel comfortable, move on to the quiz section to test your knowledge. 

CliffsNotes Pros:

• Study guides prepared by experienced teachers
• Free website with topic explanations and quizzes
• Has dedicated guides for SAT and ACT math

CliffsNotes Cons:

• No personalized feedback
• Not interactive, which may make it difficult to understand complex topics

5. Prodigy Math: Math Learning Website for Grades 1 to 8

Prodigy teaches math through several interactive games. Both parents and math teachers can access Prodigy’s platform, suitable for Grades 1 to 8. 

According to a survey , students reported twice the level of math enjoyment with Prodigy, as they completed math-related games with their friends. These games increase learners’ motivation , help them accept mistakes, and make learning fun. 

Membership prices for Prodigy start at $9.95 per month.

Prodigy Math Pros:

• Free as a teachers’ math website, flexible paid membership options for parents
• Students can play with their friends, making learning interactive
• The algorithm makes sure students learn at the right level

Prodigy Math Cons:

• No tutor feedback
• Only covers grades 1-8

6. Math Playground: Math Learning Website for Early Learning Games

Math Playground turns math into fun and games! 

The website is free and has games for students between kindergarten and 6th grade. Younger children can start by identifying shapes, while older ones can play multiplication or division games.

Math Playground Pros:

• Suitable for early learners
• Gamified learning

Math Playground Cons:

• Only covers grades 1 to 6

7. SplashLearn: Math Learning Website for Pre-K to 5

With over 4,000 games and worksheets, SplashLearn offers interactive math practice for children between pre-K and Grade 5. 

A free math site for teachers, it’s also available for parents, with membership plans starting at $7.99 per month. Kids have fun with math games, parents track their learning, and teachers get lesson ideas. A win-win situation for everyone!

SplashLearn Pros:

• Free for math teachers, and free trial for parents
• Gamified learning, increasing students’ motivation levels
• Includes progress reports and a parent app 

SplashLearn Cons:

• Only covers pre-K to 5

8. Mathplanet: Math Learning Website for High School Students

Mathplanet focuses on high school students in the US. 

Its courses include core math topics like geometry and algebra, as well as college admission exams like SAT and ACT. You can follow the lessons through texts, diagrams, or Mathplanet’s YouTube channel.

If your child goes to high school, this is an amazing free resource. That said, it probably won’t be enough to notice and correct mistakes, as there are no live tutors. 

Mathplanet Pros:

• Focused on US high school math
• Offers SAT and ACT practice

Mathplanet Cons:

• No live classes

9. Math is Fun: Math Learning Website for Gamified Learning

If you’re looking for a free math website that has both topic explanations and games, Math is Fun is a great option. 

You can find all sorts of topics, from counting to geometry , which your child can practice at their own pace. That said, if you’re looking for guided learning, you may find the platform to be too independent, as it doesn’t have instructional videos or live feedback.

Math is Fun Pros:

• Well-explained topics
• Caters to learners of different levels

Math is Fun Cons:

• Can get repetitive
• Not interactive

10. Brilliant: Math Learning Website for Advanced Learners 

Looking for help with more complex math topics? Brilliant’s platform — designed for ages 13 to 113 — has you covered. 

Start with solving equations and vectors through the foundational math course. Then move on to more advanced math such as calculus and integrals. Besides basic and complex math, the platform also includes data analysis, programming, and science courses — so it’s one of the best math help websites for university students or working professionals.

Brilliant’s basic service is free, and its premium offer starts at $24.99 per month.

Brilliant Pros:

• Interactive learning with fun, bite-sized lessons
• Suitable for advanced learners
• Great user-interface

Brilliant Cons:

• No live feedback
• The free service has limited access

11. WolframAlpha: Math Learning Website for Independent Advanced Learners

WolframAlpha has over 10,000 entries to help solve mathematical problems of different levels. 

You can use its search bar to ask what you want help with — it’s possible to type both natural language and math input. For example, you can write “equation solving” to get topic explanations for equations. Alternatively, type in a specific equation for it to give a step-by-step explanation. 

To access the step-by-step explanations, you need to be a paid subscriber at $5 per month. Although it doesn’t replace math lessons, WolframAlpha is a good website to study math, especially for independent learners who need just a little bit of extra guidance. 

WolframAlpha Pros:

• Step-by-step explanations
• Large database of math topics and answers

WolframAlpha Cons:

• Not suitable for beginners
• The free version doesn’t give full access to step-by-step explanations

12. Art of Problem Solving: Math Learning Website for Online Group Programs

One of the best school math websites, Art of Problem Solving (AoPS) offers courses, books, and an online community. 

Thanks to its comprehensive network of experts and courses, students can connect with their peers and mentors, ask questions, and join live courses. 

AoPS has three key products: AoPS Online (Grades 5-12), AoPS Beast Academy (Ages 6-13), and AoPS Academy (Grades 2-12). The prices depend on the course.

Art of Problem Solving Pros:

• Online community of experts and like-minded students
• Serves learners of different levels with age-appropriate content formats
• Includes live courses, improving math understanding

Art of Problem Solving Cons:

• Some courses are expensive
• Classes are not 1:1

13. Desmos: Math Learning Website for Graphs and Equations

With a graphing calculator, scientific calculator, and matrix calculator, Desmos is ready to be a math lover’s best friend. 

With a user-friendly interface, the website makes it a breeze to visualize graphs and get help with equations. While it’s one of the most helpful math websites for advanced students, it doesn’t provide topic explanations. For the best results, use Desmos alongside other resources, such as online math classes .

Desmos Pros:

• Useful for calculating certain equations
• Has an app on Apple Store and Google Play

Desmos Cons:

• Not a complete course, which may feel incomplete for those who want detailed feedback
• Doesn’t have topic explanations

14. Buzzmath: Math Learning Website for Children Aged Between 6 and 16

Think of Buzzmath as a virtual classroom as well as a website to help with math. Teachers can give out stars as rewards, send personalized activities to support what’s been covered in class, and use the feedback loop feature to correct mistakes automatically. 

As for parents, they can sign up to receive interactive math activities and track kids’ progress.

Designed for students between ages 6 and 16, Buzzmath is trusted by 700,000 students and 34,000 teachers around the world. A family plan with Buzzmath starts at $20 per month.

Buzzmath Pros:

• Developed by educators
• Has over 14,000 activities
• Extensive features such as immediate feedback and progress reports

Buzzmath Cons:

• Only focuses on ages 6-16
• No tutor feedback if it’s not used in class

15. MathTV: Math Learning Website for Videos

MathTV has over 10,000 tutorial videos on arithmetic, algebra, trigonometry, calculus, and other topics. 

Each video is presented by tutors and instructors, who use a whiteboard to illustrate the topics. This works well for visual learners who enjoy seeing all lesson content in one place. 

A great free math resource, MathTV is best when used alongside other websites, such as tutoring platforms or gamified subscription websites. This is because it lacks an interactive element, such as a tutor asking questions or giving direct feedback to students.

• Extensive library of free videos
• Includes diverse topics such as fundamentals, algebra, calculus, trigonometry, and statistics
• No real-time feedback
• No interactive exercises like quizzes or games

How to choose the best math learning website?

To choose the best math learning website, you need to consider the students’ needs, grade level, and learning goals. Here’s a checklist so you can decide:

• Grade level: Check if the website is suitable for the student’s grade. Some platforms only cover primary and secondary school students, whereas others have a broader range.
• Previous math knowledge: How good is the student’s math foundation? If there are gaps, choosing a tutoring service will be the best option to build a better understanding of the subject. 
• Learning goals: Casual practice? Fun games to foster a love for math? Or SAT prep? These goals will hint you what the best math help websites are.
• Budget: Some services are more expensive than others — consider if you’re willing to invest in tutoring or a subscription service, or if you’re happy using free websites to study math.

Math learning with Brighterly

Brighterly combines fun worksheets, interactive games, and expert tutors that give valuable feedback. We can say that it brings together all the advantages of the best mathematics websites, plus personalized lessons.

Find the perfect math tutor here

Say goodbye to your child’s struggles with math.

The 1:1 lesson structure creates a connection between tutors and students, so math is no longer scary numbers, but fun equations, engaging puzzles, and their favorite subject at school!

You can book a free demo to learn more about the platform or read our reviews to see what other parents think of us:

We covered 15 different mathematical websites for students of all ages and needs. For personalized feedback, tutoring websites like Brighterly would be the best choice. 

You can top that up with exam preparation websites, study guides, and games. This way, math learning would be more of a habit than an obligation! 

Book your free demo lesson with one of our math tutors today.

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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Our day-to-day activities require math, and we would struggle with the essentials without a basic understanding of maths. The main goal of teaching kids math is so that they can solve real-life problems that require math. The easiest way to ensure that your kid can understand math when they encounter it outside of the classroom […]

Aug 25, 2023

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The 7 Best AI Tools to Help Solve Math Problems

How do you make seven even? Use these tools to solve the big math problems in life.

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The test questions, wolframalpha, microsoft mathsolver.

While OpenAI's ChatGPT is one of the most widely known AI tools, there are numerous other platforms that students can use to improve their math skills.

I tested seven AI tools on two common math problems so you know what to expect from each platform and how to use each of them.

I used two math problems to test each tool and standardize the inputs.

• Solve for b: (2 / (b - 3)) - (6 / (2b + 1)) = 4
• Simplify the expression: (4 / 12) + (9 / 8) x (15 / 3) - (26 / 10)

These two problems give each AI tool a chance to show reasoning, problem-solving, accuracy, and how it can guide a learner through the process.

Thetawise provides more than simple answers; you can also opt to have the AI model tutor you by sharing a detailed step-by-step breakdown of the solution. Using the platform is fairly straightforward, given that all you need to do is navigate to the platform and key in the math problem at hand. Alternatively, you can even upload a photo of the math problem onto the platform, and the AI will analyze the image and provide you with an answer.

The AI platform gave us a step-by-step breakdown of the problem:

It resulted in the answer:

While the answer is correct, the tool also provides further options for students to generate a more detailed breakdown of the steps or ask more specific questions.

WolframAlpha is an AI tool capable of solving advanced arithmetic, calculus, and algebra equations. While WolframAlpha's free version provides you with a direct answer, the paid version of the tool generates step-by-step solutions. If you want to make the best use of WolframAlpha's capabilities, you can sign up for the Pro version, which costs $5 per month for the annual plan if you're a student.

As expected, Wolfram Alpha solved both problems, showcasing its ability to handle different problems and provide precise answers quickly.

Julius works pretty similarly to the other AI tools on this list. That said, the highlight of this platform is that it has a built-in community forum, which users can use to discuss their prompts, results, or even issues they might be facing with the platform. Its active user base helps you quickly exchange ideas and receive feedback or advice. The platform's default version uses a combination of GPT-4 and Calude-3, based on whichever model best suits the prompt you input.

We tested the platform's accuracy by submitting the same problems that we did with the other AI tools. When submitting your prompt, you have the option of typing your question or uploading an image or a Google Sheet.

Julius provided correct solutions and offered options to help users verify the solution.

One of the oldest AI platforms, Microsoft's MathSolver is a great option if you want a tool capable of providing free step-by-step solutions to calculus, algebra, and other math problems. Here's how it fared when we submitted our math problems.

Microsoft's MathSolver provided the correct answers, and you can view the steps to the solution, take a quiz, solve similar problems, and more. This can be a great way to practice and perfect your understanding of different concepts.

Symbolab allows you to practice your math skills via quizzes, track your progress, and provide solutions to mathematical problems of different types, including calculus, fractions, trigonometry, and more. You can also use the Digital Notebook feature to keep track of any math problems you solve and share them with your friends. Another highlight of this platform is that educators can use the tool to create a virtual classroom, generate assessments, and share feedback, among other things.

The platform not only displays the answer but also lets you view a breakdown of the steps involved in solving the problem. You can also share the answers and steps via email or social media or print them for reference.

Anthropic launched its Claude 3 AI models in March 2024. Anthropic stated that Claude Opus, the most advanced Claude 3 model, outperforms comparable AI tools on most benchmarks for AI systems, including basic mathematics, undergraduate-level expert knowledge, and graduate-level expert reasoning. To test the platform's accuracy and ease of use, we submitted our two math problems. Here's how the platform performed:

While Claude initially got the answer wrong, probing it and requesting further clarification led to a correct solution.

Remember that we used the free version of Claude to solve this problem; subscribing to Opus (its more advanced model) is recommended if you want to take advantage of Claude's more advanced problem-solving capabilities.

Given that Claude got the previous problem wrong, our second, more basic fraction-based problem will indicate if the AI's performance was an anomaly or part of a consistent pattern.

As you can see, Claude correctly solved this problem and provided a detailed step-by-step breakdown of how it arrived at the answer.

GPT-4 can solve problems with far greater accuracy than its predecessor, GPT-3.5. If you're using the free version of ChatGPT, you'll likely only have access to GPT 3.5 and GPT-4o . However, for $20 per month, you can subscribe to the Plus model, which gives you access to GPT-4 and allows you to input five times the number of messages per day compared to the free version. That said, let's check how it performs with math problems.

In both cases, GPT-4o provided the correct answer with a detailed breakdown of the steps. While the platform is free, unlike other models, it does not have a quiz feature or a community forum.

These AI tools offer unique features and capabilities that make them a good option for math problems. Ultimately, the best way to pick a tool is by testing different models to determine which platform best fits your preferences and learning needs.

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The Algebra Problem: How Middle School Math Became a National Flashpoint

Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it.

By Troy Closson

From suburbs in the Northeast to major cities on the West Coast, a surprising subject is prompting ballot measures, lawsuits and bitter fights among parents: algebra.

Students have been required for decades to learn to solve for the variable x, and to find the slope of a line. Most complete the course in their first year of high school. But top-achievers are sometimes allowed to enroll earlier, typically in eighth grade.

The dual pathways inspire some of the most fiery debates over equity and academic opportunity in American education.

Do bias and inequality keep Black and Latino children off the fast track? Should middle schools eliminate algebra to level the playing field? What if standout pupils lose the chance to challenge themselves?

The questions are so fraught because algebra functions as a crucial crossroads in the education system. Students who fail it are far less likely to graduate. Those who take it early can take calculus by 12th grade, giving them a potential edge when applying to elite universities and lifting them toward society’s most high-status and lucrative professions.

But racial and economic gaps in math achievement are wide in the United States, and grew wider during the pandemic. In some states, nearly four in five poor children do not meet math standards.

To close those gaps, New York City’s previous mayor, Bill de Blasio, adopted a goal embraced by many districts elsewhere. Every middle school would offer algebra, and principals could opt to enroll all of their eighth graders in the class. San Francisco took an opposite approach: If some children could not reach algebra by middle school, no one would be allowed to take it.

The central mission in both cities was to help disadvantaged students. But solving the algebra dilemma can be more complex than solving the quadratic formula.

New York’s dream of “algebra for all” was never fully realized, and Mayor Eric Adams’s administration changed the goal to improving outcomes for ninth graders taking algebra. In San Francisco, dismantling middle-school algebra did little to end racial inequities among students in advanced math classes. After a huge public outcry, the district decided to reverse course.

“You wouldn’t think that there could be a more boring topic in the world,” said Thurston Domina, a professor at the University of North Carolina. “And yet, it’s this place of incredibly high passions.”

“Things run hot,” he said.

In some cities, disputes over algebra have been so intense that parents have sued school districts, protested outside mayors’ offices and campaigned for the ouster of school board members.

Teaching math in middle school is a challenge for educators in part because that is when the material becomes more complex, with students moving from multiplication tables to equations and abstract concepts. Students who have not mastered the basic skills can quickly become lost, and it can be difficult for them to catch up.

Many school districts have traditionally responded to divergent achievement levels by simply separating children into distinct pathways, placing some in general math classes while offering others algebra as an accelerated option. Such sorting, known as tracking, appeals to parents who want their children to reach advanced math as quickly as possible.

But tracking has cast an uncomfortable spotlight on inequality. Around a quarter of all students in the United States take algebra in middle school. But only about 12 percent of Black and Latino eighth graders do, compared with roughly 24 percent of white pupils, a federal report found .

“That’s why middle school math is this flashpoint,” said Joshua Goodman, an associate professor of education and economics at Boston University. “It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up.”

In the decades-long war over math, San Francisco has emerged as a prominent battleground.

California once required that all eighth graders take algebra. But lower-performing middle school students often struggle when forced to enroll in the class, research shows. San Francisco later stopped offering the class in eighth grade. But the ban did little to close achievement gaps in more advanced math classes, recent research has found.

As the pendulum swung, the only constant was anger. Leading Bay Area academics disparaged one another’s research . A group of parents even sued the district last spring. “Denying students the opportunity to skip ahead in math when their intellectual ability clearly allows for it greatly harms their potential for future achievement,” their lawsuit said.

The city is now back to where it began: Middle school algebra — for some, not necessarily for all — will return in August. The experience underscored how every approach carries risks.

“Schools really don’t know what to do,” said Jon R. Star, an educational psychologist at Harvard who has studied algebra education. “And it’s just leading to a lot of tension.”

In Cambridge, Mass., the school district phased out middle school algebra before the pandemic. But some argued that the move had backfired: Families who could afford to simply paid for their children to take accelerated math outside of school.

“It’s the worst of all possible worlds for equity,” Jacob Barandes, a Cambridge parent, said at a school board meeting.

Elsewhere, many students lack options to take the class early: One of Philadelphia’s most prestigious high schools requires students to pass algebra before enrolling, preventing many low-income children from applying because they attend middle schools that do not offer the class.

In New York, Mr. de Blasio sought to tackle the disparities when he announced a plan in 2015 to offer algebra — but not require it — in all of the city’s middle schools. More than 15,000 eighth graders did not have the class at their schools at the time.

Since then, the number of middle schools that offer algebra has risen to about 80 percent from 60 percent. But white and Asian American students still pass state algebra tests at higher rates than their peers.

The city’s current schools chancellor, David Banks, also shifted the system’s algebra focus to high schools, requiring the same ninth-grade curriculum at many schools in a move that has won both support and backlash from educators.

And some New York City families are still worried about middle school. A group of parent leaders in Manhattan recently asked the district to create more accelerated math options before high school, saying that many young students must seek out higher-level instruction outside the public school system.

In a vast district like New York — where some schools are filled with children from well-off families and others mainly educate homeless children — the challenge in math education can be that “incredible diversity,” said Pedro A. Noguera, the dean of the University of Southern California’s Rossier School of Education.

“You have some kids who are ready for algebra in fourth grade, and they should not be denied it,” Mr. Noguera said. “Others are still struggling with arithmetic in high school, and they need support.”

Many schools are unequipped to teach children with disparate math skills in a single classroom. Some educators lack the training they need to help students who have fallen behind, while also challenging those working at grade level or beyond.

Some schools have tried to find ways to tackle the issue on their own. KIPP charter schools in New York have added an additional half-hour of math time to many students’ schedules, to give children more time for practice and support so they can be ready for algebra by eighth grade.

At Middle School 50 in Brooklyn, where all eighth graders take algebra, teachers rewrote lesson plans for sixth- and seventh-grade students to lay the groundwork for the class.

The school’s principal, Ben Honoroff, said he expected that some students would have to retake the class in high school. But after starting a small algebra pilot program a few years ago, he came to believe that exposing children early could benefit everyone — as long as students came into it well prepared.

Looking around at the students who were not enrolling in the class, Mr. Honoroff said, “we asked, ‘Are there other kids that would excel in this?’”

“The answer was 100 percent, yes,” he added. “That was not something that I could live with.”

Troy Closson reports on K-12 schools in New York City for The Times. More about Troy Closson

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