interactive math problem solving

AI Math Problem Solver

Instant step by step answers to your math homework problems. Improve your math grades today with unlimited math solutions. Try for Free 👉

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5 Million Students Helped Each Year

Interactive Mathematics helps over 5 Million students each year, who use our free lessons to help get ahead in math. We've taken that expertise and paired it with AI to provide a free to try AI math problem solver and math tutoring chat platform.

Math Problems, meet Math Solutions.

We've combined a powerful mathematical computational engine with large language model artificial intelligence to create a state of the art math problem solver and AI math calculator. More accurate than ChatGPT, more powerful than a math calculator, and faster than a math tutor! Whether it's a tough word problem, algebra equation or advanced calculus, our AI math problem solver and calculator can solve it.

Math Word Problem Solver

Math calculators and online math solver apps aren't built to handle math word problems. We've fixed that! Our solver can interpret math word problems and determine what mathematical operations needs to be used to solve the problem.

Easily snap a picture from your phone or upload a screenshot from your computer or copy/paste into the solver to get your step by step math solution.

Fast Solutions

Our proprietary AI model can answer math questions 10x faster than a human tutor and beats most other large language models on speed and solution accuracy!

Step-by-Step Solutions

Stuck on a hard math homework problem? Upload a picture of your math problem or enter it and immediately get a step-by-step solution to your math problems.

Get Math Help, 24/7

Studying for a big math test or quiz? Stuck on a difficult math homework problem in the middle of the night? Sign up and stop stressing and start improving your math grades!

AI Math Calculator + Bonuses!

We want to remove the costs getting in the way of academic success for every student! We've partnered with leading academic businesses to give you up to $1085 in exclusive discounts and free services when you sign up. You won't find these anywhere else.

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Unlimited Math Solutions plus so much more

Do you want better math grades? Do you want to stop stressing over hard math problems? Stop waiting, sign up now and in addition to our AI Math Problem Solver, we'll include free and exclusive discounts on courses, textbooks, and academic services valued at $1085.

Frequently Asked Questions

Can the math solver help me improve my grades (yes).

Now, we can't guarantee you'll get better grades, since the AI Math Solver is only half of the success equation, but the majority of students who use the application report full letter grade improvements in their grades. Most see improvements in their homework grades immediately.

How long does it take to get an answer to my math problem?

Our application is available 24/7 and will start working on a solutions immediately after you send it. The time it takes to solve each problem is dependant on the complexity of the problem. The application will post a step by step solution.

Can I really ask unlimited questions?

How is this app different from your tutoring service.

The AI Math Solver is FREE to try and powered by our proprietary mathematical computation engine and AI while our Tutoring service enables students to chat with professional (human) math tutors.

Can it answer Physics questions?

Yes, the AI has been trainined on physics concepts and problems. However if it can't answer a question, then we recommend subscribing to our Tutoring service to connect with a physics tutor.

Will it work on my phone?

Yes, the application is optimized for mobile and tablet, no need to download another app onto your phone. An internet connection is required.

Can I submit a picture of my math problem?

Yes, simply tap or click the carmera icon next to the Solve button in the application then select the image or if you're on your phone open your camera to immediately take a picture of your math problem.

The application can interpret most handwritten or typed math problems.

Is it free to use?

Yes, it's free to try! You can ask 3 questions for free before reaching the free question limit.

Which math subjects are covered?

The AI LLM has been trained on a large array of mathematical subjects including, but not limited to Basic Algebra, Advanced Algebra, Geometry, Trigonometry, Calculus, Advanced Calculus, Physics and much more.

Can it Solve Basic Math Problems?

Yep! The AI LLM has been trained on a large array of mathematical subjects including, but not limited to Basic Algebra, Advanced Algebra, Geometry, Trigonometry, Calculus, Advanced Calculus, Physics and much more.

How do I cancel my subscription?

You can cancel your subscription very easily in several ways.

1) Login, go to the Manage Account tab, then click the Cancel Plan button.

2) Click the cancel plan link in your sign up email.

3) If you can't find it or no longer have it, just send us an email at [email protected] and we'd be happy to assist you.

Can I change my subscription?

Yes you certainly can! You can change your subscription by accessing the Manage Account page within the application or using the link provided in your sign up email. If you can't find it or no longer have it, just send us an email at [email protected] or ask your tutor for assistance they will be happy to assist.

How much does it cost?

You can view the price of our subscription packages here . We're also providing freebies and exclusive deals from our large network of high quality partners. We obsess over the details to ensure you get 10x more value than the price tag!

Can it Solve Calculus Math Problems?

Can it solve geometry math problems.

P.S. We're currently working to enable in app graphing to accompany solutions.

Can it solve Trigonometric Functions?

Can it solve simple equations math problems.

Yep! The AI LLM has been trained on a large array of mathematical problems and subjects including, but not limited to Basic Algebra, Advanced Algebra, Geometry, Trigonometry, Calculus, Advanced Calculus, Physics and much more.

Can it solve any math problems and equations?

How do i get math solutions.

Simply upload an image of your math problem or enter it and click Solve. Our AI math problem solving calculator will provide a step by step solution to the problem with the answer.

Can it solve word problems?

Yes! Our AI math word problem solver will provide a step by step solution and answer to any word problem.

How do you find the answers to math word problems?

Step by step solutions and answers to any word problem or equations can be found in the chat window indicated in blue text bubbles.

Solver Title

Generating PDF...

• 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
• Pre Calculus
• Linear Algebra
• Trigonometry
• Conversions

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Number line.

• x^{2}-x-6=0
• -x+3\gt 2x+1
• line\:(1,\:2),\:(3,\:1)
• prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x)
• \frac{d}{dx}(\frac{3x+9}{2-x})
• (\sin^2(\theta))'
• \lim _{x\to 0}(x\ln (x))
• \int e^x\cos (x)dx
• \int_{0}^{\pi}\sin(x)dx
• \sum_{n=0}^{\infty}\frac{3}{2^n}
• Is there a step by step calculator for math?
• Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem.
• Is there a step by step calculator for physics?
• Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. It shows you the steps and explanations for each problem, so you can learn as you go.
• How to solve math problems step-by-step?
• To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.
• My Notebook, the Symbolab way Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back...

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Math Games offers online games and printable worksheets to make learning math fun. Kids from pre-K to 8th grade can practice math skills recommended by the Common Core State Standards in exciting game formats. Never associated learning algebra with rescuing animals or destroying zombies? Time to think again!

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Best of all? It's completely free! Click on any of our games above to get started.

Get updates on what we do by following us on Twitter at @mathgames . Send us your comments, queries or suggestions here .

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Usable Math

(formerly 4mality), a digital playground for math learning through problem solving and design.

Usable Math provides interactive problem solving practice for 3rd through 6th grade students learning mathematical reasoning and computation through creative writing, NoCode slideshow design, and human-AI collaboration.

• MATH MODULES

Math Friends

Featuring four coaches Estella Explainer, Chef Math Bear, How-to Hound, and Visual Vicuna who offer reading, computation, strategy, and visual strategies for solving math problems.

Estella Explainer

"I help children understand the language and meaning of questions using kid-friendly vocabulary."

Chef Math Bear

"I provide computational strategies (addition, subtraction, multiplication and division) for solving problems."

How-to-Hound

" I present strategic thinking clues (rounding, estimation, elimination of wrong answers). "

Visual Vicuna

" I offer ways to see problems and their solutions using animations, pictures, charts and graphs. "

The coaches annotate hints and provide feedback to help students with various levels of knowledge solve mathematical word problems using a wide range of strategies.

Math and ISTE Standards Based

Usable Math aims to teach mathematics concepts and problem solving skills based on the Massachusetts Mathematics Curriculum Framework and the Common Core State Standards for Mathematics. Usable Math supports ISTE Standards for Students : Empowered Learner (1.1), Knowledge Constructor (1.3), and Computational Thinker (1.5).

Open Education Resource

Usable Math is an open education resource project developed in the College of Education, University of Massachusetts Amherst. Usable Math received a 2023 classroom grant from MassCUE (Massachusetts Computer Using Educators) . An initial version called 4mality was developed with funding support from the Verizon Foundation and a grant from the US Department of Education, Institute of Education (IES).

BROWSE MATH MODULES

Storywriting, history, and science modules, a jenny-the-fisher math and citizen scientist adventure, math & science, a tai-the-math historian time travel adventure, math & history, ai-enhanced, a sofia-the-forester adventure, math & storywriting, math problem-solving and design modules, area and perimeter, total problems: 6.

Total problems: 8

Multiplication and Division

Algebraic Thinking

Total problems: 7

Measurement

Total problems: 10.

Geometry: Lines and Lines of Symmetry

Geometry: Maps + Grids + Ordered Pairs

Charts & Graphs

Geometry: Figures, Shapes and Angles

Total problems: 11

Add & Take Away

Place Value

Total problems: 14.

Total problems: 9

Total problems: 5

More coming soon, welcome to usable math. in this interactive website, you will find learning modules designed to develop mathematical problem solving skills among young learners in grades 3 to 6..

Our Modules explore standards-based math concepts including Fractions, Measurement, Geometry, Decimals, Money, and more. Usable Math is free to access using a computer, smartphone, or iPad.

What do we mean by Usable Math?

The word Usable can read as follows:

U Able meaning you can do math problem solving.

Us Able meaning together all of us can do math problem solving.

Usable meaning anyone is able to learn math problem solving - with practice, effort, and support.

What are the Usable Math Learning Modules?

Each learning module in Usable Math consists of a group of math word problems related to a specific mathematical concept. The problems are based on the Massachusetts Mathematics Curriculum Framework↗ as well as Common Core Standards↗ .

Each problem within a module consists of a question, three to four possible answer choices, and problem solving ideas and strategies provided by our four coaches: Estella Explainer, Chef Math Bear, How-to-Hound, and Visual Vicuna.

How are the Modules Displayed online?

Each module has been developed using Google Slides.

Click. Pause. Solve.

View each module in Slideshow.

How do teachers, students and families use each module?

We strive to make every module on Usable Math kid friendly . Clicking on a module from the selections on the Modules Homepage , each user controls what happens during the learning experience by clicking to open strategies and spending time thinking about them before answering the question. The goal is for students, by themselves, in small groups, or with a teacher, or a family member, to analyze and understand what the problem is asking them to solve before providing an answer.

A question appears without its answer choices or any problem solving strategies.

Click one time and Estella offers a problem solving strategy.

Click again and the Bear offers a different strategy.

Click again and the Hound presents a strategy.

Click again and the Vicuna has an additional strategy approach.

The next click gives the four answer choices, but not yet the correct answer.

The final click highlights the correct answer from among the answer choices.

Before going to the next problem, a motivational statement and gif appears offering encouragement to the users.

What is the purpose of the Motivational Statements between Problems?

Each motivational statement is intended to provide feedback and encouragement to students using the system. Following the insights of researchers into the use of praise and the development of growth mindsets in young learners, these motivational statements are designed to reward students’ effort, hard work, persistence, and belief in one’s self as a learner. We want youngsters to realize that they can learn anything with the right tools, the right beliefs, the right coaches, and their own work and practice.

Need more help? Or have a question?

Reach out to us and we will do our best to get back to you within 12 hours.

RESEARCH AND RESOURCES

We believe that every child deserves a strong foundation in mathematics. our platform is designed to provide engaging and effective math instruction to elementary school students, and we are proud to say that there is science behind the way we deliver this instruction..

UsableMath was formerly known as 4MALITY. As a result of our commitment to providing the best possible math instruction to elementary school students, we have rebranded our platform as UsableMath.com to better reflect our mission and approach to teaching mathematics.

Our platform is designed to provide engaging and effective math instruction to students in grades K-5, using a unique approach that emphasizes hands-on, problem-solving activities. We use interactive, multimedia elements such as videos, games, and simulations to help students understand key mathematical concepts and build a strong foundation of knowledge.

Math Coaches

The use of virtual coaches that provides students with personalized support and feedback, has become increasingly popular in the field of math education. Research has shown that learning companions can be effective in improving student engagement and motivation, as well as helping students to better understand mathematical concepts and build a stronger foundation of knowledge. UsableMath employs the concept of learning companions to help students succeed in mathematics. Our virtual math coaches serve as personal guides, providing students with individualized support and feedback as they work through mathematical concepts and problems. These coaches, or learning companions, are designed to be like friends or mentors, helping students to build their confidence, overcome challenges, and achieve their full potential.

How are we using Generative AI to enhance Usable Math Modules?

As developers of Usable Math, we are aware of both the educational potentials and complexities of Generative AI technologies. In our system, ChatGPT is used to support teachers and other adults to expand and enhance how math can be understood and taught in schools and homes. When you click on the AI icon, you are linked to a blog where we have recorded how AI proposes to solve selected math word problems found in Usable Math modules in a side-by-side view next to the hints we have authored from the perspectives of our four math coaches: Estella Explainer, Chef Math Bear, How-to-Hound, and Visual Vicuna. Our hope is that our strategies along with the AI-developed strategies will give adults more ways to inspire math learning among students.

Look for this icon for AI-enhanced guides.

Prompts for ChatGPT, BingAI and Other Generative AI Tools

Estella Explainer Prompt:

Take the personality of a math coach who provides strategies for understanding language and meaning of questions using kid-friendly vocabulary. The coach’s motto is "My job is to explain the math questions clearly so you know what you are supposed to do to solve the problem. Sometimes there are unfamiliar or confusing terms in the question. I will help you understand what they mean. The first math problem is {replace math word problem here}

Chef Math Bear Prompt:

Take the personality of a math coach who provides computational strategies (addition, subtraction, multiplication and division) for solving problems. The coach’s motto is “I am here to make sure that you know how to do the math needed to answer these questions. Sometimes you need to do addition, subtraction, multiplication or division. Some questions ask you to use fractions, decimals, large numbers, and probability. When you need ideas for what to do, I am ready.

How-to-Hound Prompt:

Take the personality of a math coach who uses strategic thinking clues (rounding, estimation, elimination of wrong answers) to solve math problems. The coach’s motto is “Answering math questions means you need a plan and my role is to help you figure out different strategies for solving problems. Sometimes you can get the correct answer by crossing out the wrong answers; other times you can round numbers up or down to make figuring a problem easier. I know other strategies as well.

Visual Vicuna Prompt:

Take the personality of a math coach who offers ways to see problems and their solutions using animations, pictures, charts and graphs. The coach’s motto is “I find math is a lot clearer when I take the numbers and words and put them into pictures and drawings or move objects around so I can see how to answer a question. When you find yourself unsure about a question, see if one of my ideas will explain what to do.

Growth Mindset Statements

As education researchers, we understand the important role that a positive attitude and motivation play in learner success. That's why we’ve integrated the use of growth mindset and motivational cues in Usable Math. After every math challenge, students receive messages that encourage them to adopt a growth mindset, reinforcing the idea that with effort and persistence, they can improve their math skills and achieve success.

A sample motivational cue from the Fractions module.

Collaborative Problem Solving

We believe in the power of collaboration and teamwork when it comes to learning mathematics. Our platform creates a learning climate that promotes collaborative problem solving, providing students with opportunities to work together and explore mathematical concepts in a supportive and inclusive environment. Whether you are a student, teacher, or parent, we invite you to explore our platform and experience the science behind the way we deliver math instruction to elementary school students. Read more about our work on the Journal of STEM Education↗

Papers, Presentations and Blogs

UsableMath GenAI Prompts: Learn Math with Our Tailor-Made Prompts for ChatGPT, Claude, and other GenAI tools. Usable Math Blog. https://blog.usablemath.org/usablemath-genai-prompts .

Maloy, R. W. & Gattupalli, S. (2024). Prompt Literacy. EdTechnica: The Open Encyclopedia of Educational Technology . https://edtechbooks.org/encyclopedia/prompt_literacy

Gattupalli, S., & Maloy, R. W. (2024). On Human-Centered AI in Education. https://doi.org/10.7275/KXAP-FN13

Gattupalli, S., Edwards, S.A, Maloy, R. W., & Rancourt, M. (2023, October). Designing for Learning: Key Decisions for an Open Online Math Tutor for Elementary Students. Digital Experiences in Mathematics Education . https://doi.org/10.1007/s40751-023-00128-3 .

Gattupalli, S., Maloy, R.W., Edwards, S.A. & Gearty, A. (2023, August 23). Prompt Literacy for STEM Educators: Enhance Your Teaching and Learning with Generative AI. Berkshire Resources for Learning and Innovation (BRLI) Teaching with Technology Conference, Pittsfield, MA. ScholarWorks@UMass.

Blending Gardens and Geometry: Socio-cultural Approaches in Math Ed. Usable Math Blog. https://blog.usablemath.org/blending-gardens-and-geometry-socio-cultural-approaches-in-math-education .

Maloy, R. W., Gattupalli, S., & Edwards, S. A. (2023). Developing Usable Math Online Tutor for Elementary Math Learners with NoCode Tools . Scholarworks@UMass.

Gattupalli, S., Maloy, R. W., & Edwards, S. A. (2023). Prompt Literacy: A Pivotal Educational Skill in the Age of AI . Scholarworks@UMass.

Gattupalli, S., Maloy, R. W., & Edwards, S. (2023). Comparing Teacher-Written and AI-Generated Math Problem Solving Strategies for Elementary School Students: Implications for Classroom Learning . https://doi.org/10.7275/8sgx-xj08

Making Math Usable for Young Learners . Guest post on Rachelle Dené Poth's EdTech blog Learning as I go: Experiences, Reflections, Lessons Learned . January, 2023.

Math Learning Digital Choice Board (2020) . ScholarWorks, University of Massachusetts Amherst.

Maloy, R.W., Razzaq, L., & Edwards, S.A. (2014). Learning by Choosing: Fourth Graders Use of an Online Multimedia Tutoring System for Math Problem Solving . Journal of Interactive Learning Research , 25(1), 51-64.

Razzaq, L., Maloy, R. W., Edwards, S. A., Arroyo, I., & Woolf, B.P. (2011). “4MALITY: Coaching Students with Different Problem Solving Strategies Using an Online Tutoring System” (p. 359-364). In J. A. Konstan, Ricardo Conejo, Jose L, Marzo & Nuria Oliver, User Modeling, Adaptation and Personalization: 19th International Conference, UMAP 2011, Girona, Spain, July 11-15 Proceedings . Berlin: Springer Verlag.

Maloy, R.W., Edwards,S. A. & Anderson G. (2010, January-June). “Teaching Math Problem Solving Using a Web-based Tutoring System, Learning Games, and Students’ Writing .” Journal of STEM Education: Innovations and Research, 11 (1&2).

Edwards, S. A., Maloy, R.W., & Anderson G. (2010, February). “Classroom Characters Coach Students to Success.” Teaching Children Mathematics, 16 (6), 342-349.

Edwards, S. A., Maloy, R. W., & Anderson G. (2009, Summer). “Reading Coaching of Math Word Problems.” Literacy Coaching Clearinghouse . http://www.literacycoachingonline.org/briefs.html .

MEET OUR TEAM

Sharon Edwards , Ph.D.

Teacher Education & Curriculum Studies

College of Education, University of Massachusetts Amherst

Sharon (she/her) is a clinical faculty in the Department of Teacher Education and Curriculum Studies in the College of Education at the University of Massachusetts Amherst. Sharon is the big brains behind the development of Usable Math online math tutor.

Email : sae at umass dot edu

Robert Maloy , Ph.D.

Elementary Math and History

Bob (he/him) is a history and math senior lecturer in the Department of Teacher Education and Curriculum Studies in the College of Education at the University of Massachusetts Amherst. Bob is the creative math content creator and storytelling artist behind Usable Math.

Email : rwm at umass dot edu

Sai Gattupalli

Math, Science & Learning Technologies (MSLT)

Sai (he/him) is a PhD candidate at the University of Massachusetts Amherst, where he researches education technology to make STEM teaching and learning and more effective. Sai is passionate about understanding learner culture to create effective learning experiences. Email : sgattupalli at umass dot edu Website : gattupalli.com

Marguerite Rancourt

Lead Teacher, Discovery School at Four Corners

Greenfield, Massachusetts

Marguerite (she/her) teaches fourth grade at the Discovery School in addition to serving as Lead Teacher for the school. She has created and taught professional development workshop for other elementary school teachers. In 2018, she received the Pioneer Valley Excellence in Teaching Award. Students in her class have been contributing to the design of system throughout the 2022-2023 school year.

Aubrey Coyne

Math Content Designer and Reviewer

College of Education, Commonwealth Honors College, University of Massachusetts Amherst.

Aubrey Coyne (she/her) is a sophomore at the University of Massachusetts Amherst. She is a math tutor and is studying to be an elementary teacher. Aubrey is passionate about finding ways to make learning accessible and enjoyable for all students.

Graduate Student, Math and Digital Media Research Assistant

Sara Shea (she/her) is a graduate student at the University of Massachusetts Amherst. She is currently part of the university’s Collaborative Teacher Education Pathway program, working towards earning her master’s degree in elementary education.

Katie Allan

Math and Digital Media Research Assistant

Katie Allan (she/her) is a senior at the University of Massachusetts Amherst. She is a math major with a concentration in education and passionate about math education.

SUGGESTIONS AND FEEDBACK

We welcome ideas from teachers, students, and families about the usable math system..

Please complete our UsableMath Module Review and Feedback↗ form.

Your responses will help us to improve how the system works instructionally and technically. Let us know any additional thoughts about the problems, characters, hints, gifs, mindset statements and more.

Your message has been received. We will get back to you shortly. The average response time is approximately 6 hours.

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SolveMe Puzzles

Math Games for Kids

Explore interactive math games for kids, perfect for preschool through grade 5! Our teacher-designed collection offers playful ways to learn essential math skills such as number sense, addition, subtraction, multiplication, division, fractions, decimals, shapes, measurement, and more. With lively characters, ... Read more vibrant graphics, and engaging challenges, learning math at home or in school becomes super-fun. Join millions of kids, teachers, and parents who love our math games! Start now for free!

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• Lesson Plans
• Math (2,046)
• Number Sense (381)
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• Number Recognition Within 5 (12)
• Number Recognition Within 10 (12)
• Number Recognition Within 20 (6)
• Number Tracing (20)
• Number Tracing Within 5 (5)
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• Number Tracing Within 20 (10)
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• Decimal Place Value (26)
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• Aiming and Precision (6)

Number Sense Games

Count back and Complete the Sequence Game

Practice the superpower of number sense by learning how to count back and complete the sequence.

Count Along with the Stars from 1 to 3 Game

Shine bright in the math world by counting along with the stars from 1 to 3.

Counting Sequence from 1 to 5 Game

Help your little one practice the counting sequence from 1 to 5.

Trace the Number One Game

Sharpen your number skills by tracing the number one.

Addition Games

Identify Turn Around Facts Game

Add more arrows to your child’s math quiver by identifying turn around facts.

Compose Numbers to make 10 Game

Begin the exciting journey of becoming a math wizard by learning how to compose numbers to make 10.

Model to Add Numbers Game

Dive deep into the world of math by modeling to add numbers.

Add and Match Game

Take a look at how to add and match with this addition game.

Subtraction Games

Solve Word Problems on Take From Scenarios Game

Enjoy the marvel of math-multiverse by learning to solve word problems on "Take From" scenarios.

Subtract and Match Game

Shine bright in the math world by learning how to subtract and match.

• Remove and Match the Number Game

Enjoy the marvel of math-multiverse by exploring how to remove and match the number.

Solve Scenarios with 'Difference Unknown' Game

Shine bright in the math world by learning how to solve scenarios with 'Difference Unknown'.

Multiplication Games

Find Facts of 2 Game

Take a deep dive into the world of math by finding facts of 2.

Skip Count to Find the Answer Game

Use your math skills to skip count to find the answer.

Multiply and Answer in Unit Form Game

Enjoy the marvel of math-multiverse by exploring how to multiply and answer in unit form.

Multiply Three Numbers Game

Unearth the wisdom of mathematics by learning how to multiply three numbers.

Division Games

Complete the Division Expression for Equal Groups Game

Take a look at how to complete the division expression for equal groups with this game.

Divide Each Expression and Match the Quotient Game

Kids must divide each expression and match the quotient to practice division.

Find the Quotient Game

Enter the madness of math-multiverse by learning to find the quotient.

Represent Division on Number Line Game

Have your own math-themed party by learning how to represent division on number lines.

Fractions Games

Compare Unit Fractions without Visual Models Game

Have your own math-themed party by learning how to compare unit fractions without visual models.

Compare and Model Greater Fraction Game

Practice the superpower of fractions by learning how to compare and model greater fractions.

Missing Numerators on Number Lines Game

Have your own math-themed party by learning how to find the missing numerators on number lines.

Partition into Equal Parts Game

Kids must partition into equal parts to practice fractions.

Decimals Games

Compare Decimals Using Place Value Chart Game

Have your own math-themed party by learning how to compare decimals using a place value chart.

Identify Decimal Numbers Using Fraction Models Game

Add more arrows to your child’s math quiver by identifying decimal numbers using fraction models.

Order Decimals with the Help of Place Value Chart Game

Use your decimal skills to order decimals with the help of a place value chart.

Round Tenths Using a Number Line Game

Enter the madness of math-multiverse by exploring how to round tenths using a number line.

Geometry Games

Find Right Angles Game

Take the first step towards building your math castle by practicing how to find right angles.

Sort Real-World Shapes Game

Add more arrows to your child’s math quiver by sorting real-world shapes.

Identify Objects Above and Below Game

Learn to solve problems by identifying objects 'above' and 'below'.

Recognize Lines, Line Segments, Rays, Angles Game

Dive deep into the world of geometry by recognizing lines, line segments, rays, angles.

Data Handling Games

Read and Interpret Data using Line Plots Game

Kids must read and interpret data using line plots.

Complete Picture Graphs Game

Apply your knowledge of measurements to complete picture graphs.

Read and Interpret Data using Bar Graphs Game

Shine bright in the math world by learning how to read and interpret data using bar graphs.

Identify Objects by Color Game

Sharpen your skills by identifying objects by their colors.

Measurement Games

Identify the Object with Shorter Length Game

Use your measurement skills to identify the object with the shorter length.

Identify the Heavier Object Game

Shine bright in the math world by learning how to identify the heavier object.

Identify the Object with Shorter Height Game

Shine bright in the math world by learning how to identify the object with the shorter height.

Guess the Correct Unit of Capacity Game

Have your own math-themed party by learning to identify the correct unit of capacity.

Relate Activities with A.M. and P.M. Game

Shine bright in the math world by learning how to relate activities with A.M. and P.M.

The Hour Hand Game

Add more arrows to your child’s math quiver by playing 'The Hour Hand' game.

Read Time in Half Hours Game

Shine bright in the math world by learning how to read time in half hours.

Identify Quarter Past and Quarter To Game

Take a look at how to identify 'Quarter Past' and 'Quarter To' with this time game.

Money Games

Count Money with Coins of a Type Game

Help your child take flight by learning how to count money with coins of a type.

Different Types of Coins Game

Explore different types of coins with your little one.

Order Coins by their Values Game

Add more arrows to your child’s math quiver by ordering coins by their values.

Add the Given Amounts of Money Game

Shine bright in the math world by learning how to add the given amounts of money.

Algebra Games

Fill in the Missing Multiples Game

Sharpen your math skills by filling in the missing multiples.

Understand the Equal Sign Game

Shine bright in the math world by understanding the equal sign.

Choose the Prime Number Out of the Given Numbers Game

Kids must choose the prime number out of the given numbers to practice algebra.

Complete the Pattern of Tens Game

Dive deep into the world of addition by completing the pattern of tens.

Word Problems Games

Solve the Word Problems Related to Multiplication Game

Unearth the wisdom of mathematics by learning to solve word problems related to multiplication.

Word Problems on How many Tens Game

Learn to solve world problems on 'How many Tens' with this game.

Solve Subtraction Scenarios Game

Apply your knowledge to solve subtraction scenarios.

Adding One by Making a Model Game

Treat yourself to an immersive learning experience with our 'Adding One by Making a Model' game.

All Math Games

Quickly Tell the Number of Things up to 10 Game

Have your own math-themed party by learning how to quickly tell the number of things up to 10.

Add Two Numbers (Up to 5) Game

Ask your little one to add two numbers (Up to 5) to play this game.

Solve 'Take Apart' Scenarios Game

Take the pressure off by simplifying subtraction by solving 'Take Apart' scenarios.

Divide Objects into Equal Groups Game

Add more arrows to your child’s math quiver by helping them divide objects into equal groups.

Use Words to Identify Decimal Notations Game

Ask your little one to use words to identify decimal notations to play this game.

The Minute Hand Game

Take a look at the minute hand with this fun game about time.

Represent Money using Symbols Game

Shine bright in the math world by learning how to represent money using symbols.

Word Problems to Count by Tens Game

Shine bright in the math world by learning how to solve word problems to count by tens.

Identify Embedded Numbers Game

Help your child take flight by learning how to identify embedded numbers.

Finding Sum (Up to 10) Game

Dive deep into the world of addition by finding the sum (up to 10).

Find One Less Game

Unearth the wisdom of mathematics by learning how to find one less.

Find Equal Groups and Size of Group Game

Practice the superpower of multiplication by learning to find equal groups and the size of group.

Use Models to Relate Multiplication and Division Game

Enjoy the marvel of mathematics by learning to use models to relate multiplication and division.

Partition to Match the Fractions Game

Have your own math-themed party by learning how to partition to match the fractions.

Fill in to Show Equivalence Between Mixed and Decimal Numbers Game

Sharpen your math skills by filling in to show the equivalence between mixed and decimal numbers.

Find Shapes All Around Us Game

Ask your little one to find and identify the different shapes around us to play this game.

Sort Objects by Color Game

Dive deep into the world of measurement by sorting objects by color.

Identify Which Object is Longer Game

Kids must identify which object is longer to practice measurement.

Use Symbols to Represent Money Game

Unearth the wisdom of mathematics by learning how to use symbols to represent money.

Identify the Equivalent Expression Game

Shine bright in the math world by learning how to identify the equivalent expression.

Solve Word Problems Related to Multiplicative Comparison Game

Use your math skills to solve word problems related to multiplicative comparison.

Solve 'Add To' Scenarios Game

Add more arrows to your child’s math quiver by solving 'Add To' scenarios.

Subtraction with Pictures Game

Shine bright in the math world by learning how to subtract with pictures.

Create Equal Groups Game

Make learning multiplication easy by creating equal groups.

Identify the Related Division Sentence Game

Enter the madness of math-multiverse by exploring how to identify related division sentences.

Choose the Correct Partition to Match the Fraction Game

Shine bright in the math world by learning to choose the correct partition to match the fraction.

Match Triangles and Squares Game

Enter the madness of math-multiverse by exploring how to match triangles and squares.

Identify Objects by their Name Game

Take a deep dive into the world of math by identifying objects by their names.

Fill in the Correct Number Using Additive Patterns Game

Fill in the correct number using additive patterns.

Count Along with the Stars from 1 to 5 Game

Count along with the stars from 1 to 5 with this number sense game.

Solve 'Put Together' Scenarios Game

Shine bright in the math world by learning how to solve 'Put Together' scenarios.

Find the Difference Using Models Game

Ask your little one to find the difference using models to play this game.

Represent Equal Groups Using Repeated Addition Game

Kids must represent equal groups using repeated addition to practice multiplication.

Solve Word Problems on Division Game

Learn to solve math problems by solving word problems on division.

Choose the Correct Partition Game

Apply your knowledge of fractions to choose the correct partition.

Fill in Color to Represent the Decimal Numbers Game

Fill in colors to represent the decimal numbers in this game.

What Is Math?

Math (Mathematics) is a field of study that deals with numbers, quantities, shapes, patterns, and their relationships. It is a fascinating subject that involves logical reasoning and problem-solving, which allows us to make sense of the world and unravel its mysteries. 

What Is the Importance of Math?

Mathematics is present in every aspect of our lives, touching upon and influencing everything that we encounter. 

• Math is an essential tool used in everyday life, from managing finances to measuring ingredients in a recipe. Math forms the backbone of many other fields of study, such as science, engineering, and technology. 
• By engaging in mathematical thinking, we develop critical thinking skills, enhance problem-solving abilities, and cultivate a logical mindset. 
• Math is like a universal language, enabling us to communicate ideas and understand the world around us with precision and clarity. It opens up a world of possibilities and empowers us to explore the wonders of our universe.

Math Topics Overview

Let’s have a look at the main domains of mathematics along with their grade level:

Number Sense

• Learning the number sequence from 1 to 20
• Tracing and writing numbers up to 20
• Counting objects up to 10 in linear and non-linear arrangements

ii) Kindergarten:

• Learning the number sequence up to 100
• Learning the counting, number names, comparing numbers up to 20
• Learning how to compose and decompose numbers into tens and ones from 11 to 19. 

iii) Grade 1:

• Learning to count to 120, starting from any number less than 120. 
• Understanding place value system 
• Comparing two-digit numbers based on the meaning of tens and ones digits.

iv) Grade 2

• Reading and writing numbers up to 1000 in the expanded form 
• Reading and Writing number names
• Even and odd numbers, Skip counting

v) Grade 3 

• Comparing Numbers
• Place Values, expanded form, standard form
• Rounding whole number to nearest 10 or 100

vi) Grade 4

• Place Values
• Rounding Numbers
• Reading and writing multi-digit numbers
• Familiarity with prime and composite numbers.

vii) Grade 5

• Introduction of decimal numbers
• Reading, writing and comparing decimals to thousandths

Visit Number Sense Games for Kids Online and enjoy simple fun math games. 

• Adding up to 5
• Understanding the concepts of ‘one more’ and ‘two more’
• Adding using pictures

ii) Kindergarten: 

• Understanding addition as putting together
• Adding within 10
• Addition sentences

iii) Grade 1:  

• Addition word problems within 20
• Adding the multiples to 10 in the range 10-90
• Learning addition strategies 
• Learning addition facts
• Addition with grouping
• Addition without regrouping
• Performing multi-digit addition
• Addition with regrouping
• Adding decimals (with and without regrouping)
• Adding multi-digit whole numbers and with decimals to hundredths.

Do check out Addition Games to explore some interactive math games for kids!

Subtraction

• Identifying ‘one less than’ within 10
• Understanding ‘taking away’
• Composing and decomposing numbers into tens and ones from 11 to 19.
• Subtraction word problems within 20
• Subtracting within 1000 (with and without regrouping)
• Subtracting within 20 using mental math strategies.
• Subtracting within 1000
• Subtraction strategies
• Multi-digit subtraction
• Subtraction with and without regrouping
• Subtracting decimals (with and without regrouping)

Visit Subtraction Games for Kids Online and master the subtraction skills with educational math games! 

Multiplication

• Working with equal groups of objects 
• Forming foundations for math multiplication

ii) Grade 3 

• Multiply one-digit whole numbers by multiples of 10 in the range 10-90.
• Properties of multiplication

iii) Grade 4

• Four-digits by a one-digit multiplication
• Two-digit by two-digit multiplication
• Familiarity with factors and multiples

iv) Grade 5

• Multiplying multi-digit whole numbers and decimals
• Multiplication area models

Practice subtraction in a fun way using some fun online math games. Do visit Multiplication Games for Kids Online .

• Solving problems involving the four operations 
• Identifying and explaining patterns in arithmetic operations.
• Factors and multiples
• Division with quotients and remainders up to four-digit dividends and one-digit divisors.
• Order of operations
• Division with decimals 

Do not miss checking out the simple Division Games for Kids Online and explore cool math games to practice division skills!

i)  Grade 3 

• Introduction to fractions (understanding of fractions as numbers)
• Identifying fractions
• Learning the representation of fraction on the number line.
• Learning about the concept of equivalent fractions 
• Comparing fractions with the same numerator or same denominator. 

ii) Grade 4

• Learning decomposition of fractions 
• Addition, subtraction, and multiplication of fractions and mixed numbers 
• Decimal notation for fractions 
• Comparing decimal numbers.

iii) Grade 5

• Addition and subtraction of fractions by making them equivalent fractions. 
• Multiplication of fractions with fractions or whole numbers.
•  Solving real world problems involving multiplication of fractions and mixed numbers. 
• Dividing whole numbers and unit fractions.

Learning fractions will be a great experience with these Fractions Games for Kids ! Do visit! 

• Understand decimal notation for fractions, and compare decimal fractions.
• Use decimal notation for fractions with denominators 10 or 100.
• Compare two decimals to hundredths using the symbols >, =, or <, and justify the conclusions by using a visual model.

ii) Grade 5

• Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. 
• Read, write, and compare decimals to thousandths.
• Rounding decimals to any place using place values.

If you want to deal with decimals fearlessly, try out Division Games and play some exciting math games online. 

i) Kindergarten:

• Describe objects using names of shapes.
• Identify and analyze shape as two-dimensional or three-dimensional.

ii) Grade 1:

• Distinguish between defining attributes and non-defining attributes of shapes.
• To partition circles and rectangles into two and four equal shares.

iii) Grade 2:  

• To recognize and draw shapes according to the number of angles or number of faces. 
• Partition circles and rectangles into two, three or four equal shares. 
• Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

iv) Grade 3:

• Recognize squares, rhombuses, and rectangles as quadrilaterals.
• To differentiate between quadrilaterals and shapes that are not quadrilaterals. 
• To partition shapes into equal parts.

v) Grade 4:

• To draw and identify lines and angles,
• To classify shapes by their properties. 
• To identify line-symmetric figures and draw lines of symmetry.
• Apply area and perimeter for rectangles in the real world. 
• Under geometric measurement, learning concepts of angles and measuring angles in whole number degrees using a protractor.

vi) Grade 5:

• To graph points on the coordinate plane to solve real world problems. 
• To classify two-dimensional figures in a hierarchy based on properties.

Explore these interesting Geometry Games that use everyday objects to describe 2D and 3D shapes.

Measurement

• Learning about measurable attributes such as weight and length. 
• Learning to compare two objects with common measurable attributes.
• Learning to measure length indirectly and by iterating length units.

iii) Grade 2:

• Introduction to the standard units of measurement like inches, feet, centimeters, and meters. 
• Measure and estimate the length of objects in standard units. 
• Relate addition and subtraction to length and work with time and money.
• To tell and write time to the nearest minute and measure time intervals in minutes and also solve word problems on this basis. 
• Introduction to the standard unit of capacity and masses like grams, kilograms, and liters. 
• Learn to draw a scaled picture graph and scaled bar graph, generate measurement data by measuring length. 
• Understand the concept of area and relate area to multiplication and addition. 
• Solve real world problems involving perimeters of polygons.
• Relate sizes of measurement units within one system of units. 
• Use the four operations to solve word problems involving intervals of time, distances, masses of objects, money and liquid volumes.
• To convert different-sized measurement units within a given measurement system.
• To learn about the concept of volume.
• Measure volume by counting unit cubes or using multiplication/addition.

Explore these interesting Measurements Games to master measurements, unit conversions, etc. with the help of amazing visuals and real-world scenarios.

i) Grade 1:

• Tell and write time in hours and half-hours using analog and digital clocks.

ii) Grade 2:

• Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

iii) Grade 3:

• Tell and write time to the nearest minute and measure time intervals in minutes. 
• Addition and subtraction of time intervals in minutes

iv) Grade 4:  

• Use the four operations to solve word problems involving intervals of time.

Now, teaching math skills like telling time, reading time will no longer be difficult as we offer these awesome Time Games for Kids Online . Try it out!

i) Grade 2:

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

ii) Grade 3:

• Counting money
• Operations with money

iii) Grade 4:

• Use the four operations to solve word problems involving money.

Get hands-on experience of counting money and operations involving money with Money Games online.

i) Grade 4:

Learn operations with algebraic thinking

ii) Grade 5:

• Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
• Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them

Algebra Games for Kids help form the strong foundation of math concepts in higher grades. Do check out! 

Word Problems

• Addition and subtraction word problems
• Multiplication and division word problems
• Money word problems

Grade 4 and Grade 5:

• Time word problems
• Multiplicative comparison

Do not forget to check out Online Word Problems Games .

How to Teach the Uses of Math to Kids in Real-life

Here are some strategies to help children see the practical uses of math in their daily lives. By incorporating these strategies, children can develop a better understanding of how math is relevant and useful in their daily lives.

• Use real-life examples : Connect math to everyday situations like shopping or cooking.
• Solve practical problems : Encourage problem-solving using math, like sharing pizza slices or calculating travel time.
• Explore math in the environment : Take field trips to observe patterns, shapes, and measurements.

How to Introduce Math to Kids Through Games

• Begin with easy math games online that are suitable for your child's level and concepts they are currently learning.
• Ensure the games are engaging with interactive elements and visuals to keep kids excited and motivated.
• Encourage problem-solving and critical thinking through game-based challenges. Introducing math through games helps children learn and enjoy math.

Benefits of Interactive Math Games Online

• Math games enhance learning experience by inspiring student engagement and facilitating effective learning. 
• Interactive Math games promote critical thinking and problem-solving skills as students explore, question, and discover mathematical concepts. 
• Math games offer an enjoyable and accessible approach to learning math, providing an alternative method for students to approach and assess their mathematical abilities.

Math Learning Experience: Games vs. Traditional Methods

• Engagement : Math games actively engage children, making learning fun and enjoyable. Traditional methods often rely on passive instruction. Learning through textbooks or flash cards do not provide the required level of active learning. Math games have the ability to put kids’ minds on a higher active mode. 
• Hands-on Learning : Math Games provide interactive and tactile experiences that help children understand abstract math concepts. Also, it provides an immediate assessment to the student, teacher, and parents. Conventional methods of learning math might become monotonous and ineffective over time.
• Problem-Solving : Games encourage critical thinking and problem-solving skills as children apply math concepts in practical situations, unlike the conventional approach.

Math games enhance understanding of math concepts by promoting engagement, hands-on learning, and problem-solving skills, overcoming the limitations of the traditional methods.

Why choose SplashLearn Math games?

Choose SplashLearn Math games for an engaging, personalized, and effective learning experience that will help your child excel in math. Here are some valuable attributes:

• Engaging Gameplay and Varied Game Formats
• Aligned with Curriculum
• Free for Teachers and Schools 
• Personalized Learning
• Comprehensive Coverage 
• Accessible Anytime, Anywhere
• Interactive Challenges and Fun Rewards
• Progress Tracking
• Weekly Reports to Parents

What are the best math games online?

There is a wide range of online math games available to children nowadays. As such, it can be hard to find games that blend fun and curriculum learning together in the best way possible. Here are some of the best math games online by SplashLearn:

• Recognize Patterns Games
• Add using Place Value Games
• Identify Decimal Number Using Fraction Models Game
• Read Time in Half Hours Games

Also, check out some best online math games for kids!

Do online math games help in developing math skills?

Absolutely! Math games are a great tool for developing math skills. They enhance reasoning abilities, deepen comprehension of math concepts, and build confidence in solving real-world math problems. These fun and practical math games provide valuable practice and support the development of key mathematical skills.

How can I make teaching math fun?

You can make math fun with online games ! Engage your students or child with interactive math games that employ innovative strategies. Boost learning through enjoyable activities and create a positive math learning experience.

What are the best math games websites for kids?

A wide range of websites and apps are available online that cater to math learning and practice. To know more, read: Best Online Math Websites

Your one stop solution for all grade learning needs.

Word Problems or Problem Solving Math Games and Worksheets

Related Pages More Math Games Math Worksheets

Our directory of Word Problems Math Games or Problem Solving Math Games available on the Internet - games that teach, build or strengthen your math problem solving skills. We categorize and review the games listed here to help you find the math games you are looking for. We have word problem games for kids and word problem games that can be solved using block models, bar models or tape diagrams. We have added more free word problem games that can be played on PCs, Tablets, iPads and Mobiles.

Word Problem Solving Games for Kids

Word problem math games using modeling, algebra worksheets.

Evaluate Expressions by Substitution Simplify Expressions by Combining Like Terms Simplify Expressions using Distributive Property Simplify Expressions using Distributive Property & Combine Like Terms

Solving Equations Solving One-Step Equations Solving Two-Step Equations Solving Equations by Combining Like Terms Solving Equations with the Variable on Both Sides Solving Equations by Distributive Property Solving Multi-Step Equations Solving Multi-Step Equations Solving Word Problems using Algebra

Solving System of Equations by Substitution Solving System of Equations by Addition Solving System of Equationsby Subtraction Solving System of Equations by Addition or Subtraction Solving System of Equations by Multiplication and then Addition or Subtraction

Number Word Problems Worksheets SAT Test Prep SAT practice problems with step-by-step video solutions.

Disaster Math

Word problems about different disasters Disaster Master Build a Kit

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Watch CBS News

Teens come up with trigonometry proof for Pythagorean Theorem, a problem that stumped math world for centuries

By Bill Whitaker

May 5, 2024 / 7:00 PM EDT / CBS News

As the school year ends, many students will be only too happy to see math classes in their rearview mirrors. It may seem to some of us non-mathematicians that geometry and trigonometry were created by the Greeks as a form of torture, so imagine our amazement when we heard two high school seniors had proved a mathematical puzzle that was thought to be impossible for 2,000 years. 

We met Calcea Johnson and Ne'Kiya Jackson at their all-girls Catholic high school in New Orleans. We expected to find two mathematical prodigies.

Instead, we found at St. Mary's Academy , all students are told their possibilities are boundless.

Come Mardi Gras season, New Orleans is alive with colorful parades, replete with floats, and beads, and high school marching bands.

In a city where uniqueness is celebrated, St. Mary's stands out – with young African American women playing trombones and tubas, twirling batons and dancing - doing it all, which defines St. Mary's, students told us.

Junior Christina Blazio says the school instills in them they have the ability to accomplish anything. 

Christina Blazio: That is kinda a standard here. So we aim very high - like, our aim is excellence for all students. 

The private Catholic elementary and high school sits behind the Sisters of the Holy Family Convent in New Orleans East. The academy was started by an African American nun for young Black women just after the Civil War. The church still supports the school with the help of alumni.

In December 2022, seniors Ne'Kiya Jackson and Calcea Johnson were working on a school-wide math contest that came with a cash prize.

Ne'Kiya Jackson: I was motivated because there was a monetary incentive.

Calcea Johnson: 'Cause I was like, "$500 is a lot of money. So I-- I would like to at least try."

Both were staring down the thorny bonus question.

Bill Whitaker: So tell me, what was this bonus question?

Calcea Johnson: It was to create a new proof of the Pythagorean Theorem. And it kind of gave you a few guidelines on how would you start a proof.

The seniors were familiar with the Pythagorean Theorem, a fundamental principle of geometry. You may remember it from high school: a² + b² = c². In plain English, when you know the length of two sides of a right triangle, you can figure out the length of the third.

Both had studied geometry and some trigonometry, and both told us math was not easy. What no one told  them  was there had been more than 300 documented proofs of the Pythagorean Theorem using algebra and geometry, but for 2,000 years a proof using trigonometry was thought to be impossible, … and that was the bonus question facing them.

Bill Whitaker: When you looked at the question did you think, "Boy, this is hard"?

Ne'Kiya Jackson: Yeah. 

Bill Whitaker: What motivated you to say, "Well, I'm going to try this"?

Calcea Johnson: I think I was like, "I started something. I need to finish it." 

Bill Whitaker: So you just kept on going.

Calcea Johnson: Yeah.

For two months that winter, they spent almost all their free time working on the proof.

CeCe Johnson: She was like, "Mom, this is a little bit too much."

CeCe and Cal Johnson are Calcea's parents.

CeCe Johnson:   So then I started looking at what she really was doing. And it was pages and pages and pages of, like, over 20 or 30 pages for this one problem.

Cal Johnson: Yeah, the garbage can was full of papers, which she would, you know, work out the problems and-- if that didn't work she would ball it up, throw it in the trash. 

Bill Whitaker: Did you look at the problem? 

Neliska Jackson is Ne'Kiya's mother.

Neliska Jackson: Personally I did not. 'Cause most of the time I don't understand what she's doing (laughter).

Michelle Blouin Williams: What if we did this, what if I write this? Does this help? ax² plus ….

Their math teacher, Michelle Blouin Williams, initiated the math contest.

Bill Whitaker: And did you think anyone would solve it?

Michelle Blouin Williams: Well, I wasn't necessarily looking for a solve. So, no, I didn't—

Bill Whitaker: What were you looking for?

Michelle Blouin Williams: I was just looking for some ingenuity, you know—

Calcea and Ne'Kiya delivered on that! They tried to explain their groundbreaking work to 60 Minutes. Calcea's proof is appropriately titled the Waffle Cone.

Calcea Johnson: So to start the proof, we start with just a regular right triangle where the angle in the corner is 90°. And the two angles are alpha and beta.

Bill Whitaker: Uh-huh

Calcea Johnson: So then what we do next is we draw a second congruent, which means they're equal in size. But then we start creating similar but smaller right triangles going in a pattern like this. And then it continues for infinity. And eventually it creates this larger waffle cone shape.

Calcea Johnson: Am I going a little too—

Bill Whitaker: You've been beyond me since the beginning. (laughter) 

Bill Whitaker: So how did you figure out the proof?

Ne'Kiya Jackson: Okay. So you have a right triangle, 90° angle, alpha and beta.

Bill Whitaker: Then what did you do?

Ne'Kiya Jackson: Okay, I have a right triangle inside of the circle. And I have a perpendicular bisector at OP to divide the triangle to make that small right triangle. And that's basically what I used for the proof. That's the proof.

Bill Whitaker: That's what I call amazing.

Ne'Kiya Jackson: Well, thank you.

There had been one other documented proof of the theorem using trigonometry by mathematician Jason Zimba in 2009 – one in 2,000 years. Now it seems Ne'Kiya and Calcea have joined perhaps the most exclusive club in mathematics. 

Bill Whitaker: So you both independently came up with proof that only used trigonometry.

Ne'Kiya Jackson: Yes.

Bill Whitaker: So are you math geniuses?

Calcea Johnson: I think that's a stretch. 

Bill Whitaker: If not genius, you're really smart at math.

Ne'Kiya Jackson: Not at all. (laugh) 

To document Calcea and Ne'Kiya's work, math teachers at St. Mary's submitted their proofs to an American Mathematical Society conference in Atlanta in March 2023.

Ne'Kiya Jackson: Well, our teacher approached us and was like, "Hey, you might be able to actually present this," I was like, "Are you joking?" But she wasn't. So we went. I got up there. We presented and it went well, and it blew up.

Bill Whitaker: It blew up.

Calcea Johnson: Yeah. 

Ne'Kiya Jackson: It blew up.

Bill Whitaker: Yeah. What was the blowup like?

Calcea Johnson: Insane, unexpected, crazy, honestly.

It took millenia to prove, but just a minute for word of their accomplishment to go around the world. They got a write-up in South Korea and a shout-out from former first lady Michelle Obama, a commendation from the governor and keys to the city of New Orleans. 

Bill Whitaker: Why do you think so many people found what you did to be so impressive?

Ne'Kiya Jackson: Probably because we're African American, one. And we're also women. So I think-- oh, and our age. Of course our ages probably played a big part.

Bill Whitaker: So you think people were surprised that young African American women, could do such a thing?

Calcea Johnson: Yeah, definitely.

Ne'Kiya Jackson: I'd like to actually be celebrated for what it is. Like, it's a great mathematical achievement.

Achievement, that's a word you hear often around St. Mary's academy. Calcea and Ne'Kiya follow a long line of barrier-breaking graduates. 

The late queen of Creole cooking, Leah Chase , was an alum. so was the first African-American female New Orleans police chief, Michelle Woodfork …

And judge for the Fifth Circuit Court of Appeals, Dana Douglas. Math teacher Michelle Blouin Williams told us Calcea and Ne'Kiya are typical St. Mary's students.  

Bill Whitaker: They're not unicorns.

Michelle Blouin Williams: Oh, no no. If they are unicorns, then every single lady that has matriculated through this school is a beautiful, Black unicorn.

Pamela Rogers: You're good?

Pamela Rogers, St. Mary's president and interim principal, told us the students hear that message from the moment they walk in the door.

Pamela Rogers: We believe all students can succeed, all students can learn. It does not matter the environment that you live in. 

Bill Whitaker: So when word went out that two of your students had solved this almost impossible math problem, were they universally applauded?

Pamela Rogers: In this community, they were greatly applauded. Across the country, there were many naysayers.

Bill Whitaker: What were they saying?

Pamela Rogers: They were saying, "Oh, they could not have done it. African Americans don't have the brains to do it." Of course, we sheltered our girls from that. But we absolutely did not expect it to come in the volume that it came.  

Bill Whitaker: And after such a wonderful achievement.

Pamela Rogers: People-- have a vision of who can be successful. And-- to some people, it is not always an African American female. And to us, it's always an African American female.

Gloria Ladson-Billings: What we know is when teachers lay out some expectations that say, "You can do this," kids will work as hard as they can to do it.

Gloria Ladson-Billings, professor emeritus at the University of Wisconsin, has studied how best to teach African American students. She told us an encouraging teacher can change a life.

Bill Whitaker: And what's the difference, say, between having a teacher like that and a whole school dedicated to the excellence of these students?

Gloria Ladson-Billings: So a whole school is almost like being in Heaven. 

Bill Whitaker: What do you mean by that?

Gloria Ladson-Billings: Many of our young people have their ceilings lowered, that somewhere around fourth or fifth grade, their thoughts are, "I'm not going to be anything special." What I think is probably happening at St. Mary's is young women come in as, perhaps, ninth graders and are told, "Here's what we expect to happen. And here's how we're going to help you get there."

At St. Mary's, half the students get scholarships, subsidized by fundraising to defray the $8,000 a year tuition. Here, there's no test to get in, but expectations are high and rules are strict: no cellphones, modest skirts, hair must be its natural color.

Students Rayah Siddiq, Summer Forde, Carissa Washington, Tatum Williams and Christina Blazio told us they appreciate the rules and rigor.

Rayah Siddiq: Especially the standards that they set for us. They're very high. And I don't think that's ever going to change.

Bill Whitaker: So is there a heart, a philosophy, an essence to St. Mary's?

Summer Forde: The sisterhood—

Carissa Washington: Sisterhood.

Tatum Williams: Sisterhood.

Bill Whitaker: The sisterhood?

Voices: Yes.

Bill Whitaker: And you don't mean the nuns. You mean-- (laughter)

Christina Blazio: I mean, yeah. The community—

Bill Whitaker: So when you're here, there's just no question that you're going to go on to college.

Rayah Siddiq: College is all they talk about. (laughter) 

Pamela Rogers: … and Arizona State University (Cheering)

Principal Rogers announces to her 615 students the colleges where every senior has been accepted.

Bill Whitaker: So for 17 years, you've had a 100% graduation rate—

Pamela Rogers: Yes.

Bill Whitaker: --and a 100% college acceptance rate?

Pamela Rogers: That's correct.

Last year when Ne'Kiya and Calcea graduated, all their classmates went to college and got scholarships. Ne'Kiya got a full ride to the pharmacy school at Xavier University in New Orleans. Calcea, the class valedictorian, is studying environmental engineering at Louisiana State University.

Bill Whitaker: So wait a minute. Neither one of you is going to pursue a career in math?

Both: No. (laugh)

Calcea Johnson: I may take up a minor in math. But I don't want that to be my job job.

Ne'Kiya Jackson: Yeah. People might expect too much out of me if (laugh) I become a mathematician. (laugh)

But math is not completely in their rear-view mirrors. This spring they submitted their high school proofs for final peer review and publication … and are still working on further proofs of the Pythagorean Theorem. Since their first two …

Calcea Johnson: We found five. And then we found a general format that could potentially produce at least five additional proofs.

Bill Whitaker: And you're not math geniuses?

Bill Whitaker: I'm not buying it. (laughs)

Produced by Sara Kuzmarov. Associate producer, Mariah B. Campbell. Edited by Daniel J. Glucksman.

Bill Whitaker is an award-winning journalist and 60 Minutes correspondent who has covered major news stories, domestically and across the globe, for more than four decades with CBS News.

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10 Helpful Worksheet Ideas for Primary School Math Lessons

M athematics is a fundamental subject that shapes the way children think and analyze the world. At the primary school level, laying a strong foundation is crucial. While hands-on activities, digital tools, and interactive discussions play significant roles in learning, worksheets remain an essential tool for reinforcing concepts, practicing skills, and assessing understanding. Here’s a look at some helpful worksheets for primary school math lessons.

Comparison Chart Worksheets

Comparison charts provide a visual means for primary school students to grasp relationships between numbers or concepts. They are easy to make at www.storyboardthat.com/create/comparison-chart-template , and here is how they can be used:

• Quantity Comparison: Charts might display two sets, like apples vs. bananas, prompting students to determine which set is larger.
• Attribute Comparison: These compare attributes, such as different shapes detailing their number of sides and characteristics.
• Number Line Comparisons: These help students understand number magnitude by placing numbers on a line to visualize their relative sizes.
• Venn Diagrams: Introduced in later primary grades, these diagrams help students compare and contrast two sets of items or concepts.
• Weather Charts: By comparing weather on different days, students can learn about temperature fluctuations and patterns.

Number Recognition and Counting Worksheets

For young learners, recognizing numbers and counting is the first step into the world of mathematics. Worksheets can offer:

• Number Tracing: Allows students to familiarize themselves with how each number is formed.
• Count and Circle: Images are presented, and students have to count and circle the correct number.
• Missing Numbers: Sequences with missing numbers that students must fill in to practice counting forward and backward.

Basic Arithmetic Worksheets

Once students are familiar with numbers, they can start simple arithmetic. 

• Addition and Subtraction within 10 or 20: Using visual aids like number lines, counters, or pictures can be beneficial.
• Word Problems: Simple real-life scenarios can help students relate math to their daily lives.
• Skip Counting: Worksheets focused on counting by 2s, 5s, or 10s.

Geometry and Shape Worksheets

Geometry offers a wonderful opportunity to relate math to the tangible world.

• Shape Identification: Recognizing and naming basic shapes such as squares, circles, triangles, etc.
• Comparing Shapes: Worksheets that help students identify differences and similarities between shapes.
• Pattern Recognition: Repeating shapes in patterns and asking students to determine the next shape in the sequence.

Measurement Worksheets

Measurement is another area where real-life application and math converge.

• Length and Height: Comparing two or more objects and determining which is longer or shorter.
• Weight: Lighter vs. heavier worksheets using balancing scales as visuals.
• Time: Reading clocks, days of the week, and understanding the calendar.

Data Handling Worksheets

Even at a primary level, students can start to understand basic data representation.

• Tally Marks: Using tally marks to represent data and counting them.
• Simple Bar Graphs: Interpreting and drawing bar graphs based on given data.
• Pictographs: Using pictures to represent data, which can be both fun and informative.

Place Value Worksheets

Understanding the value of each digit in a number is fundamental in primary math.

• Identifying Place Values: Recognizing units, tens, hundreds, etc., in a given number.
• Expanding Numbers: Breaking down numbers into their place value components, such as understanding 243 as 200 + 40 + 3.
• Comparing Numbers: Using greater than, less than, or equal to symbols to compare two numbers based on their place values.

Fraction Worksheets

Simple fraction concepts can be introduced at the primary level.

• Identifying Fractions: Recognizing half, quarter, third, etc., of shapes or sets.
• Comparing Fractions: Using visual aids like pie charts or shaded drawings to compare fractions.
• Simple Fraction Addition: Adding fractions with the same denominator using visual aids.

Money and Real-Life Application Worksheets

Understanding money is both practical and a great way to apply arithmetic.

• Identifying Coins and Notes: Recognizing different denominations.
• Simple Transactions: Calculating change, adding up costs, or determining if there’s enough money to buy certain items.
• Word Problems with Money: Real-life scenarios involving buying, selling, and saving.

Logic and Problem-Solving Worksheets

Even young students can hone their problem-solving skills with appropriate challenges.

• Sequences and Patterns: Predicting the next item in a sequence or recognizing a pattern.
• Logical Reasoning: Simple puzzles or riddles that require students to think critically.
• Story Problems: Reading a short story and solving a math-related problem based on the context.

Worksheets allow students to practice at their own pace, offer teachers a tool for assessment, and provide parents with a glimpse into their child’s learning progression. While digital tools and interactive activities are gaining prominence in education, the significance of worksheets remains undiminished. They are versatile and accessible and, when designed creatively, can make math engaging and fun for young learners.

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