types of problem solving in maths

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1.1: Introduction to Problem Solving

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• Page ID 9821

• Michelle Manes
• University of Hawaii

The Common Core State Standards for Mathematics ( http://www.corestandards.org/Math/Practice ) identify eight “Mathematical Practices” — the kinds of expertise that all teachers should try to foster in their students, but they go far beyond any particular piece of mathematics content. They describe what mathematics is really about, and why it is so valuable for students to master. The very first Mathematical Practice is:

Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

This chapter will help you develop these very important mathematical skills, so that you will be better prepared to help your future students develop them. Let’s start with solving a problem!

Draw curves connecting A to A, B to B, and C to C. Your curves cannot cross or even touch each other,they cannot cross through any of the lettered boxes, and they cannot go outside the large box or even touch it’s sides.

Think / Pair / Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it).

• What did you try?
• What makes this problem difficult?
• Can you change the problem slightly so that it would be easier to solve?

Problem Solving Strategy 1 (Wishful Thinking).

Do you wish something in the problem was different? Would it then be easier to solve the problem?

For example, what if ABC problem had a picture like this:

Can you solve this case and use it to help you solve the original case? Think about moving the boxes around once the lines are already drawn.

Here is one possible solution.

Early Math Resources for Teacher Educators

• Mathematics of Operations

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Making Sense of Problem Types

• Previous What Children Know and Need to Learn about Operations
• Next Engaging Participants around Problem Types

Considering how a young child would intuitively approach word problems helps us to explore the range of problem types within addition, subtraction, multiplication, and division.

by Angela Chan Turrou and Megan Franke

From a Child's Perspective

When we come across a word problem, we often jump directly to thinking about what operation the problem is asking for. Is it an addition, subtraction, multiplication, or division problem? Once we have decided which operation the word problem is asking for, we then decide what strategy we want to use to execute that operation. Though this approach to solving mathematics problems might be common for adults, it is quite far from how young children approach problems. Young children intuitively approach word problems not by thinking about an operation, but by thinking about the  story.   They consider what objects are in the story (is it about frogs or bananas or children on the playground?) and what is happening to the objects in the story (are they hopping away or being eaten or running around together?). 

Let's dig into this idea of a child's perspective and how it might different from an adult's perspective by taking a look at these three word problems.

• Liz had 6 apple slices. She ate 4 of them. How many apple slices does Liz have now?
• Liz has 4 rocks in her collection. How many more rocks does Liz need to collect so that she will have 6 rocks?
• Liz has 6 snow globes and her brother has 4. How many more snow globes does Liz have than her brother?

An adult might look at these word problems and see a common operation (subtraction) across all of them. They might think about subtraction as take away and use the strategy of “six take away four” to solve all three problems and get the common answer of “two.”

Examining these three problems the way a young child would allows us to see why a problem might be difficult and what strategies the child is likely to use. How might a young child solve the rock collecting or the snow globes problem? Would they solve both of those the same way? See Beginning Strategies for Problem Solving  f or a discussion of how young children intuitively approach word problems by modeling out the action or number relationships involved.

Problem Types Chart

Below is a chart of word problems organized to help you see important distinctions among addition, subtraction, multiplication, and division problems. Problems that are most applicable to young children are included in the chart. Download and explore the chart below. What do you notice about the chart and how it’s organized? How would a young child solve each problem? What number sentence could you write that matches the problem situation?  [Note: This last question is a "trick question" for the Compare problem.]

Problem-Types-Chart_0.pdf 642.8 KB

Beginning Strategies for Problem Solving

This piece explores the intuitive strategies that young children use to solve addition, subtraction, multiplication, and division problems.

Exploring Your Own Thinking

This activity was developed for our graduate students (prospective early childhood teachers). It helps adults to understand how determining...

Inservice: Introducing +, - , x , ÷

Getting started with solving addition, subtraction, multiplication, and division problems begins by asking teachers to rethink their...

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Types of Problem Solving Tasks

2. Worded contexts which require the learner to decide to use standard techniques. Majority of textbooks problems are of this type. For example:

The area of a triangular lawn is 20 square metres, and one side is 5 metres long. If I walk in straight line from the corner opposite this side, to meet it at right angles, how far have I walked?

The standard technique here is of course the recognition of the base and height of the triangle in the context used in the problem and knowledge of the area of a triangle. You can find additional problems in K-12 Math Problems .

3. Worded context in which there is no standard relationship to apply, or algorithm to use, but an answer is expected. These kind of problems usually requires setting up an equation or thinking of using specific cases or perhaps representing the problem using other representation such as graph. For example:

One side of the rectangle is reduced in length by 20%, the other side is increased by 20%; what change take place in the area?

These type of problems are best use for teaching a concept or new procedure. Here are two samples: Teaching the properties of equality via problem solving and Teaching Trigonometry through problem solving. They usually have multiple solutions or multiple correct answers.

4. Exploratory situations in which there is an ill-defined problem. Because the problem was set-up to be ill-defined, it requires the learner to mathematise by identifying variables and conjecturing relationships, choosing representations and techniques. Knowledge of a range of function is useful. Note that sometimes there may be no solution to the problem. For example:

Describe the advantages and disadvantages of raising the price of cheese rolls at the school tuck shop by 5 cents, given that cheese prices have gone down by 5% but rolls have gone up by 6 cents each.

I would include math investigations in this category.

5. Mathematical problems in which a situation is presented and a question posed for this has no obvious method. Problems in this category would be what mathematicians would call ‘problem’ since the expected line of attack is to use the forms of inquiry and mathematical thinking specific to mathematics. For example:

What happens to the relationship between the sum of squares of the two shorter sides of triangles and the square on the longer side if we allow the angle between them to vary?

As teachers, it would be good to be aware also of the features of good problem solving task and levels of problem solving skills. There is also a study that describes teachers conceptions of problem solving .

Reference: Paper 7: Modelling, problem solving and integrating concepts by Anne Watson.

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4 thoughts on “ Types of Problem Solving Tasks ”

How do I reference this article?

Hi, Really great effort. Everyone should read this article. Thanks for sharing.

I seriously consider this site needs much more attention.

I like how you state that math exercises should only be considered “problems” if they pose a barrier. Too often these are called problems when in fact there is little to no challenge involved, especially if working through the exercises as repetitive practice challenges, and the student has mastered the concept. Your breakdown of the different types of problems is a good idea to keep in mind when talking about math practice!

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5 Teaching Mathematics Through Problem Solving

Janet Stramel

In his book “How to Solve It,” George Pólya (1945) said, “One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles. The student should acquire as much experience of independent work as possible. But if he is left alone with his problem without any help, he may make no progress at all. If the teacher helps too much, nothing is left to the student. The teacher should help, but not too much and not too little, so that the student shall have a reasonable share of the work.” (page 1)

What is a problem  in mathematics? A problem is “any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method” (Hiebert, et. al., 1997). Problem solving in mathematics is one of the most important topics to teach; learning to problem solve helps students develop a sense of solving real-life problems and apply mathematics to real world situations. It is also used for a deeper understanding of mathematical concepts. Learning “math facts” is not enough; students must also learn how to use these facts to develop their thinking skills.

According to NCTM (2010), the term “problem solving” refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. When you first hear “problem solving,” what do you think about? Story problems or word problems? Story problems may be limited to and not “problematic” enough. For example, you may ask students to find the area of a rectangle, given the length and width. This type of problem is an exercise in computation and can be completed mindlessly without understanding the concept of area. Worthwhile problems  includes problems that are truly problematic and have the potential to provide contexts for students’ mathematical development.

There are three ways to solve problems: teaching for problem solving, teaching about problem solving, and teaching through problem solving.

Teaching for problem solving begins with learning a skill. For example, students are learning how to multiply a two-digit number by a one-digit number, and the story problems you select are multiplication problems. Be sure when you are teaching for problem solving, you select or develop tasks that can promote the development of mathematical understanding.

Teaching about problem solving begins with suggested strategies to solve a problem. For example, “draw a picture,” “make a table,” etc. You may see posters in teachers’ classrooms of the “Problem Solving Method” such as: 1) Read the problem, 2) Devise a plan, 3) Solve the problem, and 4) Check your work. There is little or no evidence that students’ problem-solving abilities are improved when teaching about problem solving. Students will see a word problem as a separate endeavor and focus on the steps to follow rather than the mathematics. In addition, students will tend to use trial and error instead of focusing on sense making.

Teaching through problem solving  focuses students’ attention on ideas and sense making and develops mathematical practices. Teaching through problem solving also develops a student’s confidence and builds on their strengths. It allows for collaboration among students and engages students in their own learning.

Consider the following worthwhile-problem criteria developed by Lappan and Phillips (1998):

• The problem has important, useful mathematics embedded in it.
• The problem requires high-level thinking and problem solving.
• The problem contributes to the conceptual development of students.
• The problem creates an opportunity for the teacher to assess what his or her students are learning and where they are experiencing difficulty.
• The problem can be approached by students in multiple ways using different solution strategies.
• The problem has various solutions or allows different decisions or positions to be taken and defended.
• The problem encourages student engagement and discourse.
• The problem connects to other important mathematical ideas.
• The problem promotes the skillful use of mathematics.
• The problem provides an opportunity to practice important skills.

Of course, not every problem will include all of the above. Sometimes, you will choose a problem because your students need an opportunity to practice a certain skill.

Key features of a good mathematics problem includes:

• It must begin where the students are mathematically.
• The feature of the problem must be the mathematics that students are to learn.
• It must require justifications and explanations for both answers and methods of solving.

Problem solving is not a  neat and orderly process. Think about needlework. On the front side, it is neat and perfect and pretty.

But look at the b ack.

It is messy and full of knots and loops. Problem solving in mathematics is also like this and we need to help our students be “messy” with problem solving; they need to go through those knots and loops and learn how to solve problems with the teacher’s guidance.

When you teach through problem solving , your students are focused on ideas and sense-making and they develop confidence in mathematics!

Mathematics Tasks and Activities that Promote Teaching through Problem Solving

Choosing the Right Task

Selecting activities and/or tasks is the most significant decision teachers make that will affect students’ learning. Consider the following questions:

• Teachers must do the activity first. What is problematic about the activity? What will you need to do BEFORE the activity and AFTER the activity? Additionally, think how your students would do the activity.
• What mathematical ideas will the activity develop? Are there connections to other related mathematics topics, or other content areas?
• Can the activity accomplish your learning objective/goals?

Low Floor High Ceiling Tasks

By definition, a “ low floor/high ceiling task ” is a mathematical activity where everyone in the group can begin and then work on at their own level of engagement. Low Floor High Ceiling Tasks are activities that everyone can begin and work on based on their own level, and have many possibilities for students to do more challenging mathematics. One gauge of knowing whether an activity is a Low Floor High Ceiling Task is when the work on the problems becomes more important than the answer itself, and leads to rich mathematical discourse [Hover: ways of representing, thinking, talking, agreeing, and disagreeing; the way ideas are exchanged and what the ideas entail; and as being shaped by the tasks in which students engage as well as by the nature of the learning environment].

The strengths of using Low Floor High Ceiling Tasks:

• Allows students to show what they can do, not what they can’t.
• Provides differentiation to all students.
• Promotes a positive classroom environment.
• Advances a growth mindset in students
• Aligns with the Standards for Mathematical Practice

Examples of some Low Floor High Ceiling Tasks can be found at the following sites:

• YouCubed – under grades choose Low Floor High Ceiling
• NRICH Creating a Low Threshold High Ceiling Classroom
• Inside Mathematics Problems of the Month

Math in 3-Acts

Math in 3-Acts was developed by Dan Meyer to spark an interest in and engage students in thought-provoking mathematical inquiry. Math in 3-Acts is a whole-group mathematics task consisting of three distinct parts:

Act One is about noticing and wondering. The teacher shares with students an image, video, or other situation that is engaging and perplexing. Students then generate questions about the situation.

In Act Two , the teacher offers some information for the students to use as they find the solutions to the problem.

Act Three is the “reveal.” Students share their thinking as well as their solutions.

“Math in 3 Acts” is a fun way to engage your students, there is a low entry point that gives students confidence, there are multiple paths to a solution, and it encourages students to work in groups to solve the problem. Some examples of Math in 3-Acts can be found at the following websites:

• Dan Meyer’s Three-Act Math Tasks
• Graham Fletcher3-Act Tasks ]
• Math in 3-Acts: Real World Math Problems to Make Math Contextual, Visual and Concrete

Number Talks

Number talks are brief, 5-15 minute discussions that focus on student solutions for a mental math computation problem. Students share their different mental math processes aloud while the teacher records their thinking visually on a chart or board. In addition, students learn from each other’s strategies as they question, critique, or build on the strategies that are shared.. To use a “number talk,” you would include the following steps:

• The teacher presents a problem for students to solve mentally.
• Provide adequate “ wait time .”
• The teacher calls on a students and asks, “What were you thinking?” and “Explain your thinking.”
• For each student who volunteers to share their strategy, write their thinking on the board. Make sure to accurately record their thinking; do not correct their responses.
• Invite students to question each other about their strategies, compare and contrast the strategies, and ask for clarification about strategies that are confusing.

“Number Talks” can be used as an introduction, a warm up to a lesson, or an extension. Some examples of Number Talks can be found at the following websites:

• Inside Mathematics Number Talks
• Number Talks Build Numerical Reasoning

Saying “This is Easy”

“This is easy.” Three little words that can have a big impact on students. What may be “easy” for one person, may be more “difficult” for someone else. And saying “this is easy” defeats the purpose of a growth mindset classroom, where students are comfortable making mistakes.

When the teacher says, “this is easy,” students may think,

• “Everyone else understands and I don’t. I can’t do this!”
• Students may just give up and surrender the mathematics to their classmates.
• Students may shut down.

Instead, you and your students could say the following:

• “I think I can do this.”
• “I have an idea I want to try.”
• “I’ve seen this kind of problem before.”

Tracy Zager wrote a short article, “This is easy”: The Little Phrase That Causes Big Problems” that can give you more information. Read Tracy Zager’s article here.

Using “Worksheets”

Do you want your students to memorize concepts, or do you want them to understand and apply the mathematics for different situations?

What is a “worksheet” in mathematics? It is a paper and pencil assignment when no other materials are used. A worksheet does not allow your students to use hands-on materials/manipulatives [Hover: physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics]; and worksheets are many times “naked number” with no context. And a worksheet should not be used to enhance a hands-on activity.

Students need time to explore and manipulate materials in order to learn the mathematics concept. Worksheets are just a test of rote memory. Students need to develop those higher-order thinking skills, and worksheets will not allow them to do that.

One productive belief from the NCTM publication, Principles to Action (2014), states, “Students at all grade levels can benefit from the use of physical and virtual manipulative materials to provide visual models of a range of mathematical ideas.”

You may need an “activity sheet,” a “graphic organizer,” etc. as you plan your mathematics activities/lessons, but be sure to include hands-on manipulatives. Using manipulatives can

• Provide your students a bridge between the concrete and abstract
• Serve as models that support students’ thinking
• Provide another representation
• Support student engagement
• Give students ownership of their own learning.

Adapted from “ The Top 5 Reasons for Using Manipulatives in the Classroom ”.

any task or activity for which the students have no prescribed or memorized rules or methods, nor is there a perception by students that there is a specific ‘correct’ solution method

should be intriguing and contain a level of challenge that invites speculation and hard work, and directs students to investigate important mathematical ideas and ways of thinking toward the learning

involves teaching a skill so that a student can later solve a story problem

when we teach students how to problem solve

teaching mathematics content through real contexts, problems, situations, and models

a mathematical activity where everyone in the group can begin and then work on at their own level of engagement

20 seconds to 2 minutes for students to make sense of questions

Mathematics Methods for Early Childhood Copyright © 2021 by Janet Stramel is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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Fluency, reasoning and problem solving in primary maths

Primary maths, australia and new zealand, tes resources team.

Develop fluency, reasoning and problem solving within any topic as part of a mastery approach

The skills of fluency, reasoning and problem solving are well-known to all primary maths teachers. In mastery teaching , they play an essential role in helping pupils to gain a deeper understanding of a topic. But what does this look like in practice?

For more information on mastery, check out this  handy introduction .

Firstly, problem solving is at the heart of mastering maths. While there is nothing new about using problem-solving questions to consolidate understanding, mastery gets teachers to rethink the traditional lengthy word-problem format. Instead, problem-solving questions are often open-ended, with more than one right answer. 

Problem solving is an important skill for all ages and abilities and, as such, needs to be taught explicitly. It is therefore useful to have challenges like these at the end of every lesson.

Secondly, verbal reasoning demonstrates that pupils understand the maths. Talk is an integral part of mastery as it encourages students to reason, justify and explain their thinking. This is tricky for many teachers who are not used to focusing on verbal reasoning in their maths lessons. You might, for example, get young learners to voice their thought processes. Older students could take part in class debates, giving them the space to challenge their peers using logical reasoning.

Introducing scaffolded sentence structures when talking about maths gives pupils the confidence to communicate their ideas clearly, before writing them down. A mastery classroom should never be a quiet classroom.

Finally, fluency, reasoning and problem solving underpins the deepening of understanding. Fluency alone doesn’t give students the chance to delve deeper into the mathematics. They may well be able to answer the questions, but can they also justify their answer or explore other possibilities?

Typically, teachers start new topics by developing fluency in order to give learners confidence with the skill. However, sometimes starting with a problem-solving question – eg, Prove that 4+3=7 – deepens understanding sooner. How? Pupils have to be reliant on resources they’ve used elsewhere, such as concrete manipulatives and pictorial representations, to help them explain the maths.

When planning, try not to get hung up on whether an activity focuses on either reasoning or problem solving as often it is a combination. Instead, turn your attention to using these types of questions to secure fluency and ensure that all children move beyond it into a world of deeper understanding.

Fluency, reasoning and problem solving in your classroom

Embedding these concepts into your everyday teaching can take time so patience is key! Mastery specialists recommend being more fluid with your planning and investing more time in making resources that will allow you to be reactionary to progress made in the lessons.

We’ve hand-picked these useful ideas to get you started:

This blog post was written with grateful thanks to Jenny Lewis, Primary Maths Specialist at the White Rose Maths Hub, and Helen Williams, Director of Primary at Mathematics Mastery, for their insights.

Want to know more about primary maths mastery? Check out our collection of free resources, quality assured by mastery experts and helpfully mapped by topic to year groups and learning objectives.

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3 Simple Strategies to Improve Students’ Problem-Solving Skills

These strategies are designed to make sure students have a good understanding of problems before attempting to solve them.

Research provides a striking revelation about problem solvers. The best problem solvers approach problems much differently than novices. For instance, one meta-study showed that when experts evaluate graphs , they tend to spend less time on tasks and answer choices and more time on evaluating the axes’ labels and the relationships of variables within the graphs. In other words, they spend more time up front making sense of the data before moving to addressing the task.

While slower in solving problems, experts use this additional up-front time to more efficiently and effectively solve the problem. In one study, researchers found that experts were much better at “information extraction” or pulling the information they needed to solve the problem later in the problem than novices. This was due to the fact that they started a problem-solving process by evaluating specific assumptions within problems, asking predictive questions, and then comparing and contrasting their predictions with results. For example, expert problem solvers look at the problem context and ask a number of questions:

• What do we know about the context of the problem?
• What assumptions are underlying the problem? What’s the story here?
• What qualitative and quantitative information is pertinent?
• What might the problem context be telling us? What questions arise from the information we are reading or reviewing?
• What are important trends and patterns?

As such, expert problem solvers don’t jump to the presented problem or rush to solutions. They invest the time necessary to make sense of the problem.

Now, think about your own students: Do they immediately jump to the question, or do they take time to understand the problem context? Do they identify the relevant variables, look for patterns, and then focus on the specific tasks?

If your students are struggling to develop the habit of sense-making in a problem- solving context, this is a perfect time to incorporate a few short and sharp strategies to support them.

3 Ways to Improve Student Problem-Solving

1. Slow reveal graphs: The brilliant strategy crafted by K–8 math specialist Jenna Laib and her colleagues provides teachers with an opportunity to gradually display complex graphical information and build students’ questioning, sense-making, and evaluating predictions.

For instance, in one third-grade class, students are given a bar graph without any labels or identifying information except for bars emerging from a horizontal line on the bottom of the slide. Over time, students learn about the categories on the x -axis (types of animals) and the quantities specified on the y -axis (number of baby teeth).

The graphs and the topics range in complexity from studying the standard deviation of temperatures in Antarctica to the use of scatterplots to compare working hours across OECD (Organization for Economic Cooperation and Development) countries. The website offers a number of graphs on Google Slides and suggests questions that teachers may ask students. Furthermore, this site allows teachers to search by type of graph (e.g., scatterplot) or topic (e.g., social justice).

2. Three reads: The three-reads strategy tasks students with evaluating a word problem in three different ways . First, students encounter a problem without having access to the question—for instance, “There are 20 kangaroos on the grassland. Three hop away.” Students are expected to discuss the context of the problem without emphasizing the quantities. For instance, a student may say, “We know that there are a total amount of kangaroos, and the total shrinks because some kangaroos hop away.”

Next, students discuss the important quantities and what questions may be generated. Finally, students receive and address the actual problem. Here they can both evaluate how close their predicted questions were from the actual questions and solve the actual problem.

To get started, consider using the numberless word problems on educator Brian Bushart’s site . For those teaching high school, consider using your own textbook word problems for this activity. Simply create three slides to present to students that include context (e.g., on the first slide state, “A salesman sold twice as much pears in the afternoon as in the morning”). The second slide would include quantities (e.g., “He sold 360 kilograms of pears”), and the third slide would include the actual question (e.g., “How many kilograms did he sell in the morning and how many in the afternoon?”). One additional suggestion for teams to consider is to have students solve the questions they generated before revealing the actual question.

3. Three-Act Tasks: Originally created by Dan Meyer, three-act tasks follow the three acts of a story . The first act is typically called the “setup,” followed by the “confrontation” and then the “resolution.”

This storyline process can be used in mathematics in which students encounter a contextual problem (e.g., a pool is being filled with soda). Here students work to identify the important aspects of the problem. During the second act, students build knowledge and skill to solve the problem (e.g., they learn how to calculate the volume of particular spaces). Finally, students solve the problem and evaluate their answers (e.g., how close were their calculations to the actual specifications of the pool and the amount of liquid that filled it).

Often, teachers add a fourth act (i.e., “the sequel”), in which students encounter a similar problem but in a different context (e.g., they have to estimate the volume of a lava lamp). There are also a number of elementary examples that have been developed by math teachers including GFletchy , which offers pre-kindergarten to middle school activities including counting squares , peas in a pod , and shark bait .

Students need to learn how to slow down and think through a problem context. The aforementioned strategies are quick ways teachers can begin to support students in developing the habits needed to effectively and efficiently tackle complex problem-solving.

10 Best AI Math Solvers For Instant Homework Solutions

Math ai tools make solving math problems simple. here well reveal some of the best ai math solvers for solving complex math problems..

If you need extra help with math homework, you're not alone. AI math solvers are powerful tools that can help students at all grade levels develop their math skills.

Students are not the only group that can benefit from using AI for math. Parents and educators can also use these tools to help students succeed. Math AI solvers break down math problems into small components that are easier to understand.

In this article, we'll compare some of the best AI math solver tools available. There were several things we looked for to find the best ones, such as ease of use, features, and price. Read on!

10 Best AI Math Solver Tools

1. ai math – best ai math solver overall, 2. mathful – best ai math solver for boosting your math grade.

3. HIX Tutor – Best AI Math Solver for Step-by-Step Support

4. ExamUp – Best AI Math Solver for Studying for Exams

5. homeworkai – best ai math solver for reviewing textbook material, 6. microsoft math solver – best ai math solver for use on mobile devices, 7. mathway – best ai math solver for solving algebra problems, 8. maths.ai – best ai math solver for a personalized learning experience, 9. snapxam – best ai math solver for access to online math calculators, 10. air math – best ai math solver for solving problems from the web.

For the overall best math AI tool, try AI Math. This tool enables students to master advanced math skills without the burden of scouring textbooks for answers. From deciphering word problems to simplifying algebraic expressions, AI Math covers nearly every branch of math to provide students with comprehensive support.

Use AI Math to solve math problems anytime and anywhere you have an internet connection. Along with 24/7 accessibility, the AI math solver offers near-precision with a 99% accuracy rate. Best of all, it doesn't cost anything to get started.

To begin, simply input your math question by typing the problem. In seconds, you'll receive an accurate solution and a detailed explanation that helps you learn the material.

● Provides step-by-step solutions.

● Designed to handle both simple and complex math questions.

● Gives instant feedback to reinforce math concepts.

● Requires a paid subscription after the trial period.

● May go against school policies that prohibit AI use.

Eliminate Your Math Struggles with the Versatile AI Math >>>

Mathful is an advanced AI math problem solver that uses machine learning technology and powerful algorithms to rapidly generate accurate solutions to nearly every math question imaginable.

Not all students can successfully learn new math concepts in the classroom, but Mathful is different. Students can learn at their own pace and review challenging math concepts as often as they need.

Mathful covers over 10 branches of math, including but not limited to, algebra, geometry, and calculus. It also helps younger students with elementary math subjects, such as fractions, decimals, and measurement. The platform is available 24/7 to help students study in the comfort of their homes day or night.

● Helps students gain confidence in their math skills.

● Allows students to check their answers to ensure accuracy.

● The AI math solver is available to try for free.

● Some students cannot afford a subscription after the free trial.

See Your Math Grade Skyrocket with Help from Mathful >>>

3. HIX Tutor – Best AI Math Solver for Step-by-Step Math Support

HIX Tutor is a revolutionary tool that enhances students' mathematical education. With HIX Tutor, users can get instant step-by-step explanations of homework problems, whether they need assistance with limits and derivatives or want to hone their algebraic skills.

HIX Tutor promotes streamlined learning by giving students the guidance they need each step of the way. Just submit your math query and wait seconds while the tool works its magic. You can then check the final answer against your own and gain a better understanding of how to reach the final solution.

This diverse AI math solver uses the latest in AI math technology to ensure accurate answers to math questions at all grade levels.

● Helps boost math grades and overall school success.

● Is trained in geometry, trigonometry, calculus, and more.

● Allows students to type in math questions or upload an image or file.

● Could have difficulty reading files with messy or illegible handwriting.

Leverage the Power of AI Math with HIX Tutor's AI Math AI Solver >>>

ExamUp is the perfect solution for students who want to prep for exams or have last-minute study sessions. The reliable AI homework solver can handle math topics across all branches, from number theory to applied mathematics.

ExamUp provides detailed explanations of math problems that improve student comprehension and ensure that the knowledge sticks. The AI math problem solver has a 99% accuracy rate, making it a trustworthy study sidekick.

ExamUp offers a free plan that allows students to access certain features at no cost. Gain access to additional math features and capabilities with a paid subscription.

● Supports 30+ languages, including English, Spanish, French, and Italian.

● Includes a built-in plagiarism detector.

● Offers homework help for other subjects like chemistry, physics, and biology.

● Cannot replace an in-person classroom education.

Ace Your Next Exam with ExamUp's AI Math Problem Solver Tool >>>

Math textbooks certainly have value but can be difficult to learn from due to the sheer amount of information. HomeworkAI simplifies the learning process by analyzing textbook material with practice questions and providing instant feedback and solutions to problems.

The AI homework problem solver can also help students with regular homework assignments. Type in a math problem or upload an image or text file to start the process. The platform is easy to use and is accessible 24/7 for convenience.

HomeworkAI can help users of all educational levels, from elementary age to older professionals. Students can try HomeworkAI at no cost.

● Supports a variety of file formats, such as PDF, image files, DOC, and DOCX.

● Can handle math problems with multiple solution methods.

● Helps with other school subjects like biology, chemistry, physics, and more.

● The tool does not offer advanced math features.

Get Caught Up on Your Math Assignments with Homework AI Math Solver >>>

It's inevitable that you won't always be home when you need to study or do math homework. That is why having a mobile-friendly AI math solver like Microsoft Math Solver can be a lifesaver.

Available for download in the App Store or on Google Play, Microsoft Math Solver can be used on both Android and iOS devices. After downloading the app, you'll be prompted to type in a math question, such as a quadratic equation or trigonometry problem. The tool will then provide simple steps to solve the problem and show your work.

● Covers pre-algebra, algebra, calculus, and trigonometry.

● Provides video resources for new features, tips, and more.

● Allows students to graph their math problems.

● The tool can only be used on mobile devices.

Mathway is specifically designed to help students with a variety of math subjects, such as calculus, physics, and statistics, but it is especially beneficial for algebra. The tailored AI math solver offers a simple interface with a chatbot and calculator to make completing algebra problems fast and simple.

When you enter an algebra problem, the tool will present a series of options for you to choose from. For example, it may ask if you want to “Simplify,” “Calculate in the Square Root,” or “Convert to Radical Form.” Once you've made your selection, the tool provides an answer and explanation.

● The AI math solver is free to use.

● Has a clean interface that doesn't distract you from learning.

● Can help with other math subjects like basic math, statistics, and physics.

● Requires users to sign up for advanced features.

● Explanations of math problems can sometimes be too brief.

Every student is unique in the way that they learn and comprehend information. With Maths.ai, students can learn at their own level and pace. The cutting-edge math AI solver gradually adapts to the user's learning style for a personalized academic experience.

Maths.ai prides itself on being a “safe space” in which students can ask homework questions without judgment. The tool is open to students worldwide to help them build their math skills in a way that works best for them. Students can sign up for a free trial to get started. Subscription plans start at just $3 per user, per month.

● Offers a familiar chatbot with a conversational text style.

● Uses the latest in AI technology to help students learn.

● Can be more affordable than hiring a math tutor.

● Accuracy may be reduced for complex math problems.

SnapXam doesn't just offer a one-size-fits-all math tool. Instead, it has more than 100 online math calculators that perform a wide range of mathematical functions, ranging from a condensing logarithms calculator to a polynomial factorization calculator.

The powerful AI math solver also offers step-by-step examples that walk students through different types of math problems. Students can also help SnapXam to explore different ways to solve the problem.

● Provides access to YouTube math videos and tutorials.

● Students who get different answers than the one shown can verify their answers.

● Allows students to share solutions with their friends.

● Better suited for older math students.

● Additional features are only available with a Premium account.

The ability to solve complex problems anywhere is appealing. Air Math is unique in that it offers an Air Math Homework Helper Chrome Extension that students can install, snap, and crop a math problem from the web, and instantly generate a solution.

Air Math can solve many types of problems, including challenging word problems. If the math AI solver cannot provide an accurate answer to your math question, it will recommend connecting with a real tutor who will walk you through the solution. All live tutors at Air Math are tested, certified, and consistently monitored.

● Students can type in math questions or upload photos of questions.

● The tool is available for the web and iOS and Android devices.

● A “Bookmarks” feature enables students to bookmark any solution.

● Some features are only available on the mobile version.

AI math problem solver tools are transforming the way that students approach homework assignments and prepare for exams. Leading AI math solvers like AI Math help create an engaging and intuitive learning experience that makes math a more approachable subject. Try AI Math for yourself and see how it can help you build your math skills.

Disclaimer: The above sponsored content is non-editorial and has been sourced from a third party. NDTV does not guarantee, vouch for or necessarily endorse any of the above content, nor is responsible for it in any manner whatsoever.

Mental Math & Times Tables 4+

Multiplication flash cards ‪‬, peter schmidt.

• 4.7 • 264 Ratings
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Become a mental math genius - start to practice now! FastMath will turn you into a math genius in no time! It's the ultimate way to master solving math problems quickly in your head. Perfect for students, professionals, brain training, or just for fun, FastMath offers a wide variety of exercise types, number types, and difficulty levels to improve your math skills. Discover the power of mental arithmetic with these fantastic features: - Race against time with standardized tests to evaluate your performance level - Set high scores to motivate and challenge yourself - Compete with friends on leaderboards to achieve math supremacy - Discover cool math tricks for lightning-fast problem solving - Trainer offers maximum flexibility with different number and exercise types - Monitor your progress and statistics to improve daily - Addictive challenges help you develop a lasting habit - Earn unique achievements the more you practice Supported number types: - Natural numbers - Decimal numbers - Giant numbers Supported exercise types: - Addition - Subtraction - Multiplication - Division - Squares - Square roots - Fractions - Percentages - Modulo Join thousands of learners, parents, schools, and teachers around the world who love FastMath! If there's something we can improve, or if you need help, contact our support team: [email protected] Terms of Use: https://www.apple.com/legal/internet-services/itunes/dev/stdeula Privacy Policy: https://www.fastmath.app/privacy

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We continuously improve FastMath to enhance your mental math skills. In this update, we've added new features and optimized performance to keep you swift in pursuing personal best times. Enjoy FastMath? Please consider leaving a review on the App Store. For questions or feedback, reach out to [email protected]

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264 Ratings

If you’re struggling with your mental math, use this.

After just one week I already noticed my abilities improve. It was frustrating that I used to be really good at it, but since I’ve had little practice in recent years, my skills have diminished. This app is clear and straightforward. You can get started immediately improving your math skills. Definitley recommend!

Developer Response ,

Thanks for sharing! We are happy to hear that you like Fast Math and are incredibly motivated to see that it helps you improve your mental math skills. We hope you’ll improve even further :)

Great for keeping skills sharp

Tried multiple apps (free version for all) and this was the most functional and easy to use. Thinking about upgrading to pro to use the trainer mode.

Thanks for the great feedback, we really appreciate it!

Multiplication helper

This is really good for multiplication and adding especially since you get to pick which level you’re on I don’t like that there’s a bunch of in app purchases. it is also a little glitchy when you are trying to answer the question you answer it and it stops and waits but it’s a really good multiplication, adding helper. It really helps every skill I have in math and it strengthens my grades.

Hi and thanks for your review! We are happy that you like FastMath and that it helps you to improve your mental math skills :) As for the glitches you mentioned: We will try to make sure to squash any bugs that might negatively affect the performance of the app … so keep an eye out for future updates.

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Computer Science > Computation and Language

Title: large language models are unconscious of unreasonability in math problems.

Abstract: Large language models (LLMs) demonstrate substantial capabilities in solving math problems. However, they tend to produce hallucinations when given questions containing unreasonable errors. In this paper, we study the behavior of LLMs when faced with unreasonable math problems and further explore their potential to address these problems. First, we construct the Unreasonable Math Problem (UMP) benchmark to examine the error detection ability of LLMs. Experiments show that LLMs are able to detect unreasonable errors, but still fail in generating non-hallucinatory content. In order to improve their ability of error detection and correction, we further design a strategic prompt template called Critical Calculation and Conclusion(CCC). With CCC, LLMs can better self-evaluate and detect unreasonable errors in math questions, making them more reliable and safe in practical application scenarios.

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