list all mathematical problem solving skills you know

Free Mathematics Tutorials

Skills needed for mathematical problem solving (1).

Mathematical problem solving is one of the most important topics to learn and also one of the most complex to teach. The main goal in teaching mathematical problem solving is that students develop a generic ability to solve real life problems and apply mathematics in real life situations. Problem solving can also be used, as a teaching method, for a deeper understanding of concepts. Successful mathematical problem solving depends upon many factors and skills with different characteristics. In fact one of the main difficulties in learning problem solving is the fact that many skills are needed for a learner to be an effective problem solver. Also, these factors and skills make the teaching of problem solving one of the most complex topic to teach. This paper will discuss the idea that problem solving is a process that needs to be understood by instructors so that they can develop better and more effective classroom activities and tasks. The necessary skills for problem solving as well as the methods and strategies to teach or facilitate them are discussed.

Popular Pages

• Skills Needed for Mathematical Problem Solving (2)
• Skills Needed for Mathematical Problem Solving (3)
• Math Problems, Questions and Online Self Tests

Stay In Touch

• Privacy Policy

How to Improve Problem-Solving Skills: Mathematics and Critical Thinking

In today’s rapidly changing world, problem-solving has become a quintessential skill. When we discuss the topic, it’s natural to ask, “What is problem-solving?” and “How can we enhance this skill, particularly in children?” The discipline of mathematics offers a rich platform to explore these questions. Through math, not only do we delve into numbers and equations, but we also explore how to improve problem-solving skills and how to develop critical thinking skills in math. Let’s embark on this enlightening journey together.

What is Problem-Solving?

At its core, problem-solving involves identifying a challenge and finding a solution. But it’s not always as straightforward as it sounds. So, what is problem-solving? True problem-solving requires a combination of creative thinking and logical reasoning. Mathematics, in many ways, embodies this blend. When a student approaches a math problem, they must discern the issue at hand, consider various methods to tackle it, and then systematically execute their chosen strategy.

But what is problem-solving in a broader context? It’s a life skill. Whether we’re deciding the best route to a destination, determining how to save for a big purchase, or even figuring out how to fix a broken appliance, we’re using problem-solving.

How to Develop Critical Thinking Skills in Math

Critical thinking goes hand in hand with problem-solving. But exactly how to develop critical thinking skills in math might not be immediately obvious. Here are a few strategies:

• Contextual Learning: Teaching math within a story or real-life scenario makes it relevant. When students see math as a tool to navigate the world around them, they naturally begin to think critically about solutions.
• Open-ended Questions: Instead of merely seeking the “right” answer, encourage students to explain their thought processes. This nudges them to think deeply about their approach.
• Group Discussions: Collaborative learning can foster different perspectives, prompting students to consider multiple ways to solve a problem.
• Challenging Problems: Occasionally introducing problems that are a bit beyond a student’s current skill level can stimulate critical thinking. They will have to stretch their understanding and think outside the box.

What are the Six Basic Steps of the Problem-Solving Process?

Understanding how to improve problem-solving skills often comes down to familiarizing oneself with the systematic approach to challenges. So, what are the six basic steps of the problem-solving process?

• Identification: Recognize and define the problem.
• Analysis: Understand the problem’s intricacies and nuances.
• Generation of Alternatives: Think of different ways to approach the challenge.
• Decision Making: Choose the most suitable method to address the problem.
• Implementation: Put the chosen solution into action.
• Evaluation: Reflect on the solution’s effectiveness and learn from the outcome.

By embedding these steps into mathematical education, we provide students with a structured framework. When they wonder about how to improve problem-solving skills or how to develop critical thinking skills in math, they can revert to this process, refining their approach with each new challenge.

Making Math Fun and Relevant

At Wonder Math, we believe that the key to developing robust problem-solving skills lies in making math enjoyable and pertinent. When students see math not just as numbers on a page but as a captivating story or a real-world problem to be solved, their engagement skyrockets. And with heightened engagement comes enhanced understanding.

As educators and parents, it’s crucial to continuously ask ourselves: how can we demonstrate to our children what problem-solving is? How can we best teach them how to develop critical thinking skills in math? And how can we instill in them an understanding of the six basic steps of the problem-solving process?

The answer, we believe, lies in active learning, contextual teaching, and a genuine passion for the beauty of mathematics.

The Underlying Beauty of Mathematics

Often, people perceive mathematics as a rigid discipline confined to numbers and formulas. However, this is a limited view. Math, in essence, is a language that describes patterns, relationships, and structures. It’s a medium through which we can communicate complex ideas, describe our universe, and solve intricate problems. Understanding this deeper beauty of math can further emphasize how to develop critical thinking skills in math.

Why Mathematics is the Ideal Playground for Problem-Solving

Math provides endless opportunities for problem-solving. From basic arithmetic puzzles to advanced calculus challenges, every math problem offers a chance to hone our problem-solving skills. But why is mathematics so effective in this regard?

• Structured Challenges: Mathematics presents problems in a structured manner, allowing learners to systematically break them down. This format mimics real-world scenarios where understanding the structure of a challenge can be half the battle.
• Multiple Approaches: Most math problems can be approached in various ways . This teaches learners flexibility in thinking and the ability to view a single issue from multiple angles.
• Immediate Feedback: Unlike many real-world problems where solutions might take time to show results, in math, students often get immediate feedback. They can quickly gauge if their approach works or if they need to rethink their strategy.

Enhancing the Learning Environment

To genuinely harness the power of mathematics in developing problem-solving skills, the learning environment plays a crucial role. A student who is afraid of making mistakes will hesitate to try out different approaches, stunting their critical thinking growth.

However, in a nurturing, supportive environment where mistakes are seen as learning opportunities, students thrive. They become more willing to take risks, try unconventional solutions, and learn from missteps. This mindset, where failure is not feared but embraced as a part of the learning journey, is pivotal for developing robust problem-solving skills.

Incorporating Technology

In our digital age, technology offers innovative ways to explore math. Interactive apps and online platforms can provide dynamic problem-solving scenarios, making the process even more engaging. These tools can simulate real-world challenges, allowing students to apply their math skills in diverse contexts, further answering the question of how to improve problem-solving skills.

More than Numbers 

In summary, mathematics is more than just numbers and formulas—it’s a world filled with challenges, patterns, and beauty. By understanding its depth and leveraging its structured nature, we can provide learners with the perfect platform to develop critical thinking and problem-solving skills. The key lies in blending traditional techniques with modern tools, creating a holistic learning environment that fosters growth, curiosity, and a lifelong love for learning.

Join us on this transformative journey at Wonder Math. Let’s make math an adventure, teaching our children not just numbers and equations, but also how to improve problem-solving skills and navigate the world with confidence. Enroll your child today and witness the magic of mathematics unfold before your eyes!

FAQ: Mathematics and Critical Thinking

1. what is problem-solving in the context of mathematics.

Problem-solving in mathematics refers to the process of identifying a mathematical challenge and systematically working through methods and strategies to find a solution.

2. Why is math considered a good avenue for developing problem-solving skills?

Mathematics provides structured challenges and allows for multiple approaches to find solutions. This promotes flexibility in thinking and encourages learners to view problems from various angles.

3. How does contextual learning enhance problem-solving abilities?

By teaching math within a story or real-life scenario, it becomes more relevant for the learner. This helps them see math as a tool to navigate real-world challenges , thereby promoting critical thinking.

4. What are the six basic steps of the problem-solving process in math?

The six steps are: Identification, Analysis, Generation of Alternatives, Decision Making, Implementation, and Evaluation.

5. How can parents support their children in developing mathematical problem-solving skills?

Parents can provide real-life contexts for math problems , encourage open discussions about different methods, and ensure a supportive environment where mistakes are seen as learning opportunities.

6. Are there any tools or apps that can help in enhancing problem-solving skills in math?

Yes, there are various interactive apps and online platforms designed specifically for math learning. These tools provide dynamic problem-solving scenarios and simulate real-world challenges, making the learning process engaging.

7. How does group discussion foster critical thinking in math?

Group discussions allow students to hear different perspectives and approaches to a problem. This can challenge their own understanding and push them to think about alternative methods.

8. Is it necessary to always follow the six steps of the problem-solving process sequentially?

While the six steps provide a structured approach, real-life problem-solving can sometimes be more fluid. It’s beneficial to know the steps, but adaptability and responsiveness to the situation are also crucial.

9. How does Wonder Math incorporate active learning in teaching mathematics?

Wonder Math integrates mathematics within engaging stories and real-world scenarios, making it fun and relevant. This active learning approach ensures that students are not just passive recipients but active participants in the learning process.

10. What if my child finds a math problem too challenging and becomes demotivated?

It’s essential to create a supportive environment where challenges are seen as growth opportunities. Remind them that every problem is a chance to learn, and it’s okay to seek help or approach it differently.

Related posts

Summer Math Programs: How They Can Prevent Learning Loss in Young Students

As summer approaches, parents and educators alike turn their attention to how they can support young learners during the break. Summer is a time for relaxation, fun, and travel, yet it’s also a critical period when learning loss can occur. This phenomenon, often referred to as the “summer slide,” impacts students’ progress, especially in foundational subjects like mathematics. It’s reported…

Math Programs 101: What Every Parent Should Know When Looking For A Math Program

  As a parent, you know that a solid foundation in mathematics is crucial for your child’s success, both in school and in life. But with so many math programs and math help services out there, how do you choose the right one? Whether you’re considering Outschool classes, searching for “math tutoring near me,” or exploring tutoring services online, understanding…

Mathematical Problem-Solving: Techniques and Strategies

by Ali | Mar 8, 2023 | Blog Post , Blogs | 0 comments

Introduction to Mathematical Problem-Solving

Mathematical problem-solving is the process of using logical reasoning and critical thinking to find a solution to a mathematical problem. It is an essential skill that is required in a wide range of academic and professional fields, including science, technology, engineering, and mathematics (STEM).

Importance of Mathematical Problem-Solving Skills

Mathematical problem-solving skills are critical for success in many areas of life, including education, career, and daily life. It helps students to develop analytical and critical thinking skills, enhances their ability to reason logically, and encourages them to persevere when faced with challenges.

The Process of Mathematical Problem-Solving

The process of mathematical problem-solving involves several steps that include identifying the problem, understanding the problem, making a plan, carrying out the plan, and checking the answer.

Techniques and Strategies for Mathematical Problem-Solving

1.      identify the problem.

The first step in problem-solving is to identify the problem. It involves reading the problem carefully and determining what the problem is asking.

2.      Understand the problem

The next step is to understand the problem by breaking it down into smaller parts, identifying any relevant information, and determining what needs to be solved.

3.      Make a plan

After understanding the problem, the next step is to develop a plan to solve it. This may involve identifying a formula or method to use, drawing a diagram or chart, or making a list of steps to follow.

4.      Carry out the plan

Once a plan is developed, the next step is to carry out the plan by solving the problem using the chosen method. It is important to show all steps and work neatly to avoid making mistakes.

5.      Check the answer

Finally, it is essential to check the answer to ensure it is correct. This can be done by re-reading the problem, checking the solution for accuracy, and verifying that it makes sense.

Know About: HOW TO FIND PERFECT MATH TUTOR 

Importance of using online calculators while learning math.

Utilizing online calculators can prove to be a beneficial resource for learning mathematics. There are numerous reasons why incorporating them into your studies is a wise choice.

Firstly, online calculators offer the convenience of being easily accessible at any time and from anywhere. No longer do you need to carry a physical calculator with you; you can use them on any device that has internet connectivity.

In addition, online calculators excel in accuracy and can efficiently handle complex calculations that may be difficult to do manually. They can perform arithmetic at a faster speed, saving you time and increasing productivity.

Another advantage is that some online calculators include built-in visualizations such as graphs and charts, which can help students grasp mathematical concepts better.

Furthermore, feedback can be provided by certain online calculators, assisting students in identifying and rectifying errors in their calculations. This feature can be especially useful for students who are new to learning mathematics .

Online calculators have a versatile range of functions beyond basic arithmetic, including algebraic equations, trigonometry, and calculus . This makes them useful for students at all levels of math education.

Overall, online calculators are an invaluable tool for students learning math. They are convenient, accurate, efficient, and versatile, and aid in the understanding of mathematical concepts, making them an essential component of modern-day education.

Common Errors in Mathematical Problem-Solving

There are several common errors that can occur in mathematical problem-solving, including misunderstanding the problem, using incorrect formulas or methods, making computational errors, and not checking the answer. To avoid these errors, it is essential to read the problem carefully, use the correct formulas and methods, check all computations, and double-check the answer for accuracy.

Improving Mathematical Problem-Solving Skills

There are several ways to improve mathematical problem-solving skills, including practicing regularly, working with others, seeking help from a teacher or tutor, and reviewing past problems. It is also helpful to develop a positive attitude towards problem-solving, persevere through challenges, and learn from mistakes.

Must Know: WHICH IS THE BEST WAY OF LEARNING ONLINE TUTORING OR TRADITIONAL TUTORING

Mathematical problem-solving is a crucial skill that is required for success in many academic and professional fields. By following the process of problem-solving and using the techniques and strategies outlined in this article, individuals can improve their problem-solving skills and achieve success in their academic and professional endeavors.

Frequently Asked Questions

What is mathematical problem-solving.

Mathematical problem-solving is the process of using logical reasoning and critical thinking to find a solution to a mathematical problem.

Why are mathematical problem-solving skills important?

What are the steps involved in the process of mathematical problem-solving, how can online calculators aid in learning mathematics.

Online calculators can aid in learning mathematics by providing convenience, accuracy, and efficiency. They can also help students grasp mathematical concepts better through built-in visualizations and provide feedback to identify and rectify errors in their calculations.

What are common errors to avoid in mathematical problem-solving?

Common errors to avoid in mathematical problem-solving include misunderstanding the problem, using incorrect formulas or methods, making computational errors, and not checking the answer. To avoid these errors, it is essential to read the problem carefully, use the correct formulas and methods, check all computations, and double-check the answer for accuracy.

We are committed to help students by one on one online private tutoring to maximize their e-learning potential and achieve the best results they can.

For this, we offer a free of cost trial class so that we can satisfy you. There is a free trial class for first-time students.

Problem Solving Skills: Meaning, Examples & Techniques

Table of Contents

26 January 2021

Reading Time: 2 minutes

Do your children have trouble solving their Maths homework?

Or, do they struggle to maintain friendships at school?

If your answer is ‘Yes,’ the issue might be related to your child’s problem-solving abilities. Whether your child often forgets his/her lunch at school or is lagging in his/her class, good problem-solving skills can be a major tool to help them manage their lives better.

Children need to learn to solve problems on their own. Whether it is about dealing with academic difficulties or peer issues when children are equipped with necessary problem-solving skills they gain confidence and learn to make healthy decisions for themselves. So let us look at what is problem-solving, its benefits, and how to encourage your child to inculcate problem-solving abilities

Problem-solving skills can be defined as the ability to identify a problem, determine its cause, and figure out all possible solutions to solve the problem.

• Trigonometric Problems

What is problem-solving, then? Problem-solving is the ability to use appropriate methods to tackle unexpected challenges in an organized manner. The ability to solve problems is considered a soft skill, meaning that it’s more of a personality trait than a skill you’ve learned at school, on-the-job, or through technical training. While your natural ability to tackle problems and solve them is something you were born with or began to hone early on, it doesn’t mean that you can’t work on it. This is a skill that can be cultivated and nurtured so you can become better at dealing with problems over time.

Problem Solving Skills: Meaning, Examples & Techniques are mentioned below in the Downloadable PDF. 

Benefits of learning problem-solving skills  

Promotes creative thinking and thinking outside the box.

Improves decision-making abilities.

Builds solid communication skills.

Develop the ability to learn from mistakes and avoid the repetition of mistakes.

Problem Solving as an ability is a life skill desired by everyone, as it is essential to manage our day-to-day lives. Whether you are at home, school, or work, life throws us curve balls at every single step of the way. And how do we resolve those? You guessed it right – Problem Solving.

Strengthening and nurturing problem-solving skills helps children cope with challenges and obstacles as they come. They can face and resolve a wide variety of problems efficiently and effectively without having a breakdown. Nurturing good problem-solving skills develop your child’s independence, allowing them to grow into confident, responsible adults. 

Children enjoy experimenting with a wide variety of situations as they develop their problem-solving skills through trial and error. A child’s action of sprinkling and pouring sand on their hands while playing in the ground, then finally mixing it all to eliminate the stickiness shows how fast their little minds work.

Sometimes children become frustrated when an idea doesn't work according to their expectations, they may even walk away from their project. They often become focused on one particular solution, which may or may not work.

However, they can be encouraged to try other methods of problem-solving when given support by an adult. The adult may give hints or ask questions in ways that help the kids to formulate their solutions. 

Encouraging Problem-Solving Skills in Kids

Practice problem solving through games.

Exposing kids to various riddles, mysteries, and treasure hunts, puzzles, and games not only enhances their critical thinking but is also an excellent bonding experience to create a lifetime of memories.

Create a safe environment for brainstorming

Welcome, all the ideas your child brings up to you. Children learn how to work together to solve a problem collectively when given the freedom and flexibility to come up with their solutions. This bout of encouragement instills in them the confidence to face obstacles bravely.

Invite children to expand their Learning capabilities

 Whenever children experiment with an idea or problem, they test out their solutions in different settings. They apply their teachings to new situations and effectively receive and communicate ideas. They learn the ability to think abstractly and can learn to tackle any obstacle whether it is finding solutions to a math problem or navigating social interactions.

Problem-solving is the act of finding answers and solutions to complicated problems. 

Developing problem-solving skills from an early age helps kids to navigate their life problems, whether academic or social more effectively and avoid mental and emotional turmoil.

Children learn to develop a future-oriented approach and view problems as challenges that can be easily overcome by exploring solutions. 

About Cuemath

Cuemath, a student-friendly mathematics and coding platform, conducts regular  Online Classes  for academics and skill-development, and their Mental Math App, on both  iOS  and  Android , is a one-stop solution for kids to develop multiple skills. Understand the Cuemath Fee structure and sign up for a free trial.

Frequently Asked Questions (FAQs)

How do you teach problem-solving skills.

Model a useful problem-solving method. Problem solving can be difficult and sometimes tedious. ... 1. Teach within a specific context. ... 2. Help students understand the problem. ... 3. Take enough time. ... 4. Ask questions and make suggestions. ... 5. Link errors to misconceptions.

What makes a good problem solver?

Excellent problem solvers build networks and know how to collaborate with other people and teams. They are skilled in bringing people together and sharing knowledge and information. A key skill for great problem solvers is that they are trusted by others.

• Skip to main content
• Skip to primary sidebar
• Skip to footer

Additional menu

Khan Academy Blog

Unlocking the Power of Math Learning: Strategies and Tools for Success

posted on September 20, 2023

Mathematics, the foundation of all sciences and technology, plays a fundamental role in our everyday lives. Yet many students find the subject challenging, causing them to shy away from it altogether. This reluctance is often due to a lack of confidence, a misunderstanding of unclear concepts, a move ahead to more advanced skills before they are ready, and ineffective learning methods. However, with the right approach, math learning can be both rewarding and empowering. This post will explore different approaches to learning math, strategies for success, and cutting-edge tools to help you achieve your goals.

Math Learning

Math learning can take many forms, including traditional classroom instruction, online courses, and self-directed learning. A multifaceted approach to math learning can improve understanding, engage students, and promote subject mastery. A 2014 study by the National Council of Teachers of Mathematics found that the use of multiple representations, such as visual aids, graphs, and real-world examples, supports the development of mathematical connections, reasoning, and problem-solving skills.

Moreover, the importance of math learning goes beyond solving equations and formulas. Advanced math skills are essential for success in many fields, including science, engineering, finance, health care, and technology. In fact, a report by Burning Glass Technologies found that 71% of high-salary, entry-level positions require advanced math skills.

Benefits of Math Learning

In today’s 21st-century world, having a broad knowledge base and strong reading and math skills is essential. Mathematical literacy plays a crucial role in this success. It empowers individuals to comprehend the world around them and make well-informed decisions based on data-driven understanding. More than just earning good grades in math, mathematical literacy is a vital life skill that can open doors to economic opportunities, improve financial management, and foster critical thinking. We’re not the only ones who say so:

• Math learning enhances problem-solving skills, critical thinking, and logical reasoning abilities. (Source: National Council of Teachers of Mathematics )
• It improves analytical skills that can be applied in various real-life situations, such as budgeting or analyzing data. (Source: Southern New Hampshire University )
• Math learning promotes creativity and innovation by fostering a deep understanding of patterns and relationships. (Source: Purdue University )
• It provides a strong foundation for careers in fields such as engineering, finance, computer science, and more. These careers generally correlate to high wages. (Source: U.S. Bureau of Labor Statistics )
• Math skills are transferable and can be applied across different academic disciplines. (Source: Sydney School of Education and Social Work )

How to Know What Math You Need to Learn

Often students will find gaps in their math knowledge; this can occur at any age or skill level. As math learning is generally iterative, a solid foundation and understanding of the math skills that preceded current learning are key to success. The solution to these gaps is called mastery learning, the philosophy that underpins Khan Academy’s approach to education .

Mastery learning is an educational philosophy that emphasizes the importance of a student fully understanding a concept before moving on to the next one. Rather than rushing students through a curriculum, mastery learning asks educators to ensure that learners have “mastered” a topic or skill, showing a high level of proficiency and understanding, before progressing. This approach is rooted in the belief that all students can learn given the appropriate learning conditions and enough time, making it a markedly student-centered method. It promotes thoroughness over speed and encourages individualized learning paths, thus catering to the unique learning needs of each student.

Students will encounter mastery learning passively as they go through Khan Academy coursework, as our platform identifies gaps and systematically adjusts to support student learning outcomes. More details can be found in our Educators Hub . 

Try Our Free Confidence Boosters

How to learn math.

Learning at School

One of the most common methods of math instruction is classroom learning. In-class instruction provides students with real-time feedback, practical application, and a peer-learning environment. Teachers can personalize instruction by assessing students’ strengths and weaknesses, providing remediation when necessary, and offering advanced instruction to students who need it.

Learning at Home

Supplemental learning at home can complement traditional classroom instruction. For example, using online resources that provide additional practice opportunities, interactive games, and demonstrations, can help students consolidate learning outside of class. E-learning has become increasingly popular, with a wealth of online resources available to learners of all ages. The benefits of online learning include flexibility, customization, and the ability to work at one’s own pace. One excellent online learning platform is Khan Academy, which offers free video tutorials, interactive practice exercises, and a wealth of resources across a range of mathematical topics.

Moreover, parents can encourage and monitor progress, answer questions, and demonstrate practical applications of math in everyday life. For example, when at the grocery store, parents can ask their children to help calculate the price per ounce of two items to discover which one is the better deal. Cooking and baking with your children also provides a lot of opportunities to use math skills, like dividing a recipe in half or doubling the ingredients. 

Learning Math with the Help of Artificial Intelligence (AI) 

AI-powered tools are changing the way students learn math. Personalized feedback and adaptive practice help target individual needs. Virtual tutors offer real-time help with math concepts while AI algorithms identify areas for improvement. Custom math problems provide tailored practice, and natural language processing allows for instant question-and-answer sessions. 

Using Khan Academy’s AI Tutor, Khanmigo

Transform your child’s grasp of mathematics with Khanmigo , the 24/7 AI-powered tutor that specializes in tailored, one-on-one math instruction. Available at any time, Khanmigo provides personalized support that goes beyond mere answers to nurture genuine mathematical understanding and critical thinking. Khanmigo can track progress, identify strengths and weaknesses, and offer real-time feedback to help students stay on the right track. Within a secure and ethical AI framework, your child can tackle everything from basic arithmetic to complex calculus, all while you maintain oversight using robust parental controls.

Get Math Help with Khanmigo Right Now

You can learn anything .

Math learning is essential for success in the modern world, and with the right approach, it can also be enjoyable and rewarding. Learning math requires curiosity, diligence, and the ability to connect abstract concepts with real-world applications. Strategies for effective math learning include a multifaceted approach, including classroom instruction, online courses, homework, tutoring, and personalized AI support. 

So, don’t let math anxiety hold you back; take advantage of available resources and technology to enhance your knowledge base and enjoy the benefits of math learning.

National Council of Teachers of Mathematics, “Principles to Actions: Ensuring Mathematical Success for All” , April 2014

Project Lead The Way Research Report, “The Power of Transportable Skills: Assessing the Demand and Value of the Skills of the Future” , 2020

Page. M, “Why Develop Quantitative and Qualitative Data Analysis Skills?” , 2016

Mann. EL, Creativity: The Essence of Mathematics, Journal for the Education of the Gifted. Vol. 30, No. 2, 2006, pp. 236–260, http://www.prufrock.com ’

Nakakoji Y, Wilson R.” Interdisciplinary Learning in Mathematics and Science: Transfer of Learning for 21st Century Problem Solving at University ”. J Intell. 2020 Sep 1;8(3):32. doi: 10.3390/jintelligence8030032. PMID: 32882908; PMCID: PMC7555771.

Get Khanmigo

The best way to learn and teach with AI is here. Ace the school year with our AI-powered guide, Khanmigo. 

For learners     For teachers     For parents

You are using an outdated browser. Please upgrade your browser to improve your experience.

Math Problem Solving Strategies That Make Students Say “I Get It!”

Even students who are quick with math facts can get stuck when it comes to problem solving.

As soon as a concept is translated to a word problem, or a simple mathematical sentence contains an unknown, they’re stumped.

That’s because problem solving requires us to  consciously choose the strategies most appropriate for the problem   at hand . And not all students have this metacognitive ability.

But you can teach these strategies for problem solving.  You just need to know what they are.

We’ve compiled them here divided into four categories:

Strategies for understanding a problem

Strategies for solving the problem, strategies for working out, strategies for checking the solution.

Get to know these strategies and then model them explicitly to your students. Next time they dive into a rich problem, they’ll be filling up their working out paper faster than ever!

Before students can solve a problem, they need to know what it’s asking them. This is often the first hurdle with word problems that don’t specify a particular mathematical operation.

Encourage your students to:

Read and reread the question

They say they’ve read it, but have they  really ? Sometimes students will skip ahead as soon as they’ve noticed one familiar piece of information or give up trying to understand it if the problem doesn’t make sense at first glance.

Teach students to interpret a question by using self-monitoring strategies such as:

• Rereading a question more slowly if it doesn’t make sense the first time
• Asking for help
• Highlighting or underlining important pieces of information.

Identify important and extraneous information

John is collecting money for his friend Ari’s birthday. He starts with $5 of his own, then Marcus gives him another $5. How much does he have now?

As adults looking at the above problem, we can instantly look past the names and the birthday scenario to see a simple addition problem. Students, however, can struggle to determine what’s relevant in the information that’s been given to them.

Teach students to sort and sift the information in a problem to find what’s relevant. A good way to do this is to have them swap out pieces of information to see if the solution changes. If changing names, items or scenarios has no impact on the end result, they’ll realize that it doesn’t need to be a point of focus while solving the problem.

Schema approach

This is a math intervention strategy that can make problem solving easier for all students, regardless of ability.

Compare different word problems of the same type and construct a formula, or mathematical sentence stem, that applies to them all. For example, a simple subtraction problems could be expressed as:

[Number/Quantity A] with [Number/Quantity B] removed becomes [end result].

This is the underlying procedure or  schema  students are being asked to use. Once they have a list of schema for different mathematical operations (addition, multiplication and so on), they can take turns to apply them to an unfamiliar word problem and see which one fits.

Struggling students often believe math is something you either do automatically or don’t do at all. But that’s not true. Help your students understand that they have a choice of problem-solving strategies to use, and if one doesn’t work, they can try another.

Here are four common strategies students can use for problem solving.

Visualizing

Visualizing an abstract problem often makes it easier to solve. Students could draw a picture or simply draw tally marks on a piece of working out paper.

Encourage visualization by modeling it on the whiteboard and providing graphic organizers that have space for students to draw before they write down the final number.

Guess and check

Show students how to make an educated guess and then plug this answer back into the original problem. If it doesn’t work, they can adjust their initial guess higher or lower accordingly.

Find a pattern

To find patterns, show students how to extract and list all the relevant facts in a problem so they can be easily compared. If they find a pattern, they’ll be able to locate the missing piece of information.

Work backward

Working backward is useful if students are tasked with finding an unknown number in a problem or mathematical sentence. For example, if the problem is 8 + x = 12, students can find x by:

• Starting with 12
• Taking the 8 from the 12
• Being left with 4
• Checking that 4 works when used instead of x

Now students have understood the problem and formulated a strategy, it’s time to put it into practice. But if they just launch in and do it, they might make it harder for themselves. Show them how to work through a problem effectively by:

Documenting working out

Model the process of writing down every step you take to complete a math problem and provide working out paper when students are solving a problem. This will allow students to keep track of their thoughts and pick up errors before they reach a final solution.

Check along the way

Checking work as you go is another crucial self-monitoring strategy for math learners. Model it to them with think aloud questions such as:

• Does that last step look right?
• Does this follow on from the step I took before?
• Have I done any ‘smaller’ sums within the bigger problem that need checking?

Students often make the mistake of thinking that speed is everything in math — so they’ll rush to get an answer down and move on without checking.

But checking is important too. It allows them to pinpoint areas of difficulty as they come up, and it enables them to tackle more complex problems that require multiple checks  before  arriving at a final answer.

Here are some checking strategies you can promote:

Check with a partner

Comparing answers with a peer leads is a more reflective process than just receiving a tick from the teacher. If students have two different answers, encourage them to talk about how they arrived at them and compare working out methods. They’ll figure out exactly where they went wrong, and what they got right.

Reread the problem with your solution

Most of the time, students will be able to tell whether or not their answer is correct by putting it back into the initial problem. If it doesn’t work or it just ‘looks wrong’, it’s time to go back and fix it up.

Fixing mistakes

Show students how to backtrack through their working out to find the exact point where they made a mistake. Emphasize that they can’t do this if they haven’t written down everything in the first place — so a single answer with no working out isn’t as impressive as they might think!

Need more help developing problem solving skills?

Read up on  how to set a problem solving and reasoning activity  or explore Mathseeds and Mathletics, our award winning online math programs. They’ve got over 900 teacher tested problem solving activities between them!

Get access to 900+ unique problem solving activities

You might like....

• Top Questions

Convert the following readings of pressureto kPa absolute, assuming that the barometer reads 760mm Hg:...

Show that an element and its inverse have the same order in any group.

A cubic block of wood, 10.0 cm on each side, floats at the interface between...

An ice cube tray of negligible mass contains 0.315 kg of water at17.7∘. How much...

An open tank has a vertical partition and on one side contains gasoline with a...

A 100g cube of ice at 0C is dropped into 1.0kg of water thatwas originally...

Complete the equation of the line through (2, 1) and (5, -8). Use exact numbers.

Write a function based on the given parent function and transformations in the given order....

How many solutions does the equationx1+x2+x3=13have wherex1,x2,andx3are non negative integers less than 6.

Determine whether f : Z×Z→Z is onto if a) f(m,n)=2m−nb) b) f(m,n)=m2−n2 c) f(m,n)=m+n+1 d)...

The base of S is an elliptical region with boundary curve 9x2+4y2=36. Cross-sections perpendicular to...

Create a graph of y=2x−6. Construct a graph corresponding to the linear equation y=2x−6.

Use the graphs of f and g to graph h(x) = (f + g)(x). (Graph...

find expressions for the quadratic functions whose graphs are shown. f(x)=? g(x)=?

Find the volume V of the described solid S. A cap of a sphere with...

Find a counterexample to show that each statement is false. The sum of any three...

Read the numbers and decide what the next number should be. 5 15 6 18...

In how many different orders can five runners finish a race if no ties are...

A farmer plants corn and wheat on a 180 acre farm. He wants to plant...

Find the distance between (0, 0) and (-3, 4) pair of points. If needed, show...

Whether each of these functions is a bijection from R to R.a)f(x)=−3x+4b)f(x)=−3x2+7c)f(x)=x+1x+2d)f(x)=x5+1

Find two numbers whose difference is 100 and whose product is a minimum.

Find an expression for the function whose graph is the given curve. The line segment...

Prove or disprove that if a and b are rational numbers, then ab is also...

How to find a rational number halfway between any two rational numbers given infraction form...

Fill in the blank with a number to make the expression a perfect square x2−6x+?

Look at this table: x y 1–2 2–4 3–8 4–16 5–32 Write a linear (y=mx+b),...

Part a: Assume that the height of your cylinder is 8 inches. Think of A...

The graph of a function f is shown. Which graph is an antiderivative of f?

A rectangle has area 16m2 . Express the perimeter of the rectangle as a function...

Find the equation of the quadratic function f whose graph is shown below. (5, −2)

Use the discriminant, b2−4ac, to determine the number of solutions of the following quadratic equation....

How many solutions does the equation ||2x-3|-m|=m have if m>0?

If a system of linear equations has infinitely many solutions, then the system is called...

A bacteria population is growing exponentially with a growth factor of 16 each hour.By what...

A system of linear equations with more equations than unknowns is sometimes called an overdetermined...

Express the distance between the numbers 2 and 17 using absolute value. Then find the...

Find the Laplace transform of f(t)=(sin⁡t–cos⁡t)2

Express the interval in terms of an inequality involving absolute value. (0,4)

A function is a ratio of quadratic functions and has a vertical asymptote x =4...

how do you graph y > -2

Find the weighted average of a data set where 10 has a weight of 5,...

The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume...

The population of a region is growing exponentially. There were 10 million people in 1980...

Two cables BG and BH are attached to the frame ACD as shown.Knowing that the...

A bird flies in the xy-plane with a position vector given by r→=(αt−βt3)i^+γt2j^, with α=2.4...

A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing...

Solve the following linear congruence, 25x≡15(bmod29)

For the equation, a. Write the value or values of the variable that make a...

Which of the following statements is/are correct about logistic regression? (There may be more than...

Compute 4.659×104−2.14×104. Round the answer appropriately. Express your answer as an integer using the proper...

Find the 52nd term of the arithmetic sequence -24,-7, 10

Find the 97th term of the arithmetic sequence 17, 26, 35,

An equation that expresses a relationship between two or more variables, such as H=910(220−a), is...

The football field is rectangular. a. Write a polynomial that represents the area of the...

The equation 1.5r+15=2.25r represents the number r of movies you must rent to spend the...

While standing on a ladder, you drop a paintbrush. The function represents the height y...

When does data modeling use the idea of a weak entity? Give definitions for the...

Write an equation of the line passing through (-2, 5) and parallel to the line...

Find a polar equation for the curve represented by the given Cartesian equation. y =...

Find c such that fave=f(c)

List five integers that are congruent to 4 modulo 12.

A rectangular package to be sent by a postal service can have a maximum combined...

A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s....

The One-to-One Property of natural logarithms states that if ln x = ln y, then...

Find an equation of a parabola that has curvature 4 at the origin.

Find a parametric representation of the solution set of the linear equation. 3x − 1/2y...

Find the product of the complex number and its conjugate. 2-3i

Find the prime factorization of 10!.

Find a polynomial f(x) of degree 5 that has the following zeros. -3, -7, 5...

True or False. The domain of every rational function is the set of all real...

What would be the most efficient step to suggest to a student attempting to complete...

Write a polynomial, P(x), in factored form given the following requirements. Degree: 4 Leading coefficient...

Give a geometric description of the set of points in space whose coordinates satisfy the...

Use the Cauchy-Riemann equations to show that f(z)=z― is not analytic.

Find the local maximum and minimum values and saddle points of the function. If you...

a) Evaluate the polynomial y=x3−7x2+8x−0.35 at x=1.37 . Use 3-digit arithmetic with chopping. Evaluate the...

The limit represents f'(c) for a function f and a number c. Find f and...

A man 6 feet tall walks at a rate of 5 feet per second away...

Find the Maclaurin series for the function f(x)=cos⁡4x. Use the table of power series for...

Suppose that a population develops according to the logistic equation dPdt=0.05P−0.0005P2 where t is measured...

Find transient terms in this general solution to a differential equation, if there are any...

Find the lengths of the sides of the triangle PQR. Is it a right triangle?...

Use vectors to decide whether the triangle with vertices P(1, -3, -2), Q(2, 0, -4),...

Find a path that traces the circle in the plane y=5 with radius r=2 and...

a. Find an upper bound for the remainder in terms of n.b. Find how many...

Find two unit vectors orthogonal to both j−k and i+j.

Obtain the Differential equations: parabolas with vertex and focus on the x-axis.

The amount of time, in minutes, for an airplane to obtain clearance for take off...

Use the row of numbers shown below to generate 12 random numbers between 01 and...

Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!)...

A random sample of 1200 U.S. college students was asked, "What is your perception of...

The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (The same sample data...

How many different 10 letter words (real or imaginary) can be formed from the following...

Assume that σ is unknown, the lower 100(1−α)% confidence bound on μ is: a) μ≤x―+tα,n−1sn...

A simple random sample of 60 items resulted in a sample mean of 80. The...

Decresing the sample size, while holding the confidence level and the variance the same, will...

A privately owned liquor store operates both a drive-n facility and a walk-in facility. On...

Show that the equation represents a sphere, and find its center and radius. x2+y2+z2+8x−6y+2z+17=0

Describe in words the region of R3 represented by the equation(s) or inequality. x=5

Suppose that the height, in inches, of a 25-year-old man is a normal random variable...

Find the value and interest earned if $8906.54 is invested for 9 years at %...

Which of the following statements about the sampling distribution of the sample mean is incorrect?...

The random variable x stands for the number of girls in a family of four...

The product of the ages, in years, of three (3) teenagers os 4590. None of...

A simple random sample size of 100 is selected from a population with p=0.40 What...

Which of the following statistics are unbiased estimators of population parameters? Choose the correct answer...

The probability distribution of the random variable X represents the number of hits a baseball...

Let X be a random variable with probability density function.f(x)={c(1−x2)−1<x<10otherwise(a) What is the value of...

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do...

The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is...

Given that z is a standard normal random variable, compute the following probabilities.a.P(z≤−1.0)b.P(z≥−1)c.P(z≥−1.5)d.P(−2.5≤z)e.P(−3<z≤0)

Given a standard normal distribution, find the area under the curve that lies(a) to the...

Chi-square tests are best used for which type of dependent variable? nominal, ordinal ordinal interval...

True or False 1.The goal of descriptive statistics is to simplify, summarize, and organize data....

What is the difference between probability distribution and sampling distribution?

A weather forecaster predicts that the temperature in Antarctica will decrease 8∘F each hour for...

The tallest person who ever lived was approximately 8 feet 11 inches tall. a) Write...

An in-ground pond has the shape of a rectangular prism. The pond has a depth...

The average zinc concentration recovered from a sample of measurements taken in 36 different locations...

Why is it important that a sample be random and representative when conducting hypothesis testing?...

Which of the following is true about the sampling distribution of means? A. Shape of...

Give an example of a commutative ring without zero-divisors that is not an integral domain.

List all zero-divisors in Z20. Can you see relationship between the zero-divisors of Z20 and...

Find the integer a such that a≡−15(mod27) and −26≤a≤0

Explain why the function is discontinuous at the given number a. Sketch the graph of...

Two runners start a race at the same time and finish in a tie. Prove...

Which of the following graphs represent functions that have inverse functions?

find the Laplace transform of f (t). f(t)=tsin⁡3t

Find Laplace transforms of sin⁡h3t cos22t

find the Laplace transform of f (t). f(t)=t2cos⁡2t

The Laplace transform of the product of two functions is the product of the Laplace...

The Laplace transform of u(t−2) is (a) 1s+2 (b) 1s−2 (c) e2ss(d)e−2ss

Find the Laplace Transform of the function f(t)=eat

Explain First Shift Theorem & its properties?

Solve f(t)=etcos⁡t

Find Laplace transform of the given function te−4tsin⁡3t

Reduce to first order and solve:x2y″−5xy′+9y=0 y1=x3

(D3−14D+8)y=0

A thermometer is taken from an inside room to the outside ,where the air temperature...

Find that solution of y′=2(2x−y) which passes through the point (0, 1).

Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg...

Let A, B, and C be sets. Show that (A−B)−C=(A−C)−(B−C)

Suppose that A is the set of sophomores at your school and B is the...

In how many ways can a 10-question true-false exam be answered? (Assume that no questions...

Is 2∈{2}?

How many elements are in the set { 2,2,2,2 } ?

How many elements are in the set { 0, { { 0 } }?

Draw the Hasse diagram representing the partial ordering {(a, b) | a divides b} on...

Flux through a Cube (Eigure 1) A cube has one corner at the origin and...

A well-insulated rigid tank contains 3 kg of saturated liquid-vapor mixture of water at 200...

A water pump that consumes 2 kW of electric power when operating is claimed to...

A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius...

In a truck-loading station at a post office, a small 0.200-kg package is released from...

The magnetic fieldB→in acertain region is 0.128 ,and its direction is that of the z-axis...

A marble moves along the x-axis. The potential-energy functionis shown in Fig. 1a) At which...

A proton is released in a uniform electric field, and it experiences an electric force...

A potters wheel having a radius of 0.50 m and a moment of inertia of12kg⋅m2is...

Two spherical objects are separated by a distance of 1.80×10−3m. The objects are initially electrically...

An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h....

Resolve the force F2 into components acting along the u and v axes and determine...

A conducting sphere of radius 0.01m has a charge of1.0×10−9Cdeposited on it. The magnitude of...

Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a...

In the figure a worker lifts a weightωby pulling down on a rope with a...

A stream of water strikes a stationary turbine bladehorizontally, as the drawing illustrates. The incident...

Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height...

A radar station, located at the origin of xz plane, as shown in the figure...

Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as...

You are on the roof of the physics building, 46.0 m above the ground. Your...

A block is on a frictionless table, on earth. The block accelerates at5.3ms2when a 10...

A 0.450 kg ice puck, moving east with a speed of3.00mshas a head in collision...

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three...

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope...

A ski tow operates on a 15.0 degrees slope of lenth 300m. The rope moves...

Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide...

From her bedroom window a girl drops a water-filled balloon to the ground 6.0 m...

A 730-N man stands in the middle of a frozen pond of radius 5.0 m....

A 5.00 kg package slides 1.50 m down a long ramp that is inclined at12.0∘below...

Ropes 3m and 5m in length are fastened to a holiday decoration that is suspended...

A skier of mass 70 kg is pulled up a slope by a motor driven...

A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid,...

A sled with rider having a combined mass of 120 kg travels over the perfectly...

A 7.00- kg bowling ball moves at 3.00 m/s. How fast must a 2.45- g...

Two point chargesq1=+2.40nC andq2=−6.50nC are 0.100 m apart. Point A is midway between them and...

A block of mass m slides on a horizontal frictionless table with an initial speed...

A space traveler weights 540 N on earth. what will the traveler weigh on another...

A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60...

A weatherman carried an aneroid barometer from the groundfloor to his office atop a tower....

If a negative charge is initially at rest in an electric field, will it move...

A coin with a diameter of 2.40cm is dropped on edge on to a horizontal...

An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction...

An 80.0-kg skydiver jumps out of a balloon at an altitude of1000 m and opens...

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive...

A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding...

A 500 g ball swings in a vertical circle at the end of a1.5-m-long string....

A rifle with a weight of 30 N fires a 5.0 g bullet with a...

The tires of a car make 65 revolutions as the car reduces its speed uniformly...

A 2.0- kg piece of wood slides on the surface. The curved sides are perfectly...

A 292 kg motorcycle is accelerating up along a ramp that is inclined 30.0° above...

A projectile is shot from the edge of a cliff 125 m above ground level...

A lunch tray is being held in one hand, as the drawing illustrates. The mass...

The initial velocity of a car, vi, is 45 km/h in the positivex direction. The...

An Alaskan rescue plane drops a package of emergency rations to a stranded party of...

Raindrops make an angle theta with the vertical when viewed through a moving train window....

A 0.50 kg ball that is tied to the end of a 1.1 m light...

If the coefficient of static friction between your coffeecup and the horizontal dashboard of your...

A car is initially going 50 ft/sec brakes at a constant rate (constant negative acceleration),...

A swimmer is capable of swimming 0.45m/s in still water (a) If sheaim her body...

A block is hung by a string from inside the roof of avan. When the...

A race driver has made a pit stop to refuel. Afterrefueling, he leaves the pit...

A relief airplane is delivering a food package to a group of people stranded on...

The eye of a hurricane passes over Grand Bahama Island. It is moving in a...

An extreme skier, starting from rest, coasts down a mountainthat makes an angle25.0∘with the horizontal....

Four point charges form a square with sides of length d, as shown in the...

In a scene in an action movie, a stuntman jumps from the top of one...

The spring in the figure (a) is compressed by length delta x . It launches...

An airplane propeller is 2.08 m in length (from tip to tip) and has a...

A helicopter carrying dr. evil takes off with a constant upward acceleration of5.0ms2. Secret agent...

A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force...

A box is sliding with a speed of 4.50 m/s on a horizontal surface when,...

3.19 Win the Prize. In a carnival booth, you can win a stuffed giraffe if...

A car is stopped at a traffic light. It then travels along a straight road...

a. When the displacement of a mass on a spring is12A, what fraction of the...

At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy...

A jet plane lands with a speed of 100 m/s and can accelerate at a...

In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints...

An antelope moving with constant acceleration covers the distance between two points 70.0 m apart...

A bicycle with 0.80-m-diameter tires is coasting on a level road at 5.6 m/s. A...

The rope and pulley have negligible mass, and the pulley is frictionless. The coefficient of...

A proton with an initial speed of 800,000 m/s is brought to rest by an...

The volume of a cube is increasing at the rate of 1200 cm supmin at...

An airplane starting from airport A flies 300 km east, then 350 km at 30...

To prove: In the following figure, triangles ABC and ADC are congruent. Given: Figure is...

Conduct a formal proof to prove that the diagonals of an isosceles trapezoid are congruent....

The distance between the centers of two circles C1 and C2 is equal to 10...

Segment BC is Tangent to Circle A at Point B. What is the length of...

Find an equation for the surface obtained by rotating the parabola y=x2 about the y-axis.

Find the area of the parallelogram with vertices A(-3, 0), B(-1 , 3), C(5, 2),...

If the atomic radius of lead is 0.175 nm, find the volume of its unit...

At one point in a pipeline the water’s speed is 3.00 m/s and the gauge...

Find the volume of the solid in the first octant bounded by the coordinate planes,...

A paper cup has the shape of a cone with height 10 cm and radius...

A light wave has a 670 nm wavelength in air. Its wavelength in a transparent...

An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50...

Find the equation of the sphere centered at (-9, 3, 9) with radius 5. Give...

Determine whether the congruence is true or false. 5≡8 mod 3

Find all whole number solutions of the congruence equation. (2x+1)≡5 mod 4

Determine whether the congruence is true or false. 100≡20 mod 8

I want example of an undefined term and a defined term in geometry and explaining...

Two fair dice are rolled. Let X equal the product of the 2dice. Compute P{X=i}...

Suppose that two defective refrigerators have been included in a shipment of six refrigerators. The...

Based on the Normal model N(100, 16) describing IQ scores, what percent of peoples

The probability density function of the net weight in pounds of a packaged chemical herbicide...

Let X represent the difference between the number of heads and the number of tails...

An urn contains 3 red and 7 black balls. Players A and B withdraw balls...

80% A poll is given, showing are in favor of a new building project. 8...

The probability that the San Jose Sharks will win any given game is 0.3694 based...

Find the value of P(X=7) if X is a binomial random variable with n=8 and...

Find the value of P(X=8) if X is a binomial random variable with n=12 and...

On a 8 question multiple-choice test, where each question has 2 answers, what would be...

If you toss a fair coin 11 times, what is the probability of getting all...

A coffee connoisseur claims that he can distinguish between a cup of instant coffee and...

Two firms V and W consider bidding on a road-building job, which may or may...

Two cards are drawn without replacement from an ordinary deck, find the probability that the...

In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the...

A local bank reviewed its credit card policy with the intention of recalling some of...

The accompanying table gives information on the type of coffee selected by someone purchasing a...

A batch of 500 containers for frozen orange juice contains 5 that are defective. Two...

The probability that an automobile being filled with gasoline also needs an oil change is...

Let the random variable X follow a normal distribution with μ=80 and σ2=100. a. Find...

A card is drawn randomly from a standard 52-card deck. Find the probability of the...

The next number in the series 38, 36, 30, 28, 22 is ?

What is the coefficient of x8y9 in the expansion of (3x+2y)17?

A boat on the ocean is 4 mi from the nearest point on a straight...

How many different ways can you make change for a quarter? (Different arrangements of the...

Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and...

Approximately 80,000 marriages took place in the state of New York last year. Estimate the...

The probability that a student passes the Probability and Statistics exam is 0.7. (i)Find the...

Customers at a gas station pay with a credit card (A), debit card (B), or...

It is conjectured that an impurity exists in 30% of all drinking wells in a...

Assume that the duration of human pregnancies can be described by a Normal model with...

According to a renowned expert, heavy smokers make up 70% of lung cancer patients. If...

Two cards are drawn successively and without replacement from an ordinary deck of playing cards...

Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L),...

A bag contains 6 red, 4 blue and 8 green marbles. How many marbles of...

A normal distribution has a mean of 50 and a standard deviation of 4. Please...

Seven women and nine men are on the faculty in the mathematics department at a...

An automatic machine in a manufacturing process is operating properly if the lengths of an...

Three cards are drawn without replacement from the 12 face cards (jacks, queens, and kings)...

Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a...

A TIRE MANUFACTURER WANTS TO DETERMINE THE INNER DIAMETER OF A CERTAIN GRADE OF TIRE....

Differentiate the three measures of central tendency: ungrouped data.

Find the mean of the following data: 12,10,15,10,16,12,10,15,15,13

A wallet containing four P100 bills, two P200 bills, three P500 bills, and one P1,000...

The number of hours per week that the television is turned on is determined for...

Data was collected for 259 randomly selected 10 minute intervals. For each ten-minute interval, the...

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in...

A normal distribution has a mean of 80 and a standard deviation of 14. Determine...

True or false: a. All normal distributions are symmetrical b. All normal distributions have a...

Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or...

Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8408 1374 1872 8879...

The velocity function (in meters per second) is given for a particle moving along a...

Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4),...

The integral represents the volume of a solid. Describe the solid. π∫01(y4−y8)dy a) The integral...

Two components of a minicomputer have the following joint pdf for their useful lifetimes X...

Use the table of values of f(x,y) to estimate the values of fx(3,2), fx(3,2.2), and...

Calculate net price factor and net price. Dollars list price −435.20$ Trade discount rate −26%,15%,5%.

Represent the line segment from P to Q by a vector-valued function and by a...

(x2+2xy−4y2)dx−(x2−8xy−4y2)dy=0

If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3...

Find the parametric equation of the line through a parallel to ba=[3−4],b=[−78]

Find the velocity and position vectors of a particle that has the given acceleration and...

If we know that the f is continuous and integral 0 to 4f(x)dx=10, compute the...

Integration of (y⋅tan⁡xy)

For the matrix A below, find a nonzero vector in the null space of A...

Find a nonzero vector orthogonal to the plane through the points P, Q, and R....

Suppose that the augmented matrix for a system of linear equations has been reduced by...

Find two unit vectors orthogonal to both (3 , 2, 1) and (- 1, 1,...

What is the area of the parallelogram whose vertices are listed? (0,0), (5,2), (6,4), (11,6)

Using T defined by T(x)=Ax, find a vector x whose image under T is b,...

Use the definition of Ax to write the matrix equation as a vector equation, or...

We need to find the volume of the parallelepiped with only one vertex at the...

List five vectors in Span {v1,v2}. For each vector, show the weights on v1 and...

(1) find the projection of u onto v and (2) find the vector component of...

Find the area of the parallelogram determined by the given vectors u and v. u...

(a) Find the point at which the given lines intersect. r = 2,...

(a) find the transition matrix from B toB′,(b) find the transition matrix fromB′to B,(c) verify...

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If...

Given the following vector X, find anon zero square marix A such that AX=0; You...

Construct a matrix whose column space contains (1, 1, 5) and (0, 3.1) and whose...

At what point on the paraboloid y=x2+z2 is the tangent plane parallel to the plane...

Label the following statements as being true or false. (a) If V is a vector...

Find the Euclidean distance between u and v and the cosine of the angle between...

Write an equation of the line that passes through (3, 1) and (0, 10)

There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in...

State and prove the linearity property of the Laplace transform by using the definition of...

The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that...

The Munchies Cereal Company combines a number of components to create a cereal. Oats and...

Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If...

If sin⁡x+sin⁡y=aandcos⁡x+cos⁡y=b then find tan⁡(x−y2)

Find the values of x such that the angle between the vectors (2, 1, -1),...

Find the dimensions of the isosceles triangle of largest area that can be inscribed in...

Suppose that you are headed toward a plateau 50 meters high. If the angle of...

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport....

Find an equation of the plane. The plane through the points (2, 1, 2), (3,...

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following...

two small spheres spaced 20.0cm apart have equal charges. How many extra electrons must be...

The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ft2)...

Find out these functions' domain and range. To find the domain in each scenario, identify...

Your bank account pays an interest rate of 8 percent. You are considering buying a...

Whether f is a function from Z to R ifa)f(n)=±n.b)f(n)=n2+1.c)f(n)=1n2−4.

The probability density function of X, the lifetime of a certain type of electronic device...

A sandbag is released by a balloon that is rising vertically at a speed of...

A proton is located in a uniform electric field of2.75×103NCFind:a) the magnitude of the electric...

A rectangular plot of farmland are finite on one facet by a watercourse and on...

A solenoid is designed to produce a magnetic field of 0.0270 T at its center....

I want to find the volume of the solid enclosed by the paraboloidz=2+x2+(y−2)2and the planesz=1,x=−1y=0,andy=4

Let W be the subspace spanned by the u’s, and write y as the sum...

Can u find the point on the planex+2y+3z=13that is closest to the point (1,1,1). You...

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force...

A force of 250 Newtons is applied to a hydraulic jack piston that is 0.01...

Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface...

A credit card contains 16 digits between 0 and 9. However, only 100 million numbers...

Every real number is also a complex number? True of false?

Let F be a fixed 3x2 matrix, and let H be the set of all...

Find a vector a with representation given by the directed line segment AB. Draw AB...

Find A such that the given set is Col A. {[2s+3tr+s−2t4r+s3r−s−t]:r,s,t real}

Find the vector that has the same direction as (6, 2, -3) but is four...

For the matrices (a) find k such that Nul A is a subspace of Rk,...

How many subsets with an odd number of elements does a set with 10 elements...

In how many ways can a set of five letters be selected from the English...

Suppose that f(x) = x/8 for 3 < x < 5. Determine the following probabilities:...

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to...

Find two vectors parallel to v of the given length. v=PQ→ with P(1,7,1) and Q(0,2,5);...

A dog in an open field runs 12.0 m east and then 28.0 m in...

Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning.

Use the Intermediate Value Theorem to show that there is a root of the given...

In a fuel economy study, each of 3 race cars is tested using 5 different...

A company has 34 salespeople. A board member at the company asks for a list...

A dresser drawer contains one pair of socks with each of the following colors: blue,...

A restaurant offers a $12 dinner special with seven appetizer options, 12 choices for an...

A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17...

Suppose E(X)=5 and E[X(X–1)]=27.5, find ∈(x2) and the variance.

A Major League baseball diamond has four bases forming a square whose sides measure 90...

Express f(x)=4x3+6x2+7x+2 in term of Legendre Polynomials.

Find a basis for the space of 2×2 diagonal matrices. Basis ={[],[]}

Which of the following expressions are meaningful? Which are meaningless? Explain. a) (a⋅b)⋅c (a⋅b)⋅c has...

Vectors V1 and V2 are different vectors with lengths V1 and V2 respectively. Find the...

Find an equation for the plane containing the two (parallel) lines v1=(0,1,−2)+t(2,3,−1) and v2=(2,−1,0)+t(2,3,−1).

Find, correct to the nearest degree, the three angles of the triangle with the given...

Find the vector, not with determinants, but by using properties of cross products. (i+j)×(i−j)

Find the curve’s unit tangent vector. Also, find the length of the indicated portion of...

Construct a 4×3 matrix with rank 1

Find x such that the matrix is equal to its inverse.A=[7x−8−7]

Find a polynomial with integer coefficients that satisfies the given conditions. Q has degree 3...

Write in words how to read each of the following out loud.a.{x∈R′∣0<x<1}b.{x∈R∣x≤0orx⇒1}c.{n∈Z∣nisafactorof6}d.{n∈Z⋅∣nisafactorof6}

Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets...

Find the average value of F(x, y, z) over the given region. F(x,y,z)=x2+9 over the...

Find the trace of the plane in the given coordinate plane. 3x−9y+4z=5,yz

Determine the level of measurement of the variable. Favorite color Choose the correct level of...

How wide is the chasm between what men and women earn in the workplace? According...

Write an algebraic expression for: 6 more than a number c.

Please, can u convert 3.16 (6 repeating) to a fraction.

Evaluate the expression. P(8, 3)

In a poker hand consisting of 5 cards, find the probability of holding 3 aces.

Give an expression that generates all angles coterminal with each angle. Let n represent any...

An ideal Otto cycle has a compression ratio of 10.5, takes in air at 90...

A piece of wire 10 m long is cut into two pieces. One piece is...

Put the following equation of a line into slope intercept form, simplifying all fractions 3x+3y=24

Find the point on the hyperbola xy = 8 that is closest to the point...

Water is pumped from a lower reservoir to a higher reservoir by a pump that...

A piston–cylinder device initially contains 0.07m3 of nitrogen gas at 130 kPa and 180∘. The...

Write an algebraic expression for each word phrase. 4 more than p

A club has 25 members. a) How many ways are there to choose four members...

For each of the sets below, determine whether {2} is an element of that set....

Which expression has both 8 and n as factors?

If repetitions are not permitted (a) how many 3 digit number can be formed from...

To determine the sum of all multiples of 3 between 1 and 1000

On average, there are 3 accidents per month at one intersection. We need to find...

One number is 2 more than 3 times another. Their sum is 22. Find the...

The PMF for a flash drive with X (GB) of memory that was purchased is...

An airplane needs to reach a velocity of 203.0 km/h to takeoff. On a 2000...

A racquetball strikes a wall with a speed of 30 m/s and rebounds with a...

Assuming that the random variable x has a cumulative distribution function,F(x)={0,x<00.25x,0≤x<51,5≤xDetermine the following:a)p(x<2.8)b)p(x>1.5)c)p(x<−z)d)p(x>b)

At t = 0 a grinding wheel has an angular velocity of 24.0 rad/s. It...

How many 3/4's are in 1?

You’re driving down the highway late one night at 20 m/s when a deer steps...

Table salt contains 39.33 g of sodium per 100 g of salt. The U.S. Food...

The constant-pressure heat capacity of a sample of a perfect gas was found to vary...

Coffee is draining from a conical filter into a cylindrical coffepot at the rate of...

Cart is driven by a large propeller or fan, which can accelerate or decelerate the...

A vending machine dispenses coffee into an eight-ounce cup. The amounts of coffee dispensed into...

On an essentially frictionless, horizontal ice rink, a skater moving at 3.0 m/s encounters a...

The gage pressure in a liquid at a depth of 3 m is read to...

Consider a cylindrical specimen of a steel alloy 8.5 mm (0.33 in.) in diameter and...

Calculate the total kinetic energy, in Btu, of an object with a mass of 10...

A 0.500-kg mass on a spring has velocity as a function of time given by...

An Australian emu is running due north in a straight line at a speed of...

Another pitfall cited is expecting to improve the overall performance of a computer by improving...

You throw a glob of putty straight up toward the ceiling, which is 3.60 m...

A 0.150-kg frame, when suspended from a coil spring, stretches the spring 0.070 m. A...

A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips....

A rock climber stands on top of a 50-m-high cliff overhanging a pool of water....

A tank whose bottom is a mirror is filled with water to a depth of...

Two sites are being considered for wind power generation. In the first site, the wind...

0.250 kilogram of water at75.0∘Care contained in a tiny, inert beaker. How much ice, at...

Two boats start together and race across a 60-km-wide lake and back. Boat A goes...

A roller coaster moves 200 ft horizontally and the rises 135 ft at an angle...

A tow truck drags a stalled car along a road. The chain makes an angle...

Consider the curve created by2x2+3y2–4xy=36(a) Show thatdydx=2y−2x3y−2x(b) Calculate the slope of the line perpendicular to...

The current entering the positive terminal of a device is i(t)=6e−2t mA and the voltage...

The fastest measured pitched baseball left the pitcher’s hand at a speed of 45.0 m/s....

Calculate the total potential energy, in Btu, of an object that is 20 ft below...

A chemist in an imaginary universe, where electrons have a different charge than they do...

When jumping, a flea reaches a takeoff speed of 1.0 m/s over a distance of...

Determine the energy required to accelerate a 1300-kg car from 10 to 60 km/h on...

The deepest point in the ocean is 11 km below sea level, deeper than MT....

A golfer imparts a speed of 30.3 m/s to a ball, and it travels the...

Calculate the frequency of each of the following wavelengths of electromagnetic radiation. A) 632.8 nm...

Prove that there is a positive integer that equals the sum of the positive integers...

A hurricane wind blows across a 6.00 m×15.0 m flat roof at a speed of...

If an electron and a proton are expelled at the same time,2.0×10−10mapart (a typical atomic...

The speed of sound in air at 20 C is 344 m/s. (a) What is...

Which of the following functions f has a removable discontinuity at a? If the discontinuity...

A uniform steel bar swings from a pivot at one end with a period of...

A wind farm generator uses a two-bladed propellermounted on a pylon at a height of...

A copper calorimeter can with mass 0.100 kg contains 0.160 kgof water and 0.018 kg...

Jones figures that the total number of thousands of miles that a used auto can...

Assign a binary code in some orderly manner to the 52 playingcards. Use the minimum...

A copper pot with mass 0.500 kg contains 0.170 kg of water ata temperature of...

Ea for a certain biological reaction is 50 kJ/mol, by what factor ( how many...

When a person stands on tiptoe (a strenuous position), the position of the foot is...

A solution was prepared by dissolving 1210 mg of K3Fe(CN)6 (329.2 g/mol) in sufficient waterto...

A 58-kg skier is going down a slope oriented 35 degree abovethe horizontal. The area...

The mechanics at lincoln automotive are reboring a 6-in deepcylinder to fit a new piston....

A 0.48 kg piece of wood floats in water but is found to sinkin alcohol...

A 50-g ice cube at 0oC is heated until 45-g hasbecome water at 100oC and...

A solution containing 6.23 ppm of KMnO4 had a transmittance of 0.195 in a 1.00-cm...

A black body at 7500K consists of an opening of diameter 0.0500mm, looking into an...

A new absolute temperature scale is proposed. On thisscale the ice point of water is...

A 65.0 mm focal length converging lens is 78.0 mm away from a sharp image....

A crate of fruit with mass 35.0 kg and specific heat capacity 3650 J/Kg ....

A freezer has a thermal efficiency of 2.40. Thefreezer is to convert 1.80 kg of...

A horizontal force of 210N is exerted on a 2.0 kg discus as it rotates...

Lead has a specific heat of 0.030 cal/gC. In an insulated container, 300 grams of...

A parachutist relies on air resistance mainly on her parachute to decrease her downward velocity....

The distance between a carbon atom (m=12 u) and an oxygen atom (m + 16...

A car heading north collides at an intersection with a truckheading east. If they lock...

Water stands at a depth H in a large, open tank whose sidewalls are vertical....

The heaviest invertebrate is the giant squid, which is estimated to have a weight of...

Which of the following is a correct comment? */ Comments */ ** Comment ** /*...

The concentrated sulfuric acid we use in the laboratory is 98% H2SO4 by mass. Calculate...

Consider the reaction N2(g)+3H2(g)→2NH3(g) suppose that a particular moment during the reaction molecular hydrogen on...

use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F...

• High School Questions
• College Questions
• Math Solver
• Top Questions 2
• Term of Service
• Payment Policy

Connect with us

Get Plainmath App

• Google Play

E-mail us: [email protected]

Our Service is useful for:

Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples.

2023 Plainmath. All rights reserved

• PRINT TO PLAY
• DIGITAL GAMES

Problem-Solving Strategies

October 16, 2019

There are many different ways to solve a math problem, and equipping students with problem-solving strategies is just as important as teaching computation and algorithms. Problem-solving strategies help students visualize the problem or present the given information in a way that can lead them to the solution. Solving word problems using strategies works great as a number talks activity and helps to revise many skills.

Problem-solving strategies

1. create a diagram/picture, 2. guess and check., 3. make a table or a list., 4. logical reasoning., 5. find a pattern, 6. work backward, 1. create a diagram/draw a picture.

Creating a diagram helps students visualize the problem and reach the solution. A diagram can be a picture with labels, or a representation of the problem with objects that can be manipulated. Role-playing and acting out the problem like a story can help get to the solution.

Alice spent 3/4 of her babysitting money on comic books. She is left with $6. How much money did she make from babysitting?

2. Guess and check

Teach students the same strategy research mathematicians use.

With this strategy, students solve problems by making a reasonable guess depending on the information given. Then they check to see if the answer is correct and they improve it accordingly.  By repeating this process, a student can arrive at a correct answer that has been checked. It is recommended that the students keep a record of their guesses by making a chart, a table or a list. This is a flexible strategy that works for many types of problems. When students are stuck, guessing and checking helps them start and explore the problem. However, there is a trap. Exactly because it is such a simple strategy to use, some students find it difficult to consider other strategies. As problems get more complicated, other strategies become more important and more effective.

Find two numbers that have sum 11 and product 24.

Try/guess  5 and 6  the product is 30 too high

  adjust  to 4 and 7 with product 28 still high

  adjust  again 3 and 8 product 24

3. Make a table or a list

Carefully organize the information on a table or list according to the problem information. It might be a table of numbers, a table with ticks and crosses to solve a logic problem or a list of possible answers. Seeing the given information sorted out on a table or a list will help find patterns and lead to the correct solution.

To make sure you are listing all the information correctly read the problem carefully.

Find the common factors of 24, 30 and 18

Logical reasoning is the process of using logical, systemic steps to arrive at a conclusion based on given facts and mathematic principles. Read and understand the problem. Then find the information that helps you start solving the problem. Continue with each piece of information and write possible answers.

Thomas, Helen, Bill, and Mary have cats that are black, brown, white, or gray. The cats’ names are Buddy, Lucky, Fifi, and Moo. Buddy is brown. Thoma’s cat, Lucky, is not gray. Helen’s cat is white but is not named Moo. The gray cat belongs to Bill. Which cat belongs to each student, and what is its color?

A table or list is useful in solving logic problems.

Since Lucky is not gray it can be black or brown. However, Buddy is brown so Lucky has to be black.

Buddy is brown so it cannot be Helen’s cat. Helen’s cat cannot be Moo, Buddy or Lucky, so it is Fifi.

Therefore, Moo is Bill’s cat and Buddy is Mary’s cat.

5. Find a pattern.

Finding a pattern is a strategy in which students look for patterns in the given information in order to solve the problem. When the problem consists of data like numbers or events that are repeated then it can be solved using the “find a pattern” problem-solving strategy. Data can be organized in a table or a list to reveal the pattern and help discover the “rule” of the pattern.

 The “rule” can then be used to find the answer to the question and complete the table/list.

Shannon’s Pizzeria made 5 pizzas on Sunday, 10 pizzas on Monday, 20 pizzas on Tuesday, and 40 pizzas on Wednesday. If this pattern continues, how many pizzas will the pizzeria make on Saturday?

6. Working backward

Problems that can be solved with this strategy are the ones that  list a series of events or a sequence of steps .

In this strategy, the students must start with the solution and work back to the beginning. Each operation must be reversed to get back to the beginning. So if working forwards requires addition, when students work backward they will need to subtract. And if they multiply working forwards, they must divide when working backward.

Mom bought a box of candy. Mary took 5 of them, Nick took 4 of them and 31 were given out on Halloween night. The next morning they found 8 pieces of candy in the box. How many candy pieces were in the box when mom bought it.

For this problem, we know that the final number of candy was 8, so if we work backward to “put back” the candy that was taken from the box we can reach the number of candy pieces that were in the box, to begin with.

The candy was taken away so we will normally subtract them. However, to get back to the original number of candy we need to work backward and do the opposite, which is to add them.

8 candy pieces were left + the 31 given out + plus the ones Mary took + the ones Nick took

8+31+5+4= 48   Answer: The box came with 48 pieces of candy.

Selecting the best strategy for a problem comes with practice and often problems will require the use of more than one strategies.

Print and digital activities

I have created a collection of print and digital activity cards and worksheets with word problems (print and google slides) to solve using the strategies above. The collection includes 70 problems (5 challenge ones) and their solution s and explanations.

sample below

How to use the activity cards

Allow the students to use manipulatives to solve the problems. (counters, shapes, lego blocks, Cuisenaire blocks, base 10 blocks, clocks) They can use manipulatives to create a picture and visualize the problem. They can use counters for the guess and check strategy. Discuss which strategy/strategies are better for solving each problem. Discuss the different ways. Use the activities as warm-ups, number talks, initiate discussions, group work, challenge, escape rooms, and more.

Ask your students to write their own problems using the problems in this resource, and more, as examples. Start with a simple type. Students learn a lot when trying to compose a problem. They can share the problem with their partner or the whole class. Make a collection of problems to share with another class.

For the google slides the students can use text boxes to explain their thinking with words, add shapes and lines to create diagrams, and add (insert) tables and diagrams.

Many of the problems can be solved faster by using algebraic expressions. However, since I created this resource for grades 4 and up I chose to show simple conceptual ways of solving the problems using the strategies above. You can suggest different ways of solving the problems based on the grade level.

Find the free and premium versions of the resource below. The premium version includes 70 problems (challenge problems included) and their solutions

There are 2 versions of the resource

70 google slides with explanations + 70 printable task cards

70 google slides with explanations + 11 worksheets

You might also like

Multiplying fractions/mixed numbers/simplifying

Adding and subtracting fractions

AM/PM, 24-hour clock, Elapsed Time – ideas, games, and activities

Teaching area, ideas, games, print, and digital activities

Multi-Digit Multiplication, Area model, Partial Products algorithm, Puzzles, Word problems

Place Value – Representing and adding 2/3 digit numbers with manipulatives

Multiplication Mission – arrays, properties, multiples, factors, division

Fractions Games and activities – Equivalence, make 1, compare, add, subtract, like, unlike

Diving into Division -Teaching division conceptually

Expressions with arrays

Decimals, Decimal fractions, Percentages – print and digital

Solving Word Problems- Math talks-Strategies, Ideas and Activities-print and digital

Check out our best selling card games now available at amazon.com and amazon.ca.

Chicken Escape

A multiplayer card game that makes mental math practice fun! Chicken Escape is a fast-paced multiplayer card game. While playing…

Dragon Times – A math Adventure card game

Dragon Times is an educational fantasy card game that aims to motivate children to practice multiplication and division facts while…

5 Strategies for Successful Problem Solving

• Powerful teaching strategies
• December 26, 2023
• Michaela Epstein

Blog > 5 Strategies for Successful Problem Solving

Problem solving can change the way students see maths – and how they see themselves as maths learners.

But, it's tough to help all students get the most out of a task.

To help, here are  5 Strategies for Problem Solving Success.

These are 5 valuable lessons I've learned from working with teachers across the globe .  You can use these strategies with all your students, no matter their level.

5 Strategies for Problem Solving Success

Your own enthusiasm is quickly picked up by your students. So, choose a problem, puzzle or game that you’re excited and curious about.

How do you know what will spark your curiosity? Do the task yourself!

(That’s why,  in the workshops I run , we spend a lot of time  actually  exploring problems. It’s a chance to step into students' shoes and experience maths from their perspective.)

Often, curriculum content becomes the goal of problem solving. For example, adding fractions, calculating areas or solving quadratic equations.

But, this is a mistake! Here's why-

Low floor, high ceiling tasks give students choices. Choices about what strategies to use, tools to draw on – and even what end-points to get to.

The most valuable goals focus on building confidence and capability in problem solving. For example:

• To make and break conjectures
• To use and evaluate different strategies
• To organise data in meaningful ways
• To explain and justify their conclusions.

The start of a task is what will get your students curious and hungry to get underway.

Consider: What's the least information your students will need?

At  ​our Members' online PL sessions​ , we look at one of four possibilities for launching a problem:

• Present a mystery to explore
• Present an example and non-example
• Run a demonstration game
• Show how to use a tool.

Keep the launch short – under 5 minutes. This is just enough to keep students’ attention AND share essential information.

Let’s face it, problem solving is hard, no matter your age or mathematical skill set.

Students aren’t afraid of hard work – they’re afraid of feeling or looking stupid. And, when those tricky maths moments do come, you can help.

Using questions, tools and other prompts can bring clarity and boost confidence.

(Here's a  free question catalogue  you might find handy to have in your back pocket.)

This careful support will help your students find problem solving far less daunting. Instead, it can become a chance for wonderous mathematical exploration.

Picture this: Your students are elbows deep in a problem, there’s a buzz in the air – oh, and only a minute until the bell.

The  most important  stage of a problem solving task – right at the end – is often the one that gets dropped off.

Why does ‘wrapping up’ matter?

In the last 10 minutes of a problem, students can share conjectures, strategies and solutions. It's also a chance to consider new questions that may open up further exploration.

In wrapping up, important learning will happen. Your students will observe patterns, make connections and clarify conjectures. You might even notice ‘aha’ moments.

Five strategies for problem solving success:

• Choose a task that YOU'RE keen on,
• Set a goal for strengthening problem solving skills,
• Plan a short launch to make the task widely accessible,
• Use questions, tools and prompts to support productive exploration, and
• Wrap up to create space for pivotal learning.

Join the Conversation

Dear Michaela, Greetings !! Thank you for sharing the strategies for problem solving task. These strategies will definitely enhance the skill in the mindset of young learners. In India ,Students of Grade 9 and Grade 10 have to learn and solve lot of theorems of triangle, Quadrilateral, Circle etc. Being an educator I have noticed that most of the students learn the theorems and it’s derivation by heart as a result they lack in understanding the application of these theorems.

I will appreciate if you can share your insights as how to make these topics interesting and easy to grasp.

Once again thanks for sharing such informative ideas.

Leave a comment

Cancel reply.

Your email address will not be published. Required fields are marked *

Don’t miss a thing!

Sign up to our mailing list for inspiring maths teaching ideas, event updates, free resources, and more!

Mastery-Aligned Maths Tutoring

“The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away."

FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

Maths Problem Solving: Engaging Your Students And Strengthening Their Mathematical Skills

Meriel Willatt

Maths problem solving can be challenging for pupils. There’s no ‘one size fits all’ approach or strategy and questions often combine different topic areas. Pupils often don’t know where to start. It’s no surprise that problem solving is a common topic teachers struggle to teach effectively to their pupils.

In this blog, we consider the importance of problem solving and share with you some ideas and resources for you to tackle problem solving in your maths classroom, from KS2 up to GCSE.

What is maths problem solving?

Why is maths problem solving so difficult, how to develop problem solving skills in maths, maths problem solving ks2, maths problem solving ks3, maths problem solving gcse.

Maths problem solving is when a mathematical task challenges pupils to apply their knowledge, logic and reasoning in unfamiliar contexts. Problem solving questions often combine several elements of maths.

We know from talking to the hundreds of school leaders and maths teachers that we work with as one to one online maths tutoring providers that this is one of their biggest challenges: equipping pupils with the skills and confidence necessary to approach problem solving questions.

The Ultimate Guide to Problem Solving Techniques

Download these 9 ready-to-go problem solving techniques that every pupil should know

The challenge with problem solving in maths is that there is no generic problem solving skill that can be taught in an isolated maths lesson. It’s a skill that teachers must explicitly teach to pupils, embed into their learning and revisit often.

When pupils are first introduced to a topic, they cannot start problem solving straight away using it. Problem solving relies on deep knowledge of concepts. Pupils need to become familiar with it and practice using it in different contexts before they can make connections, reason and problem solve with it. In fact, some researchers suggest that it could take up to two years to do this (Burkhardt, 2017). 

At Third Space Learning, we specialise in online one to one maths tutoring for schools, from KS1 all the way up to GCSE. Our lessons are designed by maths teachers and pedagogy experts to break down complex problems into their constituent parts. Our specialist tutors then carefully scaffold learning to build students’ confidence in key skills before combining them to tackle problem solving questions.

In order to develop problem solving skills in maths, pupils need lots of different contexts and word problems in which to practise them and the opportunity to engage in mathematical talk that draws on their metacognitive skills. 

The EEF suggests that to develop problem solving skills in maths, teachers need to teach pupils:

• To use different approaches to problem solving
• Use worked examples
• To use metacognition to plan, monitor and reflect on their approaches to problem solving

Below, we take a closer look at problem solving at each stage, from primary school all the way to GCSEs. We’ve also included links to maths resources and CPD to support you and your team’s classroom teaching.

At lower KS2, the National Curriculum states that pupils should develop their ability to solve a range of problems. However, these will involve simple calculations as pupils develop their numeracy skills. As pupils progress to upper KS2, the demand for problem solving skills increases. 

“At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems.” National curriculum in England: mathematics programmes of study (Upper key stage 2 – years 5 and 6)

KS2 problem solving can often fall into the trap of relying on acronyms, such as RICE, RIDE or even QUACK. The most popular is RUCSAC (Read, Underline, Calculate, Solve, Answer, Check). While these do aim to simplify the process for young minds, it encourages a superficial, formulaic approach to problem solving, rather than deep mathematical thinking. Also, consider how much is wrapped up within the word ‘solve’ – is this helpful?

We teach thousands of pupils KS2 maths problem solving skills every week through our one to one online tutoring programme for maths. In our interventions, we encourage deep mathematical thinking by using a simplified version of George Polya’s four stages of problem solving. Here are the four stages:

Understand the problem

• Devise a strategy for solving it
• Carry out the problem solving strategy
• Check the result

We use UCR as a simplified model: Understand, Communicate & Reflect. You may choose to adapt this depending on the age and ability of your class.

For example:

Maisy, Heidi and Freddie are children in the same family. The product of their ages is a score. How old might they be?

There are three people.

There are three numbers that multiply together to make twenty (a score is equal to 20). There will be lots of answers, but no ‘right’ answer.

Communicate

To solve the word problem we need to find the numbers that will go into 20 without a remainder (the factors).

The factors of 20 are 1, 2, 4, 5, 10 and 20.

Combinations of numbers that could work are: 1, 1, 20 1, 2, 10 1, 4, 5 2, 2, 5.

The question says children, which means ‘under 18 years’, so that would mean we could remove 1, 1, 20 from our list of possibilities. 

In our sessions, we create a nurturing learning environment where pupils feel safe to make mistakes. This is so important in the context of problem solving as the best problem solvers will be resilient and able to overcome challenges in the ‘Reflect’ stage. Read more: What is a growth mindset

Looking for more support teaching KS2 problem solving? We’ve developed a powerpoint on problem solving, reasoning and planning for depth that is designed to be used as CPD by primary school teachers, maths leads and SLT. 

The resource reflects on how metacognition can enhance reasoning and problem solving abilities, the ‘curse’ of real life maths (think ‘Carl buys 60 watermelons…) and how teachers can practically implement and teach strategies in the classroom.

You may also be interested in: 

• Developing Thinking Skills At KS2
• KS2 Maths Investigations
• Word problems for Year 6

At KS3, the importance of seeing mathematical concepts as interconnected with other skills, including problem solving, is foregrounded. The National Curriculum also stresses the importance of a strong foundation in maths before moving on to complex problem solving.

“Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems” National curriculum in England: mathematics programmes of study (Key stage 3)

“Decisions about progression should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4.” National curriculum in England: mathematics programmes of study (Key stage 3)

For many students, the transition from primary to secondary school can be a huge challenge.

Especially in the aftermath of the Covid-19 pandemic and the resultant school closures, students may arrive into Year 7 with various learning gaps and misconceptions that will hold them. Some students may need focused support to plug these gaps and grow in confidence.

You can give pupils a smoother transition from KS2 to KS3 with personalised one to one online tuition with specialist tutors with Third Space Learning. Our lessons cover content from Years 5-7 and build a solid foundation for pupils to develop their problem solving skills. Pupils are supported towards independent practice through worked examples, questioning and support slides.

The challenge for KS3 maths problem solving activities is that learners may struggle to get invested unless you start with a convincing hook. Engage your young mathematicians on topics you know well or you know they’ll be invested in and try your hand at designing your own mathematical problems. Alternatively, get some inspiration from our crossover ability and fun maths problems .

Since the new GCSE specification began in 2015, there has been an increased focus on non-routine problem solving questions. These questions demand students to make sense of lots of new information at once before they even move on to selecting the strategies they’ll use to find the correct answer. This is where many learners get stuck.

In recent years, teachers and researchers in pedagogy (including Ofsted) have recognised that open ended problem solving tasks do not in fact lead to improved student understanding. While they may be enjoyable and engage learners, they may not lead to improved results.

SSDD problems (Same Surface Different Depth) can offer a solution that develops students’ critical thinking skills, while ensuring they engage fully with the information they’re provided. The idea behind them is to provide a set of questions that look the same and use the same mathematical hook but each question requires a different mathematical process to be solved.

Read more about SSDD problems , tips on writing your own questions and download free printable examples. There are also plenty of more examples on the NRICH website.

Worked examples, careful questioning and constructing visual representations can help students to convert the information embedded in a maths challenge into mathematical notations. Read our blog on problem solving maths questions for Foundation, Crossover & Higher examples, worked solutions and strategies.

Remember that students can only move on to mathematics problem solving once they have secure knowledge in a topic. If you know there are areas your students need extra support, check our Secondary Maths Resources library for revision guides, teaching resources and worksheets for KS3 and GCSE topics.

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

Every week Third Space Learning’s specialist online maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress.

Since 2013 these personalised one to 1 lessons have helped over 169,000 primary and secondary students become more confident, able mathematicians.

Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

Related articles

Free Year 7 Maths Test With Answers And Mark Scheme: Mixed Topic Questions

What Is A Number Square? Explained For Primary School Teachers, Parents & Pupils

What Is Numicon? Explained For Primary School Teachers, Parents And Pupils

30 Problem Solving Maths Questions And Answers For GCSE

FREE Guide to Maths Mastery

All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

Ideal for running staff meetings on mastery or sense checking your own approach to mastery.

Privacy Overview

Problem Solving in Mathematics

• Math Tutorials
• Pre Algebra & Algebra
• Exponential Decay
• Worksheets By Grade

The main reason for learning about math is to become a better problem solver in all aspects of life. Many problems are multistep and require some type of systematic approach. There are a couple of things you need to do when solving problems. Ask yourself exactly what type of information is being asked for: Is it one of addition, subtraction, multiplication , or division? Then determine all the information that is being given to you in the question.

Mathematician George Pólya’s book, “ How to Solve It: A New Aspect of Mathematical Method ,” written in 1957, is a great guide to have on hand. The ideas below, which provide you with general steps or strategies to solve math problems, are similar to those expressed in Pólya’s book and should help you untangle even the most complicated math problem.

Use Established Procedures

Learning how to solve problems in mathematics is knowing what to look for. Math problems often require established procedures and knowing what procedure to apply. To create procedures, you have to be familiar with the problem situation and be able to collect the appropriate information, identify a strategy or strategies, and use the strategy appropriately.

Problem-solving requires practice. When deciding on methods or procedures to use to solve problems, the first thing you will do is look for clues, which is one of the most important skills in solving problems in mathematics. If you begin to solve problems by looking for clue words, you will find that these words often indicate an operation.

Look for Clue Words

Think of yourself as a math detective. The first thing to do when you encounter a math problem is to look for clue words. This is one of the most important skills you can develop. If you begin to solve problems by looking for clue words, you will find that those words often indicate an operation.

Common clue words for addition  problems:

Common clue words for  subtraction  problems:

• How much more

Common clue words for multiplication problems:

Common clue words for division problems:

Although clue words will vary a bit from problem to problem, you'll soon learn to recognize which words mean what in order to perform the correct operation.

Read the Problem Carefully

This, of course, means looking for clue words as outlined in the previous section. Once you’ve identified your clue words, highlight or underline them. This will let you know what kind of problem you’re dealing with. Then do the following:

• Ask yourself if you've seen a problem similar to this one. If so, what is similar about it?
• What did you need to do in that instance?
• What facts are you given about this problem?
• What facts do you still need to find out about this problem?

Develop a Plan and Review Your Work

Based on what you discovered by reading the problem carefully and identifying similar problems you’ve encountered before, you can then:

• Define your problem-solving strategy or strategies. This might mean identifying patterns, using known formulas, using sketches, and even guessing and checking.
• If your strategy doesn't work, it may lead you to an ah-ha moment and to a strategy that does work.

If it seems like you’ve solved the problem, ask yourself the following:

• Does your solution seem probable?
• Does it answer the initial question?
• Did you answer using the language in the question?
• Did you answer using the same units?

If you feel confident that the answer is “yes” to all questions, consider your problem solved.

Tips and Hints

Some key questions to consider as you approach the problem may be:

• What are the keywords in the problem?
• Do I need a data visual, such as a diagram, list, table, chart, or graph?
• Is there a formula or equation that I'll need? If so, which one?
• Will I need to use a calculator? Is there a pattern I can use or follow?

Read the problem carefully, and decide on a method to solve the problem. Once you've finished working the problem, check your work and ensure that your answer makes sense and that you've used the same terms and or units in your answer.

• Examples of Problem Solving with 4 Block
• Using Percents - Calculating Commissions
• What to Know About Business Math
• Parentheses, Braces, and Brackets in Math
• How to Solve a System of Linear Equations
• How to Solve Proportions to Adjust a Recipe
• Calculate the Exact Number of Days
• What Is a Ratio? Definition and Examples
• Changing From Base 10 to Base 2
• Finding the Percent of Change Between Numbers
• Learn About Natural Numbers, Whole Numbers, and Integers
• How to Calculate Commissions Using Percents
• Overview of the Stem-and-Leaf Plot
• Understanding Place Value
• Probability and Chance
• Evaluating Functions With Graphs

9 Ways to Improve Math Skills Quickly & Effectively

Written by Ashley Crowe

• Parent Resources

• The importance of understanding basic math skills
• 9 Ways to improve math skills
• How to use technology to improve math skills

Math class can move pretty fast. There’s so much to cover in the course of a school year. And if your child doesn’t get a new math idea right away, they can quickly get left behind.

If your child is struggling with basic math problems every day, it doesn’t mean they’re destined to be bad at math. Some students need more time to develop the problem-solving skills that math requires. Others may need to revisit past concepts before moving on. Because of how math is structured, it’s best to take each year step-by-step, lesson by lesson.

This article has tips and tricks to improve your child’s math skills while minimizing frustrations and struggles. If your child is growing to hate math, read on for ways to improve their skills and confidence, and maybe even make math fun! 

But first, the basics.

Math is a subject that builds on itself. It takes a solid understanding of past concepts to prepare for the next lesson. 

That’s why math can become frustrating when you’re forced to move on before you’re ready. You’re either stuck trying to catch up or you end up falling further behind.

But with a strong understanding of basic math skills, your child can be set up for school success. If you’re unfamiliar with the idea of sets or whole numbers , this is a great place to start. 

What are considered basic math skills?

The basic math skills required to move on to higher levels of math learning are: 

• Addition — Adding to a set.
• Subtraction — Taking away from a set.
• Multiplication — Adding equal sets together in groups (2 sets of 3 is the same as 2x3, or 6).
• Division — How many equal sets can be found in a number (12 has how many sets of two in it? 6 sets of 2).
• Percentages — A specific amount in relation to 100.
• Fractions & Decimals — Fractions are equal parts of a whole set. Decimals represent a number of parts of a whole in relation to 10. These both contrast with whole numbers. 
• Spatial Reasoning — How numbers and shapes fit together.

How to improve math skills 

People aren’t bad at math — many just need more time and practice to gain a thorough understanding.

How can you help your child improve their math abilities? Use our top 9 tips for quickly and effectively improving math skills .

1. Wrap your head around the concepts

Repetition and practice are great, but if you don’t understand the concept , it will be difficult to move forward. 

Luckily, there are many great ways to break down math concepts . The trick is finding the one that works best for your child.

Math manipulatives can be a game-changer for children who are struggling with big math ideas. Taking math off the page and putting it into their hands can bring ideas to life. Numbers become less abstract and more concrete when you’re counting toy cars or playing with blocks. Creating these “sets” of objects can bring clarity to basic math learning.

2. Try game-based learning

During math practice, repetition is important — but it can get old in a hurry. No one enjoys copying their times tables over and over and over again. If learning math has become a chore, it’s time to bring back the fun! 

Game-based learning is a great way to practice new concepts and solidify past lessons. It can even make repetition fun and engaging.

Game-based learning can look like a family board game on Friday night or an educational app , like Prodigy Math .

Take math from frustrating to fun with the right game, then watch the learning happen easily!

3. Bring math into daily life

You use basic math every day. 

As you go about your day, help your child see the math that’s all around them:  

• Tell them how fast you’re driving on the way to school
• Calculate the discount you’ll receive on your next Target trip
• Count out the number of apples you need to buy at the grocery store
• While baking, explain how 6 quarter cups is the same amount of flour as a cup and a half — then enjoy some cookies!

Relate math back to what your child loves and show them how it’s used every day. Math doesn’t have to be mysterious or abstract. Instead, use math to race monster trucks or arrange tea parties. Break it down, take away the fear, and watch their interest in math grow.

4. Implement daily practice

Math practice is important. Once you understand the concept, you have to nail down the mechanics. And often, it’s the practice that finally helps the concept click. Either way, math requires more than just reading formulas on a page.

Daily practice can be tough to implement, especially with a math-averse child. This is a great time to bring out the game-based learning mentioned above. Or find an activity that lines up with their current lesson. Are they learning about squares? Break out the math link cubes and create them. Whenever possible, step away from the worksheets and flashcards and find practice elsewhere.

5. Sketch word problems

Nothing causes a panic quite like an unexpected word problem. Something about the combination of numbers and words can cause the brain of a struggling math learner to shut down. But it doesn’t have to be that way.

Many word problems just need to be broken down, step by step . One great way to do this is to sketch it out. If Doug has five apples and four oranges, then eats two of each, how many does he have left? Draw it, talk it out, cross them off, then count. 

If you’ve been talking your child through the various math challenges you encounter every day, many word problems will start to feel familiar. 

6. Set realistic goals

If your child has fallen behind in math, then more study time is the answer. But forcing them to cram an extra hour of math in their day is not likely to produce better results. To see a positive change, first identify their biggest struggles . Then set realistic goals addressing these issues . 

Two more hours of practicing a concept they don’t understand is only going to cause more frustration. Even if they can work through the mechanics of a problem, the next lesson will leave them feeling just as lost. 

Instead, try mini practice sessions and enlist some extra help. Approach the problem in a new way, reach out to their teacher or try an online math lesson . Make sure the extra time is troubleshooting the actual problem, not just reinforcing the idea that math is hard and no fun. 

Set Goals and Rewards in Prodigy Math

Did you know that parents can set learning goals for their child in Prodigy Math? And once they achieve them, they'll unlock in-game rewards of your choice!

7. Engage with a math tutor

If your child is struggling with big picture concepts, look into finding a math tutor . Everyone learns differently, and you and your child’s teacher may be missing that “aha” moment that a little extra time and the right tutor can provide.

It’s amazing when a piece of the math puzzle finally clicks for your child. If you’re ready to get that extra help, try a free 1:1 online session from Prodigy Math Tutoring. Prodigy’s tutors are real teachers who know how to connect kids to math. With the right approach, your child can become confident in math — and who knows, they may even begin to enjoy it. 

8. Focus on one concept at a time

Math builds on itself. If your child is struggling through their current lesson, they can’t skip it and come back to it later. This is the time to practice and repeat — re-examining and reinforcing the current concept until it makes sense.

Look for other ways to approach new math ideas. Use math manipulatives to bring numbers off the page. Or try a learning app with exciting rewards and positive reinforcement to encourage extra practice. 

Take a step back when frustrations get high — but resist the temptation to just let it go. Once the concept clicks, they’ll be excited to forge ahead.

9. Teach others math you already know

Even if your child is struggling in math, they’ve still learned so much since last year. Focus on the improvements they’ve made and let them showcase their knowledge. If they have younger siblings, your older child can demonstrate addition or show them how to use a number line. This is a great way to build their confidence and encourage them to keep going.

Or let them teach you how they solve new problems. Have your child talk you through the process while you solve a long division problem . You’re likely to find yourself a little rusty on the details. Play it up and get a little silly. They’ll love teaching you the ropes of this “new math.”

Embracing technology to improve math skills

Though much of your math learning was done with pencil to paper, there are many more ways to build number skills in today’s tech world. 

Your child can take live, online math courses to work through tough concepts. Or play a variety of online games, solving math puzzles and getting consistent practice while having fun.

These technical advances can help every child learn math, no matter their preferred learning or study style. If your child is a visual learner, there’s an app for that. Do they process best while working in groups? Jump online and find one. Don’t keep repeating the same lessons from their math class over and over. Branch out, try something new and watch the learning click. 

Look online for more math help

There are so many online resources, it can be hard to know where to start. 

At Prodigy, we’re happy to help you get the ball rolling on your child’s math learning, from kindergarten through 8th grade. It’s free to sign up, fun to play and exciting to watch as your child’s math understanding grows.

Sign up for a free parent account and get instant data on your child’s progress as they build more math skills with Prodigy Math Game . It’s time to take the math struggle out of your home and enjoy learning together!

Share this article

Table of Contents

Help your child improve their math skills with the game that makes learning an adventure!

Building Problem-solving Skills for 7th-Grade Math

Mathematics is a subject that requires problem-solving skills to excel. In 7th grade, students begin to encounter more complex math concepts, and the ability to analyze and solve problems becomes increasingly important. Building problem-solving skills for math not only helps students to master math concepts but also prepares them for success in higher-level math courses and in life beyond academics. 

In this article, we will several key skills that are needed for success in 7th-grade math, and also explore how they can benefit students both academically and personally. We will also provide tips and strategies to help students develop and improve their problem-solving skills. Let’s dive in!

Building Analytical Skills

The first of seven important skills to build is that of analytical skills. These allow students to analyze a problem and break it down into smaller parts. From there, they’re able to identify the key components that need to be addressed. Analytical skills also hone students’ abilities to identify patterns. Students should be able to identify patterns in mathematical data, such as in number sequences, geometric shapes, and graphs. Importantly, students should not just be able to recognize the pattens, but they should be able to describe them (more on that in communication) and use them to make predictions and solve problems.

We alluded to this earlier, but breaking down problems is an essential component of analytical skills. Students with strong analytical skills can break problems down into smaller and more manageable parts. They are then able to identify key components of a problem and use this information to develop a strategy for solving it. 

Along with identifying patterns comes identifying relationships. Students with good mathematical analytical skills can identify relationships between different mathematical concepts, such as the relationship between addition and subtraction, or the relationship between angles and shapes. Through strengthening this skill, students will be able to describe these relationships and use them to solve problems. 

An important part of analytical skills is the ability to analyze data. Students should be able to analyzeand interpret data presented in a variety of formats, such as graphs, charts, and tables. They should be able to use this data to make predictions, draw conclusions, and solve problems.

Speaking of conclusions, reaching sound conclusions based on mathematical data is a fundamental skill needed for making predictions based on trends in a graph, or drawing inferences from a set of data.

Another skill students should master is the ability to compare and contrast mathematical concepts, such as the properties of different shapes or the strategies for solving different types of problems. Through this, they’ll be able to use the information they gather to solve problems. 

With all these skills at play comes arguably the most important: Critical thinking. This is an indicator that a student really grasps the concepts and it’s just repeating them back to you on command. Critical thinking is the ability to evaluate information and arguments, and make judgements and decisions based on evidence, and apply logic and reasoning to solve problems.

Building Creative Thinking

This is the ability for students (or anyone, really) to think outside the box and come up with innovative solutions to problems. This involves being able to approach problems from different angles and to consider multiple perspectives. For a 7th-grader, this skill can be exercised through the following:

• Thinking Outside the Box: Students should be encouraged to think creatively and come up with innovative solutions to problems. This involves thinking outside the box and considering multiple perspectives.
• Finding Multiple Solutions: Students should be able to come up with multiple solutions to a problem and evaluate each one to determine which is the most effective.
• Developing Original Ideas: Students should be able to develop original ideas and approaches to solving problems. This involves being able to come up with unique and innovative solutions that may not have been tried before.
• Making Connections: Students should be able to make connections between different mathematical concepts and apply these connections to solve problems. This involves looking for similarities and differences between concepts and using this information to make new connections.
• Visualizing Solutions : Students should be able to visualize solutions to problems and use diagrams, charts, and other visual aids to help them solve problems.
• Using Metaphors and Analogies: Students should be able to use metaphors and analogies to help them understand complex mathematical concepts. This involves using familiar concepts to explain unfamiliar ones and making connections between different ideas.

Building Problem-Solving Strategies

It may sound like the same thing, but building problem-solving strategies is not the same as building problem-solving skills. Building strategies for problem-solving lends itself to actual problem-solving. Let’s expand on this: Say your student is presented a problem that they’re struggling with, these are some of the problem-solving strategies they may use in order to solve the puzzle.

• Identify the problem: The first step in problem-solving is to identify the problem and understand what is being asked. Students should carefully read the problem and make sure they understand the question before attempting to solve it.
• Draw a diagram: Students can draw a diagram to help visualize the problem and better understand the relationships between different parts of the problem.
• Use logic: Students can use logic to identify patterns and relationships in the problem. They can use this information to develop a plan to solve the problem.
• Break the problem down: Students can break a complex problem down into smaller, more manageable parts. They can then solve each part of the problem individually before combining the solutions to get the final answer.
• Guess and check: Students can guess and check different solutions to the problem until they find the correct answer. This method involves trying different solutions and evaluating the results until the correct answer is found.
• Use algebra: Algebraic equations can be used to solve a variety of mathematical problems. Students can use algebraic equations to represent the problem and solve for the unknown variable.
• Work backward: Students can work backward from the final answer to determine the steps required to solve the problem. This method involves starting with the end goal and working backward to determine the steps needed to get there.

Building Persistence and Perseverance

In an increasingly instant-gratification world with apps, searches and AI chatbots just a click away, this is an important skill not just in the math classroom, but for life in general. Problem-solving, whether that’s a math problem or a life challenge, often requires persistence and perseverance. Student need to learn to be able to stick with a problem even when it seems challenging, difficult, or seemingly impossible. Here are ways you can encourage your students to stick it out when working on problems:

• Trying multiple approaches: When faced with a challenging problem, students can demonstrate persistence by trying multiple approaches until they find one that works. They don’t give up after one attempt but keep trying until they find a solution.
• Reframing the problem: If a problem seems particularly difficult, students can demonstrate perseverance by reframing the problem in a different way. This can help them see the problem from a new perspective and come up with a different approach to solve it.
• Asking for help: Sometimes, even with persistence, a problem may still be difficult to solve. In these cases, students can demonstrate perseverance by asking for help from their teacher or classmates. This shows that they are willing to put in the effort to find a solution, even if it means seeking assistance.
• Learning from mistakes: Making mistakes is a natural part of the problem-solving process, but students can demonstrate persistence by learning from their mistakes and using them to improve their problem-solving skills. They don’t get discouraged by their mistakes, but instead, they use them as an opportunity to learn and grow.
• Staying focused: In order to solve complex math problems, it’s important for students to stay focused and avoid distractions. Students can demonstrate perseverance by staying focused on the problem at hand and not getting distracted by other things.

Building Communication Skills

We alluded to this earlier, but a central part of building problem-solving skills is building the ability to articulate a problem or a solution. This isn’t just for the sake of personal understanding, but critical for collaboration. Students need to be able to explain their thinking, ask questions, and work with others to solve problems. Here are some examples of communication skills that can be used to build problem-solving skills:

• Clarifying understanding: Students can ask questions to clarify their understanding of the problem. They can seek clarification from their teacher or classmates to ensure they are interpreting the problem correctly.
• Explaining their reasoning: When solving a math problem, students can explain their reasoning to show how they arrived at a particular solution. This can help others understand their thought process and can also help students identify errors in their own work.
• Collaborating with peers: Problem-solving can be a collaborative effort. Students can work together in groups to solve problems and communicate their ideas and solutions with each other. This can lead to a better understanding of the problem and can also help students learn from each other.
• Writing clear explanations: When presenting their solutions to a math problem, students can write clear and concise explanations that are easy to understand. This can help others follow their thought process and can also help them communicate their ideas more effectively.
• Using math vocabulary: Math has its own language and using math vocabulary correctly is essential for effective communication. Students can demonstrate their understanding of math concepts by using correct mathematical terms and symbols when explaining their solutions.

Building Mathematical Knowledge

This would seem like a no-brainer, since you’re a math educator clicking on an article about building math problem-solving skills. However, it’s worth being explicit that problem-solving in math requires a solid understanding of mathematical concepts, including arithmetic, algebra, geometry, and data analysis. Students need to be able to apply these concepts to solve problems in real-world contexts.

7th-grade math covers a wide range of mathematical concepts and skills. Here are some examples of mathematical knowledge that 7th-grade math students should have:

• Algebraic expressions and equations: Students should be able to write and simplify algebraic expressions and solve one-step and two-step equations.
• Proportional relationships: Students should be able to understand and apply proportional relationships, including identifying proportional relationships in tables, graphs, and equations.
• Geometry: Students should have a solid understanding of geometry concepts such as angles, triangles, quadrilaterals, circles, and transformations.
• Statistics and probability: Students should be able to analyze and interpret data using measures of central tendency and variability, and understand basic probability concepts.
• Rational numbers: Students should have a solid understanding of rational numbers, including ordering, adding, subtracting, multiplying, and dividing fractions and decimals.
• Integers: Students should be able to perform operations with integers, including adding, subtracting, multiplying, and dividing.
• Ratios and proportions: Students should be able to understand and use ratios and proportions in a variety of contexts, including scale drawings and maps.

In conclusion, problem-solving skills are essential for success in 7th grade math. Analytical skills, critical and creative thinking, problem-solving strategies, persistence, communication skills, and mathematical knowledge are all important components of effective problem-solving. By developing these skills, students can approach math problems with confidence and achieve their full potential.

If you enjoyed this read, be sure to browse more of our articles . More importantly, if you want to save yourself hours of preparation time by having full math curriculums, review guides and tests available at the click of a button, be sure to sign up to our 7th Grade Newsletter . You’ll receive loads of free lesson resources, tips and advice and exclusive subscription offers!

Images Sources

Featured image by Karla Hernandez on Unsplash

https://www.freepik.com/free-photo/boy-pretends-be-superhero-uses-his-mind-draw-concept_6170411.htm#query=child%20thinking&position=21&from_view=search&track=ais

https://www.freepik.com/free-photo/happy-asian-child-student-holding-light-bulb-with-schoolbag-isolated-yellow-background_26562776.htm#query=child%20thinking%20idea&position=1&from_view=search&track=ais

https://www.freepik.com/free-photo/girl-playing-with-cube-puzzle_1267051.htm#query=child%20building&position=14&from_view=search&track=ais

https://www.freepik.com/free-photo/adorable-girl-propping-up-her-head-with-fists-being-upset-dreaming_6511917.htm#page=2&query=child%20thinking&position=0&from_view=search&track=ais

https://www.freepik.com/free-photo/boys-doing-high-five_4350791.htm#page=2&query=child%20talking&position=2&from_view=search&track=ais

https://www.freepik.com/free-photo/schoolgirl-smiling-blackboard-class_1250271.htm#query=child%20math&position=13&from_view=search&track=ais

Share this:

• Click to share on Twitter (Opens in new window)
• Click to share on Facebook (Opens in new window)

• Our Mission

6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution. 

1. Link problem-solving to reading

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it. 

3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process. 

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks. 

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.” 

6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process. 

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

• Grade 1 Lessons
• Grade 2 Lessons
• Grade 3 Lessons
• Grade 4 Lessons
• Grade 5 Lessons
• Math Activities

How to Improve Problem-Solving Skills in Math

Importance of Problem-Solving Skills in Math

Problem-solving skills are crucial in math education , enabling students to apply mathematical concepts and principles to real-world situations. Here’s why problem-solving skills are essential in math education:

1. Application of knowledge: Problem-solving in math requires encouraging students to apply the knowledge they acquire in the classroom to tackle real-life problems. It helps them understand the relevance of math in everyday life and enhances their critical thinking skills.

2. Developing critical thinking:  Problem-solving requires students to analyze, evaluate, and think critically about different approaches and strategies to solve a problem. It strengthens their mathematical abilities and improves their overall critical thinking skills.

3. Enhancing problem-solving skills:  Math problems often have multiple solutions, encouraging students to think creatively and explore different problem-solving strategies. It helps develop their problem-solving skills, which are valuable in various aspects of life beyond math.

4. Fostering perseverance:  Problem-solving in math often requires persistence and resilience. Students must be willing to try different approaches, learn from their mistakes, and keep trying until they find a solution. It fosters a growth mindset and teaches them the value of perseverance.

Benefits of strong problem-solving skills

Having strong problem-solving skills in math offers numerous benefits for students:

1. Improved academic performance:  Students with strong problem-solving skills are likelier to excel in math and other subjects that rely on logical reasoning and critical thinking.

2. Enhanced problem-solving abilities:  Strong problem-solving skills extend beyond math and can be applied to various real-life situations. It includes decision-making, analytical thinking, and solving complex problems creatively.

3. Increased confidence:  Successfully solving math problems boosts students’ self-confidence and encourages them to tackle more challenging tasks. This confidence spills over into other areas of their academic and personal lives.

4. Preparation for future careers:  Problem-solving skills are highly sought after by employers in various fields. Developing strong problem-solving skills in math sets students up for successful careers in engineering, technology, finance, and more.

Problem-solving skills are essential for math education and have numerous benefits for students. By fostering these skills, educators can empower students to become confident, critical thinkers who can apply their mathematical knowledge to solve real-world problems.

Understand the Problem

Breaking down the problem and identifying the key components.

To improve problem-solving math skills , it’s essential to first understand the problem at hand. Here are some tips to help break down the problem and identify its key components:

1. Read the problem carefully:  Take your time to read it attentively and ensure you understand what it asks. Pay attention to keywords or phrases that indicate what mathematical operation or concept to use.

2. Identify the known and unknown variables:  Determine what information is already given in the problem (known variables) and what you need to find (unknown variables). This step will help you analyze the problem more effectively.

3. Define the problem in your own words:  Restate the problem using your own words to ensure you clearly understand what needs to be solved. It can help you focus on the main objective and eliminate any distractions.

4. Break the problem into smaller parts:  Complex math problems can sometimes be overwhelming. Breaking them down into smaller, manageable parts can make them more approachable. Identify any sub-problems or intermediate steps that must be solved before reaching the final solution.

Reading and interpreting math word problems effectively

Many math problems are presented as word problems requiring reading and interpreting skills. Here are some strategies to help you effectively understand and solve math word problems:

1. Highlight key information:  As you read the word problem, underline or highlight any important details, such as numbers, units of measurement, or specific keywords related to mathematical operations.

2. Visualize the problem:  Create visual representations, such as diagrams or graphs, to help you understand the problem better. Visualizing the problem can make determining what steps to take and how to approach the solution easier.

3. Translate words into equations:  Convert the information in the word problem into mathematical equations or expressions. This translation step helps you transform the problem into a solvable math equation.

4. Solve step by step:  Break down the problem into smaller steps and solve each step individually. This approach helps you avoid confusion and progress toward the correct solution.

Improving problem-solving skills in math requires practice and patience. By understanding the problem thoroughly, breaking it into manageable parts, and effectively interpreting word problems, you can confidently enhance your ability to solve math problems.

Use Visual Representations

Using diagrams, charts, and graphs to visualize the problem.

One effective way to improve problem-solving skills in math is to utilize visual representations. Visual representations , such as diagrams, charts, and graphs, can help make complex problems more tangible and easily understood. Here are some ways to use visual representations in problem-solving:

1. Draw Diagrams:  When faced with a word problem or a complex mathematical concept, drawing a diagram can help break down the problem into more manageable parts. For example, suppose you are dealing with a geometry problem. In that case, sketching the shapes involved can provide valuable insights and help you visualize the problem better.

2. Create Charts or Tables:  For problems that involve data or quantitative information, creating charts or tables can help organize the data and identify patterns or trends. It can be particularly useful in analyzing data from surveys, experiments, or real-life scenarios.

3. Graphical Representations:  Graphs can be powerful tools in problem-solving, especially when dealing with functions, equations, or mathematical relationships. Graphically representing data or equations makes it easier to identify key features that may be hard to spot from a numerical representation alone, such as intercepts or trends.

Benefits of visual representation in problem-solving

Using visual representations in problem-solving offers several benefits:

1. Enhances Comprehension:  Visual representations provide a visual context for abstract mathematical concepts, making them easier to understand and grasp.

2. Encourages Critical Thinking:  Visual representations require active engagement and critical thinking skills. Students can enhance their problem-solving and critical thinking abilities by analyzing and interpreting visual data.

3. Promotes Pattern Recognition: Visual representations simplify identifying patterns, trends, and relationships within data or mathematical concepts. It can lead to more efficient problem-solving and a deeper understanding of mathematical principles.

4. Facilitates Communication:  Visual representations can be shared and discussed, helping students communicate their thoughts and ideas effectively. It can be particularly useful in collaborative problem-solving environments.

Incorporating visual representations into math problem-solving can significantly enhance understanding, critical thinking, pattern recognition, and communication skills. Students can approach math problems with a fresh perspective and improve their problem-solving abilities using visual tools.

Work Backwards

Understanding the concept of working backward in math problem-solving.

Working backward is a problem-solving strategy that starts with the solution and returns to the given problem. This approach can be particularly useful in math, as it helps students break down complex problems into smaller, more manageable steps. Here’s how to apply the concept of working backward in math problem-solving:

1. Identify the desired outcome : Start by clearly defining the goal or solution you are trying to reach. It could be finding the value of an unknown variable, determining a specific measurement, or solving for a particular quantity.

2. Visualize the result : Imagine the final step or solution. It will help you create a mental image of the steps needed to reach that outcome.

3. Trace the steps backward : Break down the problem into smaller steps, working backward from the desired outcome. Think about what needs to happen immediately before reaching the final solution and continue tracing the steps back to the beginning of the problem.

4. Check your work : Once you have worked backward to the beginning of the problem, double-check your calculations and steps to ensure accuracy.

Real-life examples and applications of working backward

Working backward is a valuable problem-solving technique in math and has real-life applications . Here are a few examples:

1. Financial planning : When creating a budget, you can work backward by determining your desired savings or spending amount and then calculating how much income or expenses are needed to reach that goal.

2. Project management : When planning a project, you can work backward by setting a fixed deadline and then determining the necessary steps and timelines to complete the project on time.

3. Game strategy : In games like chess or poker, working backward can help you anticipate your opponent’s moves and plan your strategy accordingly.

4. Recipe adjustments : When modifying a recipe, you can work backward by envisioning the final taste or texture you want to achieve and adjusting the ingredients or cooking methods accordingly.

By practicing working backward in math and applying it to real-life situations, you can enhance your problem-solving abilities and find creative solutions to various challenges.

Try Different Strategies

When solving math problems, it’s essential to have a repertoire of problem-solving strategies. You can improve your problem-solving skills and tackle various mathematical challenges by trying different approaches. Here are some strategies to consider:

Exploring Various Problem-Solving Strategies

1. Guess and Check:  This strategy involves making an educated guess and checking if it leads to the correct solution. It can be useful when dealing with trial-and-error problems.

2. Drawing a Diagram:  Visually representing the problem through diagrams or graphs can help you understand and solve it more effectively. This strategy is particularly useful in geometry and algebraic reasoning.

3. Using Logic:  Using logical reasoning is useful for breaking down complicated problems into smaller, more manageable components. This strategy is especially useful in mathematical proofs and logical puzzles.

4. Working Backwards:  Start with the desired outcome and return to the given information. When dealing with equations or word problems, this approach can assist.

5. Using Patterns:  Look for patterns and relationships within the problem to determine a solution. This approach can be used for different mathematical problems, such as sequences and numerical patterns.

When and How to Apply Different Strategies in Math Problem-Solving

Knowing when and how to apply different problem-solving strategies is crucial for success in math. Here are some tips:

• Understand the problem: Read the problem carefully and identify the key information and requirements.
• Select an appropriate strategy: Choose the most appropriate problem-solving strategy for the problem.
• Apply the chosen strategy: Implement the selected strategy, following the necessary steps.
• Check your solution: Verify your answer by double-checking the calculations or applying alternative methods.
• Reflect on the process: After solving the problem, take a moment to reflect and evaluate your problem-solving approach. Identify areas for improvement and consider alternative strategies that could have been used.

By exploring different problem-solving strategies and applying them to various math problems, you can enhance your problem-solving skills and develop a versatile toolkit for tackling mathematical challenges. Practice and persistence are key to honing your problem-solving abilities in math.

Key takeaways and tips for improving problem-solving skills in math

In conclusion, developing strong problem-solving skills in math is crucial for success in this subject. Here are some key takeaways and tips to help you improve your problem-solving abilities:

• Practice regularly:  The more you practice solving math problems, the better you will become at identifying patterns, applying strategies, and finding solutions.
• Break down the problem:  When faced with a complex math problem, break it into smaller, more manageable parts. It will make it easier to understand and solve.
• Understand the problem:  Before diving into a solution, fully understand the problem. Identify what information is given and what you are asked to find.
• Draw diagrams or visualize:  Use visual aids, such as diagrams or sketches, to help you better understand the problem and visualize the solution.
• Use logical reasoning:  Apply logical reasoning skills to analyze the problem and determine the most appropriate approach or strategy.
• Try different strategies:  If one approach doesn’t work, don’t be afraid to try different strategies or methods. There are often multiple ways to solve a math problem.
• Seek help and collaborate:  Don’t hesitate to seek help from your teacher, classmates, or online resources. Collaborating with others can provide different perspectives and insights.
• Learn from mistakes:  Mistakes are a valuable learning opportunity. Analyze your mistakes, understand where you went wrong, and learn from them to avoid making the same errors in the future.
• Grade 6 Lessons
• Grade 7 Lessons
• Grade 8 Lessons
• Kindergarten
• Math Lessons Online
• Math Tutorial
• Multiplication
• Subtraction
• #basic mathematic
• #Basic Mathematical Operation
• #best math online math tutor
• #Best Math OnlineTutor
• #dividing fractions
• #effective teaching
• #grade 8 math lessons
• #linear equation
• #Math Online Blog
• #mathematical rule
• #mutiplying fractions
• #odd and even numbers
• #Online Math Tutor
• #online teaching
• #order of math operations
• #pemdas rule
• #Point-Slope Form
• #Precalculus
• #Slope-Intercept Form
• #Tutoring Kids

Thank you for signing up!

GET IN TOUCH WITH US

You are using an outdated browser. Please upgrade your browser to improve your experience.

Health & Nursing

Courses and certificates.

• Bachelor's Degrees
• View all Business Bachelor's Degrees
• Business Management – B.S. Business Administration
• Healthcare Administration – B.S.
• Human Resource Management – B.S. Business Administration
• Information Technology Management – B.S. Business Administration
• Marketing – B.S. Business Administration
• Accounting – B.S. Business Administration
• Finance – B.S.
• Supply Chain and Operations Management – B.S.
• Communications – B.S.
• User Experience Design – B.S.
• Accelerated Information Technology Bachelor's and Master's Degree (from the School of Technology)
• Health Information Management – B.S. (from the Leavitt School of Health)
• View all Business Degrees

Master's Degrees

• View all Business Master's Degrees
• Master of Business Administration (MBA)
• MBA Information Technology Management
• MBA Healthcare Management
• Management and Leadership – M.S.
• Accounting – M.S.
• Marketing – M.S.
• Human Resource Management – M.S.
• Master of Healthcare Administration (from the Leavitt School of Health)
• Data Analytics – M.S. (from the School of Technology)
• Information Technology Management – M.S. (from the School of Technology)
• Education Technology and Instructional Design – M.Ed. (from the School of Education)

Certificates

• Supply Chain
• Accounting Fundamentals
• Digital Marketing and E-Commerce

Bachelor's Preparing For Licensure

• View all Education Bachelor's Degrees
• Elementary Education – B.A.
• Special Education and Elementary Education (Dual Licensure) – B.A.
• Special Education (Mild-to-Moderate) – B.A.
• Mathematics Education (Middle Grades) – B.S.
• Mathematics Education (Secondary)– B.S.
• Science Education (Middle Grades) – B.S.
• Science Education (Secondary Chemistry) – B.S.
• Science Education (Secondary Physics) – B.S.
• Science Education (Secondary Biological Sciences) – B.S.
• Science Education (Secondary Earth Science)– B.S.
• View all Education Degrees

Bachelor of Arts in Education Degrees

• Educational Studies – B.A.

Master of Science in Education Degrees

• View all Education Master's Degrees
• Curriculum and Instruction – M.S.
• Educational Leadership – M.S.
• Education Technology and Instructional Design – M.Ed.

Master's Preparing for Licensure

• Teaching, Elementary Education – M.A.
• Teaching, English Education (Secondary) – M.A.
• Teaching, Mathematics Education (Middle Grades) – M.A.
• Teaching, Mathematics Education (Secondary) – M.A.
• Teaching, Science Education (Secondary) – M.A.
• Teaching, Special Education (K-12) – M.A.

Licensure Information

• State Teaching Licensure Information

Master's Degrees for Teachers

• Mathematics Education (K-6) – M.A.
• Mathematics Education (Middle Grade) – M.A.
• Mathematics Education (Secondary) – M.A.
• English Language Learning (PreK-12) – M.A.
• Endorsement Preparation Program, English Language Learning (PreK-12)
• Science Education (Middle Grades) – M.A.
• Science Education (Secondary Chemistry) – M.A.
• Science Education (Secondary Physics) – M.A.
• Science Education (Secondary Biological Sciences) – M.A.
• Science Education (Secondary Earth Science)– M.A.
• View all Technology Bachelor's Degrees
• Cloud Computing – B.S.
• Computer Science – B.S.
• Cybersecurity and Information Assurance – B.S.
• Data Analytics – B.S.
• Information Technology – B.S.
• Network Engineering and Security – B.S.
• Software Engineering – B.S.
• Accelerated Information Technology Bachelor's and Master's Degree
• Information Technology Management – B.S. Business Administration (from the School of Business)
• User Experience Design – B.S. (from the School of Business)
• View all Technology Master's Degrees
• Cybersecurity and Information Assurance – M.S.
• Data Analytics – M.S.
• Information Technology Management – M.S.
• MBA Information Technology Management (from the School of Business)
• Full Stack Engineering
• Web Application Deployment and Support
• Front End Web Development
• Back End Web Development

3rd Party Certifications

• IT Certifications Included in WGU Degrees
• View all Technology Degrees
• View all Health & Nursing Bachelor's Degrees
• Nursing (RN-to-BSN online) – B.S.
• Nursing (Prelicensure) – B.S. (Available in select states)
• Health Information Management – B.S.
• Health and Human Services – B.S.
• Psychology – B.S.
• Health Science – B.S.
• Public Health – B.S.
• Healthcare Administration – B.S. (from the School of Business)
• View all Nursing Post-Master's Certificates
• Nursing Education—Post-Master's Certificate
• Nursing Leadership and Management—Post-Master's Certificate
• Family Nurse Practitioner—Post-Master's Certificate
• Psychiatric Mental Health Nurse Practitioner —Post-Master's Certificate
• View all Health & Nursing Degrees
• View all Nursing & Health Master's Degrees
• Nursing – Education (BSN-to-MSN Program) – M.S.
• Nursing – Leadership and Management (BSN-to-MSN Program) – M.S.
• Nursing – Nursing Informatics (BSN-to-MSN Program) – M.S.
• Nursing – Family Nurse Practitioner (BSN-to-MSN Program) – M.S. (Available in select states)
• Nursing – Psychiatric Mental Health Nurse Practitioner (BSN-to-MSN Program) – M.S. (Available in select states)
• Nursing – Education (RN-to-MSN Program) – M.S.
• Nursing – Leadership and Management (RN-to-MSN Program) – M.S.
• Nursing – Nursing Informatics (RN-to-MSN Program) – M.S.
• Master of Healthcare Administration
• Master of Public Health
• MBA Healthcare Management (from the School of Business)
• Business Leadership (with the School of Business)
• Supply Chain (with the School of Business)
• Accounting Fundamentals (with the School of Business)
• Digital Marketing and E-Commerce (with the School of Business)
• Back End Web Development (with the School of Technology)
• Front End Web Development (with the School of Technology)
• Web Application Deployment and Support (with the School of Technology)
• Full Stack Engineering (with the School of Technology)
• Single Courses
• Course Bundles

Apply for Admission

Admission requirements.

• New Students
• WGU Returning Graduates
• WGU Readmission
• Enrollment Checklist
• Accessibility
• Accommodation Request
• School of Education Admission Requirements
• School of Business Admission Requirements
• School of Technology Admission Requirements
• Leavitt School of Health Admission Requirements

Additional Requirements

• Computer Requirements
• No Standardized Testing
• Clinical and Student Teaching Information

Transferring

• FAQs about Transferring
• Transfer to WGU
• Transferrable Certifications
• Request WGU Transcripts
• International Transfer Credit
• Tuition and Fees
• Financial Aid
• Scholarships

Other Ways to Pay for School

• Tuition—School of Business
• Tuition—School of Education
• Tuition—School of Technology
• Tuition—Leavitt School of Health
• Your Financial Obligations
• Tuition Comparison
• Applying for Financial Aid
• State Grants
• Consumer Information Guide
• Responsible Borrowing Initiative
• Higher Education Relief Fund

FAFSA Support

• Net Price Calculator
• FAFSA Simplification
• See All Scholarships
• Military Scholarships
• State Scholarships
• Scholarship FAQs

Payment Options

• Payment Plans
• Corporate Reimbursement
• Current Student Hardship Assistance
• Military Tuition Assistance

WGU Experience

• How You'll Learn
• Scheduling/Assessments
• Accreditation
• Student Support/Faculty
• Military Students
• Part-Time Options
• Virtual Military Education Resource Center
• Student Outcomes
• Return on Investment
• Students and Gradutes
• Career Growth
• Student Resources
• Communities
• Testimonials
• Career Guides
• Skills Guides
• Online Degrees
• All Degrees
• Explore Your Options

Admissions & Transfers

• Admissions Overview

Tuition & Financial Aid

Student Success

• Prospective Students
• Current Students
• Military and Veterans
• Commencement
• Careers at WGU
• Advancement & Giving
• Partnering with WGU

WESTERN GOVERNORS UNIVERSITY

Developing your mathematics skills, mathematics skills.

Mathematics skills are the backbone of solving logical, pattern-based numerical problems. This broad set of skills includes numeracy, mathematical reasoning, data analysis, algebra, geometry, and critical thinking.

Mathematics skills equip you with the tools to comprehend and manipulate the complex world of mathematics, work out problems, and use analytical thinking.

This guide discusses mathematics skills, their importance, and how you can acquire them.

What Are Mathematics Skills?

Mathematics skills are the abilities and competencies you need to understand and solve mathematical problems and keep track of data. These abilities encompass various mathematical ideas, methods, and procedures that let you comprehend, evaluate, and use mathematical principles in different situations. 

Since mathematics is a universal language, mathematics skills are highly valued and applicable across different careers and professions. They are the skills that provide you with a framework for understanding and making sense of the world.

Why Are Mathematics Skills Important?

Mathematical skills are essential in day-to-day activities since they offer practical applications and the capacity to solve problems.

Here are some reasons why mathematical skills can give you an upper hand in your career:

• Practical applications: You can easily understand numerical information and make informed decisions. For example, interpreting budgets, financial statements, and project management data is essential in any organization.
• Problem-solving ability: Mathematical skills foster the development of problem-solving skills, which are extremely valuable in any profession. These skills enable you to approach challenges with a structured mindset, leading to efficient and effective solutions.
• Critical thinking: Critical thinkers can assess data, spot patterns and relationships, and reach logical conclusions. When faced with complicated problems or decision-making situations, mathematical skills enable you to make more informed decisions and exercise critical thinking.
• Cognitive development: By sharpening your mathematics skills, you’ll possess strong cognitive capacities, making you think analytically, rationally, and abstractly. These skills can be helpful in problem-solving, strategic thinking, and decision-making.

What Are the Benefits of Having Mathematics Skills?

Mathematics skills open doors to many opportunities and give you a competitive advantage in various fields. These skills will enable you to grow personally and financially and prepare you for leadership roles and new career opportunities. Here are the benefits of having mathematics skills:

• Quantitative literacy: You are able to understand, interpret, and communicate information presented in numerical or graphical form. Quantitative literacy allows you to make sense of quantitative data, critically evaluate claims, and make informed decisions based on evidence and analysis. 
• Financial management: You understand budgeting, interest rates, investments, and financial calculations. Financial management will help you in budget planning, savings, investment strategies, and evaluating financial risks, improving financial well-being and stability.
• Technology proficiency: By knowing how to leverage technology effectively, you can comfortably work with complex algorithms, and adapt to rapidly evolving technological advancements. Mathematical concepts are applied in technological fields such as computer science, data science, and engineering. 
• Data and financial analysis: Mathematics skills will enable you to analyze and interpret data accurately. Proficiency in statistical analysis, data modeling, and financial calculations enhances the ability to extract information from a large dataset.
• Risk assessment: You can assess and manage risks effectively. Mathematical concepts such as probability theory, statistical distributions, and mathematical models will equip you with the tools to evaluate and quantify risks associated with various scenarios, making you an attractive candidate in the fields of insurance, finance, project management, and investment analysis.
• Market research and forecasting: Mathematics skills are instrumental in market research and forecasting. You can analyze historical data, identify patterns, and create mathematical models that help predict market trends, making you a competitive applicant for marketing and business strategy roles.

Examples of Mathematics Skills in the Workplace

Mathematics skills are applied in everyday life and work. Below are examples of how you can apply them:

Software Development and Coding

Programmers use mathematical algorithms, logic, and problem-solving techniques to develop efficient and accurate codes. Mathematics helps in data encryption, algorithm design, optimization problems, and machine learning algorithms.

Healthcare and Medicine

As a medical professional, you would use mathematical models to analyze patient data, perform medical imaging, and simulate biological processes. Pharmacists also employ mathematical calculations to determine dosage and medication formulations. 

Supply Chain and Logistics

Applying mathematical modeling and optimization techniques, supply chain and logistics professionals optimize inventory levels, plan routes, schedule deliveries, and minimize transportation costs.  

Risk Analysis and Insurance

As an actuarial scientist, you would use mathematical models and probability theories to assess risks, calculate insurance premiums, and determine reserves.  

Data Analysis

As a data analyst, you would use mathematical skills in statistical analysis, calculating measures of central tendency and variability, creating data visualizations, and drawing meaningful conclusions from data sets.  

Financial Planning

As a financial planner, you would use mathematical calculations to create budgets, forecast income and expenses, calculate interest rates, evaluate investment opportunities, and plan for retirement.  

Engineering and Architecture

As an engineer, you would use mathematical principles and formulas to design structures, analyze structural integrity, calculate load capacities, and determine optimal configurations. You will also employ concepts such as calculus, geometry, and trigonometry to solve complex engineering problems.

How Will I Use Mathematics Skills?

As an educator, you’ll find various ways to utilize mathematics skills in your profession. 

• Education-related careers: Mathematics skills will help you become effective in education-related roles such as middle school teacher or mathematics teacher .
• Identifying patterns and trends: You will employ various mathematical skills to identify patterns and analyze data through virtual inspection, central tendency measures, variation measures, correlation analysis, regression analysis, etc.
• Critical thinking and logical reasoning: Mathematics education encourages critical thinking and logical reasoning abilities. These skills will be applied to analyze complex situations, evaluate arguments, identify patterns, and make sound judgments in personal and professional contexts.
• Data analysis and interpretation: Mathematics education will equip you with the tools to analyze and interpret data. You will use statistical techniques to examine patterns, trends, and relationships in data, enabling you to make evidence-based decisions, draw meaningful conclusions, and communicate insights effectively.
• Mathematical modeling: Mathematical modeling skills will allow you to represent real-world situations using mathematical structures. You'll be able to analyze, simulate, and predict outcomes in fields such as finance, economics, engineering, and science. You will employ mathematical models to optimize processes, solve complex problems, and make informed predictions
• Educational support: Mathematics education skills can be utilized in a teaching or tutoring role. With your knowledge, you will assist students or colleagues in understanding mathematical concepts, solving problems, and developing critical thinking skills.
• Problem-solving: Logical reasoning and critical thinking are valuable skills for solving problems. Applying mathematical problem-solving techniques will help you identify the root causes and generate potential solutions.

How Can I Learn Mathematics Skills?

WGU’s competency-based education model enables students to learn mathematics skills at their own pace, demonstrating proficiency through assessments and real-world applications. 

Through WGU’s School of Education, you can receive a solid foundation in mathematics skills. With a degree in education, you'll be equipped to:

• Solve problems using mathematics.
• Solve fundamental geometric problems.
• Perform most calculations using spreadsheets or calculators.
• Perform basic algebraic formulas.
• Interpret complex mathematical concepts, including the workings of data science models.
• Identify consequences of different sets of mathematical assumptions.
• Assemble sets of mathematical assumptions.
• Apply mathematical theories and techniques for solving practical problems.
• Apply logical and mathematical processes to challenges.
• Analyze data using basic statistical techniques.

Frequently Asked Questions

Are mathematics skills essential for non-technical careers.

Yes, mathematics skills are essential for non-technical careers.

A solid foundation in mathematics provides you with a competitive edge and improves your problem-solving abilities, making you more effective in non-technical roles.

Whether it's financial analysis, market research, or strategic planning, mathematics skills will enable you to make informed decisions and navigate challenges confidently. Whether you're pursuing a technical or non-technical career, embracing mathematics as a fundamental skill will undoubtedly improve your professional journey.

What career opportunities are available for individuals with strong mathematics skills?

Your proficiency in numbers and problem-solving can lead you to professions such as that of an actuary, assessing and managing financial risks, or in accounting , where you’ll use your mathematical skills to analyze and manage financial records. Having solid mathematics skills will open doors to exciting career opportunities in many fields. 

If you have a passion for impacting knowledge, you can also become a mathematics teacher , inspiring and shaping the minds of future generations.

How can I highlight my mathematics skills on my résumé or during job interviews?

Focus on highlighting mathematics skills directly relevant to the position and industry you are targeting. For example, if you’re applying for a retail job, you can highlight that you understand pricing and revenue management. 

Showcasing your mathematics skills demonstrates your value as a candidate and increases your chances of securing a job.

Find Your Degree

Discovering the right degree program that aligns with your goals is a crucial step. You can begin the journey toward achieving personal growth and advancement. Take our degree quiz to help you identify the degree program that best suits your interests and embark on a path of knowledge and future success.

The University

For students.

• Student Portal
• Alumni Services

Most Visited Links

• Business Programs
• Student Experience
• Diversity, Equity, and Inclusion
• Student Communities

Best 13 Strategies for solving math problems

Mathematics can often be a challenging subject for many students. The key to conquering math lies in understanding the concepts and developing effective problem-solving strategies. Let us explore a range of strategies that can help students solve math problems confidently and easily. By implementing these techniques, students can enhance their mathematical skills and achieve success in this critical subject.

Table of Contents

1. Understand the Problem

2. simplify and visualize the problem.

Complex math problems can often be overwhelming. It’s helpful to simplify and visualize the problem to make them more manageable. Break down the problem into smaller, more understandable parts. Draw diagrams or use visual aids to represent the information, relationships, or geometric figures. This approach can provide valuable insights and facilitate a better understanding of the problem.

3. Identify Relevant Concepts and Formulas

4. work backwards.

Working backward is a powerful strategy that can be employed to solve certain types of math problems. Start with the given answer and consider the steps leading to that solution. By reversing the problem, you can uncover hidden relationships, identify missing information, or even discover alternative solutions.

5. Utilize Logical Reasoning

6. practice problem-solving regularly.

Practice makes perfect, and this holds for math problem-solving as well. Regular practice strengthens your problem-solving skills and builds confidence in tackling different types of math problems. Solve various math problems from textbooks, workbooks, or online resources. The more you practice, the more familiar you become with different problem-solving techniques, enhancing your ability to effectively approach and solve math problems.

7. Seek Help and Collaborate

8. break down complex problems, 9. review and learn from mistakes.

Mistakes are an integral part of the learning process. When you encounter challenges or make errors while solving math problems, take the time to review and learn from them. Analyze your mistakes, identify where you went wrong, and understand the correct approach. This

10. Practice Mental Math

11. use problem-solving strategies, 12. develop time management skills.

Time management is essential when solving math problems, especially during exams or timed assessments. Practice working on math problems under timed conditions to improve speed and accuracy. Learn to prioritize and allocate time to different parts of a problem, ensuring you complete all necessary steps within the given timeframe.

13. Review and Reinforce Fundamentals

Conclusion – strategies for solving math problems.

Regular practice, collaboration, breaking down complex problems, and learning from mistakes are key to improving mathematical problem-solving abilities. With dedication and perseverance, students can unlock the secrets to solving math problems easily and confidently.

Share this:

Whether you are contemplating a career in applied math solving real world problems or pure mathematics expanding the realm of what is known (and unknown), make sure your CV or resume includes these 10 skills and abilities.

According to the U.S. Department of Labor , mathematicians should have at least these 10 skills and abilities if they want to succeed in mathematical research, education, or as an industrial mathematician at a Fortune 100 company.

While there are many skills and abilities that make a successful mathematician, employers will review your application materials for a high degree of competency in these skills that show your knowledge as a mathematician. Displaying the ability to exercise information ordering, inductive reasoning, and mathematical reasoning will support your case for employment no matter where you are in your career.

And don’t forget, once you land the interview, share examples of how you used these analytical skills and abilities to succeed.

Mathematics — Using mathematics to solve problems.  

Complex Problem Solving — Identifying complex problems and reviewing related information to develop and evaluate options and implement solutions.  

Critical Thinking — Using logic and reasoning to identify the strengths and weaknesses of alternative solutions, conclusions or approaches to problems.  

Reading Comprehension — Understanding written sentences and paragraphs in work related documents.  

Active Learning — Understanding the implications of new information for both current and future problem-solving and decision-making.  

Mathematical Reasoning — The ability to choose the right mathematical methods or formulas to solve a problem.  

Number Facility — The ability to add, subtract, multiply, or divide quickly and correctly.

Deductive Reasoning — The ability to apply general rules to specific problems to produce answers that make sense.  

Inductive Reasoning — The ability to combine pieces of information to form general rules or conclusions (includes finding a relationship among seemingly unrelated events).

Information Ordering — The ability to arrange things or actions in a certain order or pattern according to a specific rule or set of rules (e.g., patterns of numbers, letters, words, pictures, mathematical operations).

• Resume Help
• Professional Development
• Mathematics

Current Jobs

• Follow us on social media
• google plus

Copyright © 2017 Mathematical Association of America. All rights reserved.

Explore Jobs

• Jobs Near Me
• Remote Jobs
• Full Time Jobs
• Part Time Jobs
• Entry Level Jobs
• Work From Home Jobs

Find Specific Jobs

• $15 Per Hour Jobs
• $20 Per Hour Jobs
• Hiring Immediately Jobs
• High School Jobs
• H1b Visa Jobs

Explore Careers

• Business And Financial
• Architecture And Engineering
• Computer And Mathematical

Explore Professions

• What They Do
• Certifications
• Demographics

Best Companies

• Health Care
• Fortune 500

Explore Companies

• CEO And Executies
• Resume Builder
• Career Advice
• Explore Majors
• Questions And Answers
• Interview Questions

Mathematical Skills: What They Are And Examples

• What Are Hard Skills?
• What Are Technical Skills?
• What Are What Are Life Skills?
• What Are Social Media Skills Resume?
• What Are Administrative Skills?
• What Are Analytical Skills?
• What Are Research Skills?
• What Are Transferable Skills?
• What Are Microsoft Office Skills?
• What Are Clerical Skills?
• What Are Computer Skills?
• What Are Core Competencies?
• What Are Collaboration Skills?
• What Are Conflict Resolution Skills?
• What Are Mathematical Skills?
• How To Delegate

Find a Job You Really Want In

Mathematical skills are important to improve if you want to increase your chances for professional success, no matter what career path you pursue. Many jobs use mathematical skills regularly, and even for the rare jobs that never directly deal with numbers and figures, you’ll often need the same problem-solving and critical thinking abilities used in math to succeed. So, if you’re a job seeker who wants to know more about how to make your mathematical skills shine, stay tuned. In this article, we’ll cover the most important mathematical skills to master for the workplace and discuss how to improve and highlight your math skills during the job-search process . Key Takeaways: 10 mathematical skills that are useful in the workplace are time management, mental arithmetic, constructing logical arguments, abstract thinking, data analysis, research, visualization, creativity, forecasting, and attention to detail. Improve your mathematical skills by acquiring conceptual understandings of the skills and solving practice problems. A mathematical skill should be listed on a resume when the job listing states the skill as a requirement. Most mathematical skills are transferable and help you stand out in a crowd of applicants. In This Article    Skip to section What are mathematical skills? How to improve your mathematical skills How to highlight mathematical skills on a resume Mathematical skills resume example Mathematical Skills FAQ Sources: Sign Up For More Advice and Jobs Show More What are mathematical skills?

The term “mathematical skills” doesn’t just refer to nebulous topics taught in school, such as calculus. They’re the practical abilities that are useful no matter the industry or size of business you work in.

This includes skills such as:

Time management. Being able to manage your time efficiently is critical for your day-to-day activities, in addition to long-term planning success.

The average person wastes three entire hours each day due to inefficient time management.

Not only does that immediately translate to wasted money, but to wasted time that could be devoted to your non-work passions and activities.

Mental arithmetic. Being able to do mental math quickly will serve you well in a variety of professions.

Retail workers may need to quickly and accurately figure out a customer’s change when given a large sum of money.

Constructing logical arguments. Many careers demand the same precise, logical reasoning that’s used to solve math problems.

An attorney needs to ensure that their legal argument logically follows from the facts and evidence provided.

Abstract thinking. Abstract thinking is the ability to understand and compare non-physical concepts, such as freedom or honesty.

Improving your abstract thinking skills is useful for any career that involves creativity or navigating through complex rules.

Data analysis. A large variety of professions will require you to interpret and analyze data at some point.

Any scientific career will involve heavy interpretation of complex sets of data.

Research. Knowing how to effectively research information is crucial for developing solutions for the many problems you’ll face in your career.

In the age of the internet, there is a nearly infinite wealth of information about any topic you could wish to learn about.

Visualization. The same ability to visualize problems and outcomes is critical for finding solutions in the workplace.

Any problem you face during your career will present a variety of possible solutions with which to tackle it.

Creativity. Improving your creativity skills allows you to come up with new ideas and innovations.

Presenting fresh ideas and solutions will also help you stand out among the competition in the workplace.

Forecasting. Forecasting is the ability to extrapolate events into the future based on available data and knowledge.

This skill is critical for any job that involves planning for the future.

Attention to detail. Some jobs require more attention to small details than others.

How to improve your mathematical skills

Mathematical skills can be improved in the same way that you would improve any other skill – through consistent practice.

More specifically, there are two key actions you should follow:

Acquire conceptual understanding. You can’t improve a mathematical skill if you don’t even know what that math skill entails.

For example, suppose that you wish to improve your data analysis skills.

A quick Google search reveals that the main elements of data analysis include understanding statistics, visuals such as charts and graphs, and how to apply the data to practical problems.

Solve practice problems. It’s not enough to understand a concept to master it; you must practice practically applying it.

This piece of advice applies to certain math skills more than others. You can find plenty of online games to help you improve your hard skills , such as mental arithmetic, but maybe not your creativity.

How to highlight mathematical skills on a resume

Mathematical skills positively effect your work performance, especially when you improve them.

However, we still want to find a way to highlight them to recruiters, so they know that we’ve mastered them.

There are a few important guidelines to follow:

List or prove on your resume. The skills section of your resume can be an okay place to mention your math skills.

The job listing states the skill as a requirement. If your resume doesn’t contain the specific term, some companies’ applicant tracking systems (ATS) may automatically filter you out.

Not significant enough to waste additional resume space. Despite being required, some skills may not be essential enough to waste more than a single bullet point talking about.

For example, a job may require basic clerical skills such as multiplying and dividing small figures.

“Critical-thinking skills” and “ problem-solving skills ” are generically added to so many resumes that the terms often become meaningless.

A better way to highlight your math skills on a resume is to prove it through the results you’ve achieved. Use numbers to emphasize the positive value you created for a past employer.

Prove them in your cover letter. You want to give examples of when you used mathematical skills to create value for a past employer.

This differs from the resume strategy in that cover letters are narrower in scope.

Your resume needs to fit many examples on a single page , while your cover letter can target a few key skills to demonstrate with greater detail.

To figure out which math skills to focus on, pay attention to the essential requirements and duties listed in the job listing. Make your best judgment on the most important skills to highlight.

Explain in-depth during your job interview. Job interviews allow you the time to dive much deeper into examples of how you’ve utilized mathematical skills.

Consider the previous resume example about developing a new marketing strategy using data-analysis skills.

During the interview, you could expand on the specific technical skills and tools you used. Explain the initial problem and the thought process you employed to tackle it.

Mathematical skills resume example

Mathematical skills can be more tangible when you can see them on a resume. Luckily, we’ve provided an mathematical skills resume for you:

Finnegan Bennett 117 Melrose Ave., Austin, TX , 73301 (662)-280-0092 [email protected] Detail-orientated and organized mathematics teacher with over 10 years of experience working in high schools. Possesses a Masters in Education from Austin University. Strong skills in problem-solving and time management. Professional Experience Austin Independent School District , Austin, TX Geometry Teacher , September 2016 — Present Presented HSPA specific lessons to various classes within the mathematics department. Assist with teaching students as an entire class or in small groups as the lessons are planned. Designed, developed, and implemented courses in coordination with science curriculum Designed and implement classroom management strategies at a school wide level. Educate , Austin, TX Math Teacher , September 2013 — August 2016 Delivered and graded assessments in multiple subject areas meeting educational standards. Provide tutoring services by facilitating small groups or individual students for children in grades kindergarten through high school. Skills Pre-Calculus Classroom Management Student Learning Mathematics Special Education State Standards Clear Objectives Test Scores In-Service Training Small Groups Education University of Austin , Austin, TX Masters Degree Education , May 2016 Baker University , Austin, TX Bachelor’s Degree Business , May 2012 Graduated with honors

Mathematical Skills FAQ

What are the most important math skills?

The most important math skills in the workplace depend on your needs. The four fundamental arithmetic operations of adding, subtracting, multiplying and dividing are very important for all adults to have a basic understanding because they appear in many of our lives daily.

Time management, logic, and abstract thinking are also very important for most adults to know, regardless of profession, because they help provide structure to your life and prepare you for critical thinking.

Why are mathematical skills important?

Mathematical skills are important because they provide structure to solving problems rationally. Mathematical skills can be used everyday to make sense of a chaotic world. Recognizing patterns, using logic, building on abstract concepts all are what help keep society moving.

How do you list math skills on a resume?

List math skills under the skills section of a resume. In order to be efficient with space, make sure to only list relevant skills that are found in the job description and avoid general terms.

MAA – 10 Skills and Abilities Every Math Major Should Include on Their Resume

How useful was this post?

Click on a star to rate it!

Average rating / 5. Vote count:

No votes so far! Be the first to rate this post.

Chris Kolmar is a co-founder of Zippia and the editor-in-chief of the Zippia career advice blog. He has hired over 50 people in his career, been hired five times, and wants to help you land your next job. His research has been featured on the New York Times, Thrillist, VOX, The Atlantic, and a host of local news. More recently, he's been quoted on USA Today, BusinessInsider, and CNBC.

Related posts

How To Give An Effective Presentation (With Examples)

What Is Professionalism In The Workplace? (With Examples)

Master’s In Psychology Jobs [10 Best-Paying + 10 Entry-Level Jobs You Can Do With A Psychology Degree]

How To Write A Plan Of Action (With Examples)

• Career Advice >
• Hard Skills >
• Mathematical Skills

Stack Exchange Network

Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Q&A for work

Connect and share knowledge within a single location that is structured and easy to search.

How can I improve my problem solving/critical thinking skills and learn higher math?

I'm a rising sophomore in high school. So far, I've taken Algebra One, Two, and Geometry in school. I want to learn higher math such as precalculus/trigonometry, calculus, linear algebra, and more, so I can go into topics such as cryptography, advanced computer science, and possibly take the AMC and other olympiad tests (I'm not too interested in that).

The only problem, though, is that my abilities in problem solving and other stuff in math aren't that good. I do pretty well in my classes (high As) but that doesn't mean anything. The U.S. system doesn't seem too good in actually teaching math.

For example, I can do whatever is on my homework or tests. But, if I'm given a more difficult problem than usual concerning a topic I learned (say logarithms or something), I can't solve it.

I feel like this is going to be a hindrance to me learning higher math, doing well in more difficult subjects like calculus and linear algebra, doing well on olympiad tests, and going into math-heavy fields like computer science and cryptography.

So, how can I change all of this and improve my skills? Are there any books that teach problem-solving, mathematical thinking, and higher math (or something like precalculus)? Again, I want to better these skills so I can do well not only in math, but other fields.

Any help is really appreciated.

• algebra-precalculus
• soft-question
• self-learning
• problem-solving

• 8 $\begingroup$ Several things will help you learn higher math. You are enthusiastic about the subject. You invest time to really understand the material (forget about 'plugging into formulas). You have confidence in you abilities (don't say "I can't solve it" - try "By investing more time I will learn valuable things"). $\endgroup$ –  CopyPasteIt Commented Jun 9, 2017 at 0:05
• 2 $\begingroup$ Probably someone says that this is wishful-thinking but in my experience if you want something you generally found it (at least to some degree where you find comfortable). In this case in particular, learning mathematics, you already showed that you are good in many aspects of it. I read somewhere that some very good mathematicians were bad at calculus when young, or at least not very well. Indeed, at today, I do many mistakes in simple calculus (horrible mistakes) and I dont think I cant learn what I want to learn. $\endgroup$ –  user173262 Commented Jun 9, 2017 at 0:26
• 1 $\begingroup$ Huh. I never thought of it that way. I've almost always heard that great mathematicians displayed talent from a young age, like Gauss or Terrence Tao and his gold medal in the IMO at 13. I just wanted to learn higher math and math skills so I can apply those in other fields (like computer science). $\endgroup$ –  Ansh.23 Commented Jun 9, 2017 at 0:50
• 3 $\begingroup$ Ansh.23 I would be careful with the use of "talent." Tao didn't win the gold medal on his own, he had world class training and people behind him giving motivation. I believe talent played some role, but Tao's case does more to prove the value of early training and (this is key) being taught by people who actually know what it is like to do math than prove the innate talent hypothesis. You should look at The Road to Excellence by K. Anders Ericcson(a collection of Psychology papers on deliberate practice and elite performance) if you're interested in learning from an academic perspective. $\endgroup$ –  Retired account Commented Jun 9, 2017 at 3:01
• 1 $\begingroup$ @Ansh.23 If it seems good it probably is. This stuff hasn't really changed recently. But if you want something more interactive you could also go with Keith Devlin's intro to Math thinking course on Coursera(I actually learned proofs from this, it's a very good course). The most important thing, regardless of which source you use, is to (obviously) solve problems, but also to discuss them with others. It is very easy in writing proofs as a beginner to think your proof is good when in reality it has large logical gaps or is extremely over complicated. $\endgroup$ –  Retired account Commented Jun 9, 2017 at 5:03

12 Answers 12

I'm going to take a different approach. Yes, you should buy the Polya books, I also recommend looking at learning how to learn on Edx for an interesting take on learning techniques. But do something else as well: watch the Khan academy videos on trig, then the first couple of MIT OCW calc videos. Then take Robert Ghrists Calculus course on Coursera and take the A.P. Calculus exam (I actually did this in one year, and it wasn't very hard-not because I'm so smart, I know from experience that I am at best mediocre in a real math class. It's just A.P. Calculus doesn't take a ton of real math skill). Then, for the final step, see if you can take classes at a local Univ. in real math. Their is no way to learn math like learning from actual mathematicians, this will get you college credit, and it will look good applying to college.

• 5 $\begingroup$ He's right. AP Calculus really doesn't require much thinking to get a 5/5. They are quite basic and reiterated problems, and much what you'd find in any textbook. $\endgroup$ –  Saketh Malyala Commented Jun 9, 2017 at 2:12
• $\begingroup$ Can the down voter explain themselves? @Bob1123 was this you? $\endgroup$ –  Aperson123 Commented Jun 9, 2017 at 22:34
• $\begingroup$ I searched on Edx for learning how to learn but did not find it. Is there a link or a search phrase that will get me there? $\endgroup$ –  labyrinth Commented Apr 12 at 13:31

I highly recommend George Polya's Induction and Analogy in Mathematics . The link is to a free version on the web, but if you find it engaging you will want a hard copy. Also How to Solve It , by the same author, although I don't find it as compelling.

For just plain fun, look at Hugo Steinhaus, Mathematical Snapshots . Dover, so very inexpensive.

• $\begingroup$ Thanks for the recommendation. I've heard of Polya and How to Solve it, but not this. Do you have any recommendations for books which teach math skills (like problem-solving) and a particular subject (like precalculus or calculus)? $\endgroup$ –  Ansh.23 Commented Jun 9, 2017 at 0:00
• $\begingroup$ You've plenty of time to learn particular subjects. Now just have fun. This answer elaborates: math.stackexchange.com/questions/1714966/… . If you really want problem solving practice find a way to get involved in competitions. $\endgroup$ –  Ethan Bolker Commented Jun 9, 2017 at 0:09
• $\begingroup$ Thanks for the link to the other answer. I liked the number theory book you suggested, and I think I'll get it from a library or something. I mainly wanted problem solving practice so I can do better in other math-related stuff like programming and cryptography. Do you have any suggestions for studying for olympiads/competitions (other than the Polya suggestion)? $\endgroup$ –  Ansh.23 Commented Jun 9, 2017 at 1:07
• $\begingroup$ Can you comment on why you prefer Induction and Analogy in Mathematics to How to Solve It? $\endgroup$ –  littleO Commented Jun 9, 2017 at 2:39
• 1 $\begingroup$ @littleO Induction and Analogy has somewhat more advanced mathematics (though not very advanced) and somewhat less introspection about strategies (though a lot, of course). $\endgroup$ –  Ethan Bolker Commented Jun 9, 2017 at 12:06

For a plain precalculus textbook that's good, but not extremely challenging, you can use Basic Mathematics by Serge Lang.

Good (short) books that will improve both your problem-solving ability and your ability to appreciate proofs at the high-school level include:

• Algebra by Gelfand and Shen
• The Method of Coordinates by Gelfand, Glagoleva and Kirillov
• Functions and Graphs by Gelfand, Glagoleva and Shnol
• Invitation to Number Theory by Oystein Ore
• Introduction to Inequalities by Beckenbach and Bellman
• The Mathematics of Choice by Niven
• Numbers: Rational and Irrational by Niven

Please also have a look at the excellent bibliography in the Mathematical Olympiad Handbook by Gardiner, which is viewable on Google Books. See here: https://books.google.com/books?id=zyFLrAEVgv8C&lpg=PA41&pg=PA41&redir_esc=y#v=onepage&q&f=false

These books are all great preparation for rigorous calculus and linear algebra later on.

• 1 $\begingroup$ This is the first time I've seen someone recommend Lang's book unironically. It's always struck me as in that odd place between basics and rigor, and I guess these situations really do fit the bill. I just had to chuckle. Anyway, +1 for the books by Niven! $\endgroup$ –  A. Thomas Yerger Commented Jun 9, 2017 at 13:26
• 1 $\begingroup$ @user49640 Have you ever used the Art of Problem Solving book series? I'm debating whether I should use those or the Gelfand books and the other books you recommended. Thanks for the list and link, they're both very helpful. $\endgroup$ –  Ansh.23 Commented Jun 9, 2017 at 14:53
• $\begingroup$ Why didn't you suggest "Linear Algebra" from Gelfand? $\endgroup$ –  Dac0 Commented Jun 9, 2017 at 15:18
• $\begingroup$ @Dac0 I see linear algebra at that level as being something one would study around the same time one studies calculus, and if possible, after one has studied some basic vector geometry. $\endgroup$ –  user49640 Commented Jun 9, 2017 at 18:02
• $\begingroup$ @Ansh.23 I haven't actually seen the Art of Problem Solving books, so I can't comment on their quality. What I know is that they were mostly written by people who did well in math competitions when they were young, as opposed to actual mathematicians. All the books I'm recommending were written by accomplished mathematicians. If you're not sure, visit a library to compare the books. $\endgroup$ –  user49640 Commented Jun 9, 2017 at 18:09

I often use https://brilliant.org/ as a site with a lot of questions for every level, with really great solutions. The wikis expect a lot of focus from you if you want to learn more, but go really in depth. Pretty much every math topic is covered. If you look at topics you think you already know, you will often find questions that you will be unable to solve because they offer new perspectives.

I'll give you my advice since until now it has not been given: "Think a lot on the easy stuff". Meditate the easy definitions, work examples and exercise only to understand what's going on really well.

Try to deduce implications of "easy statement" at whatever level they are. Generalizing is easy once you understood what's going on. If you're smart you can understand a lot of geometry from the geometry of surfaces. If you're smarter you can understand a lot of geometry from the geometry of lines.

If you're in the first year an easy statement can be the definition of a group, the property of associativity, the properties of integers or elementar linear algebra stuff. If you're in a master course it can be the definition of manifold, group actions, modules. If you're first year doctorate it can newly be the definition of a group, the property of associativity and newly linear algebra :D :D :D .

I mean that the solutions to a lot of problems appear when you see the same old thing that everyone knew from a totally different perspective that gives you a hint to a road that noone had seen before. This doesn't come from knowing a lot of fancy technical stuff rather than from knowing really well what's going on.

Don't worry at all if you can't solve harder problems (in your topic) now, I've used to be just like you.

The main thing that helped me was to browse through answers to harder problems I knew I couldn't do; after following through proofs I've tried to solve similar problems, if I couldn't solve it in around ~$20$ mins I would read through the solution and I would follow that procedure until I was able to solve such problems on my own.

Such knowledge needs time to better, I was very week at $1$st grade at $2$nd grade I was way better but still sometimes I chocked on problems and had to read through solution. At $3$rd and $4$th grade I was able to exactly pinpoint what technique I could apply to the problem.

I suggest trying out easier olympiad problems they usually have elegant solutions and are usually made to test problem solving skills of the brightest minds. I suggest Art of Problem Solving site for resources.

I would suggest perfecting the math topics you learned by now than when you start learning higher math topics it will be much easier.

The most essential aspect of critical thinking is being honest with yourself.

Read Discourse on the Method of Rightly Conducting one’s Reason and Seeking Truth in the Sciences , by Rene Descartes.

Write your math work out as if you were explaining it to someone else.

Establish patterns for writing out expansions, etc. For example, if you have

$(a+b)(c+d)$, always do it as

$(a+b)(c+d)$

$=a(c+d)+b(c+d)$

$=ac+ad+bc+bd$.

Even though you know you could just as well write

$=(a+b)c+(a+b)d$

$=ac+bc+ad+bd$.

Try to preserve the order of expressions as much as possible. For example, when I produced the second example above, I copied and pasted and then edited. The original correct result was

But, in my opinion, that is bad form.

Of course, there may be good reasons for deviating from those rules from time to time. For one; the exercise of doing something the alternative way may be instructive. But having set patterns avoids a lot of mental clutter.

Read with a pencil and paper (or whiteboard, or computer, etc.), and write out the theorems and proofs in your own words and symbols. Be sure you can justify every step to yourself. But don't over do it. Sometimes it makes more sense to just read through material trying to get the gist of what is being presented. Then go back and try to get a fuller understanding.

Learn to use LyX. It's free, and it will help you post to math.stackexchange.com. https://www.lyx.org/

Consider getting a student version of Mathematica.

I dropped out of high school in the tenth grade, and was never very good at participating in academic environments. My advice comes from not doing things that way for a long time. Edit to add:

Read the paragraph prior to the discussion of Decartes' contribution to the area of critical thinking. What I mean regarding being honest with yourself is that you should guard against believing in what Francis Bacon calls "idols". A Brief History of the Idea of Critical Thinking

For example, if someone gives you sound advice on how to improve your problem solving techniques and improve your critical thinking, but it gets voted down. You are obligated to decide for yourself who is in error.

As an example of how I approach learning math, see my Mathematica notebook recording my study of C.H. Edwards, Jr.'s Advanced Calculus of Several Variables . They are a work in progress. My notation is non-standard. And the notes are terse and cryptic. (But I expect a seasoned mathematician could follow them.)

Notice also that I have noted where Edwards made an assertion for which I do not provide proof. That typically means I'm flagging that for later consideration. Also note that there are some errors in Edwards treatment which I discovered by attempting to rewrite his discussion in the way I understand it.

• $\begingroup$ That's the same Descartes who invented analytical geometry. $\endgroup$ –  Steven Thomas Hatton Commented Jun 10, 2017 at 8:47
• $\begingroup$ To be clear. I did get a GED for which I did no focused preparation. I just like to learn, so I knew enough inadvertently. I also have a degree in computer science. But that was a very long process. I even took extra math classes, in which I got decent grades. I just knew I was faking it. I wasn't really learning. $\endgroup$ –  Steven Thomas Hatton Commented Jun 10, 2017 at 19:14

I have nothing to add in terms of books and such. However, for critical thinking and problem solving part, one of the key things that helped me is to learn to identify what i don't know in a given problem. This doesn't necessarily correspond to the wanted variable in a problem. It is more like a sense of direction. You look at a problem, and most of the time you have a sense of direction, a rather flexible set of approaches that come to your mind, for the problem at hand. Some parts of the problem makes you loose that sense of direction, like "now what?!", or "i lost track of what is happening here" moments, being able to identify those parts beforehand and train yourself accordingly, is a valuable skill. I personally believe it comes with proofs as they are already mentioned, i would also add formal logic, which would teach you how anything with a set of axioms and rules work.

You know what you know and don't know what you don't know. Just learn what you don't know so you know.

Everything is easy once you've learnt it.

The number of hours you put in is everything.

You will put enough hours if you like the subject. Otherwise it will be an horror.

You've got to grow your mental model of maths. It grows with every fact you add to it. The best ones have ridiculously huge mental models of their fields. How do you want to solve something without having a mental model of it? You've got no tool then.

If you feel someone's better than you, it's because they've put more hours into it than you, and maybe of better quality (hours). You know, they might be from a family with mathematician traditions lasting centuries, they might have been being taught by the best mathematicians every day since the age of 3.

It's great though that you're wondering and asking such questions. That puts you in a better position than 99% of society. It's good, but you're probably gonna want to compete with the 1%.

I believe it's similar to becoming good at Golf. Yes, you want to have good instructors and learn efficiently but by far the largest factor is years and years of practice and dedication to your craft.

I've thought about this a lot when speaking with someone who doesn't appear to have strong critical thinking skills, or unable to easily go abstract with concepts.

The interesting part - When I get the sense they are as least as genetically smart as I am I think to myself, how are you not able to quickly slice and dice logic, generalize, etc. things that seem pretty simple to me?

My best guess is there is simply a large difference between us in the time spent practicing these skills. How do you explain that even the most gifted athletes in the world usually can't switch sports, like how Michael Jordan was not very good at baseball?

When you come across an interesting problem you can't solve, find someone to help you slowly pick it apart end to end until you understand it fundamentally. Dedicate yourself to this systematic practice and think of the amount of time it takes to become a pro at anything.

Btw, I hope you already know that people like Einstein didn't sit around working 40 hours a week and just come up with these amazing insights. He was obsessed, consumed, maniacal in his work. Not terribly different from some pro athletes. HBO Real Sports has a new episode about Larry Bird. Raw talent not withstanding, there are simply not a lot of people you can't compete with when you put in that kind of time.

• 2 $\begingroup$ The necessity of extremely hard work for years on end is a common theme in the accounts of scientists such as Weinberg and Feynman. $\endgroup$ –  Steven Thomas Hatton Commented Jun 10, 2017 at 19:33

You should also look for a good Applied Mathematics course. This really helped me go from just rules and formulas to understanding how to use mathematics to solve real world problems. Also, math is a contact sport. You just have to sit down and work on problems.

Agreed on the US school system... the best way to fix it is to forget everything they're trying to teach you! Okay maybe don't forget everything, but in my experience US math classes often try to teach you how to solve problems the wrong way, which is why many students end up hating math. Math isn't about following a series of steps towards a defined problem, computers do that. It's about creatively finding those steps.

My best advice is to do your best to forget about memorizing methods, and focus on understanding why those methods work . I'll always remember my Calculus 1 final exam where I derived the equation for arc length in the margins because I forgot it. My professor thought I wanted extra credit.

It's all well and good to be able to spit out that the area of a triangle is (1/2)bh, but it is much, much more helpful to know that a triangle is just half of a rectangle.

You must log in to answer this question.

Not the answer you're looking for browse other questions tagged algebra-precalculus soft-question self-learning problem-solving ..

• Featured on Meta
• Announcing a change to the data-dump process
• Bringing clarity to status tag usage on meta sites
• 2024 Election Results: Congratulations to our new moderator!

Hot Network Questions

• Best approach to make lasagna fill pan
• Sum[] function not computing the sum
• Is there a way to read lawyers arguments in various trials?
• Manhattan distance
• Does the average income in the US drop by $9,500 if you exclude the ten richest Americans?
• In which town of Europe (Germany ?) were this 2 photos taken during WWII?
• SOT 23-6 SMD marking code GC1MGR
• Geometry nodes: spline random
• how did the Apollo 11 know its precise gyroscopic position?
• No displayport over USBC with lenovo ideapad gaming 3 (15IHU6)
• What's the benefit or drawback of being Small?
• What prevents random software installation popups from mis-interpreting our consents
• When has the SR-71 been used for civilian purposes?
• How to sum with respect to partitions
• How to connect 20 plus external hard drives to a computer?
• Questions about LWE in NIST standards
• What does "dare not" mean in a literary context?
• Can I use Cat 6A to create a USB B 3.0 Superspeed?
• Is my magic enough to keep a person without skin alive for a month?
• Can reinforcement learning rewards be a combination of current and new state?
• help to grep a string from a site
• Remove an edge from the Hasse diagram of a finite lattice
• Children in a field trapped under a transparent dome who interact with a strange machine inside their car
• How can I play MechWarrior 2?