5 problem solving strategies for math

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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

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

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

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

What are problem-solving strategies?

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

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

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

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

The ultimate guide to problem solving techniques

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

20 Math Strategies For Problem-Solving

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

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

Strategies to understand the problem

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

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

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

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

1. Read the problem aloud

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

2. Highlight keywords 

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

3. Summarize the information

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

4. Determine the unknown

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

5. Make a plan

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

Strategies for solving the problem 

1. draw a model or diagram.

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

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

2. Act it out

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

3. Work backwards

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

For example,

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

4. Write a number sentence

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

5. Use a formula

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

Strategies for checking the solution 

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

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

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

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

2. Estimate to check for reasonableness

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

3. Plug-In Method

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

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

4. Peer Review

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

5. Use a Calculator

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

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

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

Polya’s 4 steps include:

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

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

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

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

How Third Space Learning improves problem-solving 

Resources .

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

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

One-on-one tutoring 

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

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

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

Problem-solving

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

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

READ MORE :

• 8 Common Core math examples
• Tier 3 Interventions: A School Leaders Guide
• Tier 2 Interventions: A School Leaders Guide
• Tier 1 Interventions: A School Leaders Guide

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

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

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

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

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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.

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10 Strategies for Problem-Solving in Math

reviewed by Jo-ann Caballes

Updated on August 21, 2024

It’s not surprising that kids who lack problem-solving skills feel stuck in math class. Students who are behind in problem-solving may have difficulties identifying and carrying out a plan of action to solve a problem. Math strategies for problem-solving allow children to use a range of approaches to work out math problems productively and with ease. This article explores math problem-solving strategies and how kids can use them both in traditional classes and in a virtual classroom. 

What are problem-solving strategies in math?

Problem-solving strategies for math make it easier to tackle math and work up an effective solution. When we face any kind of problem, it’s usually impossible to solve it without carrying out a good plan.In other words, these strategies were designed to make math for kids easier and more manageable. Another great benefit of these strategies is that kids can spend less time cracking math problems. 

Here are some problem-solving methods:

• Drawing a picture or diagram (helps visualize the problem)
• Breaking the problem into smaller parts (to keep track of what has been done)
• Making a table or a list (helps students to organize information)

When children have a toolkit of math problem-solving strategies at hand, it makes it easier for them to excel in math and progress faster. 

How to solve math problems?

To solve math problems, it’s worth having strategies for math problem-solving that include several steps, but it doesn’t necessarily mean they are failproof. They serve as a guide to the solution when it’s difficult to decide where and how to start. Research suggests that breaking down complex problems into smaller stages can reduce cognitive load and make it easier for students to solve problems. Essentially, a suitable strategy can help kids to find the right answers fast. 

Here are 5 math problem-solving strategies for kids:

• Recognize the Problem  
• Work up a Plan  
• Carry Out the Plan  
• Review the Work  
• Reflect and Analyze  

Understanding the Problem 

Understanding the problem is the first step in the journey of solving it. Without doing this, kids won’t be able to address it in any way. In the beginning, it’s important to read the problem carefully and make sure to understand every part of it. Next, when kids know what they are asked to do, they have to write down the information they have and determine what essentially they need to solve. 

Work Out a Plan 

Working out a plan is one of the most important steps to solving math problems. Here, the kid has to choose a good strategy that will help them with a specific math problem. Outline these steps either in mind or on paper.

Carry Out the Plan 

Being methodical at that stage is key. It involves following the plan and performing calculations with the correct operations and rules. Finally, when the work is done, the child can review and show their work to a teacher or tutor.

Review the Work

This is where checking if the answer is correct takes place. If time allows, children and the teacher can choose other methods and try to solve the same problem again with a different approach. 

Reflect and Analyze

This stage is a great opportunity to think about how the problem was solved: did any part cause confusion? Was there a more efficient method? It’s important to let the child know that they can use the insights gained for future reference. 

Ways to solve math problems

The ways to solve math problems for kids are numerous, but it doesn’t mean they all work the same for everybody. For example, some children may find visual strategies work best for them; some prefer acting out the problem using movements. Finding what kind of method or strategy works best for your kid will be extremely beneficial both for school performance and in real-life scenarios where they can apply problem-solving. 

Online tutoring platforms like Brighterly offer personalized assistance, interactive tools, and access to resources that help to determine which strategies are best for your child. Expertise-driven tutors know how to guide your kid so they won’t be stuck with the same fallacies that interfere with effective problem-solving. For example, tutors can assist kids with drawing a diagram, acting a problem out with movement, or working backward. All of these ways are highly effective, especially with a trusted supporter by your side. 

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after just one lesson!

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What are 10 strategies for solving math problems?

There are plenty of different problem-solving strategies for mathematical problems to help kids discover answers. Let’s explore 10 popular problem-solving strategies:

Understand the Problem

Figuring out the nature of math problems is the key to solving them. Kids need to identify what kind of issue this is (fraction problem, word problem, quadratic equation, etc.) and work up a plan to solve it. 

Guess and Check

With this approach, kids simply need to keep guessing until they get the answer right. While this approach may seem irrelevant, it illustrates what the kid’s thinking process is. 

Work It Out

This method encourages students to write down or say their problem-solving process instead of going straight to solving it without preparation. This minimizes the probability of mistakes. 

Work Backwords 

Working backward is a great problem-solving strategy to acquire a fresh perspective. It requires one to come up with a probable solution and decide which step to take to come to that solution. 

A visual representation of a math problem may help kids to understand it in full. One way to visualize a problem is to use a blank piece of paper and draw a picture, including all of the aspects of the issue. 

Find a Pattern 

By helping students see patterns in math problems, we help them to extract and list relevant details. This method is very effective in learning shapes and other topics that need repetition. 

It may be self-explanatory, but it’s quite helpful to ask, “What are some possible solutions to this issue?”. By giving kids time to think and reflect, we help them to develop creative and critical thinking.

Draw a Picture or Diagram

Instead of drawing the math problem yourself, ask the kid to draw it themselves. They can draw pictures of the ideas they have been taught to help them remember the concepts better.

Trial and Error Method

Not knowing clear formulas or instructions, kids won’t be able to solve anything. Ask them to make a list of possible answers based on rules they already know. Let them learn by making mistakes and trying to find a better solution. 

Review Answers with Peers

It’s so fun to solve problems alongside your peers. Kids can review their answers together and share ideas on how each problem can be solved. 

Help your kid achieve their full math potential

The best Brighterly tutors are ready to help with that.

Math problem-solving strategies for elementary students

5 problem-solving strategies for elementary students include:

Using Simple Language 

Ask students to explain the problem in their own words to make sure they understand the problem correctly.

Using Visuals and Manipulatives 

Using drawing and manipulatives like counters, blocks, or beads can help students grasp the issue faster. 

Simplifying the Problem

Breaking the problem into a step-by-step process and smaller, manageable steps will allow students to find the solution faster. 

Looking for Patterns 

Identifying patterns in numbers and operations is a great strategy to help students gain more confidence along the way. 

Using Stories

Turning math problems into stories will surely engage youngsters and make them participate more actively. 

To recap, students need to have effective math problem-solving strategies up their sleeves. Not only does it help them in the classroom, but it’s also an essential skill for real-life situations. Productive problem-solving strategies for math vary depending on the grade. But what they have in common is that kids have to know how to break the issue into smaller parts and apply critical and creative thinking to solve it. 

If you want your kid to learn how to thrive in STEM and apply problem-solving strategies to both math and real life, book a free demo lesson with Brighterly today! Make your child excited about math!

Jessica is a a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.

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17 maths problem solving strategies to boost your learning.

Worded problems getting the best of you? With this list of maths problem-solving strategies , you'll overcome any maths hurdle that comes your way.

Friday, 3rd June 2022

• What are strategies?

Understand the problem

Devise a plan, carry out the plan, look back and reflect, practise makes progress.

Problem-solving is a critical life skill that everyone needs. Whether you're dealing with everyday issues or complex challenges, being able to solve problems effectively can make a big difference to your quality of life.

While there is no one 'right' way to solve a problem, having a toolkit of different techniques that you can draw upon will give you the best chance of success. In this article, we'll explore 17 different math problem-solving strategies you can start using immediately to deepen your learning and improve your skills.

What are maths problem-solving strategies?

Before we get into the strategies themselves, let's take a step back and answer the question: what are these strategies? In simple terms, these are methods we use to solve mathematical problems—essential for anyone learning how to study maths . These can be anything from asking open-ended questions to more complex concepts like the use of algebraic equations.

The beauty of these techniques is they go beyond strictly mathematical application. It's more about understanding a given problem, thinking critically about it and using a variety of methods to find a solution.

Polya's 4-step process for solving problems

We're going to use Polya's 4-step model as the framework for our discussion of problem-solving activities . This was developed by Hungarian mathematician George Polya and outlined in his 1945 book How to Solve It. The steps are as follows:

We'll go into more detail on each of these steps as well as take a look at some specific problem-solving strategies that can be used at each stage.

This may seem like an obvious one, but it's crucial that you take the time to understand what the problem is asking before trying to solve it. Especially with a math word problem , in which the question is often disguised in language, it's easy for children to misinterpret what's being asked.

Here are some questions you can ask to help you understand the problem:

Do I understand all the words used in the problem?

What am I asked to find or show?

Can I restate the problem in my own words?

Can I think of a picture or diagram that might help me understand the problem?

Is there enough information to enable me to find a solution?

Is there anything I need to find out first in order to find the answer?

What information is extra or irrelevant?

Once you've gone through these questions, you should have a good understanding of what the problem is asking. Now let's take a look at some specific strategies that can be used at this stage.

1. Read the problem aloud

This is a great strategy for younger students who are still learning to read. By reading the problem aloud, they can help to clarify any confusion and better understand what's being asked. Teaching older students to read aloud slowly is also beneficial as it encourages them to internalise each word carefully.

2. Summarise the information

Using dot points or a short sentence, list out all the information given in the problem. You can even underline the keywords to focus on the important information. This will help to organise your thoughts and make it easier to see what's given, what's missing, what's relevant and what isn't.

3. Create a picture or diagram

This is a no-brainer for visual learners. By drawing a picture, let's say with division problems, you can better understand what's being asked and identify any information that's missing. It could be a simple sketch or a more detailed picture, depending on the problem.

4. Act it out

Visualising a scenario can also be helpful. It can enable students to see the problem in a different way and develop a more intuitive understanding of it. This is especially useful for math word problems that are set in a particular context. For example, if a problem is about two friends sharing candy, kids can act out the problem with real candy to help them understand what's happening.

5. Use keyword analysis

What does this word tell me? Which operations do I need to use? Keyword analysis involves asking questions about the words in a problem in order to work out what needs to be done. There are certain key words that can hint at what operation you need to use.

How many more?

How many left?

Equal parts

Once you understand the problem, it's time to start thinking about how you're going to solve it. This is where having a plan is vital. By taking the time to think about your approach, you can save yourself a lot of time and frustration later on.

There are many methods that can be used to figure out a pathway forward, but the key is choosing an appropriate one that will work for the specific problem you're trying to solve. Not all students understand what it means to plan a problem so we've outlined some popular problem-solving techniques during this stage.

6. Look for a pattern

Sometimes, the best way to solve a problem is to look for a pattern. This could be a number, a shape pattern or even just a general trend that you can see in the information given. Once you've found it, you can use it to help you solve the problem.

7. Guess and check

While not the most efficient method, guess and check can be helpful when you're struggling to think of an answer or when you're dealing with multiple possible solutions. To do this, you simply make a guess at the answer and then check to see if it works. If it doesn't, you make another systematic guess and keep going until you find a solution that works.

8. Working backwards

Regressive reasoning, or working backwards, involves starting with a potential answer and working your way back to figure out how you would get there. This is often used when trying to solve problems that have multiple steps. By starting with the end in mind, you can work out what each previous step would need to be in order to arrive at the answer.

9. Use a formula

There will be some problems where a specific formula needs to be used in order to solve it. Let's say we're calculating the cost of flooring panels in a rectangular room (6m x 9m) and we know that the panels cost $15 per sq. metre.

There is no mention of the word 'area', and yet that is exactly what we need to calculate. The problem requires us to use the formula for the area of a rectangle (A = l x w) in order to find the total cost of the flooring panels.

10. Eliminate the possibilities

When there are a lot of possibilities, one approach could be to start by eliminating the answers that don't work. This can be done by using a process of elimination or by plugging in different values to see what works and what doesn't.

11. Use direct reasoning

Direct reasoning, also known as top-down or forward reasoning, involves starting with what you know and then using that information to try and solve the problem . This is often used when there is a lot of information given in the problem.

By breaking the problem down into smaller chunks, you can start to see how the different pieces fit together and eventually work out a solution.

12. Solve a simpler problem

One of the most effective methods for solving a difficult problem is to start by solving a simpler version of it. For example, in order to solve a 4-step linear equation with variables on both sides, you could start by solving a 2-step one. Or if you're struggling with the addition of algebraic fractions, go back to solving regular fraction addition first.

Once you've mastered the easier problem, you can then apply the same knowledge to the challenging one and see if it works.

13. Solve an equation

Another common problem-solving technique is setting up and solving an equation. For instance, let's say we need to find a number. We know that after it was doubled, subtracted from 32, and then divided by 4, it gave us an answer of 6. One method could be to assign this number a variable, set up an equation, and solve the equation by 'backtracking and balancing the equation'.

Now that you have a plan, it's time to implement it. This is where you'll put your problem-solving skills to the test and see if your solution actually works. There are a few things to keep in mind as you execute your plan:

14. Be systematic

When trying different methods or strategies, it's important to be systematic in your approach. This means trying one problem-solving strategy at a time and not moving on until you've exhausted all possibilities with that particular approach.

15. Check your work

Once you think you've found a solution, it's important to check your work to make sure that it actually works. This could involve plugging in different values or doing a test run to see if your solution works in all cases.

16. Be flexible

If your initial plan isn't working, don't be afraid to change it. There is no one 'right' way to solve a problem, so feel free to try different things, seek help from different resources and continue until you find a more efficient strategy or one that works.

17. Don't give up

It's important to persevere when trying to solve a difficult problem. Just because you can't see a solution right away doesn't mean that there isn't one. If you get stuck, take a break and come back to the problem later with fresh eyes. You might be surprised at what you're able to see after taking some time away from it.

Once you've solved the problem, take a step back and reflect on the process that you went through. Most middle school students forget this fundamental step. This will help you to understand what worked well and what could be improved upon next time.

Whether you do this after a math test or after an individual problem, here are some questions to ask yourself:

What was the most challenging part of the problem?

Was one method more effective than another?

Would you do something differently next time?

What have you learned from this experience?

By taking the time to reflect on your process you'll be able to improve upon it in future and become an even better problem solver. Make sure you write down any insights so that you can refer back to them later.

There is never only one way to solve math problems. But the best way to become a better problem solver is to practise, practise, practise! The more you do it, the better you'll become at identifying different strategies, and the more confident you'll feel when faced with a challenging problem.

The list we've covered is by no means exhaustive, but it's a good starting point for you to begin your journey. When you get stuck, remember to keep an open mind. Experiment with different approaches. Different word problems. Be prepared to go back and try something new. And most importantly, don't forget to have fun!

The essence and beauty of mathematics lies in its freedom. So while these strategies provide nice frameworks, the best work is done by those who are comfortable with exploration outside the rules, and of course, failure! So go forth, make mistakes and learn from them. After all, that's how we improve our problem-solving skills and ability.

Lastly, don't be afraid to ask for help. If you're struggling to solve math word problems, there's no shame in seeking assistance from a certified Melbourne maths tutor . In every lesson at Math Minds, our expert teachers encourage students to think creatively, confidently and courageously.

If you're looking for a mentor who can guide you through these methods, introduce you to other problem-solving activities and help you to understand Mathematics in a deeper way - get in touch with our team today. Sign up for your free online maths assessment and discover a world of new possibilities.

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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?

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Problem-Solving Strategies

January 26, 2021 Brad Hoffman Leave a Comment

Certainly, many students find that it is possible to solve a given word problem with minimal consideration of how to approach it. People have varying degrees of “math sense.” Some find most math problems mysterious. Some, however, can very easily see what to do to find solutions; it almost seems obvious to them. But even for students with strong “math sense,” there come those situations when they don’t intuitively know what to do. For all learners, the recognition of specific problem-solving strategies to solve math problems is useful. Thinking about our own thinking (aka metacognition) is important in developing flexibility so that we can see more than one way to solve a particular problem. Math journaling supports this thinking and development.

Below you will find a list of some very useful problem-solving strategies . One thing that is particularly beneficial about this set of strategies is that they are, in fact, universal. In other words, they will work regardless of the math program a student might be using. Whether it’s Singapore Math or Everyday Math or something else entirely , these problem-solving strategies can provide a clear path toward solutions. Interestingly, they can even extend to problem-solving outside the area of math! Becoming familiar with them and comfortable using them can be a big help to students as they wend their way through problems, be they less or more complex.

10 Problem-Solving Strategies

• Make a model/Act out
• Draw a diagram or picture
• Look for a pattern
• Make an organized list
• Make a table
• Guess & Check
• Make it simpler
• Work backwards
• Use logical reasoning

Here are some examples of problems and how to use these strategies.

“How many complete turns does the hour hand on a clock make in one day?”

From the list of problem-solving strategies above, “make a model or act it out” is an excellent choice for this problem. A student could use a model or a real analog clock and turn the hands and count. Distinguishing between the minute and the hour hand and recognizing that the clock only shows 12 of the 24 hours in a day lets the student see that the hour hand makes two complete turns. A physical clock that a student can actually turn provides an important concrete experience that may prove helpful for finding the solution.

“Using each of the digits 0, 1, 2, 3, 4 only once, make a two-digit number times a three-digit number multiplication problem with the greatest product.”

Students can “ draw a diagram or picture” of an “empty” multiplication problem with a box for each digit. Consider which two digits give the largest product and put them in the highest place value spots. Then, if it’s not immediately evident to the student, use one of the other problem-solving strategies — “ guess and check” — to place the remaining digits in the remaining spots. Check by multiplying the results to identify which is actually the largest (e.g. Is it 430 x 21 or 320 x 41?)

“How many even numbers are there between 201 and 351?”

In this instance, “ look for a pattern” would be especially helpful from the list of problem-solving strategies. Either write all numbers from 201 through 351 and notice the pattern that there are 5 in every set of 10 numbers (e.g. 201-210), and then count how many sets of 10 numbers there are and multiply that by 5, or simply write one set of 10 numbers and identify the 5 in 10 pattern without writing out all of them. Either way is valid.

“You have two noses and three hats. How many different nose-hat disguises can you wear?”

For this problem, “ make an organized list ” from the problem-solving strategies listed above works well. The list will start with Hat A and match with each nose (2), then Hat B with each nose (2), then Hat C with each nose (2). This gives a total of 6 disguises.

“How many numbers between 10 and 30 give a remainder of 2 when divided by 3?” You could “ make a table” to find the solution.

As the Table continues, a pattern becomes evident (“ look for a pattern ” — overlapping strategy!) in which every third number gives a remainder of 2. Count them for a solution.

“If 25 Glinks equal a Glonk, and 15 Glonks equal a Glooie, how many Glinks equal 2 Glooies?”

Please, “ make it simpler”! That strategy is an especially good choice from the list of problem solving-strategies. Let’s look at a simpler, but similar, problem. It’s simpler because the numbers are smaller, and you could even draw a picture to prove it’s correct.

If 3 Glinks equal a Glonk. And 2 Glonks equal a Glooie. How many Glinks equal a Glooie? Multiply 3×2, which equals 6.

So, if 6 Glinks equal a Glooie, then how many Glinks equal 2 Glooies? Multiply 6×2, which equals 12. So, 12 Glinks equal 2 Glooies.

Now with the larger numbers:

If 25 Glinks equal a Glonk. And 15 Glonks equal a Glooie. How many Glinks equal a Glooie? Multiply 15×25, which equals 750. So, 750 Glinks equal a Glooie.

Then, how many Glinks equal 2 Glooies? Multiply 750×2, which equals 1500. So, there are 1500 Glinks in 2 Glooies.

It’s the same process, with bigger numbers! Much simpler!

“If I add 10 to my age and double it, I am 90. How old am I?”

From the list of problem-solving strategies, this problem begs for the student to “ work backwards”. Simply un-double the 90 and subtract ten. 90 divided by 2 = 45 and 45-10=35. Voilà! The answer is 35 years old! Then reverse again to confirm that the answer is correct.

“Arrange these digits and symbols to make a true number sentence (equation.) 3,1,4,9,+,/,= (Note: the forward slash  [/] signifies “divided by”.)

“ Use logical reasoning ” to realize that any order is possible, but a larger number needs to be divided by a smaller number with no remainder (9/3=3) Then 3+1=4, so the sentence 9/3+1=4 is the solution.

For the problems that seem absolutely impossible to solve, your best option is to “ brainstorm” , and that’s on the above list of problem-solving strategies! Try various ideas; work with a partner; explore to see what might work; try everything you can think of! It’s amazing how good ideas will sometimes just pop into one’s head!

As a student works with these problem-solving strategies, it becomes clear that they often overlap (as in the “ draw a picture” / “guess and check” example above, problem #2). Or a student becomes especially attached to a few particular strategies that often work well. Some problems seem to be especially suitable for a particular strategy, while others can be approached from several directions. Having the flexibility to move from one strategy to another helps avoid the serious “I’m STUCK!” situation. Also, using more than one strategy on the same problem allows students to check solutions more efficiently before moving on. Again, however, THINKING about how we are THINKING is very beneficial in developing skills in this area. We call this metacognition .

Solving word problems can be fun, like being a detective who has unusual insight. There are solutions! Enjoy finding them! And make effective use of problem-solving strategies!

By Jean Snyder and Brad Hoffman , Elementary Math Specialists

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Problem Solving Activities: 7 Strategies

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Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

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This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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Math problem solving strategies your teacher may have never shown you.

• Make a guess and test it
• Make a list
• Use a variable
• Draw a diagram
• Working backward

Among the math problem solving strategies, sometimes, you need to make a guess and test it

Solving a math problem by making a list.

Judy and Ramey together have 42 animals. Judy has 12 fewer animals than Ramey. How many stuffed animals does each girl have?

Again, you could make a list if you look for all combinations of 2 numbers to add to get 42 and then choose the pair with a difference of 12.

42 = 41 + 1 difference is 40 42 = 40 + 2 difference is 38 42 = 39 + 3 difference is 36 42 = 38 + 4 difference is 34 42 = 37 + 5 difference is 32 42 = 36 + 6 difference is 30 42 = 35 + 7 difference is 28 42 = 34 + 8 difference is 26 42 = 33 + 9 difference is 24 42 = 32 + 10 difference is 22 42 = 31 + 11 difference is 20 42 = 30 + 12 difference is 18 42 = 29 + 13 difference is 16 42 = 28 + 14 difference is 14 42 = 27 + 15 difference is 12

Stop! You have found what you are looking for.

The numbers are 27 and 15.

27 - 15 = 12

27 + 15 = 42

So Ramey has 27 stuffed animals and Judy has 15.

Math problem solving strategies could also make use of a variable.

Among all math problem solving strategies, my favorite is draw a diagram..

Among great math problem solving strategies, is the one when you work backward

Useful math tricks to solve math problems quickly

Math problem solving strategies

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4 Math Word Problem Solving Strategies

5 Strategies to Learn to Solve Math Word Problems

A critical step in math fluency is the ability to solve math word problems. The funny thing about solving math word problems is that it isn’t just about math. Students need to have strong reading skills as well as the growth mindset needed for problem-solving. Strong problem solving skills need to be taught as well. In this article, let’s go over some strategies to help students improve their math problem solving skills when it comes to math word problems. These skills are great for students of all levels but especially important for students that struggle with math anxiety or students with animosity toward math.

Signs of Students Struggling with Math Word Problems

It is important to look at the root cause of what is causing the student to struggle with math problems. If you are in a tutoring situation, you can check your students reading level to see if that is contributing to the issue. You can also support the student in understanding math keywords and key phrases that they might need unpacked. Next, students might need to slow their thinking down and be taught to tackle the word problem bit by bit.

The challenges students face when confronted with math word problems can be multifaceted. Identifying the root cause of difficulty is crucial. Common signs include:

• Reading comprehension issues
• Difficulty in identifying relevant information
• Trouble translating words into mathematical expressions
• Lack of a structured problem-solving approach
• Anxiety or negative attitudes towards math word problems

How to Help Students Solve Math Word Problems

Focus on math keywords and mathematical key phrases.

The first step in helping students with math word problems is focusing on keywords and phrases. For example, the words combined or increased by can mean addition. If you teach keywords and phrases they should watch out for students will gain the cues needed to go about solving a word problem. It might be a good idea to have them underline or highlight these words.

Encourage students to:

• Highlight keywords such as “sum,” “difference,” “product,” and “quotient.”
• Underline phrases that indicate operations, like “combined” for addition or “decreased by” for subtraction.

Cross out Extra Information

Along with highlighting important keywords students should also try to decipher the important from unimportant information. To help emphasize what is important in the problem, ask your students to cross out the unimportant distracting information.  This way, it will allow them to focus on what they can use to solve the problem.

Teach students to:

• Cross out irrelevant information to focus on what’s important.
• Highlight essential data to streamline the problem-solving process.

Encourage Asking Questions

As you give them time to read, allow them to have time to ask questions on what they just read. Asking questions will help them understand what to focus on and what to ignore. Once they get through that, they can figure out the right math questions and add another item under their problem-solving strategies.

Fostering a habit of asking questions can enhance comprehension:

• Allow time for students to ask questions about the problem.
• Encourage them to clarify uncertainties before attempting to solve.

Draw the Problem

A fun way to help your students understand the problem is through letting them draw it on graph paper. For example, if a math problem asks a student to count the number of fruits that Farmer John has, ask them to draw each fruit while counting them. This is a great strategy for visual learners.

Visualization helps in understanding and solving complex problems:

• Use graph paper for drawing diagrams.
• Translate the problem into a visual format, which can simplify abstract concepts.

Check Back Once They Answer

Once they figured out the answer to the math problem, ask them to recheck their answer. Checking their answer is a good habit for learning and one that should be encouraged but students need to be taught how to check their answer. So the first step would be to review the word problem to make sure that they are solving the correct problem. Then to make sure that they set it up right. This is important because sometimes students will check their equation but will not reread the word problem and make sure that the equation is set up right. So always have them do this first! Once students believe that they have read and set up the correct equation, they should be taught to check their work and redo the problem, I also like to teach them to use the opposite to double check, for example if their equation is 2+3=5, I will show them how to take 5 which is the whole and check their work backwards 5-3 and that should equal 2. This is an important step and solidifies mathematical thinking in children.

Verification ensures accuracy:

• Review the word problem to confirm understanding.
• Recheck calculations and use inverse operations to verify results.
• Teach students to redo the problem and compare answers for consistency.

Mnemonic Devices

Mnemonic devices are a great way to remember all of the types of math strategy in this post. The following are ones that I have heard of and wanted to share:

CUBES Word Problem Strategy

Cubes is a mnemonic to remember the following steps in solving math word problems:

• C ircle the numbers.
• U nderline the question.
• B ox in the key words.
• E liminate the extra information.
• S olve the problem and show your work.

RISE Word Problem Strategy

Rise is another way to explain the steps needed to solve problems:

• R ead and reread the problem.
• I llustrate the problem.
• S olve by writing equations.
• E xplain your thinking.

COINS Word Problem Strategy

C: Comprehend the questions

O: Observe the data

I: Illustrate the problem

N: Write the number sentence (equation)

Understand -Plan – Solve – Check Word Problem Strategy

This is a simple step solution to show students the big picture. I think this along with one of the mnemonic devices helps students with better understanding of the approach.

• Understand : Ensure comprehension of the problem. What is the question asking? Do you understand all the words?
• Plan : Formulate a reasonable approach. What would be a reasonable answer? In this stage students are formulating their approach to the word problem. 
• Solve : Apply appropriate strategies and show all steps. What strategies will I use to solve this problem? Am I showing my thinking? Here students use the strategies outlined in this post to attack the problem.
• Check : Verify if the solution makes sense and answers the question. Students will ask themselves if they answered the question and if their answer makes sense. 

If you need word problems to use with your classroom, you can check out my word problems resource below.

Teaching students how to approach and solve math word problems is an important skill. Solving word problems is the closest math skill that resembles math in the real world. Encouraging students to slow their thinking, examine and analyze the word problem and encourage the habit of answer checking will give your students the learning skills that can be applied not only to math but to all learning. I also wrote a blog post on a specific type of math word problem called cognitively guided instruction you can read information on that too. It is just a different way that math problems are written and worth understanding to teach problem solving, click here to read .

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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.

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Math Tech Connections

engaging printable & digital math lessons for upper elementary teachers

September 26, 2019 1 Comment

5 Problem Solving Strategies Bulletin Board (Free Download)

It can get very frustrating when students simply say they don’t know what to do. But what can we do to assist them?

We may be tempted to give students the answers or at least the first step, but that won’t help in the long run. Instead, let’s work at helping them build a variety of problem solving strategies.

Stuck on a Math Problem – Bulletin Board

We are so comfortable with modeling think aloud strategies during read alouds, we need to do this same kind of thinking aloud as we model problem solving strategies.

• Chose one area of your wall to start a ‘Stuck on a Math Problem?’ bulletin board.
• Pick two or three problem strategies to focus on first. Display those strategies on the wall and model how to use them while solving word problems.
• Encourage students to use those strategies and display their work under each header.

You may also want to print a bookmark size list of the strategies for students to glue inside their math notebook.

Where can you Find Word Problems?

• Textbook – You can always try your math textbook first. There are usually H.O.T. (higher order thinking) questions towards the end of each lesson that are perfect for this.
• Math Tri-folds  – My math tri-folds are organized by math standard, so you’ll quickly find the topics you need to cover. They also encourage students to show and explain their thinking. Below are links for grades 1-5.

Download the Resources

• Simply fill out the form below to receive the free printables . After you confirm your subscription, the free resources listed in this blog post will be sent to your inbox!
• Already a subscriber? Visit the resource library !

Free Download!

Digital Math Manipulatives

Use this fun, digital interactive activity to review place value with your students.

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My name is Mariela! I am the teacher and founder of Math Tech Connections. I started creating resources for my own students when I saw that teaching from the textbook wasn't working. Students need engaging, hands-on activities! My goal is save you time with quality, standard-aligned resources that make math fun. With over 1,000 resources and 60,000+ teacher reviews, I am certain you will find the right resource for your next lesson. Be sure to join our email list for tips and weekly freebies. :)

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Problem-Solving Strategies

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

3 Strategies to Conquer Math Word Problems

Here’s a word problem for you:

Miss Friday’s class does a daily word problem. Ten of her students are great at word problems involving addition, and only 7 seem to understand subtraction word problems. Five of her students are bored with the easy problems. Thirteen students are still struggling with basic math facts and 3 have trouble reading the word problems at all. How many of her students are engaged and learning?

Here’s a better question: “How do you grow confident and effective problem solvers?”

Why Students Struggle with Math Word Problems

Students struggle with math word problems for many reasons, but three of the biggest I’ve encountered include:

Issue #1: Student Confidence For many students, just looking at a word problem leads to anxiety. No one can think clearly with a sense of dread or fear of failure looming!

Issue #2: Flexible Thinking Many kids are taught to solve word problems methodically, with a prescriptive step-by-step plan using key words that don’t always work. Plans are great, but not when students use them as a crutch rather than a tool. Today’s standardized tests and real-world applications require creative thinking and flexibility with strategies.

Issue #3: Differentiation Teachers want students to excel quickly and often push too fast, too soon. In the case of word problems, you have to go slow to go fast. Just like in Guided Reading, you’ll want to give lots of practice with “just-right” problems and provide guided practice with problems just-above the students’ level.

3 Problem Solving Strategies

The solution is to conquer math word problems with engaging classroom strategies that counteract the above issues!

1. Teach a Problem-Solving Routine 

Kids (and adults) are notoriously impulsive problem solvers. Many students see a word problem and want to immediately snatch out those numbers and “do something” with them. When I was in elementary school, this was actually a pretty reliable strategy! But today, kids are asked to solve much more complex problems, often with tricky wording or intentional distractors.

Grow flexible thinkers and build confidence by teaching a routine. A problem solving routine simply encourages students to slow down and think before and after solving. I’ve seen lots of effective routines but my favorites always include a “before, during, and after” mindset.

To make the problem solving routine meaningful and effective:

• Use it often (daily if possible)
• Incorporate “Turn & Teach” (Students orally explain their thinking and process to a partner.)
• Allow for “Strategy Share” after solving (Selected students explain their method and thinking.)

2. Differentiate Word Problems 

No, this doesn’t mean to write a different word problem for every student! This can be as simple as adjusting the numbers in a problem or removing distractors for struggling students. Scaffolding word problems will grow confidence and improve problem solving skills by gradually increasing the level difficulty as the child is ready. This is especially effective when you are trying to teach students different structures of word problems to go with a certain operation.

For example, comparison subtraction problems are very challenging for some students. By starting with a simple version, you allow students to focus on the problem itself, rather than becoming intimidated or frustrated.

I’ve had great success in using scaffolded problems with my guided math groups. After solving the easier problem, students realize that it’s not that tricky and are ready to take on the tougher ones!

3. Compare Problems Side-by-Side 

To develop flexible thinking, nothing is more powerful than analyzing and comparing word problems. Start by using problems that have similar stories and numbers, but different problem structures. Encourage conversation, use visual representations, and have students explain the difference in structure and operation. Here’s an example showing student work on two similar problems about monkeys. Click here to download a blank copy of these problems. My freebie includes several variations to help you differentiate.

Use these three strategies to get kids thinking and talking about their problem solving strategies while building that “oh-so-important” confidence, and you CAN conquer math word problems!

Kady Dupre has worked as a classroom teacher, instructional coach, and intervention teacher in elementary grades. She loves creating learning resources for students and teachers. She authors Teacher Trap , a blog aimed at sharing her challenges, successes, and insights as a teacher.

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Why Is Math Important? 9 Reasons Why Math Skills Improve Quality of Life

Written by Ashley Crowe

• Parent Resources

• Why is math so important in life?
• 9 Benefits of a great math education
• Why students struggle to master certain math concepts
• Set your child’s math skills up for life with Prodigy Math

Math isn't just an important subject in school — it’s essential for many of your daily tasks. You likely use it every day to perform real-life skills, like grocery shopping, cooking and tracking your finances. 

What makes math special is that it’s a universal language — a powerful tool with the same meaning across the globe. Though languages divide our world, numbers unite us. Math allows us to work together towards new innovations and ideas. 

In this post, learn why math is important for kids and adults. Plus, find out why learning even the most basic math can significantly improve your family’s quality of life.

You simply can’t make it through a day without using some sort of basic math. Here’s why.

A person needs an understanding of math, measurements and fractions to cook and bake. Many people may also use math to count calories or nutrients as part of their diet or exercise routine. 

You also need math to calculate when you should leave your house to arrive on time, or how much paint you need to redo your bedroom walls. 

And then the big one, money. Financial literacy is an incredibly important skill for adults to master. It can help you budget, save and even help you make big decisions like changing careers or buying a home. 

Mathematical knowledge may even be connected to many other not-so-obvious benefits. A strong foundation in math can translate into increased understanding and regulation of your emotions, improved memory and better problem-solving skills.

The importance of math: 9 benefits of a great math education

Math offers more opportunities beyond grade school, middle school and high school. Its applications to real-life scenarios are vast. 

Though many students sit in math class wondering when they’ll ever use these things they’re learning, we know there are many times their math skills will be needed in adulthood. 

The importance of mathematics to your child’s success can’t be overstated. Basic math is a necessity, but even abstract math can help hone critical thinking skills — even if your child chooses not to pursue a STEM-style career. Math can help them succeed professionally, emotionally and cognitively. Here’s why.

1. Math promotes healthy brain function

“Use it or lose it.” We hear this said about many skills, and math is no exception. 

Solving math problems and improving our math skills gives our brain a good workout. And it improves our cognitive skills over time. Many studies have shown that routinely practicing math keeps our brain healthy and functioning well.

2. Math improves problem-solving skills

At first, classic math problems like Johnny bringing home 42 watermelons and returning 13 of them can just seem a silly exercise. But all those math word problems our children solve really do improve their problem solving skills. Word problems teach kids how to pull out the important information and then manipulate it to find a solution.

Later on, complex life problems take the place of workbooks, but problem-solving still happens the same way. When students understand algorithms and problems more deeply, they can decode the facts and more easily solve the issue. Real-life solutions are found with math and logic.

3. Math supports logical reasoning and analytical thinking

A strong understanding of math concepts means more than just number sense. It helps us see the pathways to a solution. Equations and word problems need to be examined before determining the best method for solving them. And in many cases, there’s more than one way to get to the right answer. 

It’s no surprise that logical reasoning and analytical thinking improve alongside math skills. Logic skills are necessary at all levels of mathematical education.

4. Math develops flexible thinking and creativity

Practicing math has been shown to improve investigative skills, resourcefulness and creativity.

This is because math problems often require us to bend our thinking and approach problems in more than one way. The first process we try might not work. We need flexibility and creativity to think of new pathways to the solution. And just like anything else, this way of thinking is strengthened with practice.

5. Math opens up many different career paths

There are many careers that use a large number of math concepts. These include architects, accountants, and scientists. 

But many other professionals use math skills every day to complete their jobs. CEOs use math to analyze financials. Mailmen use it to calculate how long it will take them to walk their new route. Graphic designers use math to figure out the appropriate scale and proportions in their designs. 

No matter what career path your child chooses, math skills will be beneficial.

Math skills might become even more important for today's kids!

Math can certainly open up a lot of opportunities for many of us. But did you know that careers which heavily use math are going to be among the fastest-growing jobs by the time kids today start their careers? These jobs include:

• Statisticians
• Data scientists
• Software developers
• Cybersecurity analysts

It's not just STEM jobs that will require math either. Other popular, high-growth careers like nursing and teaching now ask for a minimum knowledge of college-level math.

6. Math may boost emotional health

While this research is still in its early days, what we have seen is promising. 

The parts of the brain used to solve math problems seem to work together with the parts of the brain that regulate emotions. This suggests that math practice can actually help us cope with difficult situations. In these studies, the better someone was with numerical calculations, the better they were at regulating fear and anger. Strong math skills may even be able to help treat anxiety and depression.

7. Math improves financial literacy

Though kids may not be managing their finances now, there's going to be plenty of times where math skills are going to make a massive difference in their life as an adult.

Budgeting and saving is a big one. Where can they cut back on their spending? How will budgeting help them reach their financial goals? Can they afford this new purchase now? 

As they age into adulthood, It will benefit your child to understand how loans and interest work before purchasing a house or car. They should fully grasp profits and losses before investing in the stock market. And they will likely need to evaluate job salaries and benefits before choosing their first job.

8. Math sharpens your memory

Learning mental math starts in elementary school. Students learn addition tables, then subtraction, multiplication and division tables. As they master those skills, they’ll begin to memorize more tips and tricks, like adding a zero to the end when multiplying by 10. Students will memorize algorithms and processes throughout their education. 

Using your memory often keeps it sharp. As your child grows and continues to use math skills in adulthood, their memory will remain in tip top shape.

9. Math teaches perseverance

“I can do it!’ 

These are words heard often from our toddlers. This phrase is a marker of growth, and a point of pride. But as your child moves into elementary school, you may not hear these words as often or with as much confidence as before. 

Learning math is great for teaching perseverance. With the right math instruction, your child can see their progress and once again feel that “I can do it” attitude. The rush of excitement a child experiences when they master a new concept sticks in their memory. And they can reflect back on it when they’re struggling with a new, harder skill. 

Even when things get tough, they’ll know they can keep trying and eventually overcome it — because they’ve done it before.

Tip: Set goals to inspire and motivate your child to learn math

If your child has a  Prodigy Math Membership , you can use your parent account to set learning goals for them to achieve as they play our online math game.

The best bit? Every time they complete a goal, they'll also get a special in-game reward!

Many students experience roadblocks and hurdles throughout their math education. You might recognize some of these math struggles below in your child. But don’t worry! Any struggle is manageable with the right support and help. Together, you and your child can tackle anything. 

Here are some of the most common math struggles. 

• Increasing complexity

Sometimes the pace of class moves a bit faster than your child can keep up with. Or the concepts are just too abstract and difficult for them to wrap their mind around in one lesson. Some math ideas simply take more time to learn. 

• Wrong teaching style

A good teaching style with plenty of practice is essential to a high-quality math education. If the teacher’s style doesn’t mesh well with how your child learns, math class can be challenging. 

• Fear of failure  

Even as adults, we can feel scared to fail. It’s no surprise that our children experience this same same fear, especially with the many other pressures school can bring. 

• Lack of practice  

Sometimes, all your child needs is a little more practice. But this can be easier said than done. You can help by providing them with plenty of support and encouragement to help them get that practice time in.

• Math anxiety

Algorithms and complex problems can strike anxiety in the heart of any child (and many adults). Math anxiety is a common phenomenon. But with the right coping strategies it can be managed. 

Set your child’s math skills up for success with Prodigy Math

Now we've discovered just how important math is in both our everyday and life decisions, let's set the next generation up for success with the right tools that'll help them learn math.

Prodigy Math is a game-based, online learning platform that makes learning math fun for kids. As kids play and explore a safe, virtual world filled with fun characters and pets to collect, they'll answer math questions. These questions are curriculum-aligned and powered by an adaptive algorithm that can help them master math skills more quickly.

Plus, with a free parent account , you'll also get to be a big part of their math education without needing to be a math genius. You'll get to:

• Easily keep up with their math learning with a monthly Report Card
• See how they're doing in math class when their teacher uses Prodigy Math
• Send them motivational messages to encourage their perseverance in math

Want to play an even bigger role in helping your child master math? Try our optional Math Memberships for extra in-game content for your child to enjoy and get amazing parent tools like the ability to set in-game goals and rewards for them to achieve.

See why Prodigy can make math fun below!

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Education Math problems create false memories in the brain

30.8.2024 - 11:31

When solving math problems, the brain can create false memories. According to a new study by the University of Geneva, people sometimes believe that they have read certain information that was not actually in the problem.

30.08.2024, 11:31

30.08.2024, 11:46

This knowledge could help to improve mathematics lessons, as the University of Geneva announced on Friday. This is because it allows pupils' thought processes to be better understood.

For the study, the researchers asked 67 adults to solve math problems. They then asked the test subjects how the task was formulated. For certain math problems, more than half of the study participants added information that they had deduced when solving these problems.

Recognizing students' difficulties

As an example, the University of Geneva cited the following task in its press release: "Sophie's journey takes eight hours. When she arrives, the clock reads 11 o'clock. Fred leaves at the same time as Sophie. Fred's journey is two hours shorter than Sophie's. What time does the clock show when Fred arrives?" Many of the study participants incorrectly stated that they had read that Fred arrived two hours before Sophie.

They therefore unconsciously linked sentences that actually appeared in the task with conclusions that they drew from them while reading.

According to the researchers, teachers could make use of these false memories. By analyzing these memory errors, they could recognize the students' thinking strategies and thus better understand their difficulties in solving the problems. The study was published in the "Journal of Experimental Psychology: Learning, Memory, and Cognition".

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