what is the 4 steps for problem solving in math

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The easy 4 step problem-solving process (+ examples)

This is the 4 step problem-solving process that I taught to my students for math problems, but it works for academic and social problems as well.

Every problem may be different, but effective problem solving asks the same four questions and follows the same method.

• What’s the problem? If you don’t know exactly what the problem is, you can’t come up with possible solutions. Something is wrong. What are we going to do about this? This is the foundation and the motivation.
• What do you need to know? This is the most important part of the problem. If you don’t know exactly what the problem is, you can’t come up with possible solutions.
• What do you already know? You already know something related to the problem that will help you solve the problem. It’s not always obvious (especially in the real world), but you know (or can research) something that will help.
• What’s the relationship between the two? Here is where the heavy brainstorming happens. This is where your skills and abilities come into play. The previous steps set you up to find many potential solutions to your problem, regardless of its type.

When I used to tutor kids in math and physics , I would drill this problem-solving process into their heads. This methodology works for any problem, regardless of its complexity or difficulty. In fact, if you look at the various advances in society, you’ll see they all follow some variation of this problem-solving technique.

“The gap between understanding and misunderstanding can best be bridged by thought!” ― Ernest Agyemang Yeboah

Generally speaking, if you can’t solve the problem then your issue is step 3 or step 4; you either don’t know enough or you’re missing the connection.

Good problem solvers always believe step 3 is the issue. In this case, it’s a simple matter of learning more. Less skilled problem solvers believe step 4 is the root cause of their difficulties. In this instance, they simply believe they have limited problem-solving skills.

This is a fixed versus growth mindset and it makes a huge difference in the effort you put forth and the belief you have in yourself to make use of this step-by-step process. These two mindsets make a big difference in your learning because, at its core, learning is problem-solving.

Let’s dig deeper into the 4 steps. In this way, you can better see how to apply them to your learning journey.

Step 1: What’s the problem?

The ability to recognize a specific problem is extremely valuable.

Most people only focus on finding solutions. While a “solutions-oriented” mindset is a good thing, sometimes it pays to focus on the problem. When you focus on the problem, you often make it easier to find a viable solution to it.

When you know the exact nature of the problem, you shorten the time frame needed to find a solution. This reminds me of a story I was once told.

When does the problem-solving process start?

The process starts after you’ve identified the exact nature of the problem.

Homeowners love a well-kept lawn but hate mowing the grass.

Many companies and inventors raced to figure out a more time-efficient way to mow the lawn. Some even tried to design robots that would do the mowing. They all were chasing the solution, but only one inventor took the time to understand the root cause of the problem.

Most people figured that the problem was the labor required to maintain a lawn. The actual problem was just the opposite: maintaining a lawn was labor-intensive. The rearrangement seems trivial, but it reveals the true desire: a well-maintained lawn.

The best solution? Remove maintenance from the equation. A lawn made of artificial grass solved the problem . Hence, an application of Astroturf was discovered.

This way, the law always looked its best. Taking a few moments to apply critical thinking identified the true nature of the problem and yielded a powerful solution.

An example of choosing the right problem to work the problem-solving process on

One thing I’ve learned from tutoring high school students in math : they hate word problems.

This is because they make the student figure out the problem. Finding the solution to a math problem is already stressful. Forcing the student to also figure out what problem needs solving is another level of hell.

Word problems are not always clear about what needs to be solved. They also have the annoying habit of adding extraneous information. An ordinary math problem does not do this. For example, compare the following two problems:

What’s the height of h?

A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?

The first is a simple problem. The second is a complex problem. The end goal in both is the same.

The questions require the same knowledge (trigonometric functions), but the second is more difficult for students. Why? The second problem does not make it clear what the exact problem is. Before mathematics can even begin, you must know the problem, or else you risk solving the wrong one.

If you understand the problem, finding the solution is much easier. Understanding this, ironically, is the biggest problem for people.

Problem-solving is a universal language

Speaking of people, this method also helps settle disagreements.

When we disagree, we rarely take the time to figure out the exact issue. This happens for many reasons, but it always results in a misunderstanding. When each party is clear with their intentions, they can generate the best response.

Education systems fail when they don’t consider the problem they’re supposed to solve. Foreign language education in America is one of the best examples.

The problem is that students can’t speak the target language. It seems obvious that the solution is to have students spend most of their time speaking. Unfortunately, language classes spend a ridiculous amount of time learning grammar rules and memorizing vocabulary.

The problem is not that the students don’t know the imperfect past tense verb conjugations in Spanish. The problem is that they can’t use the language to accomplish anything. Every year, kids graduate from American high schools without the ability to speak another language, despite studying one for 4 years.

Well begun is half done

Before you begin to learn something, be sure that you understand the exact nature of the problem. This will make clear what you need to know and what you can discard. When you know the exact problem you’re tasked with solving, you save precious time and energy. Doing this increases the likelihood that you’ll succeed.

Step 2: What do you need to know?

All problems are the result of insufficient knowledge. To solve the problem, you must identify what you need to know. You must understand the cause of the problem. If you get this wrong, you won’t arrive at the correct solution.

Either you’ll solve what you thought was the problem, only to find out this wasn’t the real issue and now you’ve still got trouble or you won’t and you still have trouble. Either way, the problem persists.

If you solve a different problem than the correct one, you’ll get a solution that you can’t use. The only thing that wastes more time than an unsolved problem is solving the wrong one.

Imagine that your car won’t start. You replace the alternator, the starter, and the ignition switch. The car still doesn’t start. You’ve explored all the main solutions, so now you consider some different solutions.

Now you replace the engine, but you still can’t get it to start. Your replacements and repairs solved other problems, but not the main one: the car won’t start.

Then it turns out that all you needed was gas.

This example is a little extreme, but I hope it makes the point. For something more relatable, let’s return to the problem with language learning.

You need basic communication to navigate a foreign country you’re visiting; let’s say Mexico. When you enroll in a Spanish course, they teach you a bunch of unimportant words and phrases. You stick with it, believing it will eventually click.

When you land, you can tell everyone your name and ask for the location of the bathroom. This does not help when you need to ask for directions or tell the driver which airport terminal to drop you off at.

Finding the solution to chess problems works the same way

The book “The Amateur Mind” by IM Jeremy Silman improved my chess by teaching me how to analyze the board.

It’s only with a proper analysis of imbalances that you can make the best move. Though you may not always choose the correct line of play, the book teaches you how to recognize what you need to know . It teaches you how to identify the problem—before you create an action plan to solve it.

The problem-solving method always starts with identifying the problem or asking “What do you need to know?”. It’s only after you brainstorm this that you can move on to the next step.

Learn the method I used to earn a physics degree, learn Spanish, and win a national boxing title

• I was a terrible math student in high school who wrote off mathematics. I eventually overcame my difficulties and went on to earn a B.A. Physics with a minor in math
• I pieced together the best works on the internet to teach myself Spanish as an adult
• *I didn’t start boxing until the very old age of 22, yet I went on to win a national championship, get a high-paying amateur sponsorship, and get signed by Roc Nation Sports as a profession.

I’ve used this method to progress in mentally and physically demanding domains.

While the specifics may differ, I believe that the general methods for learning are the same in all domains.

This free e-book breaks down the most important techniques I’ve used for learning.

Step 3: What do you already know?

The only way to know if you lack knowledge is by gaining some in the first place. All advances and solutions arise from the accumulation and implementation of prior information. You must first consider what it is that you already know in the context of the problem at hand.

Isaac Newton once said, “If I have seen further, it is by standing on the shoulders of giants.” This is Newton’s way of explaining that his advancements in physics and mathematics would be impossible if it were not for previous discoveries.

Mathematics is a great place to see this idea at work. Consider the following problem:

What is the domain and range of y=(x^2)+6?

This simple algebra problem relies on you knowing a few things already. You must know:

• The definition of “domain” and “range”
• That you can never square any real number and get a negative

Once you know those things, this becomes easy to solve. This is also how we learn languages.

An example of the problem-solving process with a foreign language

Anyone interested in serious foreign language study (as opposed to a “crash course” or “survival course”) should learn the infinitive form of verbs in their target language. You can’t make progress without them because they’re the root of all conjugations. It’s only once you have a grasp of the infinitives that you can completely express yourself. Consider the problem-solving steps applied in the following example.

I know that I want to say “I don’t eat eggs” to my Mexican waiter. That’s the problem.

I don’t know how to say that, but last night I told my date “No bebo alcohol” (“I don’t drink alcohol”). I also know the infinitive for “eat” in Spanish (comer). This is what I already know.

Now I can execute the final step of problem-solving.

Step 4: What’s the relationship between the two?

I see the connection. I can use all of my problem-solving strategies and methods to solve my particular problem.

I know the infinitive for the Spanish word “drink” is “beber” . Last night, I changed it to “bebo” to express a similar idea. I should be able to do the same thing to the word for “eat”.

“No como huevos” is a pretty accurate guess.

In the math example, the same process occurs. You don’t know the answer to “What is the domain and range of y=(x^2)+6?” You only know what “domain” and “range” mean and that negatives aren’t possible when you square a real number.

A domain of all real numbers and a range of all numbers equal to and greater than six is the answer.

This is relating what you don’t know to what you already do know. The solutions appear simple, but walking through them is an excellent demonstration of the process of problem-solving.

In most cases, the solution won’t be this simple, but the process or finding it is the same. This may seem trivial, but this is a model for thinking that has served the greatest minds in history.

A recap of the 4 steps of the simple problem-solving process

• What’s the problem? There’s something wrong. There’s something amiss.
• What do you need to know? This is how to fix what’s wrong.
• What do you already know? You already know something useful that will help you find an effective solution.
• What’s the relationship between the previous two? When you use what you know to help figure out what you don’t know, there is no problem that won’t yield.

Learning is simply problem-solving. You’ll learn faster if you view it this way.

What was once complicated will become simple.

What was once convoluted will become clear.

Ed Latimore

I’m a writer, competitive chess player, Army veteran, physicist, and former professional heavyweight boxer. My work focuses on self-development, realizing your potential, and sobriety—speaking from personal experience, having overcome both poverty and addiction.

Follow me on Twitter.

Developing foreign language skills

What follows are methods I’ve discovered and used to improve in all of these areas, which have, in turn, made it even easier to use and learn the language.

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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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4 Best Steps To Problem Solving in Math That Lead to Results

Eastern Shore Math Teacher

What does problem solving in math mean, and how to develop these skills in students?  Problem solving involves tasks that are challenging and make students think.  In teaching through problem solving, learning takes place while trying to solve problems with specific concepts and skills. Therefore, teachers need to provide safe learning spaces that foster a growth mindset in math in order for students to take risks to solve problems.   In addition, providing students with problem solving steps in math builds success in solving problems.

By providing rich mathematical tasks and engaging puzzles, students improve their number sense and mindset about mathematics.  Click Here to get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students. 

Students who feel successful in math class are happier and more engaged in learning.  Check out  The Bonus Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys for students to use in your classroom to cultivate a positive classroom community in mathematics.    You can also sign up for other freebies from me Here at Easternshoremathteacher.com .

Have you ever given students a word problem or rich task, and they froze?  They have no idea how to tackle the problem, even if it is a concept they are successful with.   This is because they need problem solving strategies.  I started to incorporate more problem solving tasks into my teaching in addition to making the 4 steps for problem solving a school-wide initiative and saw results.  

What is Problem Solving in Math?

When educators use the term problem solving , they are referring to mathematical tasks that are challenging and require students to think.   Such tasks or problems can promote students’ conceptual understanding, foster their ability to reason and communicate mathematically, and capture their interests and curiosity (Hiebert & Wearne, 1993; Marcus & Fey, 2003; NCTM, 1991; van de Walle, 2003).

How Should Problem Solving For Math Be Taught?

Problem solving should not be done in isolation.  In the past, we would teach the concepts and procedures and then assign one-step “story” problems designed to provide practice on the content. Next, we would teach problem solving as a collection of strategies such as “draw a picture” or “guess and check.”  Eventually, students would be given problems to apply the skills and strategies.  Instead, we need to make problem solving an integral part of mathematics learning. 

In teaching through problem solving, learning takes place while trying to solve problems with specific concepts and skills. As students solve problems, they can use any strategy. Then, they justify their solutions with their classmates and learn new ways to solve problems. 

Students do not need every task to involve problem solving.  Sometimes the goal is to just learn a skill or strategy.   

Criteria for Problem Solving Math 

Lappan and Phillips (1998) developed a set of criteria for a good problem that they used to develop their middle school mathematics curriculum (Connected Mathematics). The problem:

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

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

The real value of these criteria is that they provide teachers with guidelines for making decisions about how to make problem solving a central aspect of their instruction.  Read more at NCTM .

Problem Solving Teaching Methods

Teaching students these 4 steps for solving problems allows them to have a process for unpacking difficult problems.  

As you teach, model the process of using these 4 steps to solve problems.   Then, encourage students to use these steps as they solve problems.   Click here for Posters, Bookmarks, and Labels to use in your classroom to promote the use of the problem solving steps in math.  

How Problem Solving Skills Develop

Problem solving skills are developed over time and are improved with effective teaching practices.  In addition, teachers need to select rich tasks that focus on the math concepts the teacher wants their students to explore. 

Problem Solving 4 Steps

Understand the problem.

 Read & Think

• Circle the needed information and underline the question. 
• Write an answer STEM sentence.  There are_____ pages left to read. 

Plan Out How to Solve the Problem

Make a Plan

• Use a strategy.  (Draw a Picture, Work Backwards, Look for a Pattern, Create a Table, Bar Model)
• Use math tools.

Do the Problem

Solve the Problem

• Show your work to solve the problem.  This could include an equation. 

Check Your Work on the Problem

Answer & Check

• Write the answer into the answer stem.
• Does your answer make sense?
• Check your work using a different strategy.

Check out these Printables for Problem Solving Steps in Math .

Teaching Problem Solving Strategies

A problem solving strategy is a plan used to find a solution.  Understanding how a variety of problem solving strategies work is important because different problems require you to approach them in different ways to find the best solution. By mastering several problem-solving strategies, you can select the right plan for solving a problem.  Here are a few strategies to use with students:

• Draw a Picture
• Work Backwards
• Look for a Pattern
• Create a Table 

Why is Using Problem Solving Steps For Math Important?

Problem solving allows students to develop an understanding of concepts rather than just memorizing a set of procedures to solve a problem.  In addition, it fosters collaboration and communication when students explain the processes they used to arrive at a solution. Through problem-solving, students develop a deeper understanding of mathematical concepts, become more engaged, and see the importance of mathematics in their lives. 

NCTM Process Standards

In 2011 the Common Core State Standards incorporated the NCTM Process Standards of problem-solving, reasoning and proof, communication, representation, and connections into the Standards for Mathematical Practice.  With these process standards, the focus became more on mathematics through problem solving.   Students could no longer just develop procedural fluency, they needed to develop conceptual understanding in order to solve new problems and make connections between mathematical ideas. 

Engaging Students to Learn in Mathematics Class

Engaging students to learn in math class will help students to love math.  Children develop a dislike of math early on and end up resenting it into adult life.   Even in the real world, students will likely have to do some form of mathematics in their personal or working life.  So how can teachers make math more interesting to engage students in the subject? Read more at 5 Best Strategies for Engaging Students to Learn in Mathematics Class

Teachers can promote number sense by providing rich mathematical tasks and encouraging students to make connections to their own experiences and previous learning.

Sign up on my webpage to get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students.  Providing opportunities to do math puzzles daily is one way to help students develop their number sense.  CLICK Here to sign up for  71 Math Number Puzzles and check out my website.

Promoting a Growth Mindset

Research shows that there is a link between a growth mindset and success. In addition, kids who have a growth mindset about their abilities perform better and are more engaged in the classroom.  Students need to be able to preserve and make mistakes when problem solving.  

Read more … 5 Powerful and Easy Lessons Teaching Students How to Get a Growth Mindset

Here are some Resources to Use to Grow a Growth Mindset

• Free Mindset Survey
• Growth Mindset Classroom Display Free
• Growth Mindset Lessons

Using Word Problems

Story Problems and word problems are one way to promote problem solving.   In addition, they provide great practice in using the 4 steps of solving problems.   Then, students are ready for more challenging problems.  

For Kindergarten

• Subtraction within 5

For First Grade

• Word Problems to 20
• Word Problems of Subtraction

For Second Grade

• Two Step Word Problems with Addition and Subtraction
• Grade 2 Addition and Subtraction Word Problems
• Word Problems with Subtraction 

For Third Grade

• Word Problems Division and Multiplication
• Multiplication Word Problems

For Fourth Grade

• Multiplication Area Model
• Multiplicative Comparison Word Problems

Resources for Problem Solving

• 3 Act Tasks
• What’s the Best Proven Way to Teach Word Problems with Two Step Equations?
• 5 Powerful and Easy Lessons Teaching Students How to Get a Growth Mindset
• 5 Powerful Ideas to Help Students Develop a Growth Mindset in Mathematics

Problem Solving Steps For Math 

In mathematics, problem solving is one of the most important topics to teach.  Learning to problem solve helps students apply mathematics to real-world situations. In addition, it is used for a deeper understanding of mathematical concepts. 

By providing rich mathematical tasks and engaging puzzles, students improve their number sense and mindset about mathematics.  Click Here to get this Freebie of 71 Math Number Puzzles delivered to your inbox to use with your students. 

Check out  The Free Ultimate Guide for Creating a Growth Mindset Classroom and Students Who Love Math for ideas, lessons, and mindset surveys to use to cultivate a growth mindset classroom.

Start by modeling using the problem solving steps in math and allowing opportunities for students to use the steps to solve problems.   As students become more comfortable with using the steps and have some strategies to use,  provide more challenging tasks.  Then, students will begin to see the importance of problem solving in math and connecting their learning to real-world situations. 

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Hi, I'm Eastern Shore Math Teacher!

I have been teaching for over 22 years in an elementary school.  I help educators plan engaging math lessons and cultivate a positive math culture in their classrooms.  

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Jul 5, 2021 Problem-Solving Steps that Actually Work Updated: Mar 6, 2023 Whenever our students encounter problems, it can be a tricky situation. On one hand, I get super excited about the idea of my students THINKING about everything they know to solve the problem. I love watching their brains work while they access that filing cabinet in their brain of math information and pull out the information to solve a challenging problem. On the other hand, that same process can become a brick wall when it becomes too overwhelming. Students can shut down and refuse to move. They can cry and become frustrated. These same students can then begin believing they are just not good at math from this point forward. That's a lot of pressure from a simple math problem. If you haven't read Jo Boaler's Mathematical Mindsets, I strongly suggest it as a way to begin helping our students see math learning with a growth mindset. It's a helpful guide in teaching our students and ourselves that knowledge is something that grows and is not fixed. It is based on Carol Dweck's work with Growth Mindsets from Mindset: The New Psychology of Success . (Another great read in helping children as a parent, teacher or coach.) So what do we do? Instead of bombarding our students with several strategies to make problem-solving easier, I think it's important to boil it down to the basics. What strategies can I give my students that help them with all problems? What's something that's easy for them to remember and recall? What's something that would give them confidence moving forward? Enter in Polya's Problem-Solving Method by George Polya who was known as the father of problem solving. These four steps sum up everything our students need to solve problems successfully. They are easy to remember and easy to implement. (This post does contain affiliate links.) Understand the Problem: This is the focus on comprehension. What is the problem asking me to do? What do I know from reading the problem? What can I comprehend? Plan: This is the time where students think about how they want to move forward. Before solving with mathematics, we want our students to determine what steps they should take. Solve : This is where students do the math. They follow the steps in their plan and work out the problem. Look Back: Now we want students to look back and see that their answer makes sense. We want them to check the answer using estimation or even by trying to solve it in another way. Four steps...that's totally manageable right? I love the simplicity of it all and even find that it carries over to all aspects of our life when solving real-life problems. Now that students have a way to solve problems, it's time to give them the tools to make a plan that will work. I've been talking about Singapore's heuristics in my Member's Facebook group, and I wanted to share some of those with you. Stay tuned in the next few weeks to learn about the heuristics and how these strategies help students determine a meaningful plan to solve problems. In the meantime, be sure to grab your problem-solving poster by clicking below! K-2 Free Math Resources Grades 3-6 Free Math Resources Recent Posts Great Big List of Math Literature Math Literature: Goodnight Numbers and a Digital Freebie Math Literature: The Action of Subtraction Thanks for submitting! AI Math Solver Graphing Calculator Popular Problems Worksheets Study Guides Cheat Sheets Calculators Verify Solution Solutions Integral Calculator Derivative Calculator Algebra Calculator Matrix Calculator More... Graphing Line Graph Exponential Graph Quadratic Graph Sine Graph More... Calculators BMI Calculator Compound Interest Calculator Percentage Calculator Acceleration Calculator More... Geometry Pythagorean Theorem Calculator Circle Area Calculator Isosceles Triangle Calculator Triangles Calculator More... Tools Notebook Groups Cheat Sheets Worksheets Study Guides Practice Verify Solution x^{\msquare} \log_{\msquare} \sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x) ▭\:\longdivision{▭} \times \twostack{▭}{▭} + \twostack{▭}{▭} - \twostack{▭}{▭} \left( \right) \times \square\frac{\square}{\square} Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Prove That Logical Sets Word Problems Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Coterminal Angle Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. 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Step 2: Devise a Plan: Below are some strategies one might use to solve a problem. Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.) 1. PDF 4-Step Process for Problem Solving Choose a strategy, or combination of strategies. Make a record of false starts, and your corrections. Carry out the plan. Clearly and precisely describe verbally each step of the plan. Verify that each step has been done correctly. Provide mathematical justification for the step (a convincing argument) Step-by-Step Math Problem Solver QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students. The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and ... Polya's Problem Solving Process Polya's 4-Step Process. George Polya was a mathematician in the 1940s. He devised a systematic process for solving problems that is now referred to by his name: the Polya 4-Step Problem-Solving ... How to Solve a Problem in Four Steps: The IDEA Model A highly sought after skill, learn a simple yet effective four step problem solving process using the concept IDEA to identify the problem, develop solutions... Step-by-Step Calculator Symbolab is the best step by step calculator for a wide range of physics problems, including mechanics, electricity and magnetism, and thermodynamics. It shows you the steps and explanations for each problem, so you can learn as you go. To solve math problems step-by-step start by reading the problem carefully and understand what you are being ... 5: Problem Solving Polya's problem-solving strategy involves four key steps: understanding the problem, devising a plan, carrying out the plan, and reviewing the solution. 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