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Problem Solving Steps

Introduction.

Solving problems is an important part of any math course. Techniques used for solving math problems are also applicable to other real-world situations. When solving problems it is important to know what to look for and to understand possible strategies for solving. As with most things, the more problems you solve, the better you will get at it. As you solve different types of math problems, you will gain a better understanding of the techniques that can be used with each type of problem.

In his book called How to Solve It, George Polya (1887 – 1985), proposed a four-step process for problem solving. In this module, we will take a look at those four common problem-solving principles as well as examples of techniques to be applied when solving problems.

Step 1: Understand the problem

In order to solve a problem, it is important to understand what you are being asked to find.

Strategies for understanding the problem:

  • Review the problem. If you are solving a word problem, read through the entire problem.
  • Seek to understand all the words used in stating the problem. Look for key words that will help you determine whether you will need to add, subtract, multiply, divide, or use a combination of these functions.
  • Determine what you are being asked to find or show.
  • Restate the problem in your own words.
  • Try drawing a picture or diagram to better understand the problem.
  • Make sure you have all of the information you need to solve the problem.

Step 2: Develop a plan

Determine how you will solve the problem. Some problems are solved by using a formula and others require you to develop an equation. Pictures, tables, or charts may also be used.

Keep in mind, you may be solving problems that require multiple steps. When you encounter these, break them down into smaller steps and solve each piece. The more problems you solve, the easier it will get to develop a plan for solving problems. You will begin to learn what techniques work best for each type of problem you solve.

Here are some of the common problem-solving techniques:

  • Guess and check
  • Make a table or list
  • Eliminate possibilities
  • Use symmetry
  • Consider special cases
  • Solve as an equation
  • Look for a pattern
  • Draw a sketch or a picture
  • Solve a simpler problem
  • Use a model
  • Start from the end - work backward
  • Use a formula

Step 3: Carry out the plan

Once you have determined your plan for solving the problem, the next step is putting that plan to work. Use the approach that makes sense for the problem and solve it. In most cases, this step will be easier than actually determining the plan. Having an understanding of basic math (pre-algebra) skills will help as you perform the necessary steps to solve the problem. Memorizing the simple multiplication and division tables at least to 10 can make solving problems much easier as well.

If you find that the problem-solving approach you chose does not work, you will need to go back to step two and choose a new approach. Having patience while carrying out your plan is important. It is not uncommon for mathematicians to have to try multiple approaches when solving problems.

Step 4: Look back and check

Here is where you check your logic. If you solved an equation, fill your answer into the equation and check to make sure it works. If you solved a word problem, consider whether or not your answer makes sense. If the problem asked for the height of a ball in the air and your answer was -10 feet, that does not make sense. Just because you get a number doesn’t mean it is right. It is important to check your answer and see if it logically makes sense. If your answer does not make sense, you should review the approach you chose as well as your math calculations. Many errors are corrected in this final step of the problem-solving process.

Example Problems

Example 1 – Difference in temperature

The hottest temperature ever recorded in Death Valley, CA was 134 degrees on July 10, 1913. The coldest temperature ever recorded there, 15 degrees, occurred earlier that year on January 8, 1913. What was the difference between these record temperatures in 1913? (www.nps.gov)

Step 1: Understand the problem: After reading through the problem, you will find that the problem to solve is clearly stated. You will need to determine the difference in temperature between the hottest and coldest recorded days in Death Valley, CA.

Step 2: Develop a plan: As you were reading the problem, you noted the key word “difference.” To find the difference between two numbers, you will need to use subtraction. You are now ready to set up an equation. You can assign the variable, x, to the unknown. In this case, the unknown is the difference in temperatures.

x = 134 - 15

Step 3: Carry out the plan: Now that you have developed your equation, go ahead and solve it. x = 134 - 15 x = 119 degrees

Step 4: Look back and check: To check your equation, fill the answer back into the equation and make sure it works. Also, consider whether or not your answer makes sense. If you had received an answer that was significantly higher or lower than either of the temperatures in the problem, that would indicate that there may be an error in your calculations. 119 = 134 – 15

Example 2 – Interest Earned

If a savings account balance of $2650 earns 4% interest in one year, how much interest is earned? What will the account balance be after the interest is earned?

Step 1: Understand the problem: After reading through the problem, you recognize that there are actually two problems to solve. You will need to determine the amount of interest on the account balance and you will need to determine what the account balance will be when the interest is earned.

Step 2: Develop a plan: The first problem you need to solve is the amount of interest earned on $2650. To find the amount of interest, you will need to multiply the current account balance by the interest rate. In order to complete the multiplication problem, you will need to change the percent into a decimal. You can assign the variable, x, to the unknown. In this case, the unknown is the amount of interest earned.

Once you determine how much interest will be earned, you can solve the second problem. You will need to add the current balance and the interest earned to determine how much will be in the account once the interest is applied. To establish an equation for the second problem, you can assign a variable, y, to the unknown. You establish this equation to solve the second problem.

y = $2650 + x

Step 3: Carry out the plan: Now that you have developed your equations, go ahead and solve them.

Part 1: x = .04 x $2650 x = $106

Part 2: y = $2650 + x y = $2650 + $106 y = $2756

Step 4: Look back and check: To check your equations, fill the answers back into them. Also, consider whether or not your answers makes sense. If you had received an answer that was lower or significantly higher than the original account balance, that would indicate there may be an error in your calculations.

Part 1: $106 = .04 x $2650

Part 2: $2756 = $2650 + $106

Example 3 - Book Buyers

In a recent sample of book buyers, 70 more shopped at large-chain bookstores than at small-chain/independent bookstores. A total of 442 book buyers shopped at these two types of stores. How many buyers shopped at each type of bookstore?

Step 1: Understand the problem: After reading through the problem, you determine you are asked to find the number of buyers shopping at each type of bookstore.

Step 2: Develop a plan: To solve this problem you will need to assign a variable, x, for one of the unknowns. If x is the number of book buyers shopping at large-chain bookstores, then (x – 70) = the number of book buyers shopping at small-chain/independent bookstores.

To solve the problem, you come up with this equation: x + x - 70 = 442

Step 3: Carry out the plan: Now that you have developed your equation, go ahead and solve it.

x + x - 70 = 442 2x – 70 + 70 = 442 + 70 2x /2= 512 /2 x = 256

After solving the equation, you determine that 256 people shopped at large-chain bookstores. You can plug 256 into the equation representing those shopping at small-chain bookstores (x - 70).

256 – 70 = 186

186 people shopped at small-chain bookstores

Step 4: Look back and check: To check your answers, fill them back into the original problem. Also, consider whether or not your answers makes sense. If the number of small-chain store shoppers was greater than the number of large-chain store shoppers or if the two numbers did not equal 442 that would indicate there was an error in your calculations.

The number of large chain shoppers (256) is 70 more than the number of small-chain store shoppers (186), and the total number of these shoppers (256 + 186) is 442.

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

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

Use Established Procedures

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

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

Look for Clue Words

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

Common clue words for addition  problems:

Common clue words for  subtraction  problems:

  • How much more

Common clue words for multiplication problems:

Common clue words for division problems:

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

Read the Problem Carefully

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

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

Develop a Plan and Review Your Work

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

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

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

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

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

Tips and Hints

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

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

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

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ALL Problems

Introduction.

MathSolvely focuses on solving mathematical problems, providing tips on how to solve the problem, step-by-step calculation steps, relevant knowledge notes and answers for each problem to help you understand the solution to this problem in detail.

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Four-Step Math Problem Solving Strategies & Techniques

Four steps to success.

There are many possible strategies and techniques you can use to solve math problems. A useful starting point is a four step approach to math problem solving. These four steps can be summarized as follows:

  • Carefully read the problem. In this careful reading, you should especially seek to clearly identify the question that is to be answered. Also, a good, general understanding of what the problem means should be sought.
  • Choose a strategy to solve the problem. Some of the possible strategies will be discussed in the rest of this article.
  • Carry out the problem solving strategy. If the first problem solving technique you try doesn’t work, try another.
  • Check the solution. This check should make sure that you have indeed answered the question that was posed and that the answer makes sense.

Step One - Understanding the Problem

As you carefully read the problem, trying to clearly understand the meaning of the problem and the question that you must answer, here are some techniques to help.

Identify given information - Highlighting or underlining facts that are given helps to visualize what is known or given.

Identify information asked for - Highlighting the unknowns in a different color helps to keep the known information visually separate from the unknowns to be determined. Ideally this will lead to a clear identification of the question to be answered.

Look for keywords or clue words - One example of clue words is those that indicate what type of mathematical operation is needed, as follows:

Clue words indicating addition: sum, total, in all, perimeter.

Clue words indicating subtraction: difference, how much more, exceed.

Clue words for multiplication: product, total, area, times.

Clue words for division: share, distribute, quotient, average.

Draw a picture - This might also be considered part of solving the problem, but a good sketch showing given information and unknowns can be very helpful in understanding the problem.

Step Two - Choose the Right Strategy

It step one has been done well, it should ease the job of choosing among the strategies presented here for approaching the problem solving step. Here are some of the many possible math problem solving strategies.

  • Look for a pattern - This might be part of understanding the problem or it might be the first part of solving the problem.
  • Make an organized list - This is another means of organizing the information as part of understanding it or beginning the solution.
  • Make a table - In some cases the problem information may be more suitable for putting in a table rather than in a list.
  • Try to remember if you’ve done a similar problem before - If you have done a similar problem before, try to use the same approach that worked in the past for the solution.
  • Guess the answer - This may seem like a haphazard approach, but if you then check whether your guess was correct, and repeat as many times as necessary until you find the right answer, it works very well. Often information from checking on whether the answer was correct helps lead you to a good next guess.
  • Work backwards - Sometimes making the calculations in the reverse order works better.

Steps Three and Four - Solving the Problem and Checking the Solution

If the first two steps have been done well, then the last two steps should be easy. If the selected problem solving strategy doesn’t seem to work when you actually try it, go back to the list and try something else. Your check on the solution should show that you have actually answered the question that was asked in the problem, and to the extent possible, you should check on whether the answer makes common sense.

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6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

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A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution. 

1. Link problem-solving to reading

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it. 

3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process. 

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks. 

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.” 

6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process. 

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

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steps problem solving math

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

Eastern Shore Math Teacher

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.

A teacher working on problem solving in math.

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.  

Bonus Growth Mindset Classroom resources to use to cultivate a growth mindset classroom.

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).

When educators use the term problem solving, they are referring to mathematical tasks that are challenging and require students to think.

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.   

List of Criteria for Problem Solving in Math

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 .

Resources to Use for Problem Solving Steps in Math.

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 .

Problem Solving steps for Math poster.

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. 

Girl Problem Solving.

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

Puzzles in Math with Answers on a computer screen.

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

Growth Mindset in Math Resources on a computer screen.

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

Word Problems of Addition and Subtraction on a computer screen.

For Second Grade

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

Problem Solving in Math with these addition and subtraction word problems with different problem structures. Can be used digitally or as a worksheet.

For Third Grade

  • Word Problems Division and Multiplication
  • Multiplication Word Problems

Use repeated addition to multiply and find the total number of items. See the connection between repeated addition and multiplication when using arrays.

For Fourth Grade

  • Multiplication Area Model
  • Multiplicative Comparison Word Problems

Solving Multiplicative comparison word problems on a computer screen.

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. 

Kids solving word problems.

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Education Corner

Strategies for Solving Math Word Problems

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Math word problems can be tricky and often challenging to solve. Employing the SQRQCQ method can make solving math word problems easier and less intimidating.

The SQRQCQ method is particularly useful for children with learning disabilities and can be used effectively in special education programs. SQRQCQ is an abbreviation for Survey, Question, Read, Question, Compute, and Question.

Step 1 – SURVEY the Math Problem

The first step to solving a math word problem is to read the problem in its entirety to understand what you are being asked to solve. After you read it, you can decide the most relevant aspects of the problem that need to be solved and what aspects are not relevant to solving the problem. The idea here is to get a general understanding.

Step 2 – QUESTION

Once you have an idea of what you’re attempting to solve, you need to determine what formulas, steps, or equations should be utilized in order to find the correct answer. It is impossible to find an answer if you can’t determine what needs to be solved. Basically, what are the questions being asked by the problem?

Step 3 – REREAD

Now that you’ve determined what needs to be solved, reread the problem and pay close attention to specific details. Determine which aspects of the problem are interrelated. Identify all relevant facts and information needed to solve the problem. As you do, write them down.

Step 4 – QUESTION

Now that you’re familiar with specific details and how different facts and information within the problem are interrelated, determine what formulas or equations must be used to set up and solve the problem. Be sure to write down what steps or operations you will use for easy reference.

Step 5 – COMPUTE

Use the formulas and/or equations identified in the previous step to complete the calculations. Be sure to follow the steps you outlined while setting up an equation or using a formula. As you complete each step, check it off your list.

Step 6 – QUESTION

Once you’ve completed the calculations, review the final answer and make sure it is correct and accurate. If it does not appear logical, review the steps you took to find the answer and look for calculation or set-up errors. Recalculate the numbers or make other changes until you get an answer that makes sense.

How does SQRQCQ help students with learning disabilities?

Math word problems tend to be especially challenging for Learning Disabled (LD) students. LD students often lack “Concept Imagery”, or the ability to visualize the whole problem by creating a complete mental image. They often jump right into calculations and computations without understanding what the problem is asking or what they’re looking for.

LD students may also struggle to understand the words or wording within math word problems correctly. The inability to correctly interpret and understand wording greatly impacts their math reasoning skills and often leads them to making the wrong calculations and arriving incorrect conclusions.

Remembering and manipulating information and details in their working memory is another challenge some LD students face as they try to see the whole picture. Slow processing of information, followed by frustration and anxiety, will often lead LD students to try and get through math word problems as quickly as possible – which is why they often jump straight into computations in their attempt to make it to the finish line as quickly as possible.

SQRQCQ is a metacognitive guide that provides LD students with a logical order for solving math word problems. It provides just enough direction to guide them through the reasoning process without overwhelming them. SQRQCQ is also a mnemonic that is easy for students to remember and which they can fall back on when completing homework or taking tests.

Read also: – A Guide for Studying Math

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