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Key Features: Provides a variety of problem-solving strategies, including guessing and checking, drawing a picture, looking for patterns, making a table, and acting it out.

Strengths: Offers clear explanations and examples of each strategy, making it easy for teachers to implement in their classrooms.

Applications: Can be used to introduce problem-solving strategies to students and provide examples of how to apply them to different types of problems.

Search method: I searched for this article using the keywords "problem-solving elementary education" in an academic journal.

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Problem Solving: An Approach to Understanding and Critiquing Our World - National Council of Teachers of Mathematics

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July 2022
Problem solving and critical thinking skills prepare students to understand and critique their world, preparing them to be contributing leaders in society. They are skills that all individuals need in decision making, in the workforce, in

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"Teaching Problem-Solving Skills in Elementary Math" 

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"Teaching Problem-Solving Skills in Elementary Math" 

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Key Features: Offers practical tips for teaching problem-solving skills, such as creating a positive classroom environment, providing opportunities for students to practice, and using real-world examples.

Strengths: Provides actionable advice that teachers can easily incorporate into their daily practice.

Applications: Can be used to guide teachers in implementing effective problem-solving instruction.

Search method: I searched for this article using the keywords "problem-solving elementary education" in an academic article.

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Your preschooler is figuring out what things are, why things are, and how things work.

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"Strategies for Encouraging Critical Thinking Skills in Students"

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"Strategies for Encouraging Critical Thinking Skills in Students"

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Key Features: Discusses the importance of fostering creativity in problem-solving and provides strategies for encouraging divergent thinking.

Strengths: Offers a fresh perspective on problem-solving and emphasizes the importance of creativity in the learning process.

Applications: This can be used to inspire teachers to create more engaging and challenging problem-solving activities.

Search method: I searched for this article using the keywords "problem-solving young learners" in an educational article.

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"20 Effective Math Strategies To Approach Problem-Solving"

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"20 Effective Math Strategies To Approach Problem-Solving"

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Key features: This article provides a specific focus on problem-solving strategies in mathematics. It offers a variety of techniques and examples to help teachers guide students in solving mathematical problems.

Strengths: The article is well-organized and easy to follow, with clear explanations and practical examples. It provides a valuable resource for teachers who want to improve their students' mathematical problem-solving skills.

Application: This article can be used as a reference for teachers to plan and deliver math problem-solving lessons. It can also be used to support students in developing their mathematical problem-solving skills.

Search method: I searched for this article using the keywords "problem-solving strategies math" in an educational article.

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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.

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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:

The problem

How to act out the problem

Gia has 6 apples. Jordan has 3 apples. How many apples do they have altogether?

Two students use counters to represent the apples. One student has 6 counters and the other student takes 3. Then, they can combine their "apples" and count the total.

Michael has 7 pencils. He gives 2 pencils to Sarah. How many pencils does Michael have now?

One student ("Michael") holds 7 pencils, the other ("Sarah") holds 2 pencils. The student playing Michael gives 2 pencils to the student playing Sarah. Then the students count how many pencils Michael is left holding.

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.

For example,

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:

1. Understand the problem

2. Devise a plan

3. Carry out the plan

4. Look back

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.

FAQs

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20 Effective Math Strategies For Problem Solving

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Math strategies for problem solving help students define the problem and highlight the key information to help them find a solution.

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"Third Grade Students' Challenges and Strategies to Solving Mathematical Word Problems"

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"Third Grade Students' Challenges and Strategies to Solving Mathematical Word Problems"

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Key Features: Provides third grade students' challenges and strategies for solving mathematical word problems. It discusses the difficulties students face and the strategies they find helpful.

Strengths: Offers helpful strategies include group discussion, self-assessment, incorporating games, and learning that math makes sense.

Applications: Can be used to inspire teachers to find effective lessons to ease the stress on problem solving.

Search method: I searched for this article using the keywords "problem-solving elementary education" in an academic journal.

Serach Method:

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Key features: This website offers a variety of resources for teaching math, including problem-solving activities, games, and lessons. It provides a user-friendly interface and high-quality content.

Strengths: The website is well-organized and easy to navigate, with a wide range of resources to choose from. It offers a variety of problem-solving activities that can be adapted to different grade levels and learning styles.

Application: This website can be used as a valuable resource for teachers to find engaging problem-solving activities and lessons. It can also be used by students to practice problem-solving skills independently.

Search method: I searched for this website using the keywords "math problem-solving resources" in a search engine.

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Explore Math in Practice in even more depth: MathInPractice.com The Math in Practice School Bundle includes 14 books altogether: one of each Grade-Level Pack plus an Administrator Pack.

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Key features: Khan Academy offers a vast collection of educational videos and exercises on various subjects, including math. It provides a personalized learning experience and is freely accessible to all.

Strengths: The website offers high-quality educational content delivered by experienced teachers. It provides a clear and concise explanation of concepts and offers ample opportunities for practice.

Application: Khan Academy can be used as a supplementary resource for students to learn problem-solving strategies and practice solving problems. It can also be used by teachers to supplement their instruction and provide additional support to students.

Search method: I searched for this website using the keywords "problem-solving math Khan Academy" in a search engine.

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If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Website Resource for 3rd Grade Problem Solving

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Website Resource for 3rd Grade Problem Solving

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Key features: Math Playground offers a variety of online math games and activities, including problem-solving challenges. It provides a fun and engaging way for students to practice their problem-solving skills.

Strengths: The website is visually appealing and easy to navigate, with a wide range of activities to choose from. It offers a variety of problem-solving challenges that can be adapted to different learning styles and abilities.

Application: Math Playground can be used as a supplementary resource for students to practice problem-solving skills independently. It can also be used by teachers to supplement their instruction and provide additional support to students.

Search method: I searched for this website using the keywords "math problem-solving games" in a search engine.

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Problem-Solving Strategies for Kids x Video

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Problem-Solving Strategies for Kids x Video

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Key features: This video provides a visual explanation of problem-solving strategies, using animated characters and real-world examples. It is engaging and easy to understand for young learners.

Strengths: The video is visually appealing and easy to follow, with clear explanations and engaging examples. It can be used to introduce problem-solving strategies to students and reinforce their understanding.

Application: This video can be used as an introductory lesson on problem-solving strategies. It can also be used as a review or reinforcement tool for students who need additional support.

Search method: I searched for this video using the keywords "problem-solving strategies for kids" on YouTube.

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Make it Simpler | Primary Math Problem Solving Strategy

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How to Teach Problem-Solving Skills x Video

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How to Teach Problem-Solving Skills x Video

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Key features: This video provides practical tips and advice for teachers on how to teach problem-solving skills effectively. It offers insights into creating a supportive learning environment and providing ample opportunities for practice.

Strengths: The video offers valuable advice for teachers on how to implement problem-solving strategies in their classrooms. It provides practical tips and examples that can be easily adapted to different teaching contexts.

Application: This video can be used by teachers to improve their teaching practices and develop effective problem-solving lessons. It can also be used as a professional development resource for teachers.

Search method: I searched for this video using the keywords "teaching problem-solving skills" on YouTube.

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How to Teach Kids Better Problem Solving | Michael Arnold | TEDxGreenville

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Rejected reason: This resource is specifically designed for gifted students and may not be appropriate for all 3rd graders. It may be too challenging or too abstract for students who are not gifted.

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How to Foster Creative Problem-Solving in Gifted and Talented Students

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Gifted and talented students might have an easier time understanding academic subjects, but these students face their own set of challenges in the classroom.

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Rejected reason: The website does not provide any information about the author or organization behind it. Without knowing who is responsible for the content, it is difficult to assess the credibility of the information.

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Reading as Problem Solving/Impact of Higher Order Thinking

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Reading is essentially a problem-solving task. Comprehending what is read, like problem solving, requires effort, planning, self-monitoring, strategy selection, and reflection. As students move through school, reading materials become more complex, thus more effortful. Students who approach reading as a problem solving activity take an active and strategic approach to reading, and are metacognitively aware of how well they understand ... Read More