how to improve word problem solving skills

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10 Best Strategies for Solving Math Word Problems

1. Understand the Problem by Paraphrasing

2. identify key information and variables, 3. translate words into mathematical symbols, 4. break down the problem into manageable parts, 5. draw diagrams or visual representations, 6. use estimation to predict answers, 7. apply logical reasoning for unknown variables, 8. leverage similar problems as templates, 9. check answers in the context of the problem, 10. reflect and learn from mistakes.

Have you ever observed the look of confusion on a student’s face when they encounter a math word problem ? It’s a common sight in classrooms worldwide, underscoring the need for effective strategies for solving math word problems . The main hurdle in solving math word problems is not just the math itself but understanding how to translate the words into mathematical equations that can be solved.

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Generic advice like “read the problem carefully” or “practice more” often falls short in addressing students’ specific difficulties with word problems. Students need targeted math word problem strategies that address the root of their struggles head-on. 

A Guide on Steps to Solving Word Problems: 10 Strategies 

One of the first steps in tackling a math word problem is to make sure your students understand what the problem is asking. Encourage them to paraphrase the problem in their own words. This means they rewrite the problem using simpler language or break it down into more digestible parts. Paraphrasing helps students grasp the concept and focus on the problem’s core elements without getting lost in the complex wording.

Original Problem: “If a farmer has 15 apples and gives away 8, how many does he have left?”

Paraphrased: “A farmer had some apples. He gave some away. Now, how many apples does he have?”

This paraphrasing helps students identify the main action (giving away apples) and what they need to find out (how many apples are left).

Play these subtraction word problem games in the classroom for free:

Students often get overwhelmed by the details in word problems. Teach them to identify key information and variables essential for solving the problem. This includes numbers , operations ( addition , subtraction , multiplication , division ), and what the question is asking them to find. Highlighting or underlining can be very effective here. This visual differentiation can help students focus on what’s important, ignoring irrelevant details.

• Encourage students to underline numbers and circle keywords that indicate operations (like ‘total’ for addition and ‘left’ for subtraction).
• Teach them to write down what they’re solving for, such as “Find: Total apples left.”

Problem: “A classroom has 24 students. If 6 more students joined the class, how many students are there in total?”

Key Information:

• Original number of students (24)
• Students joined (6)
• Looking for the total number of students

Here are some fun addition word problems that your students can play for free:

The transition from the language of word problems to the language of mathematics is a critical skill. Teach your students to convert words into mathematical symbols and equations. This step is about recognizing keywords and phrases corresponding to mathematical operations and expressions .

Common Translations:

• “Total,” “sum,” “combined” → Addition (+)
• “Difference,” “less than,” “remain” → Subtraction (−)
• “Times,” “product of” → Multiplication (×)
• “Divided by,” “quotient of” → Division (÷)
• “Equals” → Equals sign (=)

Problem: “If one book costs $5, how much would 4 books cost?”

Translation: The word “costs” indicates a multiplication operation because we find the total cost of multiple items. Therefore, the equation is 4 × 5 = $20

Complex math word problems can often overwhelm students. Incorporating math strategies for problem solving, such as teaching them to break down the problem into smaller, more manageable parts, is a powerful approach to overcome this challenge. This means looking at the problem step by step rather than simultaneously trying to solve it. Breaking it down helps students focus on one aspect of the problem at a time, making finding the solution more straightforward.

Problem: “John has twice as many apples as Sarah. If Sarah has 5 apples, how many apples do they have together?”

Steps to Break Down the Problem:

Find out how many apples John has: Since John has twice as many apples as Sarah, and Sarah has 5, John has 5 × 2 = 10

Calculate the total number of apples: Add Sarah’s apples to John’s to find the total,  5 + 10 = 15

By splitting the problem into two parts, students can solve it without getting confused by all the details at once.

Explore these fun multiplication word problem games:

Diagrams and visual representations can be incredibly helpful for students, especially when dealing with spatial or quantity relationships in word problems. Encourage students to draw simple sketches or diagrams to represent the problem visually. This can include drawing bars for comparison, shapes for geometry problems, or even a simple distribution to better understand division or multiplication problems .

Problem: “A garden is 3 times as long as it is wide. If the width is 4 meters, how long is the garden?”

Visual Representation: Draw a rectangle and label the width as 4 meters. Then, sketch the length to represent it as three times the width visually, helping students see that the length is 4 × 3 = 12

Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer’s ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

Problem: “If a book costs $4.95 and you buy 3 books, approximately how much will you spend?”

Estimation Strategy: Round $4.95 to the nearest dollar ($5) and multiply by the number of books (3), so 5 × 3 = 15. Hence, the estimated total cost is about $15.

Estimation helps students understand whether their final answer is plausible, providing a quick way to check their work against a rough calculation.

Check out these fun estimation and prediction word problem worksheets that can be of great help:

When students encounter problems with unknown variables, it’s crucial to introduce them to logical reasoning. This strategy involves using the information in the problem to deduce the value of unknown variables logically. One of the most effective strategies for solving math word problems is working backward from the desired outcome. This means starting with the result and thinking about the steps leading to that result, which can be particularly useful in algebraic problems.

Problem: “A number added to three times itself equals 32. What is the number?”

Working Backward:

Let the unknown number be x.

The equation based on the problem is  x + 3x = 32

Solve for x by simplifying the equation to 4x=32, then dividing by 4 to find x=8.

By working backward, students can more easily connect the dots between the unknown variable and the information provided.

Practicing problems of similar structure can help students recognize patterns and apply known strategies to new situations. Encourage them to leverage similar problems as templates, analyzing how a solved problem’s strategy can apply to a new one. Creating a personal “problem bank”—a collection of solved problems—can be a valuable reference tool, helping students see the commonalities between different problems and reinforcing the strategies that work.

Suppose students have solved a problem about dividing a set of items among a group of people. In that case, they can use that strategy when encountering a similar problem, even if it’s about dividing money or sharing work equally.

It’s essential for students to learn the habit of checking their answers within the context of the problem to ensure their solutions make sense. This step involves going back to the original problem statement after solving it to verify that the answer fits logically with the given information. Providing a checklist for this process can help students systematically review their answers.

Checklist for Reviewing Answers:

• Re-read the problem: Ensure the question was understood correctly.
• Compare with the original problem: Does the answer make sense given the scenario?
• Use estimation: Does the precise answer align with an earlier estimation?
• Substitute back: If applicable, plug the answer into the problem to see if it works.

Problem: “If you divide 24 apples among 4 children, how many apples does each child get?”

After solving, students should check that they understood the problem (dividing apples equally).

Their answer (6 apples per child) fits logically with the number of apples and children.

Their estimation aligns with the actual calculation.

Substituting back 4×6=24 confirms the answer is correct.

Teaching students to apply logical reasoning, leverage solved problems as templates, and check their answers in context equips them with a robust toolkit for tackling math word problems efficiently and effectively.

One of the most effective ways for students to improve their problem-solving skills is by reflecting on their errors, especially with math word problems. Using word problem worksheets is one of the most effective strategies for solving word problems, and practicing word problems as it fosters a more thoughtful and reflective approach to problem-solving

These worksheets can provide a variety of problems that challenge students in different ways, allowing them to encounter and work through common pitfalls in a controlled setting. After completing a worksheet, students can review their answers, identify any mistakes, and then reflect on them in their mistake journal. This practice reinforces mathematical concepts and improves their math problem solving strategies over time.

3 Additional Tips for Enhancing Word Problem-Solving Skills

Before we dive into the importance of reflecting on mistakes, here are a few impactful tips to enhance students’ word problem-solving skills further:

1. Utilize Online Word Problem Games

Incorporate online games that focus on math word problems into your teaching. These interactive platforms make learning fun and engaging, allowing students to practice in a dynamic environment. Games can offer instant feedback and adaptive challenges, catering to individual learning speeds and styles.

Here are some word problem games that you can use for free:

2. Practice Regularly with Diverse Problems

Consistent practice with a wide range of word problems helps students become familiar with different questions and mathematical concepts. This exposure is crucial for building confidence and proficiency.

Start Practicing Word Problems with these Printable Word Problem Worksheets:

3. Encourage Group Work

Solving word problems in groups allows students to share strategies and learn from each other. A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students’ problem-solving toolkit.

Conclusion 

Mastering math word problems is a journey of small steps. Encourage your students to practice regularly, stay curious, and learn from their mistakes. These strategies for solving math word problems are stepping stones to turning challenges into achievements. Keep it simple, and watch your students grow their confidence and skills, one problem at a time.

Frequently Asked Questions (FAQs)

How can i help my students stay motivated when solving math word problems.

Encourage small victories and use engaging tools like online games to make practice fun and rewarding.

What's the best way to teach beginners word problems?

Begin with simple problems that integrate everyday scenarios to make the connection between math and real-life clear and relatable.

How often should students practice math word problems?

Regular, daily practice with various problems helps build confidence and problem-solving skills over time.

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• Problem Solving

How to Improve Problem Solving Skills

Last Updated: January 27, 2024 Fact Checked

This article was co-authored by Erin Conlon, PCC, JD . Erin Conlon is an Executive Life Coach, the Founder of Erin Conlon Coaching, and the host of the podcast "This is Not Advice." She specializes in aiding leaders and executives to thrive in their career and personal lives. In addition to her private coaching practice, she teaches and trains coaches and develops and revises training materials to be more diverse, equitable, and inclusive. She holds a BA in Communications and History and a JD from The University of Michigan. Erin is a Professional Certified Coach with The International Coaching Federation. There are 13 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 235,253 times.

The ability to solve problems applies to more than just mathematics homework. Analytical thinking and problem-solving skills are a part of many jobs, ranging from accounting and computer programming to detective work and even creative occupations like art, acting, and writing. While individual problems vary, there are certain general approaches to problem-solving like the one first proposed by mathematician George Polya in 1945. [1] X Research source By following his principles of understanding the problem, devising a plan, carrying out the plan, and looking back, you can improve your problem-solving and tackle any issue systematically.

Define the problem clearly.

• Try to formulate questions. Say that as a student you have very little money and want to find an effective solution. What is at issue? Is it one of income – are you not making enough money? Is it one of over-spending? Or perhaps you have run into unexpected expenses or your financial situation has changed?

State your objective.

• Say that your problem is still money. What is your goal? Perhaps you never have enough to go out on the weekend and have fun at the movies or a club. You decide that your goal is to have more spending cash. Good! With a clear goal, you have better defined the problem.

Gather information systematically.

• To solve your money shortage, for example, you would want to get as detailed a picture of your financial situation as possible. Collect data through your latest bank statements and to talk to a bank teller. Track your earnings and spending habits in a notebook, and then create a spreadsheet or chart to show your income alongside your expenditures.

Analyze information.

• Say you have now collected all your bank statements. Look at them. When, how, and from where is your money coming? Where, when, and how are you spending it? What is the overall pattern of your finances? Do you have a net surplus or deficit? Are there any unexplained items?

Generate possible solutions.

• Your problem is a lack of money. Your goal is to have more spending cash. What are your options? Without evaluating them, come up with possible options. Perhaps you can acquire more money by getting a part-time job or by taking out a student loan. On the other hand, you might try to save by cutting your spending or by lowering other costs.
• Divide and conquer. Break the problem into smaller problems and brainstorm solutions for them separately, one by one.
• Use analogies and similarities. Try to find a resemblance with a previously solved or common problem. If you can find commonalities between your situation and one you've dealt with before, you may be able to adapt some of the solutions for use now.

Evaluate the solutions and choose.

• How can you raise money? Look at expenditures – you aren’t spending much outside of basic needs like tuition, food, and housing. Can you cut costs in other ways like finding a roommate to split rent? Can you afford to take a student loan just to have fun on the weekend? Can you spare time from your studies to work part-time?
• Each solution will produce its own set of circumstances that need evaluation. Run projections. Your money problem will require you to draw up budgets. But it will also take personal consideration. For example, can you cut back on basic things like food or housing? Are you willing to prioritize money over school or to take on debt?

Implement a solution.

• You decide to cut costs, because you were unwilling to take on debt, to divert time away from school, or to live with a roommate. You draw up a detailed budget, cutting a few dollars here and there, and commit to a month-long trial.

Review and evaluate the outcome.

• The results of your trial are mixed. On one hand, you have saved enough during the month for fun weekend activities. But there are new problems. You find that you must choose between spending cash and buying basics like food. You also need a new pair of shoes but can’t afford it, according to your budget. You may need to a different solution.

Adjust if necessary.

• After a month, you decide to abandon your first budget and to look for part-time work. You find a work-study job on campus. Making a new budget, you now have extra money without taking too much time away from your studies. You may have an effective solution.

Do regular mental exercises.

• Word games work great. In a game like “Split Words,” for example, you have to match word fragments to form words under a given theme like “philosophy.” In the game, “Tower of Babel,” you will need to memorize and then match words in a foreign language to the proper picture.
• Mathematical games will also put your problem solving to the test. Whether it be number or word problems, you will have to activate the parts of your brain that analyze information. For instance: “James is half as old now as he will be when he is 60 years older than he was six years before he was half as old as he is now. How old will James be when his age is twice what it was 10 years after he was half his current age?”

Play video games.

• Play something that will force you to think strategically or analytically. Try a puzzle game like Tetris. Or, perhaps you would rather prefer a role-playing or strategy game. In that case, something like “Civilization” or “Sim-City” might suit you better.

Take up a hobby.

• Web design, software programming, jigsaw puzzles, Sudoku, and chess are also hobbies that will force you to think strategically and systematically. Any of these will help you improve your overall problem solving.

Expert Q&A

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• ↑ https://math.berkeley.edu/~gmelvin/polya.pdf
• ↑ https://www.healthywa.wa.gov.au/Articles/N_R/Problem-solving
• ↑ https://asq.org/quality-resources/problem-solving
• ↑ https://ctb.ku.edu/en/table-of-contents/evaluate/evaluate-community-interventions/collect-analyze-data/main
• ↑ https://www.mindtools.com/pages/article/newCT_96.htm
• ↑ https://www.skillsyouneed.com/ips/problem-solving.html
• ↑ Erin Conlon, PCC, JD. Executive Life Coach. Expert Interview. 31 August 2021.
• ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5930973/
• ↑ https://www.theguardian.com/lifeandstyle/2018/oct/13/mental-exercises-to-keep-your-brain-sharp
• ↑ https://www.apa.org/monitor/2014/02/video-game
• ↑ https://www.nature.com/articles/d41586-018-05449-7

About This Article

To improve your problem-solving skills, start by clearly defining the problem and your objective or goal. Next, gather as much information as you can about the problem and organize the data by rewording, condensing, or summarizing it. Then, analyze the information you've gathered, looking for important links, patterns, and relationships in the data. Finally, brainstorm possible solutions, evaluate the solutions, and choose one to implement. For tips on implementing solutions successfully, read on! Did this summary help you? Yes No

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14 Effective Ways to Help Your Students Conquer Math Word Problems

If a train leaving Minneapolis is traveling at 87 miles an hour…

Word problems can be tricky for a lot of students, but they’re incredibly important to master. After all, in the real world, most math is in the form of word problems. “If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?” “This sweater costs $135, but it’s on sale for 35% off. So how much is that?” Here are the best teacher-tested ideas for helping kids get a handle on these problems.

1. Solve word problems regularly

This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so they’ll get comfortable with the process.

Learn more: Teaching With Jennifer Findlay

2. Teach problem-solving routines

There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time.

Learn more: Word Problems Made Easy

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3. Visualize or model the problem

Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link.

Learn more: Math Geek Mama

4. Make sure they identify the actual question

Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed. 

Learn more: Robert Kaplinsky

5. Remove the numbers

It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking. 

Learn more: Where the Magic Happens Teaching

6. Try the CUBES method

This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked.

Learn more: Teaching With a Mountain View

7. Show word problems the LOVE

Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use. 

8. Consider teaching word problem key words

This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it.

Learn more: Book Units Teacher

9. Determine the operation for the situation

Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link.

Learn more: Solving Word Problems With Jennifer Findlay

10. Differentiate word problems to build skills

Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves.

Learn more: Differentiating Math 

11. Ensure they can justify their answers

One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now.

Learn more: Madly Learning

12. Write the answer in a sentence

When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer.

Learn more: Multi-Step Word Problems

13. Add rigor to your word problems

A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems.

Learn more: The Routty Math Teacher and Alyssa Teaches

14. Use a problem-solving rounds activity.

Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer.

Learn more: Teacher Trap

Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies .

Plus, 60+ Awesome Websites For Teaching and Learning Math .

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3 Strategies to Conquer Math Word Problems

Here’s a word problem for you:

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

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

Why Students Struggle with Math Word Problems

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

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

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

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

3 Problem Solving Strategies

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

1. Teach a Problem-Solving Routine 

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

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

To make the problem solving routine meaningful and effective:

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

2. Differentiate Word Problems 

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

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

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

3. Compare Problems Side-by-Side 

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

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

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

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3 Word Problem Solving Strategies To Improve Word Problem Performance

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The ability to solve word problems doesn’t necessarily come easily to all students. We can improve our students’ ability to solve story problems with a few simple word problem-solving strategies. When it comes to comprehending, understanding, and solving word problems, sometimes it is helpful to move beyond traditional word problems and try a new word problem type that is designed to support students in tackling these tricky skills!

In order to solve word problems, students need to be able to:

• Comprehend the action or context of a word problem
• Understand the question or missing piece of information
• Develop a mathematically sound plan for solving for the missing information.
• Accurately calculate to find their solution.

It’s a balance between comprehension, an understanding of math concepts, and an ability to carry out math concepts. Identifying which of these steps are strengths or needs for your students can help you to choose a strategy that will best improve their word problem performance.

Word Problem Solving Strategy #1: Numberless Word Problems

Who is this strategy for? If your students are struggling to understand the action, context or question in a story problem, discussion and numberless word problems will be a word problem-solving strategy that can help your students tremendously! This strategy also helps your “number pluckers” who see numbers, pluck and add together regardless of context! Numberless word problems slow your students down!

Using a tool such as numberless word problems can help your students in their understanding precisely because the numberless word problem strategy emphasizes discussion every step of the way!

How do I use this strategy? As you solve numberless word problems you begin with a problem with no numbers at all and ask a variety of questions as you discuss and slowly add information back into the problem.

Reagan picked flowers for a bouquet! She picked both roses and carnations.

When you initially present the problem, ask your students questions such as

• Who is the story problem about?
• What is happening in this story?
• What are you wondering about?

Reagan picked flowers for a bouquet! She picked 7 roses and also some carnations.

• What new information do we have?
• What do you think we might learn next?
• What *could* be the number of carnations in the bouquet? What might make sense?

Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations.

• What new information do we know?
• What do you know about the story?
• What happened in the story?
• Could we draw a picture or diagram to match the story?
• What might we be wondering about the bouquet?
• What questions could we answer about the bouquet?

Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations. How many flowers are in the bouquet in all?

• What is the question wondering?
• Do we have enough information to answer that question?
• Where do we see the 7 roses in our diagram?
• Where do we see the 8 carnations in our diagram?
• How can we use the diagram to answer the question of how many flowers are in the bouquet in all?

DONE FOR YOU NUMBERLESS WORD PROBLEMS

Kindergarten | 1st Grade | 2nd Grade | 3rd Grade | 4th Grade

Word Problem Solving Strategy #2: Guided Visual Models

Who is this strategy for? Visual models help your students to organize the information they know as well as to visualize the missing piece of information. Drawing visual models helps lead your students to an equation. This strategy is ideal for students who understand what a word problem is asking but have difficulty connecting the action of a word problem to an equation.

A visual model might include:

• A math drawing (simple circles or an organic representation)
• A number bond (number bonds can be used beyond addition and subtraction! Adding more “parts” can help to visualize multiplication and division as well!)
• Tape diagrams

How can I use this strategy? As you are supporting your students in using these visual models, continually ask questions and draw connections between the word problem and their diagram.

Frank built a tower using 16 blocks. He took 7 blocks off of his tower and gave them to Declan so he could build a tower as well. How many blocks does Frank have left?

• Could you draw a picture that shows what happened?
• Frank had 16 blocks. Was that all of the blocks in the story or part of them? Where would we put the total in our number bond?
• Frank gave away 7 blocks. Was that all of the blocks or a part of the blocks? Where would we put the part in our number bond?
• And we’re wondering how many blocks Frank has left. Where is the missing part in our number bond? Could we write a question mark in that part?

If your students are familiar with number bonds or tape diagrams, knowing that they are missing a part will lead them to writing a subtraction equation or a missing addend addition equation to solve.

**If your students are not familiar with how to find a missing part or missing whole in an equation this is a topic that needs to be addressed as well! Your students are missing foundational math understandings that are critical to their word problem-solving strategy. Additional practice with both fact families and missing numbers in an equation will be helpful to your students!

Word Problem Strategy #3: Problem Sorts

Who is this strategy for? This strategy is for ALL students! When your students examine problems to help understand the underlying structures and problem types , solving word problems becomes easier.

If you were to be asked to cook dinner for a group of people at the drop of a hat, you would likely have a much easier time putting together a pizza than you would a complicated curry dish. You understand the underlying structure of a pizza- crust, sauce, cheese, toppings- and because you know this structure, given any different type of pizza (BBQ, Traditional, Garlic, Buffalo Chicken) you would be able to use the structure to come up with a recipe quickly and easily.

Understanding and recognizing problem types can do the same thing for our students! Understanding that in a “put together” problem there are going to be parts and that those parts can be put together using addition makes these problems much easier to solve!

How can I use this strategy? One way to help your students to recognize and understand problem types is to sort word problems. In a problem sort, you aren’t attending to the matter of solving the problem at all . Instead, you are reading the problems and sorting them based on whether the problem is missing a part or missing the total. If you are working on multiplication and division word problems you might sort based on whether the problem is missing the total , missing the number of groups or missing the group size. Other problem types will lend themselves to different sorting activities.

Additional Word Problem Resources

Using different types of word problem resources can help you to support your students in different ways.

Word Problem Sort Cards   can be a useful tool when you want your students to attend to the structure of math problems. Sort the cards based on problem type or based on the operation your students would use to solve. After sorting, solve the problems together. Reuse the sort as a math center!

Word Problem Notebooks  are a useful tool when you want your students to draw models and visual representations of word problems and to connect these models to an equation.

Numberless Word Problems   help get to the heart of the action or context of a word problem. Because you start with no numbers and employ a great deal of conversation these problems are simple to differentiate and give all students a point of access into the activity.

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Strategies for Solving Word Problems – Math

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

• Circle any numbers you’ll use.
• Lightly cross out any information you don’t need.
• Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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4 Math Word Problem Solving Strategies

5 Strategies to Learn to Solve Math Word Problems

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

Signs of Students Struggling with Math Word Problems

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

How to Help Students Solve Math Word Problems

Focus on math keywords and mathematical key phrases.

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

Cross out Extra Information

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

Encourage Asking Questions

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

Draw the Problem

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

Check Back Once They Answer

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

Mnemonic Devices

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

CUBES Word Problem Strategy

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

C: Circle the numbers

U: Underline the question

B: Box in the key words

E: Eliminate the information

S: Solve the problem & show your work

RISE Word Problem Strategy

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

R: Read and reread

I: Illustrate what is being asked

S: Solve by writing your equation or number sentences

E: Explain your thinking

COINS Word Problem Strategy

C: Comprehend the questions

O: Observe the data

I: Illustrate the problem

N: Write the number sentence (equation)

Understand -Plan – Solve – Check Word Problem Strategy

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

Understand: What is the question asking? Do you understand all the words?

Plan: What would be a reasonable answer? In this stage students are formulating their approach to the word problem. 

Solve: What strategies will I use to solve this problem? Am I showing my thinking? Here students use the strategies outlined in this post to attack the problem.

Check: Students will ask themselves if they answered the question and if their answer makes sense. 

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

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

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Module 10: Linear Equations

Apply a problem-solving strategy to word problems, learning outcomes.

• Approach word problems with a positive attitude
• Use a problem solving strategy for word problems
• Translate more complex word problems into algebraic expressions and equations

 Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in the cartoon below?

Negative thoughts about word problems can be barriers to success.

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts, like the student in the cartoon below. Read the positive thoughts and say them out loud.

When it comes to word problems, a positive attitude is a big step toward success.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn’t do three years ago. Whether it’s driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-Solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then, you’ve increased your math vocabulary as you learned about more algebraic procedures, and you’ve had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we’ll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We’ll demonstrate the strategy as we solve the following problem.

Pete bought a shirt on sale for $[latex]18[/latex], which is one-half the original price. What was the original price of the shirt?

Solution: Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the Internet.

• In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It’s hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

• In this problem, the words “what was the original price of the shirt” tell you what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

• Let [latex]p=[/latex] the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

Step 6. Check the answer in the problem and make sure it makes sense.

• We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.

Step 7. Answer the question with a complete sentence.

• The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”

If this were a homework exercise, our work might look like this:

https://ohm.lumenlearning.com/multiembedq.php?id=142694&theme=oea&iframe_resize_id=mom1

We list the steps we took to solve the previous example.

Problem-Solving Strategy

• Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don’t understand, look them up in a dictionary or on the internet.
• Identify what you are looking for.  Determine the constants and variables in the problem.  A constant is a number in the problem that is not going to change.  A variable is a number that you don’t yet know its value.
• Name what you are looking for. Choose a letter to represent that quantity.
• Translate words into algebraic expressions and equations.  Write an equation to represent the problem. It may be helpful to first restate the problem in one sentence before translating.
• Solve the equation using good algebra techniques.
• Check the answer in the problem. Make sure it makes sense.
• Answer the question with a complete sentence.

Translate word problems into expressions

One of the first steps to solving word problems is converting an English sentence into a mathematical sentence. In the table below, words or phrases commonly associated with mathematical operators are categorized. Word problems often contain these or similar words, so it’s good to see what mathematical operators are associated with them.

Some examples follow:

• “[latex]x\text{ is }5[/latex]” becomes [latex]x=5[/latex]
• “Three more than a number” becomes [latex]x+3[/latex]
• “Four less than a number” becomes [latex]x-4[/latex]
• “Double the cost” becomes [latex]2\cdot\text{ cost }[/latex]
• “Groceries and gas together for the week cost $250” means [latex]\text{ groceries }+\text{ gas }=250[/latex]
• “The difference of [latex]9[/latex] and a number” becomes [latex]9-x[/latex]. Notice how [latex]9[/latex] is first in the sentence and the expression.

Let’s practice translating a few more English phrases into algebraic expressions.

Translate the table into algebraic expressions:

In this example video, we show how to translate more words into mathematical expressions.

For another review of how to translate algebraic statements into words, watch the following video.

The power of algebra is how it can help you model real situations in order to answer questions about them.  Let’s use this approach with another example.

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought [latex]11[/latex] apples to the picnic. How many bananas did he bring?

https://ohm.lumenlearning.com/multiembedq.php?id=142722&theme=oea&iframe_resize_id=mom2

Twenty-eight less than five times a certain number is [latex]232[/latex]. What is the number?

Following the steps provided:

• Read and understand: we are looking for a number.
• Constants and variables:  [latex]28[/latex] and [latex]232[/latex] are constants, “a certain number” is our variable, because we don’t know its value, and we are asked to find it. We will call it [latex]x[/latex].
• Translate:  five times a certain number translates to [latex]5x[/latex] Twenty-eight less than five times a certain number translates to [latex]5x-28[/latex], because subtraction is built backward. “is 232” translates to “[latex]=232″[/latex] since “is” is associated with equals.
• Write an equation:  [latex]5x-28=232[/latex]

[latex]\begin{array}{r}5x-28=232\\5x=260\\x=52\,\,\,\end{array}[/latex]

[latex]\begin{array}{r}5\left(52\right)-28=232\\5\left(52\right)=260\\260=260\end{array}[/latex]

In the video that follows, we show another example of how to translate a sentence into a mathematical expression using a problem solving method.

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?

https://ohm.lumenlearning.com/multiembedq.php?id=142735&theme=oea&iframe_resize_id=mom3

https://ohm.lumenlearning.com/multiembedq.php?id=142761&theme=oea&iframe_resize_id=mom4

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• Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
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March 29, 2023

Demystifying Word Problems: Effective Techniques for Teaching Problem-Solving Skills

As a teacher, I understand the struggles students often face when it comes to solving word problems. Whether it’s reading challenges, a lack of executive functioning skills for multi-step problems, information overload, or language barriers for English language learners, word problems can be tricky! That’s why I want to share some effective techniques for teaching word problem-solving skills that can empower our students to tackle these tasks with confidence (and accuracy).

Importance of Word Problem-Solving Skills

Before diving into these techniques, let’s explore why it’s important to teach our students word problem-solving skills. First and foremost, these skills have real-world application and relevance, as students will encounter problem-solving scenarios throughout their lives. Furthermore, developing these skills fosters critical thinking and reasoning abilities that are invaluable in various subjects, including math, science, and social studies.

Techniques for Teaching Word Problem-Solving Skills

Understanding the problem.

Teach students to identify important information and keywords. Help students recognize what information is relevant and which words signal specific mathematical operations. A strategy I like to use with my students is to underline the question, box in the keywords, and circle the numbers needed.

Visualization

Use diagrams, drawings, mental movies, or manipulatives to represent the problem: Encourage students to create visual representations of the problem to better understand the situation. A strategy I like to use for this is to have my students make a mental movie, then they share their ideas with a partner, and finally, they use manipulatives to explore a solution.

You can also use pictures or comic strips to illustrate the problem. I like to introduce primary students to word problems with the Kindergarten Word Problems because they have an illustration on each game card giving the students context and helping them build prior knowledge.

Developing a Plan

Teach students to choose appropriate strategies for solving word problems: Help students understand that different problems require different approaches and provide them with a toolkit of strategies.

Again, referencing the kindergarten word problems, I like these because there’s a balance between solving for the missing beginning, middle, and end and even comparing the two addends. This gives students a variety of problems to solve.

I recommend starting with concrete strategies like mental movies, pictures, and acting out the problem. After students demonstrate understanding, move on to pictures and diagrams. I find that tape diagrams and number lines are most useful for elementary students.

Encourage Collaboration and Discussion

Another great strategy is to promote peer collaboration and group problem-solving. Foster a classroom environment where students feel comfortable working together and sharing ideas.

I do this with students by projecting one game card problem on our interactive whiteboard. Next, I partner students together using ClassDojo’s partner generator; however, you can use any partner-generating method. Our routine before each lesson is to think about the problem for one minute. Then, we talk about the problem with a partner. Finally, we explore solutions for the problem independently and share our thinking with the whole group.

Using Word Problems to Support Instruction

Word problems are essential to academic success. I have a set of word problems included in each grade-level bundle of math games, and if I’m being honest, I don’t like using them as a stand-alone games.

I know what you’re thinking, “YOU DON’T LIKE YOUR OWN GAME?”

It’s not that I don’t like it because I know it’s necessary. It’s just that it’s too challenging and takes more time and perseverance to solve than basic math facts.

Instead of using them as a game, I sprinkle word problems into other games. I also use them as discussion starters or warm-ups before beginning our math lesson. I have learned that consistency is key. It’s such a routine that my students could lead this lesson without a teacher.

Implementing word problems can help create a more engaging, effective, and supportive learning environment for students as they develop their problem-solving skills.

Teaching word problem-solving skills is crucial for students’ success, both in the classroom and beyond. I hope the techniques discussed in this blog post inspire you to implement them in your classroom and explore the word problems in my math game bundles. I invite you to share your experiences teaching problem-solving skills or any additional techniques you’ve found effective in the comments below.

Together, let’s empower our students to become more confident problem-solvers!

Want some fun ideas for teaching word problems? Make sure to read this blog post 7 Fun Activities for Teaching Word Problems That Actually Work !

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How to Tackle Math Word Problems & Make Sense of Operations

Do your students struggle to make sense of math word problems? They’re not alone! Using meaningful word problem strategies can help kids make sense of operations & have confidence solving word problems.

As students learn the four math operations, it’s imperative that they learn to apply the operations to show higher level thinking.  Students should be able to determine which one to use and apply it to real-life situations , especially considering that our end goal is to create productive thinkers who can change the world.

One way we do this is by providing students with word problems that highlight the math operation and include problems that may happen in the real world .  Let’s explore some common reasons why students struggle with math word problems and learn two word problem strategies to help them overcome these challenges.

*This is a guest post from Jessica at Math with Purpose .

Common Reasons Students Struggle with Word Problems:

1. they’re developing reading comprehension skills.

It’s no surprise that word problems can be a challenge for many students.  After all, many of these students are developing their own reading skills and then being asked to read and interpret informational text in a word problem.

Many word problems include multiple steps which require students to infer what to do first.  In fact, the National Foundation for Educational Research found that poor inferring skills lead to poor comprehension.

It is a skill that students must be explicitly taught and is usually one of the later skills due to its complexity. That means our students are expected to do a higher level of reading comprehension every time they read that short word problem in math class !

2. They’re Relying Only On Keywords (Rather than the Meaning of Operations)

Students can encounter difficulty when translating words into mathematical symbols or equations. They may struggle to identify which mathematical operations are needed to solve the problem and how to represent the problem in a mathematical format.  Many teachers teach students to circle key words and memorize them to determine which operation to use.

Students may learn that addition means to “add to” or “make a total” while subtraction is an action of “taking away”.  Students look for keywords that they can circle to determine whether adding or subtracting.   But what happens when the action is there, but students actually need to solve using a different math operation? Here’s an example:

Gabbi had some stickers.  She earned 12 more stickers for completing her homework.  Now she has 56 stickers.  How many stickers did she have at first?

In this problem, it’s clearly an “add to” situation.  Gabbi is adding to her collection.  However, to solve the problem, a student would need to subtract from the total to find the missing part .

While keywords can help with some problems, they don’t actually work for the variety of word problems students will encounter .

In fact, according to the University of Arizona, students will solve 15 different addition and subtraction problem types by the end of Grade 2 and 9 different multiplication and division problem types by the end of Grade 4.

Read more about the problems with relying on key words in word problems here .

Word Problem Strategies to Help Students Comprehend Operations Before Solving

In order to help students comprehend and solve complicated word problems, math educators have to think like a reading teacher and acknowledge there is a whole set of skills required for students to do the mathematics.

Instead of using basic strategies such as circling key words and plugging in numbers that may work some of the time, teachers can push for greater depth and understanding using two easy word problem strategies .

1. Make connections to prior knowledge and experiences:

One of the first reading strategies students learn is to make a movie of the text in their head and make real-world connections to the story.  The most meaningful connections are text to self connections where students relate the text to their own lives.

Students can do the same thing with a word problem!  They can read the story and make a picture of what’s happening – maybe even act it out with real life objects .

Teachers can also change the nouns in the word problem to be more relatable for each class including student names in the problems and objects that they enjoy doing each day.  This one simple change will help students engage with the text and want to find out more.

2. Visualize the problem by drawing a picture:

Once students are connected to the story of the word problem, it’s time to connect it to mathematics .

Instead of relying on keywords, students can draw visuals of the part-whole, comparison or equal groups models to show what operation will be needed to solve the problem.

Through drawing bar models , students will identify the variable and lay the strong foundation for algebra even beginning in Grade 2.

These visuals aren’t complicated and can be taught easily while students are comprehending the word problem.  You can find out more about these visual models for word problems in this blog post and even snag free posters for each representation for your classroom.

Solving math word problems is a valuable skill that empowers students to apply mathematical knowledge in real-life situations , but it also requires students to use a variety of skills to accomplish.  By thinking like a reading teacher, math educators can employ the skills they use during reading to truly help students master word problems by making connections and visualizing the problem .

If you are looking for more support to help students walk through the variety of word problems they will encounter, consider The Problem Solving Handbook .

It includes 3 video lessons for each problem type, plus practice and challenge problems for students to truly master word problems.

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A Game-Changing Practice Fuses Math and Literacy

A program that scaffolds math with reading and writing has a formerly struggling elementary school in the Bronx dramatically outperforming the state in math.

When Concourse Village Elementary School (CVES) opened in 2013 in the wake of the planned phaseout of P.S. 385, which the New York City Department of Education had tagged with a D, students were struggling academically.

“When we arrived, we found a major deficit across all content areas,” said incoming principal and school founder Alexa Sorden, who was particularly alarmed by the reading scores. “The first year was challenging because we were trying to come up with a plan and say, ‘OK, how are we going to make sure that all the children are reading on grade level so that they’re prepared?’”

Sorden, a former literacy specialist and teacher, felt that a strong foundation in reading and writing underpinned success across all content areas—and she made it the school’s mission to be literacy-first. Today, students employ collaborative literacy strategies to support science and social studies units, for example, and bring their narrative skills to bear while making predictions and inferences as they analyze artwork .

In mathematics, a subject area not traditionally associated with literacy, Concourse Village has developed an especially innovative model that reinforces both reading and computational skills. Students tackle tough mathematical word problems through two literacy strategies: a group reading exercise that relies on what Sorden calls “the power of repeated reading,” and a problem-solving procedure developed by Exemplars, Inc , along with the problems, that requires students to produce an organized body of written artifacts.   

Despite the statistics stacked against them—the school is situated in the poorest congressional district in the nation , and 96 percent of children at CVES are on free and reduced lunch, while 15 percent are homeless—students are now outperforming the averages in both New York State English and math exams by over 40 percent .

What are the details of the math program? We visited the school and spoke to Sorden and fourth-grade mathematics teacher Blair Pacheco at length, and we provide an outline and some video of the school’s practices below.

Translating Math Into Words, and Back Into Numbers

In math classes, CVES students approach challenging word problems by reading, annotating, and writing to tease out the meaning—breaking the problems down into smaller parts and using the power of storytelling and narrative to bolster their insights. Word problems are above grade level to ensure that students are stretching to master difficult concepts.

Before considering solutions to a problem, the students start small by trying to clarify what it is actually saying. Numbers and questions are stripped out, and the class uses a three-read protocol that fosters both group and individual learning: The teacher reads the problem, then the students read it, and then everyone reads it together.

“Sometimes when kids see numbers, they start to get confused,” said Pacheco. “If we take out those numbers for a brief moment, they’re reading it as a story and they’re getting that understanding. It’s no longer just about math.”

For example, in one of Pacheco’s classes, students read: “Jaci and Emma are playing a game on their computer where a player earns points.” Students relay the gist of the story back to the teacher, who writes it on the board for reference.

The word problem—now with numbers included, but still without the questions that ask students to perform calculations or mathematical comparisons—is then shown on the interactive whiteboard, and the students read it aloud and process the information together.

One student annotates the word problem on the board with input from the class—underlining important information, including numbers and key words. In the example from Pacheco’s class, students underline the repeated word round  to indicate that there will likely be several rounds of numbers that might require a comparison or a computation.

Based on the annotations, students then create a “What I Know” chart as a class. For example, Pacheco’s students agree on how many points each player made in each round.

Using the information they have already identified, students hypothesize about what questions might be asked. For example, Pacheco’s students might guess that the question would ask the total number of points for all rounds. Brainstorming possible questions requires students to call on prior knowledge about what they can do with the numbers—compare through greater or lesser than or equal signs, for example, or compute by adding or subtracting.

Finally, the actual question is revealed on the board—and the class reads the whole problem aloud.

From Group to Independent Problem-Solving

After rereading the above-grade-level problem as a class, each student receives a word problem printout differentiated based on their ability. Students work through a five-step problem-solving procedure based on the reading protocol they use as a class. They work independently, or in small groups if they need more support. A checklist of the steps guides them through the problem.

Students scaffold their understanding—and make it visible to themselves and their teachers—by underlining important words, circling the question the problem is asking, and then writing an “I Have To” statement that clarifies what the student must do to arrive at the answer. For example, a student might write, “I have to find out who made the most points in each round.”

Then each student devises a mathematical strategy to solve the problem. They might write, “I will use addition,” “I will multiply,” or “I will use the comparison strategy.”

Finally students solve the problem and double-check their work. They write their answer in a complete sentence, put a box around it, and label it “answer.” They write out an explanation of how they solved the problem using at least two math words, like multiply  and add , and then write a complete sentence making connections to previous math they have learned. They might comment on an observation they made, a pattern or rule they found, a different strategy they could have used, or a comparison they noticed. Writing their takeaways in words reinforces their prior knowledge and how it can be applied in new ways.

“We ask them to make their thinking visible,” says Sorden, explaining the rationale behind all the writing in her school’s math courses. “Create a plan. Make your thinking visible and clear on paper so that anyone that picks it up is able to make meaning about what you were trying to share. We want them to be able to communicate orally and in writing so that their ideas are clearly communicated with the world.”

The problem-solving procedure and math tasks that CVES uses were developed by Exemplars , a company that provides a library of rich performance tasks and professional development for K-12 schools.

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Reading Comprehension and Math Word Problems: Enhancing Problem-Solving Skills

Reading comprehension and math word problems are two key components of a solid educational foundation. Many students often face challenges when understanding complex texts and solving word problems. This article explores the relationship between reading comprehension and math word problems and how students can develop efficient strategies to excel in both areas.

Understanding the basics of reading comprehension is crucial for learners, as it equips them with the necessary skills to decipher meaning from age-appropriate texts. Similarly, when solving mathematical word problems, students must utilize their comprehension abilities to interpret and extract relevant information from the problem. By applying reading comprehension strategies to word problems, learners can boost their problem-solving skills and excel in subjects that require textual analysis.

Bridging the gap between reading comprehension and word problem-solving is achievable by equipping students with the right tools and techniques. Students can benefit from learning strategies that can be applied across different subjects, ensuring a well-rounded education. The following sections of the article offer valuable insights into using these strategies and commonly asked questions.

Key Takeaways

Strengthening reading comprehension skills supports success in math word problems.

Application of comprehension strategies improves problem-solving across various subjects.

Learners should focus on versatile techniques for a well-rounded education.

Understanding the Basics of Reading Comprehension

Reading comprehension is a critical skill for all students, as it enables them to grasp the meaning and significance of text. Students can develop their reading comprehension by focusing on accuracy, understanding the context, and applying the acquired information.

In the context of reading comprehension, accuracy refers to the ability of students to read words and sentences correctly. It is essential for students to have a solid foundation in phonics and vocabulary in order to improve their reading accuracy. To achieve this, they can frequently practice reading texts that are appropriate to their level and gradually increase the difficulty as they gain confidence.

The next aspect of reading comprehension is understanding the context in which a text is written. This requires the students to comprehend the meaning of individual words and phrases and their relationships within the text. To enhance their contextual understanding, students should learn to identify the main ideas, supporting details, and implicit information present in a text.

Additionally, students should consciously try to apply the information they have comprehended. This can be achieved by summarizing, discussing, or even responding to questions related to the text. By actively engaging with the material, students are more likely to retain the information and improve their overall reading comprehension.

Providing students with various types of texts, such as fiction, non-fiction, and poetry, can help them enhance their comprehension skills. Exposure to different genres allows them to encounter diverse language styles, themes, and structures, which in turn contributes to the development of their cognitive abilities.

Reading comprehension is an essential skill that not only improves a student’s academic performance but also contributes to their overall development. With continued practice, patience, and effort, students are capable of enhancing their comprehension skills, enabling them to better understand and appreciate the world around them.

Understanding Word Problems

Mathematics in word problems.

Word problems are essential in mathematics, as they present real-life situations where math is required to find a solution. They involve various mathematical operations, such as addition, subtraction, multiplication, and division. Geometry word problems may also include concepts like area, volume, or angle measures. Solving these problems is crucial for developing a deeper understanding of mathematical concepts and enhancing problem-solving skills.

Relevance of Word Problems

Math word problems are highly relevant in daily life as well as in various professions. They help students develop critical thinking and decision-making abilities. In subjects like science, engineering, and finance, mathematical word problems often serve as the foundation for complex problem-solving tasks. Thus, mastering word problems is critical for success in both academic and professional settings.

Challenges in Word Problems

Solving word problems can be challenging for multiple reasons:.

• Language Processing: Students must first understand the problem’s context, which sometimes requires them to process challenging vocabulary or complex sentence structures.
• Identifying Operations: Once the problem is understood, students need to identify the appropriate mathematical operation(s) (add, subtract, multiply, divide) and apply them to the given numbers.
• Working with Fractions: Dividing fractions and solving problems that involve fractions can be particularly tricky for some learners.
• Decoding: Translation of a problem from words to mathematical notation may be an obstacle for certain students.

Despite the challenges, learning to solve mathematical word problems is essential in developing mathematical literacy and problem-solving abilities. By practicing and mastering various types of word problems, students can build confidence in their mathematical skills and apply them in real-life situations.

Strategies to Solve Word Problems Identifying Key Words

To effectively solve mathematical word problems, it is important to identify key words within the text. These words often indicate the operation to perform or provide crucial information for solving the problem. Common key words for addition include sum , total , more , and added to , while subtraction problems often include words like difference , less , fewer , and minus . Multiplication and division problems may contain key words like times , product , divided by , and quotient . Recognizing these words can help guide the problem-solving process.

Problem-Solving Framework

A structured problem-solving framework can aid in approaching these types of problems systematically. Following a simple four-step process can improve students’ ability to find solutions:

• Understand the problem: Read the problem carefully, identifying the key information and unknowns.
• Devise a plan: Determine the appropriate operation(s), using the key words and other contextual clues.
• Implement the plan: Perform the necessary calculations, ensuring accuracy and understanding of each step.
• Review the solution: Check the solution against the original problem statement to ensure it is reasonable and complete.

Applying this framework to each word problem will build confidence and increase success in problem-solving.

Using Visual and Manipulative Resources

Visual representations and manipulatives can be extremely beneficial in helping students understand and solve word problems. For example, using diagrams, tables, or number lines can help visualize the problem, making it easier to identify the necessary steps for solving.

• Diagrams : Sketching simple diagrams can clarify relationships between values and simplify complex problems. Examples include bar models, area models, and Venn diagrams.
• Tables : Organizing data into a table can illustrate patterns, highlight relationships, and streamline calculations.
• Number Lines : Using a number line can help visualize addition, subtraction, multiplication, and division operations, making it easier to grasp the concept of a given problem.

Similarly, manipulatives such as counters, fraction strips, or base-ten blocks can provide a hands-on approach to understanding abstract concepts and visualizing mathematical relationships. Students can physically manipulate these tools to explore, discover, and demonstrate their understanding of the problem-solving process.

In conclusion, using strategic approaches like identifying key words, employing a problem-solving framework, and incorporating visual representations and manipulatives can greatly enhance the ability to tackle complex math word problems, ultimately leading to a more successful and enjoyable learning experience.

Reading Comprehension and Word Problem Solving in Different Subjects

Math and science.

Reading comprehension is crucial in math and science subjects, as it involves understanding complex concepts and word problems. Students must be able to interpret the information given and apply mathematical and scientific principles to solve problems accurately. This involves breaking down the problem into smaller parts, identifying key terms and variables, and selecting the appropriate formulas or methods to use.

• Math: In math, word problems can involve a wide range of topics, such as algebra, geometry, and calculus. Students need to decipher the context, translate it into mathematical expressions, and solve for the desired variables.
• Science: Science subjects like physics, chemistry, and biology also require reading comprehension skills. Students need to understand scientific texts, grasp experiment procedures, and analyze data presented in various formats (tables, graphs, etc.).

Narrative and Social Studies

Reading comprehension and word problem-solving skills are also essential in understanding the context and drawing accurate conclusions in narrative and social studies subjects.

• Narrative: In literature, reading comprehension involves analyzing the plot, characters, and themes, as well as understanding the author’s purpose and perspective. Additionally, it requires deciphering figurative language, symbolism, and other literary devices.
• Social Studies: In subjects like history and geography, students need to read and comprehend texts about different cultures, political systems, and historical events. They may need to analyze primary and secondary sources, compare different perspectives, and evaluate the reliability of the information provided.

Both math/science and narrative/social studies subjects require strong reading comprehension skills to navigate and solve word problems or understand complex concepts successfully. By honing these skills, students can improve their overall academic performance and develop a more comprehensive understanding of various topics across different disciplines.

Application of Reading Comprehension Strategies

Reading comprehension strategies are essential for understanding and solving math word problems. By applying these strategies, students can significantly improve their ability to analyze and solve complex problems.

Firstly, identifying the main idea of a problem helps students focus on the most important information. This involves recognizing the key elements of the given problem and disregarding any unnecessary details. For example, in a problem about calculating the total price of items, the main idea is to find the product of the quantity and the unit price.

Visualizing the problem is another effective strategy. By creating a mental or physical image of the problem, students can better understand the relationships between the different elements involved. This may include drawing a diagram or sketch, or even using physical objects to represent the components of the problem.

Utilizing context clues can help students infer meaning and fill in any gaps in their understanding. Context clues can come in the form of definitions, examples, or descriptions that help to clarify unfamiliar terms or concepts. This is particularly helpful for problems with complex or technical language.

Making connections to prior knowledge or experiences allows students to apply previously learned concepts to new problems. This encourages critical thinking and fosters a deeper understanding of the subject matter. When confronted with a math word problem that uses similar concepts or ideas, students can draw on their past experiences to approach the problem confidently.

Another strategy is asking questions while reading through the problem. This practices active engagement with the text and promotes comprehension. Students should pose questions to themselves, such as “What is the problem asking?” or “What information is necessary for solving this problem?”. By doing so, they are better equipped to identify important information and organize their approach in a logical manner.

 In summary, incorporating reading comprehension strategies into math word problems enables students to better decipher complex problems, recognize important information, and develop critical thinking skills. By mastering these strategies, students are well on their way to becoming confident and proficient problem solvers.

Frequently Asked Questions

What are effective strategies for solving math word problems.

To solve math word problems effectively, try the following strategies:

• Read the problem carefully and identify critical information.
• Visualize the problem by drawing a model or diagram.
• Translate words into mathematical expressions or equations.
• Determine the proper operations to apply.
• Solve the equation step by step, continuously checking for accuracy.
• Verify the solution by plugging it back into the original problem.

How can I improve my child's reading comprehension skills for math?

To help your child enhance their reading comprehension skills in math, consider these approaches:

• Encourage regular reading to develop vocabulary and language skills.
• Discuss word problems, exploring how language and math concepts are connected.
• Practice breaking problems down into smaller, more manageable parts.
• Teach strategies for identifying key words and phrases that signal mathematical operations.
• Provide opportunities to practice problem-solving in a variety of contexts.

What is the impact of reading comprehension on problem-solving in mathematics?

Reading comprehension greatly impacts problem-solving in mathematics, as it enables students to understand and interpret word problems accurately. Strong reading comprehension skills allow students to identify relevant information, choose appropriate strategies, and apply mathematical concepts to arrive at the correct solution.

How can teachers support special education students with word problems?

Teachers can support special education students in tackling math word problems by:

• Providing clear instructions and explanations.
• Using visual aids and manipulatives to represent mathematical concepts.
• Breaking problems down into smaller steps.
• Encouraging students to use personal strategies, such as highlighting keywords or drawing diagrams.
• Offering additional practice opportunities and targeted interventions as needed.

What is the correlation between reading comprehension competence and mathematical problem-solving skills?

There is a strong correlation between reading comprehension competence and mathematical problem-solving skills. Improved reading comprehension fosters better understanding of word problems and the ability to select appropriate strategies to solve them. Consequently, increased proficiency in reading comprehension contributes to enhanced math performance.

Can you provide examples of common math word problems and their solutions?

Sure, here are two examples:

• Problem: Sarah has 12 apples, and she wants to share them equally between her and two friends. How many apples does each person get?

Solution: Divide the total number of apples (12) by the number of people (3):

12 ÷ 3 = 4.

Each person gets 4 apples.

• Problem: A rectangular garden is 18 meters long and 4 meters wide. What is the perimeter of the garden?

Solution: Add the lengths of all sides:

(18 + 4) x 2 = 22 x 2 = 44.

The perimeter of the garden is 44 meters.

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20 Word Problems For 2nd Grade: Develop Their Problem Solving Skills Across Single and Mixed Topics

Emma Johnson

Word problems for second grade are an important tool for improving number fluency. The key focus of math in second grade is on ensuring students are becoming more fluent with number facts and the concept of place value. Children are starting to develop more efficient written methods by this stage and are beginning to carry out calculations with increasingly larger whole numbers.

As children progress through school, they are exposed to a wider variety of problem solving questions covering a range of concepts. In second grade, these include addition, subtraction, measurement and data.  

It is important that children are regularly exposed to reasoning and problem solving questions, alongside the fluency work each lesson. It is also important to remember that all children need exposure to reasoning and problem solving questions, not just the higher attaining students who finish quickest.

We have put together a collection of 20 word problems, aimed at second grade students.

Word Problems Grade 2 Addition and Subtraction

11 grade 2 addition and subtraction questions to develop reasoning and problem solving skills.

Place value

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In second grade, students focus on one-step problems, covering a range of topics. At this stage the majority of word problems students are tackling will have one-step, but they may also start to be introduced to simple two-step word problems. Here is a breakdown of topics that will be covered and expectations in second grade. 

Solve number problems and practical problems involving recognizing the place value of each digit of a 3-digit number; comparing and ordering numbers up to 1,000 and identifying, representing and estimating numbers using different representations.

Solve problems, including missing number problems, using number facts, place value and more complex addition and subtraction word problems .

Solve problems involving length; adding and subtracting within money word problems involving dollar bills, quarters, dimes, nickels and pennies.

Solve-step and two-step questions (For example, ‘How many more?’ and ‘How many fewer’?) using information presented in scaled bar charts, pictograms and tables.

By second grade, children are starting to learn how to use some of the formal written methods of addition and subtraction. It is important that the link between math in school and math in real-life continues to be made. Word problems are a key element in helping students to make this link. 

How to teach problem solving in second grade

When teaching math problems to second grade, it’s important to think of ways to make them fun, engaging and something the children are able to relate to. This might include acting out the problem, using concrete resources and providing visual images, to bring the problems to life. 

Children should have plenty of opportunity to talk in pairs, groups and as a whole class, to share their understanding of what is being asked and their strategies for solving the problem. The use of manipulatives is important and all children should have access to a range of math resources when solving problems like this.

Students need to be encouraged to read word problems carefully and to make sure they understand what is being asked, before attempting to tackle the problem. This is where the use of a partner and group discussion can really help children’s understanding. Students then need to think about what they already know and how they can use this to help them answer the question. Where appropriate, students should also be encouraged to draw diagrams and pictures to help them solve the question.

Here is an example:

Mason has 24 glass jars to put flowers in.

He gives 5 to Marcy and drops 2 while carrying them inside the shop.

How many glass jars does Mason have left?

How to solve:

What do you already know?

• Mason has a total of 24 glass jars.
• We know he gives Marcy 5 jars, which means we will need to subtract 5 from 4. 
• He also dropped 2, also meaning we will need to subtract.
• In second grade, children should be building confidence with adding and subtracting within 20, and should be able to do these calculations in their heads.
• Children who aren’t able to recall quickly could use counters to represent the jars, or draw a bar model to help solve it.

How can this be drawn/represented visually?

We can draw a bar model or counters to represent this problem:

• To calculate how many jars are left, we can either use or draw 24 counters. We can then remove or cross out the 5 jars given to Marcy, and then 2 jars that were broken.
• Using the bar model, we can first subtract 5 from 24, representing the jars given to Marcy, leaving 19 jars. Then subtract 2 more from 19, to represent the two jars broken.
• Mason had 17 glass jars left. 

Addition word problems for second grade

In second grade, students are exposed to a range of addition word problems, including problems involving mental addition and addition of up to 3-digits using formal written methods.

See also: Mental math second grade

A family driving on holiday travel 146 miles from home to the first service station.

They then drive a further 175 miles to reach their destination.

How far have they traveled altogether?

Answer : 321 miles

146 + 175 = 321

Elvie is buying a can of soda from a vending machine. She has put in 2 quarters, 2 dimes, and 3 nickels. 

How much is the can of soda?

Answer : 85¢

50¢ + 20¢ + 15¢ = 85¢

Jamie scored 443 on his new online game.

Jared scored 468.

How many points did they score between them?

Answer : 911 points

443 + 468 = 911

At Third Space Learning we often tie word problems into our one-to-one online tuition. With each programme personalized to the needs of each individual student, children are able to develop their problem solving skills, math fluency and grow confidence in math.

Subtraction word problems for second grade

Subtraction word problems in second grade also need to comprise of a combination of mental calculation questions and those involving formal written subtraction up to 3-digits. Children should also be starting to estimate answers and check their calculations by using the inverse.

Ahmed collects 374 stickers.

He needs 526 stickers to fill his sticker album.

How many more stickers does he need to collect?

Answer : 152 stickers

526 – 374 = 152

 A bag of carrots weigh 360g

A bag of tomatoes weighs 235g.

How much heavier is the bag of carrots?

Answer : 125g

360 – 235 = 125

 Ahmed buys a bag of candy with 200 pieces in it.

Over 2 weeks, he eats 145 pieces. How many pieces of candy does Ahmed have left?

Answer : 55 pieces of candy

200 – 145 or count up from 145 to 200.

Multi-step word problems in second grade

When children first move into elementary school, word problems are predominantly one-step. As they become more confident they can be exposed to more word problems, requiring a second step or multi-step word problems. When first introducing two-step problems, keep the numbers used in the problems low and manageable to allow students to focus on reasoning over calculations.

Oliver had 3 bags of candies.

Each bag contained 15 candies.

Oliver’s little brother ate 17 pieces of the candy. How many pieces of candy does Oliver have left?

Answer : 9 sweets

15 + 15 + 15 = 45 

45  – 17 = 28

A teacher photocopies 95 math worksheets and 80 English worksheets in one week.

Teachers can print a maximum of 300 worksheets per week. 

How many can the teacher print for other subjects?

Answer : 125 worksheets

 95 + 80 = 175

300 – 175 = 125

A flower shop picks 19 roses and 25 daisies fresh from their garden.

A customer orders a dozen flowers for a birthday gift.

How many flowers will the flower shop have left?

Answer : 32 flowers

19 + 25 = 44 flowers (roses and daisies combined)

44 – 12 = 32 flowers

We hope that this collection of word problems for second grade becomes a useful resource in your second grade math classroom. 

For more resources, take a look at our library. Third Space Learning offers a wide array of math and word problems resources for other grades. These include worksheets , end of year assessments and a range of math games and activities for students from kindergarten through to 6th grade. 

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

The content in this article was originally written by former Deputy Headteacher Emma Johnson and has since been revised and adapted for US schools by elementary math teacher Christi Kulesza.

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What’s the Importance of Word Problems?

“If Johnny has eight apples, and he gives three of them away to Sally, how many apples does he have left?” Word problems have long been met with dread by math students from all walks of life. Normally, when people think of mathematics, words are not the first visual that comes to mind; it’s numbers! However, the importance of word problems cannot be discounted. Studies on education have shown that word problems have many benefits. Of course, we at A Grade Ahead definitely see the value of word problems; our math curriculum has an emphasis on building the skills needed and completing word problems in our unique enrichment program . Let’s explore the benefits of word problems below!

Why Are Word Problems Important?

Strengthen problem-solving skills.

Although number-based math involves problem solving, thinking about solutions in the form of words is much more impactful and applicable to other areas of a student’s learning and cognitive development. As in life, when certain problems arise, people must be able to think about solutions in different formats in order to conjure up the best possible solution. This website offers some tips on how to help children improve their abilities to work through word problems, and therefore, improve their problem-solving skills.

Improve Comprehension and Analysis

Math isn’t the subject where people would imagine comprehension skills could be built, but that is just another testament to how important word problems are! Word problems offer a way to practice close reading, visualizing, interpreting, and analyzing. Students are presented with a story in a word problem. They must read closely to understand what information is important, and visualize it to gain a complete view of the goal. They must know what the question means and analyze the question for clues to how to solve the problem. All these skills are practiced before the student even begins applying any math equations!

Build Logical and Critical Thinking Skills

Students must transform numbers to visuals in their minds, and then back into numbers again – all while addressing all the logical limitations of the problem.

Including numbers in real-life scenarios makes math more interesting for students! Often, when just using math rules and not thinking critically about the problem, students can make mistakes and come up with nonsensible answers. However, because there is no scenario attached, students may not understand why such answers don’t work. For example:

Solve for x: 15x – 170= 100.

The correct answer is 18, but students who are unsure about the correct process for solving this problem could answer anything from -163 to 4 to 4,050! Without any context, these students won’t necessarily notice a logical problem with their answers. Let’s try again in the form of a word problem.

A car company must sell 100 cars each week in order to make a profit. It costs the company $170 to pay its fifteen employees each week. How many cars does each employee have to sell this week in order for the company to make a profit?

Using the scenario given, students may set up the problem as it is shown numerically and solve. However, now that we have a situation to go along with, answers like -163, 4, and 4,050 really don’t make sense, and students will be able to notice that. Word problems are important for learning because they develop a child’s logical thinking skills.

Develop Creativity

Becoming a word-problem master is one step toward becoming a master at life! This blog post by John Marsh gives some examples about why that is. When students can use their imaginations to visualize and explore the dimensions of various word problems, they can become more motivated to solve scenarios than if they are looking at monotonous number combinations.

Plus, this will help students when they are looking at numeric equations. They may be able to apply the word-problem thinking to come up with solutions to a math problem by imagining an equation as a word problem! Creativity is key both in the classroom and in life satisfaction, so we should probably start teaching our kids its importance through word problems!

Get Invested

One of the main struggles that teachers face in the math classroom is engaging students and making them feel excited to learn. This website gives some creative word problems that students will enjoy working on for a wide variety of math topics.

How often do you think teachers hear the question: “Why are we learning this?” (Hint: It’s a lot!) Word problems are one way to show students how they might be able to use math in their lives now, or in the future. What student doesn’t want to imagine they have 10 cookies? The bottom line is students will be more inclined to practice skills if they are convinced that it will actually be useful.

Practice, Practice, Practice!

Word problems give students a way to practice all the tools they have learned. Especially in higher levels, word problems involve multiple steps and can use many different types of math. Often, students are able to bring in concepts learned in past chapters or even past grades. This helps reinforce previously learned topics and show students the benefits of learning a concept instead of memorizing it for a test!

Demonstrate Knowledge

Word problems are a key tool in determining what material a student feels comfortable. With multiple choice problems, or even basic solving, there are many opportunities for children to get the right answer without actually understanding the process or rationale behind the math. But, with word problems, students must display the higher levels of thinking that is required, meaning that they must display that they have the knowledge needed to solve the question. Word problems make it easier to see what concepts students need extra help on.

After reading this, we hope you see the importance of word problems, too! If your child is struggling to apply his or her knowledge to word problems, consider an enrichment program at an academy or at home and practice the skills above.

Can you think of any more reasons that show the importance of word problems for student learning? Do you think word problems have helped your child? Let us know in the comments below!

Author: Morgan L., Writer and Teacher at A Grade Ahead ; Brenna Waugaman, Writer and Teacher at  A Grade Ahead

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August 16, 2017 · Leave a Comment

5 Ways to Build Math Problem Solving Skills (based on brain research)

Whether talking about state tests or meeting with your team to plan the next math unit, the conversation inevitably turns to word problems. But knowing how to build math problem-solving skills without resorting to pages of boring story problem practice can be hard.

These days word problems aren’t the basic one-step wonders that many of us dealt with as students. Instead, multi-step story problems that require students to apply multiple concepts and skills are incorporated into instruction and state assessments.

Understanding brain research can help simply the process of teaching this challenging format of math problem-solving to students, including those who struggle.

What research says about building master problem solvers in math

Have you seen how many math skills we must teach these days? No teacher has enough time to build critical math skills AND effectively teach problem-solving…or do they?

Research would argue we are going about these tasks all wrong. They say there are many reasons students struggle with math word problems , but one big one is that we aren’t doing what’s best for the brain. Instead, here’s what the brain research says about the must-have elements for building step-by-step math problem-solving mastery.

Finding #1: Becoming a master problem solver requires repetition.

Duh, right? Any good teacher knows this…but what’s the best recipe for repetition if you want students to master math word problems? How much practice? How often?

Let’s start with the concept of mastery.

How do you develop math problem solving skills?

In the 1990’s, Anders Ericsson studied experts to explore what made some people excel. Findings showed a positive correlation between the amount of deliberate practice (activities that require a high level of concentration and aren’t necessarily inherently fun) and skill level.

In other words, the more practice someone gets, the more they improve. This became the basis of Malcolm Gladwell’s 10,000-hour rule, which stated that it takes 10,000 hours to make you an expert in a field.

But what should that practice look like for students who struggle with word problems? Is it better to have a deep dive into story problems, or do short bursts of practice do more for long-term understanding?

Designing Better Word Problem Activities: Building Step-by-step Math Problem-Solving Practice

We can look at Ebbinghaus’ work on memory & retention to answer that.  He found spacing practice over time decreased the number of exposures needed. In other words, small amounts of practice over several days, weeks, or even months actually means you need LESS practice than if you try to cram it all in at once.

For over 80 years, this finding has stood the test of time. While research has shown that students who engage in mass practice (lots of practice all at once) might do better on an assessment that takes place tomorrow, students who engage in repeated practice over a period of time retain more skills long-term (Bloom & Shuell, 1981; Rea & Modigliani, 1985).

And how long does the research say you should spend reviewing?

How long should problem-solving practice really be?

Shorter is better. As discussed earlier, peak attention required for deliberate practice can only be maintained for so long. And the majority of research supports 8-10 minutes as the ideal lesson length (Robertson, 2010).

This means practice needs to be focused so that during those minutes of discussion, you can dive deep – breaking down the word problem and discussing methods to solve it.

Teacher Tip: Applying this finding to your classroom

Less is actually more as long as you plan to practice regularly. While students who struggle with word problems may need a great deal of practice to master word problems, ideally, this practice should be provided in short, regular intervals with no more than 8-10 minutes spent in whole group discussion.

Here are a few simple steps to apply these findings to your math classroom:

• Find 8-12 minutes in your daily schedule to focus on problem-solving – consider this time sacred & only for problem-solving.
• Select only 1-2 word problems per day. Target step-by-step math problem-solving to build math problem-solving skills through a less-is-more approach using Problem of the Day .

Finding #2: Students who are challenged & supported have better outcomes.

Productive struggle, as it is called in the research, focuses on the effortful practice that builds long-term understanding.

Important to this process are opportunities for choice, collaboration, and the use of materials or topics of interest (which will be discussed later).

This productive struggle also helps students build flexible thinking so that they can apply previously learned skills to new or unfamiliar tasks (Bransford, Brown, & Cocking, 2000).

“Meaningful learning tasks need to challenge ever student in some way. It is crucial that no student be able to coast to success time after time; this experience can create the belief that you are smart only if you can succeed without effort.” -Carol Dweck

It is also critical to provide support and feedback during the challenging task (Cimpian, Arce, Markman, & Dweck, 2007). This prevents frustration and fear of failure when the goal seems out of reach or when a particularly challenging task arises.

Simple ways to build productive struggle into your math classroom

Giving students who struggle with word problems a chance to struggle with challenging word problems is critical to building confidence and skills. However, this challenge must be reasonable, or the learner’s self-esteem will falter, and students need support and regular feedback to achieve their potential.

Here are a few simple things to try:

• Select problems that are just at the edge of students’ Zone of Proximal Development.
• Scaffold or model with more challenging problems to support risk-taking.
• Give regular feedback & support – go over the work and discuss daily.

Finding #3: Novelty & variation are keys to engagement.

When it comes to standardized testing (and life in general), problems that arise aren’t labeled with the skills and strategies required to solve them.

This makes it important to provide mixed practice opportunities so students are focused on asking themselves questions about what the problem is asking and what they are trying to find.

This type of variation not only supports a deeper level of engagement, it also supports the metacognitive strategies needed to analyze and develop a strategy to solve (Rohrer & Taylor, 2014).

The benefits of novelty in learning

A 2013 study also supports the importance of novelty in supporting reinforcement learning (aka review). The findings suggested that when task variation was provided for an already familiar skill, it offered the following benefits:

• reduced errors due to lack of focus
• helped learners maintain attention to task
• motivated and engaged student

Using variety to build connections & deepen understanding

In addition, by providing variations in practice, we can also help learners understand the skills and strategies they are using on a deeper level.  

When students who struggle with word problems are forced to apply their toolbox of strategies to novel problem formats, they begin to analyze and observe patterns in how problems are structured and the meaning they bring.

This requires much more engagement than being handed a sheet full of multiplication story problems, where students can pull the numbers and compute with little focus on understanding.

Designing word problems that incorporate variety & novelty

Don’t be afraid to shake things up!

Giving students practice opportunities with different skills or problem formats mixed in is a great way to boost engagement and develop meta-cognitive skills.

Here are a few tips for trying it out in the classroom:

• Change it up! Word problem practice doesn’t have to match the day’s math lesson.
• Give opportunities to practice the same skill or strategy in via different formats.
• Adjust the wording and/or topic in word problems to help students generalize skills.

Finding #4: Interest and emotion increase retention and skill development.

Attention and emotion are huge for learning. We’ve all seen it in our classroom.

Those magical lessons that hook learners are the ones that stick with them for years to come, but what does the research say?

The Science Behind Emotion & Learning

Neuroscientists have shown that emotions create connections among different sections of the brain (Immordino-Yang, 2016) . This supports long-term retrieval of the skills taught and a deeper connection to the learning.

This means if you can connect problem-solving with a scenario or a feeling, your students will be more likely to internalize the skills being practiced. Whether this is by “wowing” them with a little-known fact or solving real-world problems, the emotional trigger can be huge for learning.

What about incorporating student interests?

As for student interests, a long line of research supports the benefits of using these to increase educational outcomes and student motivation, including for students who struggle with word problems (Chen, 2001; Chen & Ennis, 2004; Solomon, 1996).

Connecting classwork with student interests has increased students’ intentions to participate in future learning endeavors (Chen, 2001).

And interests don’t just mean that love of Pokemon!

It means allowing social butterflies to work collaboratively. Providing students with opportunities to manipulate real objects or create models. Allowing kids to be authentic while digging in and developing the skills they need to master their learning objectives.

What this looks like in a math class

Evoke emotion and use student interests to engage the brain in deep, long-lasting learning whenever possible.

This will help with today’s learning and promote long-term engagement, even when later practice might not be as interesting for students who struggle with word problems.

Here’s how to start applying this research today:

• Find word problems that match student interests.
• Connect real-life situations and emotions to story problem practice.
• Consider a weekly theme to connect practice throughout the week.

Finding #5: Student autonomy builds confidence & independence.

Autonomy is a student’s ability to be in control of their learning. In other words, it is their ability to take ownership over the learning process and how they demonstrate mastery.

Why students need to control their learning

Research shows that providing students a sense of control and supporting their choices is way to help engage learners and build independent thinking. It also increased intrinsic motivation (Reeve, Nix, & Hamm, 2003).

However, this doesn’t mean we just let kids learn independently. Clearly, some things require repeated guidance and modeling. Finding small ways that students can take control of the learning process is much better in these instances.

We know that giving at least partial autonomy has been linked to numerous positive student learning outcomes (Wielenga-Meijer, Taris, Widboldus, & Kompier, 2011).

But how can we foster this independence and autonomy, especially with those students who struggle to self-regulate behavior?

Fostering independence in students who struggle to stay on task

Well, the research says several conditions support building toward independence.

The first (and often neglected) is to explain unappealing choices and why they are one of the options.

When it comes to word problems, this might include explaining the rationale behind one of the strategies that appears to be a lot more work than the others.

It is also important to acknowledge students’ negative feelings about a task or their ability to complete it. While we want them to be able to build independence, we don’t want them to drown in overwhelm.

By providing emotional support, we can help determine whether a student is stuck with the learning or with the emotions from the cognitive challenge.

Finally, giving choices is recommended. Identifying choices you and your students who struggle with word problems can live with is an important step.

Whether this is working in partners, trying an alternative method, or skipping a problem and coming back, students need to feel like they have some ownership over the challenge they are working through.

By building in opportunities for autonomy, and choice, teachers help students build a sense of self-efficacy and confidence in their ability to be successful learners across various contexts (McCombs, 2002,2006).

We know this leads to numerous positive outcomes and has even been linked to drop-out prevention (Christenson & Thurlow, 2004).

Fostering autonomy in your classroom

You’re not going to be able to hold their hands forever.

Giving opportunities to work through challenges independently and to feel ownership for their choices will help build both confidence and skills.

Here’s how to get started letting go:

• Give students time to tackle the problem independently (or in partners).
• Don’t get hyper-focused on a single method to solve – give opportunities to share & learn together.
• Provide appropriate support (where needed) to build autonomy for all learners – like reading the problem orally.

Finding #6: Students need to be taught how to fail & recover from it.

Despite Ericsson’s findings discussed early on in this post, talent does matter, and it is important to teach students to recover from failure because those are the moments when they learn the most.

A 2014 study by Brooke Macnamara analyzed 88 studies to determine how talent factored into deliberate practice.

Her findings show what we (as teachers) already know, students may require different amounts of practice to reach the same skill level…but how do we keep those struggling students from keeping up?

Growth mindset research gives us insight into ways to support students who struggle with word problems, encourage all students in math problem-solving, and harness the power of failure through “yet.”

You might not be able to do something yet, but if you keep trying, you will. This opens the door for multiple practice opportunities where students learn from each other.

And what about the advanced students?

Many of these students have not experienced failure, but they may have met their match when it comes to complex word problems.

To support these students, who may be experiencing their first true challenge, we need to have high standards and provide constructive, supportive feedback on how to grow.

Then we need to give them space to try again.

There is great power in allowing students to revise and try again, but our grading system often discourages being comfortable with failure.

Building the confidence to fail in your classroom

Many students feel the pressure always to have the right answer. Allowing students to fail safely means you can help them learn from these failures so they don’t make the same mistake twice.

Here’s how you can safely foster growth and build math problem solving skills through failure in your classroom:

• Build in time to analyze errors & reflect.
• Reward effort & growth as much as, if not more than, accuracy.
• ​At least initially, skip the grading so students aren’t afraid to be wrong.

Getting started with brain-based problem solving

The brain research is clear.

Spending 45 minutes focused on a sheet of word problems following the same format isn’t the answer.

By implementing this research, you can save yourself time and the frustration from a disengaged class.

Based on this research, I’ve created Daily Problem Solving bundles to save you time and build math problem-solving skills. You can get each month separately or buy the full-year bundle at a major discount.

Currently, I offer these bundles for several grade levels, including:

Try Daily Problem Solving with your Learners

Of course, you do! Start working to build step-by-step math problem-solving skills today by clicking the button below to sign up for a free set of Daily Problem Solving.

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How to Train Your Problem-Solving Skills

From the hiccups that disrupt your morning routines to the hurdles that define your professional paths, there is always a problem to be solved. 

The good news is that every obstacle is an opportunity to develop problem-solving skills and become the best version of yourself. That’s right: It turns out you can get better at problem-solving, which will help you increase success in daily life and long-term goals.  

Read on to learn how to improve your problem-solving abilities through scientific research and practical strategies.

Understanding Problem-Solving Skills

You may be surprised to learn that your problem-solving skills go beyond just trying to find a solution. Problem-solving skills involve cognitive abilities such as analytical thinking, creativity, decision-making, logical reasoning, and memory. 

Strong problem-solving skills boost critical thinking, spark creativity, and hone decision-making abilities. For you or anyone looking to improve their mental fitness , these skills are necessary for career advancement, personal growth, and positive interpersonal relationships. 

Core Components of Problem-Solving Skills Training

To effectively train your problem-solving skills, it’s important to practice all of the steps required to solve the problem. Think of it this way: Before attempting to solve a problem, your brain has already been hard at work evaluating the situation and picking the best action plan. After you’ve worked hard preparing, you’ll need to implement your plan and assess the outcome by following these steps:  

• Identify and define problems: Recognizing and clearly articulating issues is the foundational step in solving them.
• Generate solutions: Employing brainstorming techniques helps you develop multiple potential solutions.
• Evaluate and select solutions: Using specific criteria to assess solutions helps you choose the most effective one.
• Implement solutions: Developing and executing action plans, including preparing for potential obstacles, guides you to positive outcomes.
• Review and learn from outcomes: Assessing the success of solutions and learning from the results for future improvement facilitates future success. 

Strategies for Developing Problem-Solving Skills

There are many practical exercises and activities that can improve problem-solving abilities.

Cultivate a Problem-Solving Mindset

• Adopt a growth mindset: A growth mindset involves transforming phrases like “I can’t” into “I can’t yet.” Believing in the capacity to improve your skills through effort and perseverance can lead to greater success in problem-solving.
• Practice mindfulness: Mindfulness can enhance cognitive flexibility , allowing you to view problems from multiple perspectives and find creative solutions.

Enhance Core Cognitive Skills 

• Strengthen your memory: Engage in activities that challenge your memory since accurately recalling information is crucial in problem-solving. Techniques such as mnemonic devices or memory palaces can be particularly effective.
• Build your critical thinking: Regularly question assumptions, evaluate arguments, and engage in activities that require reasoning, such as strategy games or debates.

Apply Structured Problem-Solving Techniques

• Use the STOP method: This stands for Stop , Think , Observe , and Plan . It's a simple yet effective way to approach any problem methodically, ensuring you consider all aspects before taking action.
• Try reverse engineering: Start with the desired outcome and work backward to understand the steps needed to achieve that result. This approach can be particularly useful for complex problems with unclear starting points.

Incorporate Technology into Your Training

• Engage with online courses and workshops: Many platforms offer courses specifically designed to enhance problem-solving skills, ranging from critical thinking to creative problem-solving techniques.
• Use cognitive training apps: Apps like Elevate provide targeted, research-backed games and workouts to improve cognitive skills including attention, processing speed, and more. 

Practice with Real-World Applications and Learn from Experience

• Tackle daily challenges: Use everyday issues as opportunities to practice problem-solving. Whether figuring out a new recipe or managing a tight budget, applying your skills in real-world situations can reinforce learning.
• Keep a problem-solving journal: Record the challenges you face, the strategies you employ, and the outcomes you achieve. Reflecting on your problem-solving process over time can provide insights into your strengths and areas for improvement.

Embracing Problem-Solving as a Lifelong Journey

Since problems arise daily, it’s important to feel confident in solving them. 

And you can do just that by downloading the Elevate brain training app. Elevate offers 40+ games and activities designed to improve problem-solving, communication, and other cognitive skills in a personalized way that’s backed by science. Pretty cool, right? 

Consider downloading the Elevate app on Android or iOS now—it’ll be the easiest problem you solve all day. 

Related Articles

How Problem-Solving Games Can Boost Your Brain

• Discover why problem-solving games are fun and effective ways to train your brain. 

Improving Your Problem-Solving Skills

• Discover how to improve your problem-solving skills and make logical, informed decisions.  

Best Ways to Boost Your Mental Fitness

• Mental fitness refers to your ability to sustain your overall well-being. Learn tips to improve yours.  

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

How to improve your problem solving skills and build effective problem solving strategies

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Effective problem solving is all about using the right process and following a plan tailored to the issue at hand. Recognizing your team or organization has an issue isn’t enough to come up with effective problem solving strategies. 

To truly understand a problem and develop appropriate solutions, you will want to follow a solid process, follow the necessary problem solving steps, and bring all of your problem solving skills to the table.  

We’ll first guide you through the seven step problem solving process you and your team can use to effectively solve complex business challenges. We’ll also look at what problem solving strategies you can employ with your team when looking for a way to approach the process. We’ll then discuss the problem solving skills you need to be more effective at solving problems, complete with an activity from the SessionLab library you can use to develop that skill in your team.

Let’s get to it! 

What is a problem solving process?

• What are the problem solving steps I need to follow?

Problem solving strategies

What skills do i need to be an effective problem solver, how can i improve my problem solving skills.

Solving problems is like baking a cake. You can go straight into the kitchen without a recipe or the right ingredients and do your best, but the end result is unlikely to be very tasty!

Using a process to bake a cake allows you to use the best ingredients without waste, collect the right tools, account for allergies, decide whether it is a birthday or wedding cake, and then bake efficiently and on time. The result is a better cake that is fit for purpose, tastes better and has created less mess in the kitchen. Also, it should have chocolate sprinkles. Having a step by step process to solve organizational problems allows you to go through each stage methodically and ensure you are trying to solve the right problems and select the most appropriate, effective solutions.

What are the problem solving steps I need to follow? 

All problem solving processes go through a number of steps in order to move from identifying a problem to resolving it.

Depending on your problem solving model and who you ask, there can be anything between four and nine problem solving steps you should follow in order to find the right solution. Whatever framework you and your group use, there are some key items that should be addressed in order to have an effective process.

We’ve looked at problem solving processes from sources such as the American Society for Quality and their four step approach , and Mediate ‘s six step process. By reflecting on those and our own problem solving processes, we’ve come up with a sequence of seven problem solving steps we feel best covers everything you need in order to effectively solve problems.

1. Problem identification 

The first stage of any problem solving process is to identify the problem or problems you might want to solve. Effective problem solving strategies always begin by allowing a group scope to articulate what they believe the problem to be and then coming to some consensus over which problem they approach first. Problem solving activities used at this stage often have a focus on creating frank, open discussion so that potential problems can be brought to the surface.

2. Problem analysis 

Though this step is not a million miles from problem identification, problem analysis deserves to be considered separately. It can often be an overlooked part of the process and is instrumental when it comes to developing effective solutions.

The process of problem analysis means ensuring that the problem you are seeking to solve is the right problem . As part of this stage, you may look deeper and try to find the root cause of a specific problem at a team or organizational level.

Remember that problem solving strategies should not only be focused on putting out fires in the short term but developing long term solutions that deal with the root cause of organizational challenges. 

Whatever your approach, analyzing a problem is crucial in being able to select an appropriate solution and the problem solving skills deployed in this stage are beneficial for the rest of the process and ensuring the solutions you create are fit for purpose.

3. Solution generation

Once your group has nailed down the particulars of the problem you wish to solve, you want to encourage a free flow of ideas connecting to solving that problem. This can take the form of problem solving games that encourage creative thinking or problem solving activities designed to produce working prototypes of possible solutions. 

The key to ensuring the success of this stage of the problem solving process is to encourage quick, creative thinking and create an open space where all ideas are considered. The best solutions can come from unlikely places and by using problem solving techniques that celebrate invention, you might come up with solution gold. 

4. Solution development

No solution is likely to be perfect right out of the gate. It’s important to discuss and develop the solutions your group has come up with over the course of following the previous problem solving steps in order to arrive at the best possible solution. Problem solving games used in this stage involve lots of critical thinking, measuring potential effort and impact, and looking at possible solutions analytically. 

During this stage, you will often ask your team to iterate and improve upon your frontrunning solutions and develop them further. Remember that problem solving strategies always benefit from a multitude of voices and opinions, and not to let ego get involved when it comes to choosing which solutions to develop and take further.

Finding the best solution is the goal of all problem solving workshops and here is the place to ensure that your solution is well thought out, sufficiently robust and fit for purpose. 

5. Decision making 

Nearly there! Once your group has reached consensus and selected a solution that applies to the problem at hand you have some decisions to make. You will want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

The decision making stage is a part of the problem solving process that can get missed or taken as for granted. Fail to properly allocate roles and plan out how a solution will actually be implemented and it less likely to be successful in solving the problem.

Have clear accountabilities, actions, timeframes, and follow-ups. Make these decisions and set clear next-steps in the problem solving workshop so that everyone is aligned and you can move forward effectively as a group. 

Ensuring that you plan for the roll-out of a solution is one of the most important problem solving steps. Without adequate planning or oversight, it can prove impossible to measure success or iterate further if the problem was not solved. 

6. Solution implementation 

This is what we were waiting for! All problem solving strategies have the end goal of implementing a solution and solving a problem in mind. 

Remember that in order for any solution to be successful, you need to help your group through all of the previous problem solving steps thoughtfully. Only then can you ensure that you are solving the right problem but also that you have developed the correct solution and can then successfully implement and measure the impact of that solution.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way.

7. Solution evaluation 

So you and your team developed a great solution to a problem and have a gut feeling its been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback. You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives. 

None of that is possible without taking the time to evaluate the success of the solution you developed in your problem solving model and adjust if necessary.

Remember that the problem solving process is often iterative and it can be common to not solve complex issues on the first try. Even when this is the case, you and your team will have generated learning that will be important for future problem solving workshops or in other parts of the organization. 

It’s worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time. Data and insight is invaluable at every stage of the problem solving process and this one is no different.

Problem solving workshops made easy

Problem solving strategies are methods of approaching and facilitating the process of problem-solving with a set of techniques , actions, and processes. Different strategies are more effective if you are trying to solve broad problems such as achieving higher growth versus more focused problems like, how do we improve our customer onboarding process?

Broadly, the problem solving steps outlined above should be included in any problem solving strategy though choosing where to focus your time and what approaches should be taken is where they begin to differ. You might find that some strategies ask for the problem identification to be done prior to the session or that everything happens in the course of a one day workshop.

The key similarity is that all good problem solving strategies are structured and designed. Four hours of open discussion is never going to be as productive as a four-hour workshop designed to lead a group through a problem solving process.

Good problem solving strategies are tailored to the team, organization and problem you will be attempting to solve. Here are some example problem solving strategies you can learn from or use to get started.

Use a workshop to lead a team through a group process

Often, the first step to solving problems or organizational challenges is bringing a group together effectively. Most teams have the tools, knowledge, and expertise necessary to solve their challenges – they just need some guidance in how to use leverage those skills and a structure and format that allows people to focus their energies.

Facilitated workshops are one of the most effective ways of solving problems of any scale. By designing and planning your workshop carefully, you can tailor the approach and scope to best fit the needs of your team and organization. 

Problem solving workshop

• Creating a bespoke, tailored process
• Tackling problems of any size
• Building in-house workshop ability and encouraging their use

Workshops are an effective strategy for solving problems. By using tried and test facilitation techniques and methods, you can design and deliver a workshop that is perfectly suited to the unique variables of your organization. You may only have the capacity for a half-day workshop and so need a problem solving process to match. 

By using our session planner tool and importing methods from our library of 700+ facilitation techniques, you can create the right problem solving workshop for your team. It might be that you want to encourage creative thinking or look at things from a new angle to unblock your groups approach to problem solving. By tailoring your workshop design to the purpose, you can help ensure great results.

One of the main benefits of a workshop is the structured approach to problem solving. Not only does this mean that the workshop itself will be successful, but many of the methods and techniques will help your team improve their working processes outside of the workshop. 

We believe that workshops are one of the best tools you can use to improve the way your team works together. Start with a problem solving workshop and then see what team building, culture or design workshops can do for your organization!

Run a design sprint

Great for: 

• aligning large, multi-discipline teams
• quickly designing and testing solutions
• tackling large, complex organizational challenges and breaking them down into smaller tasks

By using design thinking principles and methods, a design sprint is a great way of identifying, prioritizing and prototyping solutions to long term challenges that can help solve major organizational problems with quick action and measurable results.

Some familiarity with design thinking is useful, though not integral, and this strategy can really help a team align if there is some discussion around which problems should be approached first. 

The stage-based structure of the design sprint is also very useful for teams new to design thinking.  The inspiration phase, where you look to competitors that have solved your problem, and the rapid prototyping and testing phases are great for introducing new concepts that will benefit a team in all their future work. 

It can be common for teams to look inward for solutions and so looking to the market for solutions you can iterate on can be very productive. Instilling an agile prototyping and testing mindset can also be great when helping teams move forwards – generating and testing solutions quickly can help save time in the long run and is also pretty exciting!

Break problems down into smaller issues

Organizational challenges and problems are often complicated and large scale in nature. Sometimes, trying to resolve such an issue in one swoop is simply unachievable or overwhelming. Try breaking down such problems into smaller issues that you can work on step by step. You may not be able to solve the problem of churning customers off the bat, but you can work with your team to identify smaller effort but high impact elements and work on those first.

This problem solving strategy can help a team generate momentum, prioritize and get some easy wins. It’s also a great strategy to employ with teams who are just beginning to learn how to approach the problem solving process. If you want some insight into a way to employ this strategy, we recommend looking at our design sprint template below!

Use guiding frameworks or try new methodologies

Some problems are best solved by introducing a major shift in perspective or by using new methodologies that encourage your team to think differently.

Props and tools such as Methodkit , which uses a card-based toolkit for facilitation, or Lego Serious Play can be great ways to engage your team and find an inclusive, democratic problem solving strategy. Remember that play and creativity are great tools for achieving change and whatever the challenge, engaging your participants can be very effective where other strategies may have failed.

LEGO Serious Play

• Improving core problem solving skills
• Thinking outside of the box
• Encouraging creative solutions

LEGO Serious Play is a problem solving methodology designed to get participants thinking differently by using 3D models and kinesthetic learning styles. By physically building LEGO models based on questions and exercises, participants are encouraged to think outside of the box and create their own responses. 

Collaborate LEGO Serious Play exercises are also used to encourage communication and build problem solving skills in a group. By using this problem solving process, you can often help different kinds of learners and personality types contribute and unblock organizational problems with creative thinking. 

Problem solving strategies like LEGO Serious Play are super effective at helping a team solve more skills-based problems such as communication between teams or a lack of creative thinking. Some problems are not suited to LEGO Serious Play and require a different problem solving strategy.

Card Decks and Method Kits

• New facilitators or non-facilitators 
• Approaching difficult subjects with a simple, creative framework
• Engaging those with varied learning styles

Card decks and method kids are great tools for those new to facilitation or for whom facilitation is not the primary role. Card decks such as the emotional culture deck can be used for complete workshops and in many cases, can be used right out of the box. Methodkit has a variety of kits designed for scenarios ranging from personal development through to personas and global challenges so you can find the right deck for your particular needs.

Having an easy to use framework that encourages creativity or a new approach can take some of the friction or planning difficulties out of the workshop process and energize a team in any setting. Simplicity is the key with these methods. By ensuring everyone on your team can get involved and engage with the process as quickly as possible can really contribute to the success of your problem solving strategy.

Source external advice

Looking to peers, experts and external facilitators can be a great way of approaching the problem solving process. Your team may not have the necessary expertise, insights of experience to tackle some issues, or you might simply benefit from a fresh perspective. Some problems may require bringing together an entire team, and coaching managers or team members individually might be the right approach. Remember that not all problems are best resolved in the same manner.

If you’re a solo entrepreneur, peer groups, coaches and mentors can also be invaluable at not only solving specific business problems, but in providing a support network for resolving future challenges. One great approach is to join a Mastermind Group and link up with like-minded individuals and all grow together. Remember that however you approach the sourcing of external advice, do so thoughtfully, respectfully and honestly. Reciprocate where you can and prepare to be surprised by just how kind and helpful your peers can be!

Mastermind Group

• Solo entrepreneurs or small teams with low capacity
• Peer learning and gaining outside expertise
• Getting multiple external points of view quickly

Problem solving in large organizations with lots of skilled team members is one thing, but how about if you work for yourself or in a very small team without the capacity to get the most from a design sprint or LEGO Serious Play session? 

A mastermind group – sometimes known as a peer advisory board – is where a group of people come together to support one another in their own goals, challenges, and businesses. Each participant comes to the group with their own purpose and the other members of the group will help them create solutions, brainstorm ideas, and support one another. 

Mastermind groups are very effective in creating an energized, supportive atmosphere that can deliver meaningful results. Learning from peers from outside of your organization or industry can really help unlock new ways of thinking and drive growth. Access to the experience and skills of your peers can be invaluable in helping fill the gaps in your own ability, particularly in young companies.

A mastermind group is a great solution for solo entrepreneurs, small teams, or for organizations that feel that external expertise or fresh perspectives will be beneficial for them. It is worth noting that Mastermind groups are often only as good as the participants and what they can bring to the group. Participants need to be committed, engaged and understand how to work in this context. 

Coaching and mentoring

• Focused learning and development
• Filling skills gaps
• Working on a range of challenges over time

Receiving advice from a business coach or building a mentor/mentee relationship can be an effective way of resolving certain challenges. The one-to-one format of most coaching and mentor relationships can really help solve the challenges those individuals are having and benefit the organization as a result.

A great mentor can be invaluable when it comes to spotting potential problems before they arise and coming to understand a mentee very well has a host of other business benefits. You might run an internal mentorship program to help develop your team’s problem solving skills and strategies or as part of a large learning and development program. External coaches can also be an important part of your problem solving strategy, filling skills gaps for your management team or helping with specific business issues. 

Now we’ve explored the problem solving process and the steps you will want to go through in order to have an effective session, let’s look at the skills you and your team need to be more effective problem solvers.

Problem solving skills are highly sought after, whatever industry or team you work in. Organizations are keen to employ people who are able to approach problems thoughtfully and find strong, realistic solutions. Whether you are a facilitator , a team leader or a developer, being an effective problem solver is a skill you’ll want to develop.

Problem solving skills form a whole suite of techniques and approaches that an individual uses to not only identify problems but to discuss them productively before then developing appropriate solutions.

Here are some of the most important problem solving skills everyone from executives to junior staff members should learn. We’ve also included an activity or exercise from the SessionLab library that can help you and your team develop that skill. 

If you’re running a workshop or training session to try and improve problem solving skills in your team, try using these methods to supercharge your process!

Active listening

Active listening is one of the most important skills anyone who works with people can possess. In short, active listening is a technique used to not only better understand what is being said by an individual, but also to be more aware of the underlying message the speaker is trying to convey. When it comes to problem solving, active listening is integral for understanding the position of every participant and to clarify the challenges, ideas and solutions they bring to the table.

Some active listening skills include:

• Paying complete attention to the speaker.
• Removing distractions.
• Avoid interruption.
• Taking the time to fully understand before preparing a rebuttal.
• Responding respectfully and appropriately.
• Demonstrate attentiveness and positivity with an open posture, making eye contact with the speaker, smiling and nodding if appropriate. Show that you are listening and encourage them to continue.
• Be aware of and respectful of feelings. Judge the situation and respond appropriately. You can disagree without being disrespectful.   
• Observe body language. 
• Paraphrase what was said in your own words, either mentally or verbally.
• Remain neutral. 
• Reflect and take a moment before responding.
• Ask deeper questions based on what is said and clarify points where necessary.   

Active Listening   #hyperisland   #skills   #active listening   #remote-friendly   This activity supports participants to reflect on a question and generate their own solutions using simple principles of active listening and peer coaching. It’s an excellent introduction to active listening but can also be used with groups that are already familiar with it. Participants work in groups of three and take turns being: “the subject”, the listener, and the observer.

Analytical skills

All problem solving models require strong analytical skills, particularly during the beginning of the process and when it comes to analyzing how solutions have performed.

Analytical skills are primarily focused on performing an effective analysis by collecting, studying and parsing data related to a problem or opportunity. 

It often involves spotting patterns, being able to see things from different perspectives and using observable facts and data to make suggestions or produce insight. 

Analytical skills are also important at every stage of the problem solving process and by having these skills, you can ensure that any ideas or solutions you create or backed up analytically and have been sufficiently thought out.

Nine Whys   #innovation   #issue analysis   #liberating structures   With breathtaking simplicity, you can rapidly clarify for individuals and a group what is essentially important in their work. You can quickly reveal when a compelling purpose is missing in a gathering and avoid moving forward without clarity. When a group discovers an unambiguous shared purpose, more freedom and more responsibility are unleashed. You have laid the foundation for spreading and scaling innovations with fidelity.

Collaboration

Trying to solve problems on your own is difficult. Being able to collaborate effectively, with a free exchange of ideas, to delegate and be a productive member of a team is hugely important to all problem solving strategies.

Remember that whatever your role, collaboration is integral, and in a problem solving process, you are all working together to find the best solution for everyone. 

Marshmallow challenge with debriefing   #teamwork   #team   #leadership   #collaboration   In eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top. The Marshmallow Challenge was developed by Tom Wujec, who has done the activity with hundreds of groups around the world. Visit the Marshmallow Challenge website for more information. This version has an extra debriefing question added with sample questions focusing on roles within the team.

Communication  

Being an effective communicator means being empathetic, clear and succinct, asking the right questions, and demonstrating active listening skills throughout any discussion or meeting. 

In a problem solving setting, you need to communicate well in order to progress through each stage of the process effectively. As a team leader, it may also fall to you to facilitate communication between parties who may not see eye to eye. Effective communication also means helping others to express themselves and be heard in a group.

Bus Trip   #feedback   #communication   #appreciation   #closing   #thiagi   #team   This is one of my favourite feedback games. I use Bus Trip at the end of a training session or a meeting, and I use it all the time. The game creates a massive amount of energy with lots of smiles, laughs, and sometimes even a teardrop or two.

Creative problem solving skills can be some of the best tools in your arsenal. Thinking creatively, being able to generate lots of ideas and come up with out of the box solutions is useful at every step of the process. 

The kinds of problems you will likely discuss in a problem solving workshop are often difficult to solve, and by approaching things in a fresh, creative manner, you can often create more innovative solutions.

Having practical creative skills is also a boon when it comes to problem solving. If you can help create quality design sketches and prototypes in record time, it can help bring a team to alignment more quickly or provide a base for further iteration.

The paper clip method   #sharing   #creativity   #warm up   #idea generation   #brainstorming   The power of brainstorming. A training for project leaders, creativity training, and to catalyse getting new solutions.

Critical thinking

Critical thinking is one of the fundamental problem solving skills you’ll want to develop when working on developing solutions. Critical thinking is the ability to analyze, rationalize and evaluate while being aware of personal bias, outlying factors and remaining open-minded.

Defining and analyzing problems without deploying critical thinking skills can mean you and your team go down the wrong path. Developing solutions to complex issues requires critical thinking too – ensuring your team considers all possibilities and rationally evaluating them. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Data analysis 

Though it shares lots of space with general analytical skills, data analysis skills are something you want to cultivate in their own right in order to be an effective problem solver.

Being good at data analysis doesn’t just mean being able to find insights from data, but also selecting the appropriate data for a given issue, interpreting it effectively and knowing how to model and present that data. Depending on the problem at hand, it might also include a working knowledge of specific data analysis tools and procedures. 

Having a solid grasp of data analysis techniques is useful if you’re leading a problem solving workshop but if you’re not an expert, don’t worry. Bring people into the group who has this skill set and help your team be more effective as a result.

Decision making

All problems need a solution and all solutions require that someone make the decision to implement them. Without strong decision making skills, teams can become bogged down in discussion and less effective as a result. 

Making decisions is a key part of the problem solving process. It’s important to remember that decision making is not restricted to the leadership team. Every staff member makes decisions every day and developing these skills ensures that your team is able to solve problems at any scale. Remember that making decisions does not mean leaping to the first solution but weighing up the options and coming to an informed, well thought out solution to any given problem that works for the whole team.

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

Dependability

Most complex organizational problems require multiple people to be involved in delivering the solution. Ensuring that the team and organization can depend on you to take the necessary actions and communicate where necessary is key to ensuring problems are solved effectively.

Being dependable also means working to deadlines and to brief. It is often a matter of creating trust in a team so that everyone can depend on one another to complete the agreed actions in the agreed time frame so that the team can move forward together. Being undependable can create problems of friction and can limit the effectiveness of your solutions so be sure to bear this in mind throughout a project. 

Team Purpose & Culture   #team   #hyperisland   #culture   #remote-friendly   This is an essential process designed to help teams define their purpose (why they exist) and their culture (how they work together to achieve that purpose). Defining these two things will help any team to be more focused and aligned. With support of tangible examples from other companies, the team members work as individuals and a group to codify the way they work together. The goal is a visual manifestation of both the purpose and culture that can be put up in the team’s work space.

Emotional intelligence

Emotional intelligence is an important skill for any successful team member, whether communicating internally or with clients or users. In the problem solving process, emotional intelligence means being attuned to how people are feeling and thinking, communicating effectively and being self-aware of what you bring to a room. 

There are often differences of opinion when working through problem solving processes, and it can be easy to let things become impassioned or combative. Developing your emotional intelligence means being empathetic to your colleagues and managing your own emotions throughout the problem and solution process. Be kind, be thoughtful and put your points across care and attention. 

Being emotionally intelligent is a skill for life and by deploying it at work, you can not only work efficiently but empathetically. Check out the emotional culture workshop template for more!

Facilitation

As we’ve clarified in our facilitation skills post, facilitation is the art of leading people through processes towards agreed-upon objectives in a manner that encourages participation, ownership, and creativity by all those involved. While facilitation is a set of interrelated skills in itself, the broad definition of facilitation can be invaluable when it comes to problem solving. Leading a team through a problem solving process is made more effective if you improve and utilize facilitation skills – whether you’re a manager, team leader or external stakeholder.

The Six Thinking Hats   #creative thinking   #meeting facilitation   #problem solving   #issue resolution   #idea generation   #conflict resolution   The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Flexibility 

Being flexible is a vital skill when it comes to problem solving. This does not mean immediately bowing to pressure or changing your opinion quickly: instead, being flexible is all about seeing things from new perspectives, receiving new information and factoring it into your thought process.

Flexibility is also important when it comes to rolling out solutions. It might be that other organizational projects have greater priority or require the same resources as your chosen solution. Being flexible means understanding needs and challenges across the team and being open to shifting or arranging your own schedule as necessary. Again, this does not mean immediately making way for other projects. It’s about articulating your own needs, understanding the needs of others and being able to come to a meaningful compromise.

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

Working in any group can lead to unconscious elements of groupthink or situations in which you may not wish to be entirely honest. Disagreeing with the opinions of the executive team or wishing to save the feelings of a coworker can be tricky to navigate, but being honest is absolutely vital when to comes to developing effective solutions and ensuring your voice is heard. 

Remember that being honest does not mean being brutally candid. You can deliver your honest feedback and opinions thoughtfully and without creating friction by using other skills such as emotional intelligence. 

Explore your Values   #hyperisland   #skills   #values   #remote-friendly   Your Values is an exercise for participants to explore what their most important values are. It’s done in an intuitive and rapid way to encourage participants to follow their intuitive feeling rather than over-thinking and finding the “correct” values. It is a good exercise to use to initiate reflection and dialogue around personal values.

Initiative 

The problem solving process is multi-faceted and requires different approaches at certain points of the process. Taking initiative to bring problems to the attention of the team, collect data or lead the solution creating process is always valuable. You might even roadtest your own small scale solutions or brainstorm before a session. Taking initiative is particularly effective if you have good deal of knowledge in that area or have ownership of a particular project and want to get things kickstarted.

That said, be sure to remember to honor the process and work in service of the team. If you are asked to own one part of the problem solving process and you don’t complete that task because your initiative leads you to work on something else, that’s not an effective method of solving business challenges.

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

Impartiality

A particularly useful problem solving skill for product owners or managers is the ability to remain impartial throughout much of the process. In practice, this means treating all points of view and ideas brought forward in a meeting equally and ensuring that your own areas of interest or ownership are not favored over others. 

There may be a stage in the process where a decision maker has to weigh the cost and ROI of possible solutions against the company roadmap though even then, ensuring that the decision made is based on merit and not personal opinion. 

Empathy map   #frame insights   #create   #design   #issue analysis   An empathy map is a tool to help a design team to empathize with the people they are designing for. You can make an empathy map for a group of people or for a persona. To be used after doing personas when more insights are needed.

Being a good leader means getting a team aligned, energized and focused around a common goal. In the problem solving process, strong leadership helps ensure that the process is efficient, that any conflicts are resolved and that a team is managed in the direction of success.

It’s common for managers or executives to assume this role in a problem solving workshop, though it’s important that the leader maintains impartiality and does not bulldoze the group in a particular direction. Remember that good leadership means working in service of the purpose and team and ensuring the workshop is a safe space for employees of any level to contribute. Take a look at our leadership games and activities post for more exercises and methods to help improve leadership in your organization.

Leadership Pizza   #leadership   #team   #remote-friendly   This leadership development activity offers a self-assessment framework for people to first identify what skills, attributes and attitudes they find important for effective leadership, and then assess their own development and initiate goal setting.

In the context of problem solving, mediation is important in keeping a team engaged, happy and free of conflict. When leading or facilitating a problem solving workshop, you are likely to run into differences of opinion. Depending on the nature of the problem, certain issues may be brought up that are emotive in nature. 

Being an effective mediator means helping those people on either side of such a divide are heard, listen to one another and encouraged to find common ground and a resolution. Mediating skills are useful for leaders and managers in many situations and the problem solving process is no different.

Conflict Responses   #hyperisland   #team   #issue resolution   A workshop for a team to reflect on past conflicts, and use them to generate guidelines for effective conflict handling. The workshop uses the Thomas-Killman model of conflict responses to frame a reflective discussion. Use it to open up a discussion around conflict with a team.

Planning 

Solving organizational problems is much more effective when following a process or problem solving model. Planning skills are vital in order to structure, deliver and follow-through on a problem solving workshop and ensure your solutions are intelligently deployed.

Planning skills include the ability to organize tasks and a team, plan and design the process and take into account any potential challenges. Taking the time to plan carefully can save time and frustration later in the process and is valuable for ensuring a team is positioned for success.

3 Action Steps   #hyperisland   #action   #remote-friendly   This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme. The group discusses and agrees on a vision, then creates some action steps that will lead them towards that vision. The scope of the challenge is also defined, through discussion of the helpful and harmful factors influencing the group.

Prioritization

As organisations grow, the scale and variation of problems they face multiplies. Your team or is likely to face numerous challenges in different areas and so having the skills to analyze and prioritize becomes very important, particularly for those in leadership roles.

A thorough problem solving process is likely to deliver multiple solutions and you may have several different problems you wish to solve simultaneously. Prioritization is the ability to measure the importance, value, and effectiveness of those possible solutions and choose which to enact and in what order. The process of prioritization is integral in ensuring the biggest challenges are addressed with the most impactful solutions.

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

Project management

Some problem solving skills are utilized in a workshop or ideation phases, while others come in useful when it comes to decision making. Overseeing an entire problem solving process and ensuring its success requires strong project management skills. 

While project management incorporates many of the other skills listed here, it is important to note the distinction of considering all of the factors of a project and managing them successfully. Being able to negotiate with stakeholders, manage tasks, time and people, consider costs and ROI, and tie everything together is massively helpful when going through the problem solving process. 

Record keeping

Working out meaningful solutions to organizational challenges is only one part of the process.  Thoughtfully documenting and keeping records of each problem solving step for future consultation is important in ensuring efficiency and meaningful change. 

For example, some problems may be lower priority than others but can be revisited in the future. If the team has ideated on solutions and found some are not up to the task, record those so you can rule them out and avoiding repeating work. Keeping records of the process also helps you improve and refine your problem solving model next time around!

Personal Kanban   #gamestorming   #action   #agile   #project planning   Personal Kanban is a tool for organizing your work to be more efficient and productive. It is based on agile methods and principles.

Research skills

Conducting research to support both the identification of problems and the development of appropriate solutions is important for an effective process. Knowing where to go to collect research, how to conduct research efficiently, and identifying pieces of research are relevant are all things a good researcher can do well. 

In larger groups, not everyone has to demonstrate this ability in order for a problem solving workshop to be effective. That said, having people with research skills involved in the process, particularly if they have existing area knowledge, can help ensure the solutions that are developed with data that supports their intention. Remember that being able to deliver the results of research efficiently and in a way the team can easily understand is also important. The best data in the world is only as effective as how it is delivered and interpreted.

Customer experience map   #ideation   #concepts   #research   #design   #issue analysis   #remote-friendly   Customer experience mapping is a method of documenting and visualizing the experience a customer has as they use the product or service. It also maps out their responses to their experiences. To be used when there is a solution (even in a conceptual stage) that can be analyzed.

Risk management

Managing risk is an often overlooked part of the problem solving process. Solutions are often developed with the intention of reducing exposure to risk or solving issues that create risk but sometimes, great solutions are more experimental in nature and as such, deploying them needs to be carefully considered. 

Managing risk means acknowledging that there may be risks associated with more out of the box solutions or trying new things, but that this must be measured against the possible benefits and other organizational factors. 

Be informed, get the right data and stakeholders in the room and you can appropriately factor risk into your decision making process. 

Decisions, Decisions…   #communication   #decision making   #thiagi   #action   #issue analysis   When it comes to decision-making, why are some of us more prone to take risks while others are risk-averse? One explanation might be the way the decision and options were presented.  This exercise, based on Kahneman and Tversky’s classic study , illustrates how the framing effect influences our judgement and our ability to make decisions . The participants are divided into two groups. Both groups are presented with the same problem and two alternative programs for solving them. The two programs both have the same consequences but are presented differently. The debriefing discussion examines how the framing of the program impacted the participant’s decision.

Team-building 

No single person is as good at problem solving as a team. Building an effective team and helping them come together around a common purpose is one of the most important problem solving skills, doubly so for leaders. By bringing a team together and helping them work efficiently, you pave the way for team ownership of a problem and the development of effective solutions. 

In a problem solving workshop, it can be tempting to jump right into the deep end, though taking the time to break the ice, energize the team and align them with a game or exercise will pay off over the course of the day.

Remember that you will likely go through the problem solving process multiple times over an organization’s lifespan and building a strong team culture will make future problem solving more effective. It’s also great to work with people you know, trust and have fun with. Working on team building in and out of the problem solving process is a hallmark of successful teams that can work together to solve business problems.

9 Dimensions Team Building Activity   #ice breaker   #teambuilding   #team   #remote-friendly   9 Dimensions is a powerful activity designed to build relationships and trust among team members. There are 2 variations of this icebreaker. The first version is for teams who want to get to know each other better. The second version is for teams who want to explore how they are working together as a team.

Time management 

The problem solving process is designed to lead a team from identifying a problem through to delivering a solution and evaluating its effectiveness. Without effective time management skills or timeboxing of tasks, it can be easy for a team to get bogged down or be inefficient.

By using a problem solving model and carefully designing your workshop, you can allocate time efficiently and trust that the process will deliver the results you need in a good timeframe.

Time management also comes into play when it comes to rolling out solutions, particularly those that are experimental in nature. Having a clear timeframe for implementing and evaluating solutions is vital for ensuring their success and being able to pivot if necessary.

Improving your skills at problem solving is often a career-long pursuit though there are methods you can use to make the learning process more efficient and to supercharge your problem solving skillset.

Remember that the skills you need to be a great problem solver have a large overlap with those skills you need to be effective in any role. Investing time and effort to develop your active listening or critical thinking skills is valuable in any context. Here are 7 ways to improve your problem solving skills.

Share best practices

Remember that your team is an excellent source of skills, wisdom, and techniques and that you should all take advantage of one another where possible. Best practices that one team has for solving problems, conducting research or making decisions should be shared across the organization. If you have in-house staff that have done active listening training or are data analysis pros, have them lead a training session. 

Your team is one of your best resources. Create space and internal processes for the sharing of skills so that you can all grow together. 

Ask for help and attend training

Once you’ve figured out you have a skills gap, the next step is to take action to fill that skills gap. That might be by asking your superior for training or coaching, or liaising with team members with that skill set. You might even attend specialized training for certain skills – active listening or critical thinking, for example, are business-critical skills that are regularly offered as part of a training scheme.

Whatever method you choose, remember that taking action of some description is necessary for growth. Whether that means practicing, getting help, attending training or doing some background reading, taking active steps to improve your skills is the way to go.

Learn a process 

Problem solving can be complicated, particularly when attempting to solve large problems for the first time. Using a problem solving process helps give structure to your problem solving efforts and focus on creating outcomes, rather than worrying about the format. 

Tools such as the seven-step problem solving process above are effective because not only do they feature steps that will help a team solve problems, they also develop skills along the way. Each step asks for people to engage with the process using different skills and in doing so, helps the team learn and grow together. Group processes of varying complexity and purpose can also be found in the SessionLab library of facilitation techniques . Using a tried and tested process and really help ease the learning curve for both those leading such a process, as well as those undergoing the purpose.

Effective teams make decisions about where they should and shouldn’t expend additional effort. By using a problem solving process, you can focus on the things that matter, rather than stumbling towards a solution haphazardly. 

Create a feedback loop

Some skills gaps are more obvious than others. It’s possible that your perception of your active listening skills differs from those of your colleagues. 

It’s valuable to create a system where team members can provide feedback in an ordered and friendly manner so they can all learn from one another. Only by identifying areas of improvement can you then work to improve them. 

Remember that feedback systems require oversight and consideration so that they don’t turn into a place to complain about colleagues. Design the system intelligently so that you encourage the creation of learning opportunities, rather than encouraging people to list their pet peeves.

While practice might not make perfect, it does make the problem solving process easier. If you are having trouble with critical thinking, don’t shy away from doing it. Get involved where you can and stretch those muscles as regularly as possible. 

Problem solving skills come more naturally to some than to others and that’s okay. Take opportunities to get involved and see where you can practice your skills in situations outside of a workshop context. Try collaborating in other circumstances at work or conduct data analysis on your own projects. You can often develop those skills you need for problem solving simply by doing them. Get involved!

Use expert exercises and methods

Learn from the best. Our library of 700+ facilitation techniques is full of activities and methods that help develop the skills you need to be an effective problem solver. Check out our templates to see how to approach problem solving and other organizational challenges in a structured and intelligent manner.

There is no single approach to improving problem solving skills, but by using the techniques employed by others you can learn from their example and develop processes that have seen proven results. 

Try new ways of thinking and change your mindset

Using tried and tested exercises that you know well can help deliver results, but you do run the risk of missing out on the learning opportunities offered by new approaches. As with the problem solving process, changing your mindset can remove blockages and be used to develop your problem solving skills.

Most teams have members with mixed skill sets and specialties. Mix people from different teams and share skills and different points of view. Teach your customer support team how to use design thinking methods or help your developers with conflict resolution techniques. Try switching perspectives with facilitation techniques like Flip It! or by using new problem solving methodologies or models. Give design thinking, liberating structures or lego serious play a try if you want to try a new approach. You will find that framing problems in new ways and using existing skills in new contexts can be hugely useful for personal development and improving your skillset. It’s also a lot of fun to try new things. Give it a go!

Encountering business challenges and needing to find appropriate solutions is not unique to your organization. Lots of very smart people have developed methods, theories and approaches to help develop problem solving skills and create effective solutions. Learn from them!

Books like The Art of Thinking Clearly , Think Smarter, or Thinking Fast, Thinking Slow are great places to start, though it’s also worth looking at blogs related to organizations facing similar problems to yours, or browsing for success stories. Seeing how Dropbox massively increased growth and working backward can help you see the skills or approach you might be lacking to solve that same problem. Learning from others by reading their stories or approaches can be time-consuming but ultimately rewarding.

A tired, distracted mind is not in the best position to learn new skills. It can be tempted to burn the candle at both ends and develop problem solving skills outside of work. Absolutely use your time effectively and take opportunities for self-improvement, though remember that rest is hugely important and that without letting your brain rest, you cannot be at your most effective. 

Creating distance between yourself and the problem you might be facing can also be useful. By letting an idea sit, you can find that a better one presents itself or you can develop it further. Take regular breaks when working and create a space for downtime. Remember that working smarter is preferable to working harder and that self-care is important for any effective learning or improvement process.

Want to design better group processes?

Over to you

Now we’ve explored some of the key problem solving skills and the problem solving steps necessary for an effective process, you’re ready to begin developing more effective solutions and leading problem solving workshops.

Need more inspiration? Check out our post on problem solving activities you can use when guiding a group towards a great solution in your next workshop or meeting. Have questions? Did you have a great problem solving technique you use with your team? Get in touch in the comments below. We’d love to chat!

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How to Improve Problem-Solving Skills in Math

Importance of Problem-Solving Skills in Math

Problem-solving skills are crucial in math education , enabling students to apply mathematical concepts and principles to real-world situations. Here’s why problem-solving skills are essential in math education:

1. Application of knowledge: Problem-solving in math requires encouraging students to apply the knowledge they acquire in the classroom to tackle real-life problems. It helps them understand the relevance of math in everyday life and enhances their critical thinking skills.

2. Developing critical thinking:  Problem-solving requires students to analyze, evaluate, and think critically about different approaches and strategies to solve a problem. It strengthens their mathematical abilities and improves their overall critical thinking skills.

3. Enhancing problem-solving skills:  Math problems often have multiple solutions, encouraging students to think creatively and explore different problem-solving strategies. It helps develop their problem-solving skills, which are valuable in various aspects of life beyond math.

4. Fostering perseverance:  Problem-solving in math often requires persistence and resilience. Students must be willing to try different approaches, learn from their mistakes, and keep trying until they find a solution. It fosters a growth mindset and teaches them the value of perseverance.

Benefits of strong problem-solving skills

Having strong problem-solving skills in math offers numerous benefits for students:

1. Improved academic performance:  Students with strong problem-solving skills are likelier to excel in math and other subjects that rely on logical reasoning and critical thinking.

2. Enhanced problem-solving abilities:  Strong problem-solving skills extend beyond math and can be applied to various real-life situations. It includes decision-making, analytical thinking, and solving complex problems creatively.

3. Increased confidence:  Successfully solving math problems boosts students’ self-confidence and encourages them to tackle more challenging tasks. This confidence spills over into other areas of their academic and personal lives.

4. Preparation for future careers:  Problem-solving skills are highly sought after by employers in various fields. Developing strong problem-solving skills in math sets students up for successful careers in engineering, technology, finance, and more.

Problem-solving skills are essential for math education and have numerous benefits for students. By fostering these skills, educators can empower students to become confident, critical thinkers who can apply their mathematical knowledge to solve real-world problems.

Understand the Problem

Breaking down the problem and identifying the key components.

To improve problem-solving math skills, it’s essential to first understand the problem at hand. Here are some tips to help break down the problem and identify its key components:

1. Read the problem carefully:  Take your time to read it attentively and ensure you understand what it asks. Pay attention to keywords or phrases that indicate what mathematical operation or concept to use.

2. Identify the known and unknown variables:  Determine what information is already given in the problem (known variables) and what you need to find (unknown variables). This step will help you analyze the problem more effectively.

3. Define the problem in your own words:  Restate the problem using your own words to ensure you clearly understand what needs to be solved. It can help you focus on the main objective and eliminate any distractions.

4. Break the problem into smaller parts:  Complex math problems can sometimes be overwhelming. Breaking them down into smaller, manageable parts can make them more approachable. Identify any sub-problems or intermediate steps that must be solved before reaching the final solution.

Reading and interpreting math word problems effectively

Many math problems are presented as word problems requiring reading and interpreting skills. Here are some strategies to help you effectively understand and solve math word problems:

1. Highlight key information:  As you read the word problem, underline or highlight any important details, such as numbers, units of measurement, or specific keywords related to mathematical operations.

2. Visualize the problem:  Create visual representations, such as diagrams or graphs, to help you understand the problem better. Visualizing the problem can make determining what steps to take and how to approach the solution easier.

3. Translate words into equations:  Convert the information in the word problem into mathematical equations or expressions. This translation step helps you transform the problem into a solvable math equation.

4. Solve step by step:  Break down the problem into smaller steps and solve each step individually. This approach helps you avoid confusion and progress toward the correct solution.

Improving problem-solving skills in math requires practice and patience. By understanding the problem thoroughly, breaking it into manageable parts, and effectively interpreting word problems, you can confidently enhance your ability to solve math problems.

Use Visual Representations

Using diagrams, charts, and graphs to visualize the problem.

One effective way to improve problem-solving skills in math is to utilize visual representations. Visual representations , such as diagrams, charts, and graphs, can help make complex problems more tangible and easily understood. Here are some ways to use visual representations in problem-solving:

1. Draw Diagrams:  When faced with a word problem or a complex mathematical concept, drawing a diagram can help break down the problem into more manageable parts. For example, suppose you are dealing with a geometry problem. In that case, sketching the shapes involved can provide valuable insights and help you visualize the problem better.

2. Create Charts or Tables:  For problems that involve data or quantitative information, creating charts or tables can help organize the data and identify patterns or trends. It can be particularly useful in analyzing data from surveys, experiments, or real-life scenarios.

3. Graphical Representations:  Graphs can be powerful tools in problem-solving, especially when dealing with functions, equations, or mathematical relationships. Graphically representing data or equations makes it easier to identify key features that may be hard to spot from a numerical representation alone, such as intercepts or trends.

Benefits of visual representation in problem-solving

Using visual representations in problem-solving offers several benefits:

1. Enhances Comprehension:  Visual representations provide a visual context for abstract mathematical concepts, making them easier to understand and grasp.

2. Encourages Critical Thinking:  Visual representations require active engagement and critical thinking skills. Students can enhance their problem-solving and critical thinking abilities by analyzing and interpreting visual data.

3. Promotes Pattern Recognition: Visual representations simplify identifying patterns, trends, and relationships within data or mathematical concepts. It can lead to more efficient problem-solving and a deeper understanding of mathematical principles.

4. Facilitates Communication:  Visual representations can be shared and discussed, helping students communicate their thoughts and ideas effectively. It can be particularly useful in collaborative problem-solving environments.

Incorporating visual representations into math problem-solving can significantly enhance understanding, critical thinking, pattern recognition, and communication skills. Students can approach math problems with a fresh perspective and improve their problem-solving abilities using visual tools.

Work Backwards

Understanding the concept of working backward in math problem-solving.

Working backward is a problem-solving strategy that starts with the solution and returns to the given problem. This approach can be particularly useful in math, as it helps students break down complex problems into smaller, more manageable steps. Here’s how to apply the concept of working backward in math problem-solving:

1. Identify the desired outcome : Start by clearly defining the goal or solution you are trying to reach. It could be finding the value of an unknown variable, determining a specific measurement, or solving for a particular quantity.

2. Visualize the result : Imagine the final step or solution. It will help you create a mental image of the steps needed to reach that outcome.

3. Trace the steps backward : Break down the problem into smaller steps, working backward from the desired outcome. Think about what needs to happen immediately before reaching the final solution and continue tracing the steps back to the beginning of the problem.

4. Check your work : Once you have worked backward to the beginning of the problem, double-check your calculations and steps to ensure accuracy.

Real-life examples and applications of working backward

Working backward is a valuable problem-solving technique in math and has real-life applications. Here are a few examples:

1. Financial planning : When creating a budget, you can work backward by determining your desired savings or spending amount and then calculating how much income or expenses are needed to reach that goal.

2. Project management : When planning a project, you can work backward by setting a fixed deadline and then determining the necessary steps and timelines to complete the project on time.

3. Game strategy : In games like chess or poker, working backward can help you anticipate your opponent’s moves and plan your strategy accordingly.

4. Recipe adjustments : When modifying a recipe, you can work backward by envisioning the final taste or texture you want to achieve and adjusting the ingredients or cooking methods accordingly.

By practicing working backward in math and applying it to real-life situations, you can enhance your problem-solving abilities and find creative solutions to various challenges.

Try Different Strategies

When solving math problems, it’s essential to have a repertoire of problem-solving strategies. You can improve your problem-solving skills and tackle various mathematical challenges by trying different approaches. Here are some strategies to consider:

Exploring Various Problem-Solving Strategies

1. Guess and Check:  This strategy involves making an educated guess and checking if it leads to the correct solution. It can be useful when dealing with trial-and-error problems.

2. Drawing a Diagram:  Visually representing the problem through diagrams or graphs can help you understand and solve it more effectively. This strategy is particularly useful in geometry and algebraic reasoning.

3. Using Logic:  Using logical reasoning is useful for breaking down complicated problems into smaller, more manageable components. This strategy is especially useful in mathematical proofs and logical puzzles.

4. Working Backwards:  Start with the desired outcome and return to the given information. When dealing with equations or word problems, this approach can assist.

5. Using Patterns:  Look for patterns and relationships within the problem to determine a solution. This approach can be used for different mathematical problems, such as sequences and numerical patterns.

When and How to Apply Different Strategies in Math Problem-Solving

Knowing when and how to apply different problem-solving strategies is crucial for success in math. Here are some tips:

• Understand the problem: Read the problem carefully and identify the key information and requirements.
• Select an appropriate strategy: Choose the most appropriate problem-solving strategy for the problem.
• Apply the chosen strategy: Implement the selected strategy, following the necessary steps.
• Check your solution: Verify your answer by double-checking the calculations or applying alternative methods.
• Reflect on the process: After solving the problem, take a moment to reflect and evaluate your problem-solving approach. Identify areas for improvement and consider alternative strategies that could have been used.

By exploring different problem-solving strategies and applying them to various math problems, you can enhance your problem-solving skills and develop a versatile toolkit for tackling mathematical challenges. Practice and persistence are key to honing your problem-solving abilities in math.

Key takeaways and tips for improving problem-solving skills in math

In conclusion, developing strong problem-solving skills in math is crucial for success in this subject. Here are some key takeaways and tips to help you improve your problem-solving abilities:

• Practice regularly:  The more you practice solving math problems, the better you will become at identifying patterns, applying strategies, and finding solutions.
• Break down the problem:  When faced with a complex math problem, break it into smaller, more manageable parts. It will make it easier to understand and solve.
• Understand the problem:  Before diving into a solution, fully understand the problem. Identify what information is given and what you are asked to find.
• Draw diagrams or visualize:  Use visual aids, such as diagrams or sketches, to help you better understand the problem and visualize the solution.
• Use logical reasoning:  Apply logical reasoning skills to analyze the problem and determine the most appropriate approach or strategy.
• Try different strategies:  If one approach doesn’t work, don’t be afraid to try different strategies or methods. There are often multiple ways to solve a math problem.
• Seek help and collaborate:  Don’t hesitate to seek help from your teacher, classmates, or online resources. Collaborating with others can provide different perspectives and insights.
• Learn from mistakes:  Mistakes are a valuable learning opportunity. Analyze your mistakes, understand where you went wrong, and learn from them to avoid making the same errors in the future.
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7 Problem Solving Skills That Aren’t Just Buzzwords (+ Resume Example)

• Julia Mlcuchova , 
• Updated April 8, 2024 9 min read

Problem-solving skills are something everybody should include on their resume, yet only a few seem to understand what these skills actually are. If you've always felt that the term "problem-solving skills" is rather vague and wanted to know more, you've come to the right place.

In this article, we're going to explain what problem-solving skills really mean. We'll talk about what makes up good problem-solving skills and give you tips on how to get better at them. You'll also find out how to make your problem-solving abilities look more impressive to those who might want to hire you.

Sounds good, right? Curious to learn more? 

In this article we’ll show you:

• What are problem solving skills;
• Why are they important; 
• Specific problem solving skills examples;
• How to develop your problem solving skills;
• And, how to showcase them on your resume.

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What are problem solving skills?

Why are problem solving skills important, the best 7 problem solving skills examples, how to develop problem solving skills, problem solving skills resume example, key takeaways: problem solving skills.

First of all, they're more than just a buzzword!

Problem-solving skills are a set of specific abilities that allow you to deal with unexpected situations in the workplace, whether it be job related or team related. 

It's a complex process that involves several “sub skills” or “sub steps,” namely:

• Recognizing and identifying the issue at hand.
• Breaking the problem down into smaller parts and analyzing how they relate to one another. 
• Creating potential solutions to the problem, evaluating them and picking the best one.  
• Applying the chosen solution and assessing its outcome. 
• Learning from the whole process to deal with future problems more effectively. 

As you can see, it's not just about solving problems that are right in front of us, but also about predicting potential issues and being prepared to deal with them before they arise.  

Despite what you may believe, problem-solving skills aren't just for managers . 

Think about it this way: Why do employers hire employees in the first place? To solve problems for them!

And, as we all know, problems don't discriminate. In other words, it doesn't matter whether you're just an intern, an entry-level professional, or a seasoned veteran, you'll constantly face some kind of challenges. And the only difference is in how complex they will get.

This is also reflected in the way employers assess suitability of potential job candidates. 

In fact, research shows that the ability to deal with unexpected complications is prioritized by an overwhelming 60% of employers across all industries, making it one of the most compelling skills on your resume.

So, regardless of your job description or your career level, you're always expected to find solutions for problems, either independently or as a part of a team. 

And that's precisely what makes problem-solving skills so invaluable and universal ! 

Wondering how good is your resume?

Find out with our AI Resume Checker! Just upload your resume and see what can be improved.

As we've said before, problem-solving isn't really just one single skill. 

Instead, your ability to handle workplace issues with composure depends on several different “sub-skills”. 

So, which specific skills make an employee desirable even for the most demanding of recruiters? 

In no particular order, you should focus on these 7 skills : 

• Analytical skills
• Research skills
• Critical thinking 
• Decision-making
• Collaboration
• Having a growth mindset

Let's have a look at each of them in greater detail!

#1 Analytical skills

Firstly, to truly understand complex problems, you need to break them down into more manageable parts . Then, you observe them closely and ask yourself: “ Which parts work and which don't,” How do these parts contribute to the problem as a whole,” and "What exactly needs to be fixed?” In other words, you gather data , you study it, and compare it - all to pinpoint the cause of the issue as closely as possible.

#2 Research skills

Another priceless tool is your research skills (sometimes relying on just one source of information isn't enough). Besides, to make a truly informed decision , you'll have to dig a little deeper. Being a good researcher means looking for potential solutions to a problem in a wider context. For example: going through team reports, customer feedback, quarterly sales or current market trends.  

#3 Critical thinking

Every employer wants to hire people who can think critically. Yet, the ability to evaluate situations objectively and from different perspectives , is actually pretty hard to come by. But as long as you stay open-minded, inquisitive, and with a healthy dose of skepticism, you'll be able to assess situations based on facts and evidence more successfully. Plus, critical thinking comes in especially handy when you need to examine your own actions and processes. 

 #4 Creativity

Instead of following the old established processes that don't work anymore, you should feel comfortable thinking outside the box. The thing is, problems have a nasty habit of popping up unexpectedly and rapidly. And sometimes, you have to get creative in order to solve them fast. Especially those that have no precedence. But this requires a blend of intuition, industry knowledge, and quick thinking - a truly rare combination. 

#5 Decision-making

The analysis, research, and brainstorming are done. Now, you need to look at the possible solutions, and make the final decision (informed, of course). And not only that, you also have to stand by it ! Because once the train gets moving, there's no room for second guessing. Also, keep in mind that you need to be prepared to take responsibility for all decisions you make. That's no small feat! 

#6 Collaboration

Not every problem you encounter can be solved by yourself alone. And this is especially true when it comes to complex projects. So, being able to actively listen to your colleagues, take their ideas into account, and being respectful of their opinions enables you to solve problems together. Because every individual can offer a unique perspective and skill set. Yes, democracy is hard, but at the end of the day, it's teamwork that makes the corporate world go round. 

#7 Having a growth mindset

Let's be honest, no one wants their work to be riddled with problems. But facing constant challenges and changes is inevitable. And that can be scary! However, when you're able to see these situations as opportunities to grow instead of issues that hold you back, your problem solving skills reach new heights. And the employers know that too!

Now that we've shown you the value problem-solving skills can add to your resume, let's ask the all-important question: “How can I learn them?”

Well…you can't. At least not in the traditional sense of the word. 

Let us explain: Since problem-solving skills fall under the umbrella of soft skills , they can't be taught through formal education, unlike computer skills for example. There's no university course that you can take and graduate as a professional problem solver. 

But, just like other interpersonal skills, they can be nurtured and refined over time through practice and experience. 

Unfortunately, there's no one-size-fits-all approach, but the following tips can offer you inspiration on how to improve your problem solving skills:

• Cultivate a growth mindset. Remember what we've said before? Your attitude towards obstacles is the first step to unlocking your problem-solving potential. 
• Gain further knowledge in your specialized field. Secondly, it's a good idea to delve a little deeper into your chosen profession. Because the more you read on a subject, the easier it becomes to spot certain patterns and relations.  
• Start with small steps. Don't attack the big questions straight away — you'll only set yourself up for failure. Instead, start with more straightforward tasks and work your way up to more complex problems. 
• Break problems down into more digestible pieces. Complex issues are made up of smaller problems. And those can be further divided into even smaller problems, and so on. Until you're left with only the basics. 
• Don't settle for a single solution. Instead, keep on exploring other possible answers.
• Accept failure as a part of the learning process. Finally, don't let your failures discourage you. After all, you're bound to misstep a couple of times before you find your footing. Just keep on practicing. 

How to improve problem solving skills with online courses

While it’s true that formal education won’t turn you into a master problem solver, you can still hone your skills with courses and certifications offered by online learning platforms :

• Analytical skills. You can sharpen your analytical skills with Data Analytics Basics for Everyone from IBM provided by edX (Free); or Decision Making and Analytical Thinking: Fortune 500 provided by Udemy (＄21,74).
• Creativity. And, to unlock your inner creative mind, you can try Creative Thinking: Techniques and Tools for Success from the Imperial College London provided by Coursera (Free).
• Critical thinking. Try Introduction to Logic and Critical Thinking Specialization from Duke University provided by Coursera (Free); or Logical and Critical Thinking offered by The University of Auckland via FutureLearn.  
• Decision-making. Or, you can learn how to become more confident when it's time to make a decision with Decision-Making Strategies and Executive Decision-Making both offered by LinkedIn Learning (1 month free trial).
• Communication skills . Lastly, to improve your collaborative skills, check out Communicating for Influence and Impact online at University of Cambridge. 

The fact that everybody and their grandmothers put “ problem-solving skills ” on their CVs has turned the phrase into a cliche. 

But there's a way to incorporate these skills into your resume without sounding pretentious and empty. Below, we've prepared a mock-up resume that manages to do just that.

FYI, if you like this design, you can use the template to create your very own resume. Just click the red button and fill in your information (or let the AI do it for you).

Problem solving skills on resume example

This resume was written by our experienced resume writers specifically for this profession.

Why this example works?

• Firstly, the job description itself is neatly organized into bullet points .  
• Instead of simply listing soft skills in a skills section , you can incorporate them into the description of your work experience entry.  
• Also, the language here isn't vague . This resume puts each problem-solving skill into a real-life context by detailing specific situations and obstacles. 
• And, to highlight the impact of each skill on your previous job position, we recommend quantifying your results whenever possible. 
• Finally, starting each bullet point with an action verb (in bold) makes you look more dynamic and proactive.

To sum it all up, problem-solving skills continue gaining popularity among employers and employees alike. And for a good reason!

Because of them, you can overcome any obstacles that stand in the way of your professional life more efficiently and systematically. 

In essence, problem-solving skills refer to the ability to recognize a challenge, identify its root cause, think of possible solutions , and then implement the most effective one. 

Believing that these skills are all the same would be a serious misconception. In reality, this term encompasses a variety of different abilities , including:

In short, understanding, developing, and showcasing these skills, can greatly boost your chances at getting noticed by the hiring managers. So, don't hesitate and start working on your problem-solving skills right now!

Julia has recently joined Kickresume as a career writer. From helping people with their English to get admitted to the uni of their dreams to advising them on how to succeed in the job market. It would seem that her career is on a steadfast trajectory. Julia holds a degree in Anglophone studies from Metropolitan University in Prague, where she also resides. Apart from creative writing and languages, she takes a keen interest in literature and theatre.

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Barking Orders

David Kahn makes progress step by step.

By Sam Corbin

Jump to: Today’s Theme | Tricky Clues

MONDAY PUZZLE — Lewis Carroll is said to have popularized the word ladder puzzle, in which the solver is tasked with transforming a four-letter word into another by changing its letters one at a time. The number of “rungs” on the ladder depends entirely on the two words selected. The game has also had other names, including “doublets” and “word-links.” I might have called it “The quip of Theseus.” ( Sorry ).

An impressive word ladder appears in today’s crossword, which was constructed by David Kahn. Traveling from one end of the puzzle to the other reveals a meaningful message. Mr. Kahn, it should be noted, is nearing the top of another ladder, as he inches toward his 200th puzzle for The New York Times. Phew. What’s my excuse?

Today’s Theme

The eight-step ladder in Mr. Kahn’s puzzle begins with a “Nonrenewable energy source”: COAL (1A). From there, we travel through a couple of unremarkable words in the theme set — COOL (21A) and WOOL (30A) — and pause briefly on two energy sources, WOOD (35A) and FOOD (39A). The production of each of these, we learn, contributes to a certain “symptom of climate change” at 36-Across. This entry may be obvious to most solvers since the term is often used interchangeably in discussions about climate change: GLOBAL WARMING.

But Mr. Kahn isn’t finished. After trading FOOD’s letters to get FOND (42A) and then FIND (52A), we land on a final “Renewable energy source” that completes the ladder: WIND. And I got that renewable energy source knocked right out of me as I felt the significance of the completed theme.

It also seems apt to have “Goes extinct” (49A) as a clue in today’s puzzle after a Sunday crossword by John Rippe and Jeff Chen that tackled this very subject, and which Caitlin Lovinger cited as the first instance in recent memory of being so “emotionally moved by a theme.”

Tricky Clues

18A. “Sustainably produced electricity” falls into a subcategory of renewable energy and is referred to as GREEN POWER.

58A. It seems odd to have such an endless supply of words to describe, well, nothing. “Diddly-squat” means NADA. Other terms that mean nothing — which is distinct from not meaning anything, mind you — include zero, nil, zilch and zippo.

62A. “Barking orders, say” evokes the idea of marching orders, which makes it hard to discern that this clue hints at an adjective as opposed to a plural noun. It also had me picturing dogs in military formation. The correct answer is BOSSY.

8D. A “Work of fiction?” is no book, but a simple LIE. Then again, isn’t any novel just a long and convincingly recounted lie?

24D. If a three-legged stand is a tripod, then it follows that a “Two-legged stand” is a BIPOD — though it shouldn’t be confused with a creature that stands on two legs, which is a biped .

33D. Even though clues must match tense with their entries, they can take different verb forms. The entry for “Talked incessantly,” for instance, is RAN ON, as opposed to a single word ending in -ed.

42D. “Done, in Dijon” wants an answer in French: FINI. (“The end” in Dijon is just “fin.”)

Constructor Notes

The subject of climate change is pretty serious, so I was trying to say something about it in a fun way. At first, I was going to have seven steps in the word ladder (COAL, cool, fool, FOOD, FOND, FIND, WIND). But by changing “fool” to WOOL and adding WOOD, I was able to add more theme content and put GLOBAL WARMING in the middle of the grid while keeping the theme symmetrical.

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Sam Corbin writes about language, wordplay and the daily crossword for The Times. More about Sam Corbin

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