easy problem solving examples

39 Best Problem-Solving Examples

Problem-solving is a process where you’re tasked with identifying an issue and coming up with the most practical and effective solution.

This indispensable skill is necessary in several aspects of life, from personal relationships to education to business decisions.

Problem-solving aptitude boosts rational thinking, creativity, and the ability to cooperate with others. It’s also considered essential in 21st Century workplaces.

If explaining your problem-solving skills in an interview, remember that the employer is trying to determine your ability to handle difficulties. Focus on explaining exactly how you solve problems, including by introducing your thoughts on some of the following frameworks and how you’ve applied them in the past.

Problem-Solving Examples

1. divergent thinking.

Divergent thinking refers to the process of coming up with multiple different answers to a single problem. It’s the opposite of convergent thinking, which would involve coming up with a singular answer .

The benefit of a divergent thinking approach is that it can help us achieve blue skies thinking – it lets us generate several possible solutions that we can then critique and analyze .

In the realm of problem-solving, divergent thinking acts as the initial spark. You’re working to create an array of potential solutions, even those that seem outwardly unrelated or unconventional, to get your brain turning and unlock out-of-the-box ideas.

This process paves the way for the decision-making stage, where the most promising ideas are selected and refined.

Go Deeper: Divervent Thinking Examples

2. Convergent Thinking

Next comes convergent thinking, the process of narrowing down multiple possibilities to arrive at a single solution.

This involves using your analytical skills to identify the best, most practical, or most economical solution from the pool of ideas that you generated in the divergent thinking stage.

In a way, convergent thinking shapes the “roadmap” to solve a problem after divergent thinking has supplied the “destinations.”

Have a think about which of these problem-solving skills you’re more adept at: divergent or convergent thinking?

Go Deeper: Convergent Thinking Examples

3. Brainstorming

Brainstorming is a group activity designed to generate a multitude of ideas regarding a specific problem. It’s divergent thinking as a group , which helps unlock even more possibilities.

A typical brainstorming session involves uninhibited and spontaneous ideation, encouraging participants to voice any possible solutions, no matter how unconventional they might appear.

It’s important in a brainstorming session to suspend judgment and be as inclusive as possible, allowing all participants to get involved.

By widening the scope of potential solutions, brainstorming allows better problem definition, more creative solutions, and helps to avoid thinking “traps” that might limit your perspective.

Go Deeper: Brainstorming Examples

4. Thinking Outside the Box

The concept of “thinking outside the box” encourages a shift in perspective, urging you to approach problems from an entirely new angle.

Rather than sticking to traditional methods and processes, it involves breaking away from conventional norms to cultivate unique solutions.

In problem-solving, this mindset can bypass established hurdles and bring you to fresh ideas that might otherwise remain undiscovered.

Think of it as going off the beaten track when regular routes present roadblocks to effective resolution.

5. Case Study Analysis

Analyzing case studies involves a detailed examination of real-life situations that bear relevance to the current problem at hand.

For example, if you’re facing a problem, you could go to another environment that has faced a similar problem and examine how they solved it. You’d then bring the insights from that case study back to your own problem.

This approach provides a practical backdrop against which theories and assumptions can be tested, offering valuable insights into how similar problems have been approached and resolved in the past.

See a Broader Range of Analysis Examples Here

6. Action Research

Action research involves a repetitive process of identifying a problem, formulating a plan to address it, implementing the plan, and then analyzing the results. It’s common in educational research contexts.

The objective is to promote continuous learning and improvement through reflection and action. You conduct research into your problem, attempt to apply a solution, then assess how well the solution worked. This becomes an iterative process of continual improvement over time.

For problem-solving, this method offers a way to test solutions in real-time and allows for changes and refinements along the way, based on feedback or observed outcomes. It’s a form of active problem-solving that integrates lessons learned into the next cycle of action.

Go Deeper: Action Research Examples

7. Information Gathering

Fundamental to solving any problem is the process of information gathering.

This involves collecting relevant data , facts, and details about the issue at hand, significantly aiding in the understanding and conceptualization of the problem.

In problem-solving, information gathering underpins every decision you make.

This process ensures your actions are based on concrete information and evidence, allowing for an informed approach to tackle the problem effectively.

8. Seeking Advice

Seeking advice implies turning to knowledgeable and experienced individuals or entities to gain insights on problem-solving.

It could include mentors, industry experts, peers, or even specialized literature.

The value in this process lies in leveraging different perspectives and proven strategies when dealing with a problem. Moreover, it aids you in avoiding pitfalls, saving time, and learning from others’ experiences.

9. Creative Thinking

Creative thinking refers to the ability to perceive a problem in a new way, identify unconventional patterns, or produce original solutions.

It encourages innovation and uniqueness, often leading to the most effective results.

When applied to problem-solving, creative thinking can help you break free from traditional constraints, ideal for potentially complex or unusual problems.

Go Deeper: Creative Thinking Examples

10. Conflict Resolution

Conflict resolution is a strategy developed to resolve disagreements and arguments, often involving communication, negotiation, and compromise.

When employed as a problem-solving technique, it can diffuse tension, clear bottlenecks, and create a collaborative environment.

Effective conflict resolution ensures that differing views or disagreements do not become roadblocks in the process of problem-solving.

Go Deeper: Conflict Resolution Examples

11. Addressing Bottlenecks

Bottlenecks refer to obstacles or hindrances that slow down or even halt a process.

In problem-solving, addressing bottlenecks involves identifying these impediments and finding ways to eliminate them.

This effort not only smooths the path to resolution but also enhances the overall efficiency of the problem-solving process.

For example, if your workflow is not working well, you’d go to the bottleneck – that one point that is most time consuming – and focus on that. Once you ‘break’ this bottleneck, the entire process will run more smoothly.

12. Market Research

Market research involves gathering and analyzing information about target markets, consumers, and competitors.

In sales and marketing, this is one of the most effective problem-solving methods. The research collected from your market (e.g. from consumer surveys) generates data that can help identify market trends, customer preferences, and competitor strategies.

In this sense, it allows a company to make informed decisions, solve existing problems, and even predict and prevent future ones.

13. Root Cause Analysis

Root cause analysis is a method used to identify the origin or the fundamental reason for a problem.

Once the root cause is determined, you can implement corrective actions to prevent the problem from recurring.

As a problem-solving procedure, root cause analysis helps you to tackle the problem at its source, rather than dealing with its surface symptoms.

Go Deeper: Root Cause Analysis Examples

14. Mind Mapping

Mind mapping is a visual tool used to structure information, helping you better analyze, comprehend and generate new ideas.

By laying out your thoughts visually, it can lead you to solutions that might not have been apparent with linear thinking.

In problem-solving, mind mapping helps in organizing ideas and identifying connections between them, providing a holistic view of the situation and potential solutions.

15. Trial and Error

The trial and error method involves attempting various solutions until you find one that resolves the problem.

It’s an empirical technique that relies on practical actions instead of theories or rules.

In the context of problem-solving, trial and error allows you the flexibility to test different strategies in real situations, gaining insights about what works and what doesn’t.

16. SWOT Analysis

SWOT is an acronym standing for Strengths, Weaknesses, Opportunities, and Threats.

It’s an analytic framework used to evaluate these aspects in relation to a particular objective or problem.

In problem-solving, SWOT Analysis helps you to identify favorable and unfavorable internal and external factors. It helps to craft strategies that make best use of your strengths and opportunities, whilst addressing weaknesses and threats.

Go Deeper: SWOT Analysis Examples

17. Scenario Planning

Scenario planning is a strategic planning method used to make flexible long-term plans.

It involves imagining, and then planning for, multiple likely future scenarios.

By forecasting various directions a problem could take, scenario planning helps manage uncertainty and is an effective tool for problem-solving in volatile conditions.

18. Six Thinking Hats

The Six Thinking Hats is a concept devised by Edward de Bono that proposes six different directions or modes of thinking, symbolized by six different hat colors.

Each hat signifies a different perspective, encouraging you to switch ‘thinking modes’ as you switch hats. This method can help remove bias and broaden perspectives when dealing with a problem.

19. Decision Matrix Analysis

Decision Matrix Analysis is a technique that allows you to weigh different factors when faced with several possible solutions.

After listing down the options and determining the factors of importance, each option is scored based on each factor.

Revealing a clear winner that both serves your objectives and reflects your values, Decision Matrix Analysis grounds your problem-solving process in objectivity and comprehensiveness.

20. Pareto Analysis

Also known as the 80/20 rule, Pareto Analysis is a decision-making technique.

It’s based on the principle that 80% of problems are typically caused by 20% of the causes, making it a handy tool for identifying the most significant issues in a situation.

Using this analysis, you’re likely to direct your problem-solving efforts more effectively, tackling the root causes producing most of the problem’s impact.

21. Critical Thinking

Critical thinking refers to the ability to analyze facts to form a judgment objectively.

It involves logical, disciplined thinking that is clear, rational, open-minded, and informed by evidence.

For problem-solving, critical thinking helps evaluate options and decide the most effective solution. It ensures your decisions are grounded in reason and facts, and not biased or irrational assumptions.

Go Deeper: Critical Thinking Examples

22. Hypothesis Testing

Hypothesis testing usually involves formulating a claim, testing it against actual data, and deciding whether to accept or reject the claim based on the results.

In problem-solving, hypotheses often represent potential solutions. Hypothesis testing provides verification, giving a statistical basis for decision-making and problem resolution.

Usually, this will require research methods and a scientific approach to see whether the hypothesis stands up or not.

Go Deeper: Types of Hypothesis Testing

23. Cost-Benefit Analysis

A cost-benefit analysis (CBA) is a systematic process of weighing the pros and cons of different solutions in terms of their potential costs and benefits.

It allows you to measure the positive effects against the negatives and informs your problem-solving strategy.

By using CBA, you can identify which solution offers the greatest benefit for the least cost, significantly improving efficacy and efficiency in your problem-solving process.

Go Deeper: Cost-Benefit Analysis Examples

24. Simulation and Modeling

Simulations and models allow you to create a simplified replica of real-world systems to test outcomes under controlled conditions.

In problem-solving, you can broadly understand potential repercussions of different solutions before implementation.

It offers a cost-effective way to predict the impacts of your decisions, minimizing potential risks associated with various solutions.

25. Delphi Method

The Delphi Method is a structured communication technique used to gather expert opinions.

The method involves a group of experts who respond to questionnaires about a problem. The responses are aggregated and shared with the group, and the process repeats until a consensus is reached.

This method of problem solving can provide a diverse range of insights and solutions, shaped by the wisdom of a collective expert group.

26. Cross-functional Team Collaboration

Cross-functional team collaboration involves individuals from different departments or areas of expertise coming together to solve a common problem or achieve a shared goal.

When you bring diverse skills, knowledge, and perspectives to a problem, it can lead to a more comprehensive and innovative solution.

In problem-solving, this promotes communal thinking and ensures that solutions are inclusive and holistic, with various aspects of the problem being addressed.

27. Benchmarking

Benchmarking involves comparing one’s business processes and performance metrics to the best practices from other companies or industries.

In problem-solving, it allows you to identify gaps in your own processes, determine how others have solved similar problems, and apply those solutions that have proven to be successful.

It also allows you to compare yourself to the best (the benchmark) and assess where you’re not as good.

28. Pros-Cons Lists

A pro-con analysis aids in problem-solving by weighing the advantages (pros) and disadvantages (cons) of various possible solutions.

This simple but powerful tool helps in making a balanced, informed decision.

When confronted with a problem, a pro-con analysis can guide you through the decision-making process, ensuring all possible outcomes and implications are scrutinized before arriving at the optimal solution. Thus, it helps to make the problem-solving process both methodical and comprehensive.

29. 5 Whys Analysis

The 5 Whys Analysis involves repeatedly asking the question ‘why’ (around five times) to peel away the layers of an issue and discover the root cause of a problem.

As a problem-solving technique, it enables you to delve into details that you might otherwise overlook and offers a simple, yet powerful, approach to uncover the origin of a problem.

For example, if your task is to find out why a product isn’t selling your first answer might be: “because customers don’t want it”, then you ask why again – “they don’t want it because it doesn’t solve their problem”, then why again – “because the product is missing a certain feature” … and so on, until you get to the root “why”.

30. Gap Analysis

Gap analysis entails comparing current performance with potential or desired performance.

You’re identifying the ‘gaps’, or the differences, between where you are and where you want to be.

In terms of problem-solving, a Gap Analysis can help identify key areas for improvement and design a roadmap of how to get from the current state to the desired one.

31. Design Thinking

Design thinking is a problem-solving approach that involves empathy, experimentation, and iteration.

The process focuses on understanding user needs, challenging assumptions , and redefining problems from a user-centric perspective.

In problem-solving, design thinking uncovers innovative solutions that may not have been initially apparent and ensures the solution is tailored to the needs of those affected by the issue.

32. Analogical Thinking

Analogical thinking involves the transfer of information from a particular subject (the analogue or source) to another particular subject (the target).

In problem-solving, you’re drawing parallels between similar situations and applying the problem-solving techniques used in one situation to the other.

Thus, it allows you to apply proven strategies to new, but related problems.

33. Lateral Thinking

Lateral thinking requires looking at a situation or problem from a unique, sometimes abstract, often non-sequential viewpoint.

Unlike traditional logical thinking methods, lateral thinking encourages you to employ creative and out-of-the-box techniques.

In solving problems, this type of thinking boosts ingenuity and drives innovation, often leading to novel and effective solutions.

Go Deeper: Lateral Thinking Examples

34. Flowcharting

Flowcharting is the process of visually mapping a process or procedure.

This form of diagram can show every step of a system, process, or workflow, enabling an easy tracking of the progress.

As a problem-solving tool, flowcharts help identify bottlenecks or inefficiencies in a process, guiding improved strategies and providing clarity on task ownership and process outcomes.

35. Multivoting

Multivoting, or N/3 voting, is a method where participants reduce a large list of ideas to a prioritized shortlist by casting multiple votes.

This voting system elevates the most preferred options for further consideration and decision-making.

As a problem-solving technique, multivoting allows a group to narrow options and focus on the most promising solutions, ensuring more effective and democratic decision-making.

36. Force Field Analysis

Force Field Analysis is a decision-making technique that identifies the forces for and against change when contemplating a decision.

The ‘forces’ represent the differing factors that can drive or hinder change.

In problem-solving, Force Field Analysis allows you to understand the entirety of the context, favoring a balanced view over a one-sided perspective. A comprehensive view of all the forces at play can lead to better-informed problem-solving decisions.

TRIZ, which stands for “The Theory of Inventive Problem Solving,” is a problem-solving, analysis, and forecasting methodology.

It focuses on finding contradictions inherent in a scenario. Then, you work toward eliminating the contraditions through finding innovative solutions.

So, when you’re tackling a problem, TRIZ provides a disciplined, systematic approach that aims for ideal solutions and not just acceptable ones. Using TRIZ, you can leverage patterns of problem-solving that have proven effective in different cases, pivoting them to solve the problem at hand.

38. A3 Problem Solving

A3 Problem Solving, derived from Lean Management, is a structured method that uses a single sheet of A3-sized paper to document knowledge from a problem-solving process.

Named after the international paper size standard of A3 (or 11-inch by 17-inch paper), it succinctly records all key details of the problem-solving process from problem description to the root cause and corrective actions.

Used in problem-solving, this provides a straightforward and logical structure for addressing the problem, facilitating communication between team members, ensuring all critical details are included, and providing a record of decisions made.

39. Scenario Analysis

Scenario Analysis is all about predicting different possible future events depending upon your decision.

To do this, you look at each course of action and try to identify the most likely outcomes or scenarios down the track if you take that course of action.

This technique helps forecast the impacts of various strategies, playing each out to their (logical or potential) end. It’s a good strategy for project managers who need to keep a firm eye on the horizon at all times.

When solving problems, Scenario Analysis assists in preparing for uncertainties, making sure your solution remains viable, regardless of changes in circumstances.

How to Answer “Demonstrate Problem-Solving Skills” in an Interview

When asked to demonstrate your problem-solving skills in an interview, the STAR method often proves useful. STAR stands for Situation, Task, Action, and Result.

Situation: Begin by describing a specific circumstance or challenge you encountered. Make sure to provide enough detail to allow the interviewer a clear understanding. You should select an event that adequately showcases your problem-solving abilities.

For instance, “In my previous role as a project manager, we faced a significant issue when our key supplier abruptly went out of business.”

Task: Explain what your responsibilities were in that situation. This serves to provide context, allowing the interviewer to understand your role and the expectations placed upon you.

For instance, “It was my task to ensure the project remained on track despite this setback. Alternative suppliers needed to be found without sacrificing quality or significantly increasing costs.”

Action: Describe the steps you took to manage the problem. Highlight your problem-solving process. Mention any creative approaches or techniques that you used.

For instance, “I conducted thorough research to identify potential new suppliers. After creating a shortlist, I initiated contact, negotiated terms, assessed samples for quality and made a selection. I also worked closely with the team to re-adjust the project timeline.”

Result: Share the outcomes of your actions. How did the situation end? Did your actions lead to success? It’s particularly effective if you can quantify these results.

For instance, “As a result of my active problem solving, we were able to secure a new supplier whose costs were actually 10% cheaper and whose quality was comparable. We adjusted the project plan and managed to complete the project just two weeks later than originally planned, despite the major vendor setback.”

Remember, when you’re explaining your problem-solving skills to an interviewer, what they’re really interested in is your approach to handling difficulties, your creativity and persistence in seeking a resolution, and your ability to carry your solution through to fruition. Tailoring your story to highlight these aspects will help exemplify your problem-solving prowess.

Go Deeper: STAR Interview Method Examples

Benefits of Problem-Solving

Problem-solving is beneficial for the following reasons (among others):

• It can help you to overcome challenges, roadblocks, and bottlenecks in your life.
• It can save a company money.
• It can help you to achieve clarity in your thinking.
• It can make procedures more efficient and save time.
• It can strengthen your decision-making capacities.
• It can lead to better risk management.

Whether for a job interview or school, problem-solving helps you to become a better thinking, solve your problems more effectively, and achieve your goals. Build up your problem-solving frameworks (I presented over 40 in this piece for you!) and work on applying them in real-life situations.

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 5 Top Tips for Succeeding at University
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 50 Durable Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 100 Consumer Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 30 Globalization Pros and Cons

Leave a Comment Cancel Reply

Your email address will not be published. Required fields are marked *

• Prodigy Math
• Prodigy English

From our blog

• Is a Premium Membership Worth It?
• Promote a Growth Mindset
• Help Your Child Who's Struggling with Math
• Parent's Guide to Prodigy
• Assessments
• Math Curriculum Coverage
• English Curriculum Coverage
• Game Portal

120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

Hey teachers! 👋

Use Prodigy to spark a love for math in your students – including when solving word problems!

• Teaching Tools
• Subtraction
• Multiplication
• Mixed operations
• Ordering and number sense
• Comparing and sequencing
• Physical measurement
• Ratios and percentages
• Probability and data relationships

You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

120 Math word problems, categorized by skill

Addition word problems.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

Practice math word problems with Prodigy Math

Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

Multiplication word problems

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

Mixed operations word problems

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

Variables word problems

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

How to easily make your own math word problems & word problems worksheets

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

• Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
• Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
• Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
• Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem.
• Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
• Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
• Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

35 problem-solving techniques and methods for solving complex problems

Design your next session with SessionLab

Join the 150,000+ facilitators 
using SessionLab.

Recommended Articles

A step-by-step guide to planning a workshop, how to create an unforgettable training session in 8 simple steps, 47 useful online tools for workshop planning and meeting facilitation.

All teams and organizations encounter challenges as they grow. There are problems that might occur for teams when it comes to miscommunication or resolving business-critical issues . You may face challenges around growth , design , user engagement, and even team culture and happiness. In short, problem-solving techniques should be part of every team’s skillset.

Problem-solving methods are primarily designed to help a group or team through a process of first identifying problems and challenges , ideating possible solutions , and then evaluating the most suitable .

Finding effective solutions to complex problems isn’t easy, but by using the right process and techniques, you can help your team be more efficient in the process.

So how do you develop strategies that are engaging, and empower your team to solve problems effectively?

In this blog post, we share a series of problem-solving tools you can use in your next workshop or team meeting. You’ll also find some tips for facilitating the process and how to enable others to solve complex problems.

Let’s get started! 

How do you identify problems?

How do you identify the right solution.

• Tips for more effective problem-solving

Complete problem-solving methods

• Problem-solving techniques to identify and analyze problems
• Problem-solving techniques for developing solutions

Problem-solving warm-up activities

Closing activities for a problem-solving process.

Before you can move towards finding the right solution for a given problem, you first need to identify and define the problem you wish to solve. 

Here, you want to clearly articulate what the problem is and allow your group to do the same. Remember that everyone in a group is likely to have differing perspectives and alignment is necessary in order to help the group move forward. 

Identifying a problem accurately also requires that all members of a group are able to contribute their views in an open and safe manner. It can be scary for people to stand up and contribute, especially if the problems or challenges are emotive or personal in nature. Be sure to try and create a psychologically safe space for these kinds of discussions.

Remember that problem analysis and further discussion are also important. Not taking the time to fully analyze and discuss a challenge can result in the development of solutions that are not fit for purpose or do not address the underlying issue.

Successfully identifying and then analyzing a problem means facilitating a group through activities designed to help them clearly and honestly articulate their thoughts and produce usable insight.

With this data, you might then produce a problem statement that clearly describes the problem you wish to be addressed and also state the goal of any process you undertake to tackle this issue.  

Finding solutions is the end goal of any process. Complex organizational challenges can only be solved with an appropriate solution but discovering them requires using the right problem-solving tool.

After you’ve explored a problem and discussed ideas, you need to help a team discuss and choose the right solution. Consensus tools and methods such as those below help a group explore possible solutions before then voting for the best. They’re a great way to tap into the collective intelligence of the group for great results!

Remember that the process is often iterative. Great problem solvers often roadtest a viable solution in a measured way to see what works too. While you might not get the right solution on your first try, the methods below help teams land on the most likely to succeed solution while also holding space for improvement.

Every effective problem solving process begins with an agenda . A well-structured workshop is one of the best methods for successfully guiding a group from exploring a problem to implementing a solution.

In SessionLab, it’s easy to go from an idea to a complete agenda . Start by dragging and dropping your core problem solving activities into place . Add timings, breaks and necessary materials before sharing your agenda with your colleagues.

The resulting agenda will be your guide to an effective and productive problem solving session that will also help you stay organized on the day!

Tips for more effective problem solving

Problem-solving activities are only one part of the puzzle. While a great method can help unlock your team’s ability to solve problems, without a thoughtful approach and strong facilitation the solutions may not be fit for purpose.

Let’s take a look at some problem-solving tips you can apply to any process to help it be a success!

Clearly define the problem

Jumping straight to solutions can be tempting, though without first clearly articulating a problem, the solution might not be the right one. Many of the problem-solving activities below include sections where the problem is explored and clearly defined before moving on.

This is a vital part of the problem-solving process and taking the time to fully define an issue can save time and effort later. A clear definition helps identify irrelevant information and it also ensures that your team sets off on the right track.

Don’t jump to conclusions

It’s easy for groups to exhibit cognitive bias or have preconceived ideas about both problems and potential solutions. Be sure to back up any problem statements or potential solutions with facts, research, and adequate forethought.

The best techniques ask participants to be methodical and challenge preconceived notions. Make sure you give the group enough time and space to collect relevant information and consider the problem in a new way. By approaching the process with a clear, rational mindset, you’ll often find that better solutions are more forthcoming.  

Try different approaches  

Problems come in all shapes and sizes and so too should the methods you use to solve them. If you find that one approach isn’t yielding results and your team isn’t finding different solutions, try mixing it up. You’ll be surprised at how using a new creative activity can unblock your team and generate great solutions.

Don’t take it personally 

Depending on the nature of your team or organizational problems, it’s easy for conversations to get heated. While it’s good for participants to be engaged in the discussions, ensure that emotions don’t run too high and that blame isn’t thrown around while finding solutions.

You’re all in it together, and even if your team or area is seeing problems, that isn’t necessarily a disparagement of you personally. Using facilitation skills to manage group dynamics is one effective method of helping conversations be more constructive.

Get the right people in the room

Your problem-solving method is often only as effective as the group using it. Getting the right people on the job and managing the number of people present is important too!

If the group is too small, you may not get enough different perspectives to effectively solve a problem. If the group is too large, you can go round and round during the ideation stages.

Creating the right group makeup is also important in ensuring you have the necessary expertise and skillset to both identify and follow up on potential solutions. Carefully consider who to include at each stage to help ensure your problem-solving method is followed and positioned for success.

Document everything

The best solutions can take refinement, iteration, and reflection to come out. Get into a habit of documenting your process in order to keep all the learnings from the session and to allow ideas to mature and develop. Many of the methods below involve the creation of documents or shared resources. Be sure to keep and share these so everyone can benefit from the work done!

Bring a facilitator 

Facilitation is all about making group processes easier. With a subject as potentially emotive and important as problem-solving, having an impartial third party in the form of a facilitator can make all the difference in finding great solutions and keeping the process moving. Consider bringing a facilitator to your problem-solving session to get better results and generate meaningful solutions!

Develop your problem-solving skills

It takes time and practice to be an effective problem solver. While some roles or participants might more naturally gravitate towards problem-solving, it can take development and planning to help everyone create better solutions.

You might develop a training program, run a problem-solving workshop or simply ask your team to practice using the techniques below. Check out our post on problem-solving skills to see how you and your group can develop the right mental process and be more resilient to issues too!

Design a great agenda

Workshops are a great format for solving problems. With the right approach, you can focus a group and help them find the solutions to their own problems. But designing a process can be time-consuming and finding the right activities can be difficult.

Check out our workshop planning guide to level-up your agenda design and start running more effective workshops. Need inspiration? Check out templates designed by expert facilitators to help you kickstart your process!

In this section, we’ll look at in-depth problem-solving methods that provide a complete end-to-end process for developing effective solutions. These will help guide your team from the discovery and definition of a problem through to delivering the right solution.

If you’re looking for an all-encompassing method or problem-solving model, these processes are a great place to start. They’ll ask your team to challenge preconceived ideas and adopt a mindset for solving problems more effectively.

• Six Thinking Hats
• Lightning Decision Jam
• Problem Definition Process
• Discovery & Action Dialogue

Design Sprint 2.0

• Open Space Technology

1. Six Thinking Hats

Individual approaches to solving a problem can be very different based on what team or role an individual holds. It can be easy for existing biases or perspectives to find their way into the mix, or for internal politics to direct a conversation.

Six Thinking Hats is a classic method for identifying the problems that need to be solved and enables your team to consider them from different angles, whether that is by focusing on facts and data, creative solutions, or by considering why a particular solution might not work.

Like all problem-solving frameworks, Six Thinking Hats is effective at helping teams remove roadblocks from a conversation or discussion and come to terms with all the aspects necessary to solve complex problems.

2. Lightning Decision Jam

Featured courtesy of Jonathan Courtney of AJ&Smart Berlin, Lightning Decision Jam is one of those strategies that should be in every facilitation toolbox. Exploring problems and finding solutions is often creative in nature, though as with any creative process, there is the potential to lose focus and get lost.

Unstructured discussions might get you there in the end, but it’s much more effective to use a method that creates a clear process and team focus.

In Lightning Decision Jam, participants are invited to begin by writing challenges, concerns, or mistakes on post-its without discussing them before then being invited by the moderator to present them to the group.

From there, the team vote on which problems to solve and are guided through steps that will allow them to reframe those problems, create solutions and then decide what to execute on. 

By deciding the problems that need to be solved as a team before moving on, this group process is great for ensuring the whole team is aligned and can take ownership over the next stages. 

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

3. Problem Definition Process

While problems can be complex, the problem-solving methods you use to identify and solve those problems can often be simple in design. 

By taking the time to truly identify and define a problem before asking the group to reframe the challenge as an opportunity, this method is a great way to enable change.

Begin by identifying a focus question and exploring the ways in which it manifests before splitting into five teams who will each consider the problem using a different method: escape, reversal, exaggeration, distortion or wishful. Teams develop a problem objective and create ideas in line with their method before then feeding them back to the group.

This method is great for enabling in-depth discussions while also creating space for finding creative solutions too!

Problem Definition   #problem solving   #idea generation   #creativity   #online   #remote-friendly   A problem solving technique to define a problem, challenge or opportunity and to generate ideas.

4. The 5 Whys 

Sometimes, a group needs to go further with their strategies and analyze the root cause at the heart of organizational issues. An RCA or root cause analysis is the process of identifying what is at the heart of business problems or recurring challenges. 

The 5 Whys is a simple and effective method of helping a group go find the root cause of any problem or challenge and conduct analysis that will deliver results. 

By beginning with the creation of a problem statement and going through five stages to refine it, The 5 Whys provides everything you need to truly discover the cause of an issue.

The 5 Whys   #hyperisland   #innovation   This simple and powerful method is useful for getting to the core of a problem or challenge. As the title suggests, the group defines a problems, then asks the question “why” five times, often using the resulting explanation as a starting point for creative problem solving.

5. World Cafe

World Cafe is a simple but powerful facilitation technique to help bigger groups to focus their energy and attention on solving complex problems.

World Cafe enables this approach by creating a relaxed atmosphere where participants are able to self-organize and explore topics relevant and important to them which are themed around a central problem-solving purpose. Create the right atmosphere by modeling your space after a cafe and after guiding the group through the method, let them take the lead!

Making problem-solving a part of your organization’s culture in the long term can be a difficult undertaking. More approachable formats like World Cafe can be especially effective in bringing people unfamiliar with workshops into the fold. 

World Cafe   #hyperisland   #innovation   #issue analysis   World Café is a simple yet powerful method, originated by Juanita Brown, for enabling meaningful conversations driven completely by participants and the topics that are relevant and important to them. Facilitators create a cafe-style space and provide simple guidelines. Participants then self-organize and explore a set of relevant topics or questions for conversation.

6. Discovery & Action Dialogue (DAD)

One of the best approaches is to create a safe space for a group to share and discover practices and behaviors that can help them find their own solutions.

With DAD, you can help a group choose which problems they wish to solve and which approaches they will take to do so. It’s great at helping remove resistance to change and can help get buy-in at every level too!

This process of enabling frontline ownership is great in ensuring follow-through and is one of the methods you will want in your toolbox as a facilitator.

Discovery & Action Dialogue (DAD)   #idea generation   #liberating structures   #action   #issue analysis   #remote-friendly   DADs make it easy for a group or community to discover practices and behaviors that enable some individuals (without access to special resources and facing the same constraints) to find better solutions than their peers to common problems. These are called positive deviant (PD) behaviors and practices. DADs make it possible for people in the group, unit, or community to discover by themselves these PD practices. DADs also create favorable conditions for stimulating participants’ creativity in spaces where they can feel safe to invent new and more effective practices. Resistance to change evaporates as participants are unleashed to choose freely which practices they will adopt or try and which problems they will tackle. DADs make it possible to achieve frontline ownership of solutions.

7. Design Sprint 2.0

Want to see how a team can solve big problems and move forward with prototyping and testing solutions in a few days? The Design Sprint 2.0 template from Jake Knapp, author of Sprint, is a complete agenda for a with proven results.

Developing the right agenda can involve difficult but necessary planning. Ensuring all the correct steps are followed can also be stressful or time-consuming depending on your level of experience.

Use this complete 4-day workshop template if you are finding there is no obvious solution to your challenge and want to focus your team around a specific problem that might require a shortcut to launching a minimum viable product or waiting for the organization-wide implementation of a solution.

8. Open space technology

Open space technology- developed by Harrison Owen – creates a space where large groups are invited to take ownership of their problem solving and lead individual sessions. Open space technology is a great format when you have a great deal of expertise and insight in the room and want to allow for different takes and approaches on a particular theme or problem you need to be solved.

Start by bringing your participants together to align around a central theme and focus their efforts. Explain the ground rules to help guide the problem-solving process and then invite members to identify any issue connecting to the central theme that they are interested in and are prepared to take responsibility for.

Once participants have decided on their approach to the core theme, they write their issue on a piece of paper, announce it to the group, pick a session time and place, and post the paper on the wall. As the wall fills up with sessions, the group is then invited to join the sessions that interest them the most and which they can contribute to, then you’re ready to begin!

Everyone joins the problem-solving group they’ve signed up to, record the discussion and if appropriate, findings can then be shared with the rest of the group afterward.

Open Space Technology   #action plan   #idea generation   #problem solving   #issue analysis   #large group   #online   #remote-friendly   Open Space is a methodology for large groups to create their agenda discerning important topics for discussion, suitable for conferences, community gatherings and whole system facilitation

Techniques to identify and analyze problems

Using a problem-solving method to help a team identify and analyze a problem can be a quick and effective addition to any workshop or meeting.

While further actions are always necessary, you can generate momentum and alignment easily, and these activities are a great place to get started.

We’ve put together this list of techniques to help you and your team with problem identification, analysis, and discussion that sets the foundation for developing effective solutions.

Let’s take a look!

• The Creativity Dice
• Fishbone Analysis
• Problem Tree
• SWOT Analysis
• Agreement-Certainty Matrix
• The Journalistic Six
• LEGO Challenge
• What, So What, Now What?
• Journalists

Individual and group perspectives are incredibly important, but what happens if people are set in their minds and need a change of perspective in order to approach a problem more effectively?

Flip It is a method we love because it is both simple to understand and run, and allows groups to understand how their perspectives and biases are formed. 

Participants in Flip It are first invited to consider concerns, issues, or problems from a perspective of fear and write them on a flip chart. Then, the group is asked to consider those same issues from a perspective of hope and flip their understanding.  

No problem and solution is free from existing bias and by changing perspectives with Flip It, you can then develop a problem solving model quickly and effectively.

Flip It!   #gamestorming   #problem solving   #action   Often, a change in a problem or situation comes simply from a change in our perspectives. Flip It! is a quick game designed to show players that perspectives are made, not born.

10. The Creativity Dice

One of the most useful problem solving skills you can teach your team is of approaching challenges with creativity, flexibility, and openness. Games like The Creativity Dice allow teams to overcome the potential hurdle of too much linear thinking and approach the process with a sense of fun and speed. 

In The Creativity Dice, participants are organized around a topic and roll a dice to determine what they will work on for a period of 3 minutes at a time. They might roll a 3 and work on investigating factual information on the chosen topic. They might roll a 1 and work on identifying the specific goals, standards, or criteria for the session.

Encouraging rapid work and iteration while asking participants to be flexible are great skills to cultivate. Having a stage for idea incubation in this game is also important. Moments of pause can help ensure the ideas that are put forward are the most suitable. 

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.

11. Fishbone Analysis

Organizational or team challenges are rarely simple, and it’s important to remember that one problem can be an indication of something that goes deeper and may require further consideration to be solved.

Fishbone Analysis helps groups to dig deeper and understand the origins of a problem. It’s a great example of a root cause analysis method that is simple for everyone on a team to get their head around. 

Participants in this activity are asked to annotate a diagram of a fish, first adding the problem or issue to be worked on at the head of a fish before then brainstorming the root causes of the problem and adding them as bones on the fish. 

Using abstractions such as a diagram of a fish can really help a team break out of their regular thinking and develop a creative approach.

Fishbone Analysis   #problem solving   ##root cause analysis   #decision making   #online facilitation   A process to help identify and understand the origins of problems, issues or observations.

12. Problem Tree 

Encouraging visual thinking can be an essential part of many strategies. By simply reframing and clarifying problems, a group can move towards developing a problem solving model that works for them. 

In Problem Tree, groups are asked to first brainstorm a list of problems – these can be design problems, team problems or larger business problems – and then organize them into a hierarchy. The hierarchy could be from most important to least important or abstract to practical, though the key thing with problem solving games that involve this aspect is that your group has some way of managing and sorting all the issues that are raised.

Once you have a list of problems that need to be solved and have organized them accordingly, you’re then well-positioned for the next problem solving steps.

Problem tree   #define intentions   #create   #design   #issue analysis   A problem tree is a tool to clarify the hierarchy of problems addressed by the team within a design project; it represents high level problems or related sublevel problems.

13. SWOT Analysis

Chances are you’ve heard of the SWOT Analysis before. This problem-solving method focuses on identifying strengths, weaknesses, opportunities, and threats is a tried and tested method for both individuals and teams.

Start by creating a desired end state or outcome and bare this in mind – any process solving model is made more effective by knowing what you are moving towards. Create a quadrant made up of the four categories of a SWOT analysis and ask participants to generate ideas based on each of those quadrants.

Once you have those ideas assembled in their quadrants, cluster them together based on their affinity with other ideas. These clusters are then used to facilitate group conversations and move things forward. 

SWOT analysis   #gamestorming   #problem solving   #action   #meeting facilitation   The SWOT Analysis is a long-standing technique of looking at what we have, with respect to the desired end state, as well as what we could improve on. It gives us an opportunity to gauge approaching opportunities and dangers, and assess the seriousness of the conditions that affect our future. When we understand those conditions, we can influence what comes next.

14. Agreement-Certainty Matrix

Not every problem-solving approach is right for every challenge, and deciding on the right method for the challenge at hand is a key part of being an effective team.

The Agreement Certainty matrix helps teams align on the nature of the challenges facing them. By sorting problems from simple to chaotic, your team can understand what methods are suitable for each problem and what they can do to ensure effective results. 

If you are already using Liberating Structures techniques as part of your problem-solving strategy, the Agreement-Certainty Matrix can be an invaluable addition to your process. We’ve found it particularly if you are having issues with recurring problems in your organization and want to go deeper in understanding the root cause. 

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.

Organizing and charting a team’s progress can be important in ensuring its success. SQUID (Sequential Question and Insight Diagram) is a great model that allows a team to effectively switch between giving questions and answers and develop the skills they need to stay on track throughout the process. 

Begin with two different colored sticky notes – one for questions and one for answers – and with your central topic (the head of the squid) on the board. Ask the group to first come up with a series of questions connected to their best guess of how to approach the topic. Ask the group to come up with answers to those questions, fix them to the board and connect them with a line. After some discussion, go back to question mode by responding to the generated answers or other points on the board.

It’s rewarding to see a diagram grow throughout the exercise, and a completed SQUID can provide a visual resource for future effort and as an example for other teams.

SQUID   #gamestorming   #project planning   #issue analysis   #problem solving   When exploring an information space, it’s important for a group to know where they are at any given time. By using SQUID, a group charts out the territory as they go and can navigate accordingly. SQUID stands for Sequential Question and Insight Diagram.

16. Speed Boat

To continue with our nautical theme, Speed Boat is a short and sweet activity that can help a team quickly identify what employees, clients or service users might have a problem with and analyze what might be standing in the way of achieving a solution.

Methods that allow for a group to make observations, have insights and obtain those eureka moments quickly are invaluable when trying to solve complex problems.

In Speed Boat, the approach is to first consider what anchors and challenges might be holding an organization (or boat) back. Bonus points if you are able to identify any sharks in the water and develop ideas that can also deal with competitors!   

Speed Boat   #gamestorming   #problem solving   #action   Speedboat is a short and sweet way to identify what your employees or clients don’t like about your product/service or what’s standing in the way of a desired goal.

17. The Journalistic Six

Some of the most effective ways of solving problems is by encouraging teams to be more inclusive and diverse in their thinking.

Based on the six key questions journalism students are taught to answer in articles and news stories, The Journalistic Six helps create teams to see the whole picture. By using who, what, when, where, why, and how to facilitate the conversation and encourage creative thinking, your team can make sure that the problem identification and problem analysis stages of the are covered exhaustively and thoughtfully. Reporter’s notebook and dictaphone optional.

The Journalistic Six – Who What When Where Why How   #idea generation   #issue analysis   #problem solving   #online   #creative thinking   #remote-friendly   A questioning method for generating, explaining, investigating ideas.

18. LEGO Challenge

Now for an activity that is a little out of the (toy) box. LEGO Serious Play is a facilitation methodology that can be used to improve creative thinking and problem-solving skills. 

The LEGO Challenge includes giving each member of the team an assignment that is hidden from the rest of the group while they create a structure without speaking.

What the LEGO challenge brings to the table is a fun working example of working with stakeholders who might not be on the same page to solve problems. Also, it’s LEGO! Who doesn’t love LEGO! 

LEGO Challenge   #hyperisland   #team   A team-building activity in which groups must work together to build a structure out of LEGO, but each individual has a secret “assignment” which makes the collaborative process more challenging. It emphasizes group communication, leadership dynamics, conflict, cooperation, patience and problem solving strategy.

19. What, So What, Now What?

If not carefully managed, the problem identification and problem analysis stages of the problem-solving process can actually create more problems and misunderstandings.

The What, So What, Now What? problem-solving activity is designed to help collect insights and move forward while also eliminating the possibility of disagreement when it comes to identifying, clarifying, and analyzing organizational or work problems. 

Facilitation is all about bringing groups together so that might work on a shared goal and the best problem-solving strategies ensure that teams are aligned in purpose, if not initially in opinion or insight.

Throughout the three steps of this game, you give everyone on a team to reflect on a problem by asking what happened, why it is important, and what actions should then be taken. 

This can be a great activity for bringing our individual perceptions about a problem or challenge and contextualizing it in a larger group setting. This is one of the most important problem-solving skills you can bring to your organization.

W³ – What, So What, Now What?   #issue analysis   #innovation   #liberating structures   You can help groups reflect on a shared experience in a way that builds understanding and spurs coordinated action while avoiding unproductive conflict. It is possible for every voice to be heard while simultaneously sifting for insights and shaping new direction. Progressing in stages makes this practical—from collecting facts about What Happened to making sense of these facts with So What and finally to what actions logically follow with Now What . The shared progression eliminates most of the misunderstandings that otherwise fuel disagreements about what to do. Voila!

20. Journalists  

Problem analysis can be one of the most important and decisive stages of all problem-solving tools. Sometimes, a team can become bogged down in the details and are unable to move forward.

Journalists is an activity that can avoid a group from getting stuck in the problem identification or problem analysis stages of the process.

In Journalists, the group is invited to draft the front page of a fictional newspaper and figure out what stories deserve to be on the cover and what headlines those stories will have. By reframing how your problems and challenges are approached, you can help a team move productively through the process and be better prepared for the steps to follow.

Journalists   #vision   #big picture   #issue analysis   #remote-friendly   This is an exercise to use when the group gets stuck in details and struggles to see the big picture. Also good for defining a vision.

Problem-solving techniques for developing solutions 

The success of any problem-solving process can be measured by the solutions it produces. After you’ve defined the issue, explored existing ideas, and ideated, it’s time to narrow down to the correct solution.

Use these problem-solving techniques when you want to help your team find consensus, compare possible solutions, and move towards taking action on a particular problem.

• Improved Solutions
• Four-Step Sketch
• 15% Solutions
• How-Now-Wow matrix
• Impact Effort Matrix

21. Mindspin  

Brainstorming is part of the bread and butter of the problem-solving process and all problem-solving strategies benefit from getting ideas out and challenging a team to generate solutions quickly. 

With Mindspin, participants are encouraged not only to generate ideas but to do so under time constraints and by slamming down cards and passing them on. By doing multiple rounds, your team can begin with a free generation of possible solutions before moving on to developing those solutions and encouraging further ideation. 

This is one of our favorite problem-solving activities and can be great for keeping the energy up throughout the workshop. Remember the importance of helping people become engaged in the process – energizing problem-solving techniques like Mindspin can help ensure your team stays engaged and happy, even when the problems they’re coming together to solve are complex. 

MindSpin   #teampedia   #idea generation   #problem solving   #action   A fast and loud method to enhance brainstorming within a team. Since this activity has more than round ideas that are repetitive can be ruled out leaving more creative and innovative answers to the challenge.

22. Improved Solutions

After a team has successfully identified a problem and come up with a few solutions, it can be tempting to call the work of the problem-solving process complete. That said, the first solution is not necessarily the best, and by including a further review and reflection activity into your problem-solving model, you can ensure your group reaches the best possible result. 

One of a number of problem-solving games from Thiagi Group, Improved Solutions helps you go the extra mile and develop suggested solutions with close consideration and peer review. By supporting the discussion of several problems at once and by shifting team roles throughout, this problem-solving technique is a dynamic way of finding the best solution. 

Improved Solutions   #creativity   #thiagi   #problem solving   #action   #team   You can improve any solution by objectively reviewing its strengths and weaknesses and making suitable adjustments. In this creativity framegame, you improve the solutions to several problems. To maintain objective detachment, you deal with a different problem during each of six rounds and assume different roles (problem owner, consultant, basher, booster, enhancer, and evaluator) during each round. At the conclusion of the activity, each player ends up with two solutions to her problem.

23. Four Step Sketch

Creative thinking and visual ideation does not need to be confined to the opening stages of your problem-solving strategies. Exercises that include sketching and prototyping on paper can be effective at the solution finding and development stage of the process, and can be great for keeping a team engaged. 

By going from simple notes to a crazy 8s round that involves rapidly sketching 8 variations on their ideas before then producing a final solution sketch, the group is able to iterate quickly and visually. Problem-solving techniques like Four-Step Sketch are great if you have a group of different thinkers and want to change things up from a more textual or discussion-based approach.

Four-Step Sketch   #design sprint   #innovation   #idea generation   #remote-friendly   The four-step sketch is an exercise that helps people to create well-formed concepts through a structured process that includes: Review key information Start design work on paper,  Consider multiple variations , Create a detailed solution . This exercise is preceded by a set of other activities allowing the group to clarify the challenge they want to solve. See how the Four Step Sketch exercise fits into a Design Sprint

24. 15% Solutions

Some problems are simpler than others and with the right problem-solving activities, you can empower people to take immediate actions that can help create organizational change. 

Part of the liberating structures toolkit, 15% solutions is a problem-solving technique that focuses on finding and implementing solutions quickly. A process of iterating and making small changes quickly can help generate momentum and an appetite for solving complex problems.

Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process.   

It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things they cannot change. 

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.

25. How-Now-Wow Matrix

The problem-solving process is often creative, as complex problems usually require a change of thinking and creative response in order to find the best solutions. While it’s common for the first stages to encourage creative thinking, groups can often gravitate to familiar solutions when it comes to the end of the process. 

When selecting solutions, you don’t want to lose your creative energy! The How-Now-Wow Matrix from Gamestorming is a great problem-solving activity that enables a group to stay creative and think out of the box when it comes to selecting the right solution for a given problem.

Problem-solving techniques that encourage creative thinking and the ideation and selection of new solutions can be the most effective in organisational change. Give the How-Now-Wow Matrix a go, and not just for how pleasant it is to say out loud. 

How-Now-Wow Matrix   #gamestorming   #idea generation   #remote-friendly   When people want to develop new ideas, they most often think out of the box in the brainstorming or divergent phase. However, when it comes to convergence, people often end up picking ideas that are most familiar to them. This is called a ‘creative paradox’ or a ‘creadox’. The How-Now-Wow matrix is an idea selection tool that breaks the creadox by forcing people to weigh each idea on 2 parameters.

26. Impact and Effort Matrix

All problem-solving techniques hope to not only find solutions to a given problem or challenge but to find the best solution. When it comes to finding a solution, groups are invited to put on their decision-making hats and really think about how a proposed idea would work in practice. 

The Impact and Effort Matrix is one of the problem-solving techniques that fall into this camp, empowering participants to first generate ideas and then categorize them into a 2×2 matrix based on impact and effort.

Activities that invite critical thinking while remaining simple are invaluable. Use the Impact and Effort Matrix to move from ideation and towards evaluating potential solutions before then committing to them. 

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.

27. Dotmocracy

If you’ve followed each of the problem-solving steps with your group successfully, you should move towards the end of your process with heaps of possible solutions developed with a specific problem in mind. But how do you help a group go from ideation to putting a solution into action? 

Dotmocracy – or Dot Voting -is a tried and tested method of helping a team in the problem-solving process make decisions and put actions in place with a degree of oversight and consensus. 

One of the problem-solving techniques that should be in every facilitator’s toolbox, Dot Voting is fast and effective and can help identify the most popular and best solutions and help bring a group to a decision effectively. 

Dotmocracy   #action   #decision making   #group prioritization   #hyperisland   #remote-friendly   Dotmocracy is a simple method for group prioritization or decision-making. It is not an activity on its own, but a method to use in processes where prioritization or decision-making is the aim. The method supports a group to quickly see which options are most popular or relevant. The options or ideas are written on post-its and stuck up on a wall for the whole group to see. Each person votes for the options they think are the strongest, and that information is used to inform a decision.

All facilitators know that warm-ups and icebreakers are useful for any workshop or group process. Problem-solving workshops are no different.

Use these problem-solving techniques to warm up a group and prepare them for the rest of the process. Activating your group by tapping into some of the top problem-solving skills can be one of the best ways to see great outcomes from your session.

• Check-in/Check-out
• Doodling Together
• Show and Tell
• Constellations
• Draw a Tree

28. Check-in / Check-out

Solid processes are planned from beginning to end, and the best facilitators know that setting the tone and establishing a safe, open environment can be integral to a successful problem-solving process.

Check-in / Check-out is a great way to begin and/or bookend a problem-solving workshop. Checking in to a session emphasizes that everyone will be seen, heard, and expected to contribute. 

If you are running a series of meetings, setting a consistent pattern of checking in and checking out can really help your team get into a groove. We recommend this opening-closing activity for small to medium-sized groups though it can work with large groups if they’re disciplined!

Check-in / Check-out   #team   #opening   #closing   #hyperisland   #remote-friendly   Either checking-in or checking-out is a simple way for a team to open or close a process, symbolically and in a collaborative way. Checking-in/out invites each member in a group to be present, seen and heard, and to express a reflection or a feeling. Checking-in emphasizes presence, focus and group commitment; checking-out emphasizes reflection and symbolic closure.

29. Doodling Together  

Thinking creatively and not being afraid to make suggestions are important problem-solving skills for any group or team, and warming up by encouraging these behaviors is a great way to start. 

Doodling Together is one of our favorite creative ice breaker games – it’s quick, effective, and fun and can make all following problem-solving steps easier by encouraging a group to collaborate visually. By passing cards and adding additional items as they go, the workshop group gets into a groove of co-creation and idea development that is crucial to finding solutions to problems. 

Doodling Together   #collaboration   #creativity   #teamwork   #fun   #team   #visual methods   #energiser   #icebreaker   #remote-friendly   Create wild, weird and often funny postcards together & establish a group’s creative confidence.

30. Show and Tell

You might remember some version of Show and Tell from being a kid in school and it’s a great problem-solving activity to kick off a session.

Asking participants to prepare a little something before a workshop by bringing an object for show and tell can help them warm up before the session has even begun! Games that include a physical object can also help encourage early engagement before moving onto more big-picture thinking.

By asking your participants to tell stories about why they chose to bring a particular item to the group, you can help teams see things from new perspectives and see both differences and similarities in the way they approach a topic. Great groundwork for approaching a problem-solving process as a team! 

Show and Tell   #gamestorming   #action   #opening   #meeting facilitation   Show and Tell taps into the power of metaphors to reveal players’ underlying assumptions and associations around a topic The aim of the game is to get a deeper understanding of stakeholders’ perspectives on anything—a new project, an organizational restructuring, a shift in the company’s vision or team dynamic.

31. Constellations

Who doesn’t love stars? Constellations is a great warm-up activity for any workshop as it gets people up off their feet, energized, and ready to engage in new ways with established topics. It’s also great for showing existing beliefs, biases, and patterns that can come into play as part of your session.

Using warm-up games that help build trust and connection while also allowing for non-verbal responses can be great for easing people into the problem-solving process and encouraging engagement from everyone in the group. Constellations is great in large spaces that allow for movement and is definitely a practical exercise to allow the group to see patterns that are otherwise invisible. 

Constellations   #trust   #connection   #opening   #coaching   #patterns   #system   Individuals express their response to a statement or idea by standing closer or further from a central object. Used with teams to reveal system, hidden patterns, perspectives.

32. Draw a Tree

Problem-solving games that help raise group awareness through a central, unifying metaphor can be effective ways to warm-up a group in any problem-solving model.

Draw a Tree is a simple warm-up activity you can use in any group and which can provide a quick jolt of energy. Start by asking your participants to draw a tree in just 45 seconds – they can choose whether it will be abstract or realistic. 

Once the timer is up, ask the group how many people included the roots of the tree and use this as a means to discuss how we can ignore important parts of any system simply because they are not visible.

All problem-solving strategies are made more effective by thinking of problems critically and by exposing things that may not normally come to light. Warm-up games like Draw a Tree are great in that they quickly demonstrate some key problem-solving skills in an accessible and effective way.

Draw a Tree   #thiagi   #opening   #perspectives   #remote-friendly   With this game you can raise awarness about being more mindful, and aware of the environment we live in.

Each step of the problem-solving workshop benefits from an intelligent deployment of activities, games, and techniques. Bringing your session to an effective close helps ensure that solutions are followed through on and that you also celebrate what has been achieved.

Here are some problem-solving activities you can use to effectively close a workshop or meeting and ensure the great work you’ve done can continue afterward.

• One Breath Feedback
• Who What When Matrix
• Response Cards

How do I conclude a problem-solving process?

All good things must come to an end. With the bulk of the work done, it can be tempting to conclude your workshop swiftly and without a moment to debrief and align. This can be problematic in that it doesn’t allow your team to fully process the results or reflect on the process.

At the end of an effective session, your team will have gone through a process that, while productive, can be exhausting. It’s important to give your group a moment to take a breath, ensure that they are clear on future actions, and provide short feedback before leaving the space. 

The primary purpose of any problem-solving method is to generate solutions and then implement them. Be sure to take the opportunity to ensure everyone is aligned and ready to effectively implement the solutions you produced in the workshop.

Remember that every process can be improved and by giving a short moment to collect feedback in the session, you can further refine your problem-solving methods and see further success in the future too.

33. One Breath Feedback

Maintaining attention and focus during the closing stages of a problem-solving workshop can be tricky and so being concise when giving feedback can be important. It’s easy to incur “death by feedback” should some team members go on for too long sharing their perspectives in a quick feedback round. 

One Breath Feedback is a great closing activity for workshops. You give everyone an opportunity to provide feedback on what they’ve done but only in the space of a single breath. This keeps feedback short and to the point and means that everyone is encouraged to provide the most important piece of feedback to them. 

One breath feedback   #closing   #feedback   #action   This is a feedback round in just one breath that excels in maintaining attention: each participants is able to speak during just one breath … for most people that’s around 20 to 25 seconds … unless of course you’ve been a deep sea diver in which case you’ll be able to do it for longer.

34. Who What When Matrix 

Matrices feature as part of many effective problem-solving strategies and with good reason. They are easily recognizable, simple to use, and generate results.

The Who What When Matrix is a great tool to use when closing your problem-solving session by attributing a who, what and when to the actions and solutions you have decided upon. The resulting matrix is a simple, easy-to-follow way of ensuring your team can move forward. 

Great solutions can’t be enacted without action and ownership. Your problem-solving process should include a stage for allocating tasks to individuals or teams and creating a realistic timeframe for those solutions to be implemented or checked out. Use this method to keep the solution implementation process clear and simple for all involved. 

Who/What/When Matrix   #gamestorming   #action   #project planning   With Who/What/When matrix, you can connect people with clear actions they have defined and have committed to.

35. Response cards

Group discussion can comprise the bulk of most problem-solving activities and by the end of the process, you might find that your team is talked out! 

Providing a means for your team to give feedback with short written notes can ensure everyone is head and can contribute without the need to stand up and talk. Depending on the needs of the group, giving an alternative can help ensure everyone can contribute to your problem-solving model in the way that makes the most sense for them.

Response Cards is a great way to close a workshop if you are looking for a gentle warm-down and want to get some swift discussion around some of the feedback that is raised. 

Response Cards   #debriefing   #closing   #structured sharing   #questions and answers   #thiagi   #action   It can be hard to involve everyone during a closing of a session. Some might stay in the background or get unheard because of louder participants. However, with the use of Response Cards, everyone will be involved in providing feedback or clarify questions at the end of a session.

Save time and effort discovering the right solutions

A structured problem solving process is a surefire way of solving tough problems, discovering creative solutions and driving organizational change. But how can you design for successful outcomes?

With SessionLab, it’s easy to design engaging workshops that deliver results. Drag, drop and reorder blocks  to build your agenda. When you make changes or update your agenda, your session  timing   adjusts automatically , saving you time on manual adjustments.

Collaborating with stakeholders or clients? Share your agenda with a single click and collaborate in real-time. No more sending documents back and forth over email.

Explore  how to use SessionLab  to design effective problem solving workshops or  watch this five minute video  to see the planner in action!

Over to you

The problem-solving process can often be as complicated and multifaceted as the problems they are set-up to solve. With the right problem-solving techniques and a mix of creative exercises designed to guide discussion and generate purposeful ideas, we hope we’ve given you the tools to find the best solutions as simply and easily as possible.

Is there a problem-solving technique that you are missing here? Do you have a favorite activity or method you use when facilitating? Let us know in the comments below, we’d love to hear from you! 

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Leave a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Going from a mere idea to a workshop that delivers results for your clients can feel like a daunting task. In this piece, we will shine a light on all the work behind the scenes and help you learn how to plan a workshop from start to finish. On a good day, facilitation can feel like effortless magic, but that is mostly the result of backstage work, foresight, and a lot of careful planning. Read on to learn a step-by-step approach to breaking the process of planning a workshop into small, manageable chunks.  The flow starts with the first meeting with a client to define the purposes of a workshop.…

How does learning work? A clever 9-year-old once told me: “I know I am learning something new when I am surprised.” The science of adult learning tells us that, in order to learn new skills (which, unsurprisingly, is harder for adults to do than kids) grown-ups need to first get into a specific headspace.  In a business, this approach is often employed in a training session where employees learn new skills or work on professional development. But how do you ensure your training is effective? In this guide, we'll explore how to create an effective training session plan and run engaging training sessions. As team leader, project manager, or consultant,…

Effective online tools are a necessity for smooth and engaging virtual workshops and meetings. But how do you choose the right ones? Do you sometimes feel that the good old pen and paper or MS Office toolkit and email leaves you struggling to stay on top of managing and delivering your workshop? Fortunately, there are plenty of online tools to make your life easier when you need to facilitate a meeting and lead workshops. In this post, we’ll share our favorite online tools you can use to make your job as a facilitator easier. In fact, there are plenty of free online workshop tools and meeting facilitation software you can…

Design your next workshop with SessionLab

Join the 150,000 facilitators using SessionLab

Sign up for free

What is Problem Solving? (Steps, Techniques, Examples)

By Status.net Editorial Team on May 7, 2023 — 5 minutes to read

What Is Problem Solving?

Definition and importance.

Problem solving is the process of finding solutions to obstacles or challenges you encounter in your life or work. It is a crucial skill that allows you to tackle complex situations, adapt to changes, and overcome difficulties with ease. Mastering this ability will contribute to both your personal and professional growth, leading to more successful outcomes and better decision-making.

Problem-Solving Steps

The problem-solving process typically includes the following steps:

• Identify the issue : Recognize the problem that needs to be solved.
• Analyze the situation : Examine the issue in depth, gather all relevant information, and consider any limitations or constraints that may be present.
• Generate potential solutions : Brainstorm a list of possible solutions to the issue, without immediately judging or evaluating them.
• Evaluate options : Weigh the pros and cons of each potential solution, considering factors such as feasibility, effectiveness, and potential risks.
• Select the best solution : Choose the option that best addresses the problem and aligns with your objectives.
• Implement the solution : Put the selected solution into action and monitor the results to ensure it resolves the issue.
• Review and learn : Reflect on the problem-solving process, identify any improvements or adjustments that can be made, and apply these learnings to future situations.

Defining the Problem

To start tackling a problem, first, identify and understand it. Analyzing the issue thoroughly helps to clarify its scope and nature. Ask questions to gather information and consider the problem from various angles. Some strategies to define the problem include:

• Brainstorming with others
• Asking the 5 Ws and 1 H (Who, What, When, Where, Why, and How)
• Analyzing cause and effect
• Creating a problem statement

Generating Solutions

Once the problem is clearly understood, brainstorm possible solutions. Think creatively and keep an open mind, as well as considering lessons from past experiences. Consider:

• Creating a list of potential ideas to solve the problem
• Grouping and categorizing similar solutions
• Prioritizing potential solutions based on feasibility, cost, and resources required
• Involving others to share diverse opinions and inputs

Evaluating and Selecting Solutions

Evaluate each potential solution, weighing its pros and cons. To facilitate decision-making, use techniques such as:

• SWOT analysis (Strengths, Weaknesses, Opportunities, Threats)
• Decision-making matrices
• Pros and cons lists
• Risk assessments

After evaluating, choose the most suitable solution based on effectiveness, cost, and time constraints.

Implementing and Monitoring the Solution

Implement the chosen solution and monitor its progress. Key actions include:

• Communicating the solution to relevant parties
• Setting timelines and milestones
• Assigning tasks and responsibilities
• Monitoring the solution and making adjustments as necessary
• Evaluating the effectiveness of the solution after implementation

Utilize feedback from stakeholders and consider potential improvements. Remember that problem-solving is an ongoing process that can always be refined and enhanced.

Problem-Solving Techniques

During each step, you may find it helpful to utilize various problem-solving techniques, such as:

• Brainstorming : A free-flowing, open-minded session where ideas are generated and listed without judgment, to encourage creativity and innovative thinking.
• Root cause analysis : A method that explores the underlying causes of a problem to find the most effective solution rather than addressing superficial symptoms.
• SWOT analysis : A tool used to evaluate the strengths, weaknesses, opportunities, and threats related to a problem or decision, providing a comprehensive view of the situation.
• Mind mapping : A visual technique that uses diagrams to organize and connect ideas, helping to identify patterns, relationships, and possible solutions.

Brainstorming

When facing a problem, start by conducting a brainstorming session. Gather your team and encourage an open discussion where everyone contributes ideas, no matter how outlandish they may seem. This helps you:

• Generate a diverse range of solutions
• Encourage all team members to participate
• Foster creative thinking

When brainstorming, remember to:

• Reserve judgment until the session is over
• Encourage wild ideas
• Combine and improve upon ideas

Root Cause Analysis

For effective problem-solving, identifying the root cause of the issue at hand is crucial. Try these methods:

• 5 Whys : Ask “why” five times to get to the underlying cause.
• Fishbone Diagram : Create a diagram representing the problem and break it down into categories of potential causes.
• Pareto Analysis : Determine the few most significant causes underlying the majority of problems.

SWOT Analysis

SWOT analysis helps you examine the Strengths, Weaknesses, Opportunities, and Threats related to your problem. To perform a SWOT analysis:

• List your problem’s strengths, such as relevant resources or strong partnerships.
• Identify its weaknesses, such as knowledge gaps or limited resources.
• Explore opportunities, like trends or new technologies, that could help solve the problem.
• Recognize potential threats, like competition or regulatory barriers.

SWOT analysis aids in understanding the internal and external factors affecting the problem, which can help guide your solution.

Mind Mapping

A mind map is a visual representation of your problem and potential solutions. It enables you to organize information in a structured and intuitive manner. To create a mind map:

• Write the problem in the center of a blank page.
• Draw branches from the central problem to related sub-problems or contributing factors.
• Add more branches to represent potential solutions or further ideas.

Mind mapping allows you to visually see connections between ideas and promotes creativity in problem-solving.

Examples of Problem Solving in Various Contexts

In the business world, you might encounter problems related to finances, operations, or communication. Applying problem-solving skills in these situations could look like:

• Identifying areas of improvement in your company’s financial performance and implementing cost-saving measures
• Resolving internal conflicts among team members by listening and understanding different perspectives, then proposing and negotiating solutions
• Streamlining a process for better productivity by removing redundancies, automating tasks, or re-allocating resources

In educational contexts, problem-solving can be seen in various aspects, such as:

• Addressing a gap in students’ understanding by employing diverse teaching methods to cater to different learning styles
• Developing a strategy for successful time management to balance academic responsibilities and extracurricular activities
• Seeking resources and support to provide equal opportunities for learners with special needs or disabilities

Everyday life is full of challenges that require problem-solving skills. Some examples include:

• Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
• Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
• Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
• How to Resolve Employee Conflict at Work [Steps, Tips, Examples]
• How to Write Inspiring Core Values? 5 Steps with Examples
• 30 Employee Feedback Examples (Positive & Negative)

• Pre-algebra lessons
• Pre-algebra word problems
• Algebra lessons

Algebra word problems

• Algebra proofs
• Advanced algebra
• Geometry lessons
• Geometry word problems
• Geometry proofs
• Trigonometry lessons
• Consumer math
• Baseball math
• Math for nurses
• Statistics made easy
• High school physics
• Basic mathematics store
• SAT Math Prep
• Math skills by grade level
• Ask an expert
• Other websites
• K-12 worksheets
• Worksheets generator
• Algebra worksheets
• Geometry worksheets
• Free math problem solver
• Pre-algebra calculators
• Algebra Calculators
• Geometry Calculators
• Math puzzles
• Math tricks
• Member login

Basic math word problems

You encounter and solve basic math word problems on a daily basis without thinking about it. Knowing how to tackle and solve word problems is an important skill in school. You may find it useful to review some math problem solving strategies .

Whole number word problems

Fractions word problems, ratio and proportion word problems .

Ratio word problems Six carefully selected ratio word problems with solutions to help you master ratios. Proportion word problems Four carefully selected proportion word problems with solutions.

Convert square feet to acres See how you can use proportion to convert square feet to acres

Percentage word problems

Average word problems.

Average word problems Word problems about finding the average from easy to challenging

Comparison word problems

Comparison word problems A variety of comparison word problems from easy to challenging

Venn diagram word problems

Venn diagram word problems A variety of word problems from easy to challenging

Have A Great Basic Math Word Problem?

Share it here with a very detailed solution!

Enter Your Title

Add a Picture/Graphic Caption (optional)  

Click here to upload more images (optional)

Author Information (optional)

To receive credit as the author, enter your information below.

Submit Your Contribution

• Check box to agree to these   submission guidelines .
• I am at least 16 years of age.
• I understand and accept the privacy policy .
• I understand that you will display my submission on your website.

(You can preview and edit on the next page)

What Other Visitors Have Said

Click below to see contributions from other visitors to this page...

Click here to write your own.

Recent Articles

How to divide any number by 5 in 2 seconds.

Feb 28, 24 11:07 AM

Math Trick to Square Numbers from 50 to 59

Feb 23, 24 04:46 AM

Sum of Consecutive Odd Numbers

Feb 22, 24 10:07 AM

100 Tough Algebra Word Problems. If you can solve these problems with no help, you must be a genius!

 Recommended

About me :: Privacy policy :: Disclaimer :: Donate   Careers in mathematics  

Copyright © 2008-2021. Basic-mathematics.com. All right reserved

From Dilemmas to Solutions: Problem-Solving Examples to Learn From

• by the PsychNewsDaily Staff
• May 21, 2023

Introduction to Problem-Solving

Life is full of challenges and dilemmas, both big and small.

But if there’s one skill that can help you navigate these, it’s problem-solving .

So, what exactly is problem-solving? And why is it such a crucial skill in daily life?

Understanding the Concept of Problem-Solving

Problem-solving is a mental process that involves identifying, analyzing, and resolving challenges or difficulties.

It’s like a journey that starts with a problem and ends with a solution.

It’s a skill that’s not just used in the field of psychology but in all aspects of life.

Whether you’re trying to decide on the best route to work, dealing with a disagreement with a friend, or figuring out how to fix a leaky faucet, you’re using your problem-solving skills.

When you’re faced with a problem, your brain goes through a series of steps to find a solution.

This process can be conscious or unconscious and can involve logical thinking, creativity, and prior knowledge.

Effective problem-solving can lead to better decisions and outcomes, making it a valuable tool in your personal and professional life.

Importance of Problem-Solving in Daily Life

Why is problem-solving so important in daily life? Well, it’s simple.

Problems are a part of life.

They arise in different shapes and sizes, and in different areas of life, including work, relationships, health, and personal growth.

Having strong problem-solving skills can help you navigate these challenges effectively and efficiently.

In your personal life, problem-solving can help you manage stress and conflict, make better decisions, and achieve your goals.

In the workplace, it can help you navigate complex projects, improve processes, and foster innovation.

Problem-solving is also a key skill in many professions and industries, from engineering and science to healthcare and customer service.

Moreover, problem-solving can contribute to your overall mental well-being.

It can give you a sense of control and agency, reduce feelings of stress and anxiety, and foster a positive attitude.

It’s also a key component of resilience, the ability to bounce back from adversity.

In conclusion, problem-solving is a fundamental skill in life.

It’s a tool you can use to tackle challenges, make informed decisions, and drive change.

By understanding the concept of problem-solving and recognizing its importance in daily life, you’re taking the first step toward becoming a more effective problem solver.

As we delve deeper into this topic, you’ll discover practical problem-solving examples, learn about different problem-solving techniques, and gain insights on how to improve your own problem-solving skills.

So, stay tuned and continue your exploration of introduction to psychology with us.

Stages of Problem-Solving

The process of problem-solving can be broken down into three key stages: identifying the problem , developing possible solutions , and implementing the best solution .

Each stage requires a different set of skills and strategies.

By understanding these stages, you can enhance your problem-solving abilities and tackle various challenges more effectively.

Identifying the Problem

The first step in problem-solving is recognizing that a problem exists.

This involves defining the issue clearly and understanding its root cause.

You might need to gather information, ask questions, and analyze the situation from multiple perspectives.

It can be helpful to write down the problem and think about how it impacts you or others involved.

For instance, if you’re struggling with time management, the problem might be that you have too many obligations and not enough time.

Or perhaps your methods of organizing your tasks aren’t effective.

It’s important to be as specific as possible when identifying the problem, as this will guide the rest of the problem-solving process.

Developing Possible Solutions

Once you’ve identified the problem, the next step is to brainstorm possible solutions.

This is where creativity comes into play.

Don’t limit yourself; even ideas that seem unrealistic or out of the box can lead to effective solutions.

Consider different strategies and approaches.

You could try using techniques like mind mapping, listing pros and cons, or consulting with others for fresh perspectives.

Remember, the goal is to generate a variety of options, not to choose a solution at this stage.

Implementing the Best Solution

The final stage of problem-solving is to select the best solution and put it into action.

Review the options you’ve developed, evaluate their potential effectiveness, and make a decision.

Keep in mind that the “best” solution isn’t necessarily the perfect one (as there might not be a perfect solution), but rather the one that seems most likely to achieve your desired outcome given the circumstances.

Once you’ve chosen a solution, plan out the steps needed to implement it and then take action.

Monitor the results and adjust your approach as necessary.

If the problem persists, don’t be discouraged; return to the previous stages, reassess the problem and your potential solutions, and try again.

Remember, problem-solving is a dynamic process that often involves trial and error.

It’s an essential skill in many areas of life, from everyday challenges to workplace dilemmas.

To learn more about the psychology behind problem-solving and decision-making, check out our introduction to psychology article.

Problem-Solving Examples

Understanding the concept of problem-solving is one thing, but seeing it in action is another.

To help you grasp the practical application of problem-solving strategies, let’s explore three different problem-solving examples from daily life, the workplace, and relationships.

Daily Life Problem-Solving Example

Imagine you’re trying to lose weight but struggle with late-night snacking.

The issue isn’t uncommon, but it’s hindering your progress towards your weight loss goal.

• Identifying the Problem : Late-night snacking is causing you to consume extra calories, preventing weight loss.
• Developing Possible Solutions : You could consider eating an earlier dinner, having a healthier snack option, or practicing mindful eating.
• Implementing the Best Solution : After trying out different solutions, you find that preparing a healthy snack in advance minimizes your calorie intake and satisfies your late-night cravings, helping you stay on track with your weight loss goal.

Workplace Problem-Solving Example

Let’s consider a scenario where a team at work is failing to meet project deadlines consistently.

• Identifying the Problem : The team is not completing projects on time, causing delays in the overall project timeline.
• Developing Possible Solutions : The team could consider improving their time management skills, using project management tools, or redistributing tasks among team members.
• Implementing the Best Solution : After trying out different strategies, the team finds that using a project management tool helps them stay organized, delegate tasks effectively, and complete projects within the given timeframe.

For more insights on effective management styles that can help in problem-solving at the workplace, check out our articles on autocratic leadership , democratic leadership style , and laissez faire leadership .

Relationship Problem-Solving Example

In a romantic relationship, conflicts can occasionally arise.

Let’s imagine a common issue where one partner feels the other isn’t spending enough quality time with them.

• Identifying the Problem : One partner feels neglected due to a lack of quality time spent together.
• Developing Possible Solutions : The couple could consider scheduling regular date nights, engaging in shared hobbies, or setting aside a specific time each day for undisturbed conversation.
• Implementing the Best Solution : The couple decides to implement a daily “unplugged” hour where they focus solely on each other without distractions. This results in improved relationship satisfaction.

For more on navigating relationship challenges, check out our articles on anxious avoidant attachment and emotional awareness .

These problem-solving examples illustrate how the process of identifying a problem, developing possible solutions, and implementing the best solution can be applied to various situations.

By understanding and applying these strategies, you can improve your problem-solving skills and navigate challenges more effectively.

Techniques for Effective Problem-Solving

As you navigate the world of problem-solving, you’ll find that there are multiple techniques you can use to arrive at a solution.

Each technique offers a unique approach to identifying issues, generating potential solutions, and choosing the best course of action.

In this section, we’ll explore three common techniques: Brainstorming , Root Cause Analysis , and SWOT Analysis .

Brainstorming

Brainstorming is a free-thinking method used to generate a large number of ideas related to a specific problem.

You do this by suspending criticism and allowing your creativity to flow.

The aim is to produce as many ideas as possible, even if they seem far-fetched.

You then evaluate these ideas to identify the most beneficial solutions.

By using brainstorming, you can encourage out-of-the-box thinking and possibly discover innovative solutions to challenging problems.

Root Cause Analysis

Root Cause Analysis (RCA) is a method used to identify the underlying causes of a problem.

The goal is to address these root causes rather than the symptoms of the problem.

This technique helps to prevent the same issue from recurring in the future.

There are several RCA methods, such as the “5 Whys” technique, where you ask “why” multiple times until you uncover the root cause of the problem.

By identifying and addressing the root cause, you tackle the problem at its source, which can lead to more effective and long-lasting solutions.

SWOT Analysis

SWOT Analysis is a strategic planning technique that helps you identify your Strengths, Weaknesses, Opportunities, and Threats related to a problem.

This approach encourages you to examine the problem from different angles, helping you understand the resources you have at your disposal (Strengths), the areas where you could improve (Weaknesses), the external factors that could benefit you (Opportunities), and the external factors that could cause problems (Threats).

With this comprehensive understanding, you can develop a well-informed strategy to solve the problem.

Each of these problem-solving techniques provides a distinct approach to identifying and resolving issues.

By understanding and utilizing these methods, you can enhance your problem-solving skills and increase your effectiveness in dealing with challenges.

For more insights into effective problem-solving and other psychological topics, explore our introduction to psychology .

Improving Your Problem-Solving Skills

Learning to solve problems effectively is a skill that can be honed with time and practice.

The following are some ways to enhance your problem-solving capabilities.

Practice Makes Perfect

The saying “practice makes perfect” holds true when it comes to problem-solving.

The more problems you tackle, the better you’ll become at devising and implementing effective solutions.

Seek out opportunities to practice your problem-solving skills both in everyday life and in more complex situations.

This could involve resolving a dispute at work, figuring out a puzzle, or even strategizing in a board game.

Each problem you encounter is a new opportunity to apply and refine your skills.

Learning from Others’ Experiences

There’s much to be gained from observing how others approach problem-solving.

Whether it’s reading about problem solving examples from renowned psychologists or discussing strategies with colleagues, you can learn valuable techniques and perspectives from the experiences of others.

Consider participating in group activities that require problem-solving, such as escape rooms or team projects.

Observe how team members identify problems, brainstorm solutions, and decide on the best course of action.

Embracing a Growth Mindset

A key component of effective problem-solving is adopting a growth mindset.

This mindset, coined by psychologist Carol Dweck, is the belief that abilities and intelligence can be developed through dedication and hard work.

When you embrace a growth mindset, you view challenges as opportunities to learn and grow rather than as insurmountable obstacles.

Believing in your ability to develop and enhance your problem-solving skills over time can make the process less daunting and more rewarding.

So, when you encounter a problem, instead of thinking, “I can’t do this,” try thinking, “I can’t do this yet, but with effort and practice, I can learn.”

For more on the growth mindset, you might want to check out our article on what is intrinsic motivation which includes how a growth mindset can fuel your motivation to improve.

By practicing regularly, learning from others, and embracing a growth mindset, you can continually improve your problem-solving skills and become more adept at overcoming challenges you encounter.

Related posts:

• Embrace the Change: Embodying the Democratic Leadership Style
• Taking Charge by Doing Nothing: Understanding Laissez Faire Leadership
• Mastering Leadership: Unraveling the Contingency Theory

• Bipolar Disorder
• Therapy Center
• When To See a Therapist
• Types of Therapy
• Best Online Therapy
• Best Couples Therapy
• Best Family Therapy
• Managing Stress
• Sleep and Dreaming
• Understanding Emotions
• Self-Improvement
• Healthy Relationships
• Student Resources
• Personality Types
• Verywell Mind Insights
• 2023 Verywell Mind 25
• Mental Health in the Classroom
• Editorial Process
• Meet Our Review Board
• Crisis Support

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.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

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."

• Skip to main content
• Skip to primary sidebar
• Skip to footer

Additional menu

Khan Academy Blog

Free Math Worksheets — Over 100k free practice problems on Khan Academy

Looking for free math worksheets.

You’ve found something even better!

That’s because Khan Academy has over 100,000 free practice questions. And they’re even better than traditional math worksheets – more instantaneous, more interactive, and more fun!

Just choose your grade level or topic to get access to 100% free practice questions:

Kindergarten, basic geometry, pre-algebra, algebra basics, high school geometry.

• Trigonometry

Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

• Addition and subtraction
• Place value (tens and hundreds)
• Addition and subtraction within 20
• Addition and subtraction within 100
• Addition and subtraction within 1000
• Measurement and data
• Counting and place value
• Measurement and geometry
• Place value
• Measurement, data, and geometry
• Add and subtract within 20
• Add and subtract within 100
• Add and subtract within 1,000
• Money and time
• Measurement
• Intro to multiplication
• 1-digit multiplication
• Addition, subtraction, and estimation
• Intro to division
• Understand fractions
• Equivalent fractions and comparing fractions
• More with multiplication and division
• Arithmetic patterns and problem solving
• Quadrilaterals
• Represent and interpret data
• Multiply by 1-digit numbers
• Multiply by 2-digit numbers
• Factors, multiples and patterns
• Add and subtract fractions
• Multiply fractions
• Understand decimals
• Plane figures
• Measuring angles
• Area and perimeter
• Units of measurement
• Decimal place value
• Add decimals
• Subtract decimals
• Multi-digit multiplication and division
• Divide fractions
• Multiply decimals
• Divide decimals
• Powers of ten
• Coordinate plane
• Algebraic thinking
• Converting units of measure
• Properties of shapes
• Ratios, rates, & percentages
• Arithmetic operations
• Negative numbers
• Properties of numbers
• Variables & expressions
• Equations & inequalities introduction
• Data and statistics
• Negative numbers: addition and subtraction
• Negative numbers: multiplication and division
• Fractions, decimals, & percentages
• Rates & proportional relationships
• Expressions, equations, & inequalities
• Numbers and operations
• Solving equations with one unknown
• Linear equations and functions
• Systems of equations
• Geometric transformations
• Data and modeling
• Volume and surface area
• Pythagorean theorem
• Transformations, congruence, and similarity
• Arithmetic properties
• Factors and multiples
• Reading and interpreting data
• Negative numbers and coordinate plane
• Ratios, rates, proportions
• Equations, expressions, and inequalities
• Exponents, radicals, and scientific notation
• Foundations
• Algebraic expressions
• Linear equations and inequalities
• Graphing lines and slope
• Expressions with exponents
• Quadratics and polynomials
• Equations and geometry
• Algebra foundations
• Solving equations & inequalities
• Working with units
• Linear equations & graphs
• Forms of linear equations
• Inequalities (systems & graphs)
• Absolute value & piecewise functions
• Exponents & radicals
• Exponential growth & decay
• Quadratics: Multiplying & factoring
• Quadratic functions & equations
• Irrational numbers
• Performing transformations
• Transformation properties and proofs
• Right triangles & trigonometry
• Non-right triangles & trigonometry (Advanced)
• Analytic geometry
• Conic sections
• Solid geometry
• Polynomial arithmetic
• Complex numbers
• Polynomial factorization
• Polynomial division
• Polynomial graphs
• Rational exponents and radicals
• Exponential models
• Transformations of functions
• Rational functions
• Trigonometric functions
• Non-right triangles & trigonometry
• Trigonometric equations and identities
• Analyzing categorical data
• Displaying and comparing quantitative data
• Summarizing quantitative data
• Modeling data distributions
• Exploring bivariate numerical data
• Study design
• Probability
• Counting, permutations, and combinations
• Random variables
• Sampling distributions
• Confidence intervals
• Significance tests (hypothesis testing)
• Two-sample inference for the difference between groups
• Inference for categorical data (chi-square tests)
• Advanced regression (inference and transforming)
• Analysis of variance (ANOVA)
• Scatterplots
• Data distributions
• Two-way tables
• Binomial probability
• Normal distributions
• Displaying and describing quantitative data
• Inference comparing two groups or populations
• Chi-square tests for categorical data
• More on regression
• Prepare for the 2020 AP®︎ Statistics Exam
• AP®︎ Statistics Standards mappings
• Polynomials
• Composite functions
• Probability and combinatorics
• Limits and continuity
• Derivatives: definition and basic rules
• Derivatives: chain rule and other advanced topics
• Applications of derivatives
• Analyzing functions
• Parametric equations, polar coordinates, and vector-valued functions
• Applications of integrals
• Differentiation: definition and basic derivative rules
• Differentiation: composite, implicit, and inverse functions
• Contextual applications of differentiation
• Applying derivatives to analyze functions
• Integration and accumulation of change
• Applications of integration
• AP Calculus AB solved free response questions from past exams
• AP®︎ Calculus AB Standards mappings
• Infinite sequences and series
• AP Calculus BC solved exams
• AP®︎ Calculus BC Standards mappings
• Integrals review
• Integration techniques
• Thinking about multivariable functions
• Derivatives of multivariable functions
• Applications of multivariable derivatives
• Integrating multivariable functions
• Green’s, Stokes’, and the divergence theorems
• First order differential equations
• Second order linear equations
• Laplace transform
• Vectors and spaces
• Matrix transformations
• Alternate coordinate systems (bases)

Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

What are teachers saying about Khan Academy’s interactive math worksheets?

“My students love Khan Academy because they can immediately learn from their mistakes, unlike traditional worksheets.”

Is Khan Academy free?

Khan Academy’s practice questions are 100% free—with no ads or subscriptions.

What do Khan Academy’s interactive math worksheets cover?

Our 100,000+ practice questions cover every math topic from arithmetic to calculus, as well as ELA, Science, Social Studies, and more.

Is Khan Academy a company?

Khan Academy is a nonprofit with a mission to provide a free, world-class education to anyone, anywhere.

Want to get even more out of Khan Academy?

Then be sure to check out our teacher tools . They’ll help you assign the perfect practice for each student from our full math curriculum and track your students’ progress across the year. Plus, they’re also 100% free — with no subscriptions and no ads.

Get Khanmigo

The best way to learn and teach with AI is here. Ace the school year with our AI-powered guide, Khanmigo. 

For learners     For teachers     For parents

• Mathematicians
• Math Lessons
• Square Roots
• Math Calculators

Simple Algebra Problems – Easy Exercises with Solutions for Beginners

JUMP TO TOPIC

Understanding Algebraic Expressions

Breaking down algebra problems, solving algebraic equations, tackling algebra word problems, types of algebraic equations, algebra for different grades.

For instance, solving the equation (3x = 7) for (x) helps us understand how to isolate the variable to find its value.

I always find it fascinating how algebra serves as the foundation for more advanced topics in mathematics and science. Starting with basic problems such as ( $(x-1)^2 = [4\sqrt{(x-4)}]^2$ ) allows us to grasp key concepts and build the skills necessary for tackling more complex challenges.

So whether you’re refreshing your algebra skills or just beginning to explore this mathematical language, let’s dive into some examples and solutions to demystify the subject. Trust me, with a bit of practice, you’ll see algebra not just as a series of problems, but as a powerful tool that helps us solve everyday puzzles.

Simple Algebra Problems and Strategies

When I approach simple algebra problems, one of the first things I do is identify the variable.

The variable is like a placeholder for a number that I’m trying to find—a mystery I’m keen to solve. Typically represented by letters like ( x ) or ( y ), variables allow me to translate real-world situations into algebraic expressions and equations.

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables (like ( x ) or ( y )), and operators (like add, subtract, multiply, and divide). For example, ( 4x + 7 ) is an algebraic expression where ( x ) is the variable and the numbers ( 4 ) and ( 7 ) are terms. It’s important to manipulate these properly to maintain the equation’s balance.

Solving algebra problems often starts with simplifying expressions. Here’s a simple method to follow:

• Combine like terms : Terms that have the same variable can be combined. For instance, ( 3x + 4x = 7x ).
• Isolate the variable : Move the variable to one side of the equation. If the equation is ( 2x + 5 = 13 ), my job is to get ( x ) by itself by subtracting ( 5 ) from both sides, giving me ( 2x = 8 ).

With algebraic equations, the goal is to solve for the variable by performing the same operation on both sides. Here’s a table with an example:

Algebra word problems require translating sentences into equations. If a word problem says “I have six less than twice the number of apples than Bob,” and Bob has ( b ) apples, then I’d write the expression as ( 2b – 6 ).

Understanding these strategies helps me tackle basic algebra problems efficiently. Remember, practice makes perfect, and each problem is an opportunity to improve.

In algebra, we encounter a variety of equation types and each serves a unique role in problem-solving. Here, I’ll brief you about some typical forms.

Linear Equations : These are the simplest form, where the highest power of the variable is one. They take the general form ( ax + b = 0 ), where ( a ) and ( b ) are constants, and ( x ) is the variable. For example, ( 2x + 3 = 0 ) is a linear equation.

Polynomial Equations : Unlike for linear equations, polynomial equations can have variables raised to higher powers. The general form of a polynomial equation is ( $a_nx^n + a_{n-1}x^{n-1} + … + a_2x^2 + a_1x + a_0 = 0$ ). In this equation, ( n ) is the highest power, and ( $a_n$ ), ( $a_{n-1} $), …, ( $a_0$ ) represent the coefficients which can be any real number.

• Binomial Equations : They are a specific type of polynomial where there are exactly two terms. Like ($ x^2 – 4 $), which is also the difference of squares, a common format encountered in factoring.

To understand how equations can be solved by factoring, consider the quadratic equation ( $x^2$ – 5x + 6 = 0 ). I can factor this into ( (x-2)(x-3) = 0 ), which allows me to find the roots of the equation.

Here’s how some equations look when classified by degree:

Remember, identification and proper handling of these equations are essential in algebra as they form the basis for complex problem-solving.

In my experience with algebra, I’ve found that the journey begins as early as the 6th grade, where students get their first taste of this fascinating subject with the introduction of variables representing an unknown quantity.

I’ve created worksheets and activities aimed specifically at making this early transition engaging and educational.

6th Grade :

Moving forward, the complexity of algebraic problems increases:

7th and 8th Grades :

• Mastery of negative numbers: students practice operations like ( -3 – 4 ) or ( -5 $\times$ 2 ).
• Exploring the rules of basic arithmetic operations with negative numbers.
• Worksheets often contain numeric and literal expressions that help solidify their concepts.

Advanced topics like linear algebra are typically reserved for higher education. However, the solid foundation set in these early grades is crucial. I’ve developed materials to encourage students to understand and enjoy algebra’s logic and structure.

Remember, algebra is a tool that helps us quantify and solve problems, both numerical and abstract. My goal is to make learning these concepts, from numbers to numeric operations, as accessible as possible, while always maintaining a friendly approach to education.

I’ve walked through various simple algebra problems to help establish a foundational understanding of algebraic concepts. Through practice, you’ll find that these problems become more intuitive, allowing you to tackle more complex equations with confidence.

Remember, the key steps in solving any algebra problem include:

• Identifying variables and what they represent.
• Setting up the equation that reflects the problem statement.
• Applying algebraic rules such as the distributive property ($a(b + c) = ab + ac$), combining like terms, and inverse operations.
• Checking your solutions by substituting them back into the original equations to ensure they work.

As you continue to engage with algebra, consistently revisiting these steps will deepen your understanding and increase your proficiency. Don’t get discouraged by mistakes; they’re an important part of the learning process.

I hope that the straightforward problems I’ve presented have made algebra feel more manageable and a little less daunting. Happy solving!

• Pre Calculus
• Probability
• Sets & Set Theory
• Trigonometry

Examples for

Mathematical Word Problems

Math word problems is one of the most complex parts of the elementary math curriculum since translating text into symbolic math is required to solve the problem. Because the Wolfram Language has powerful symbolic computation ability, Wolfram|Alpha can interpret basic mathematical word problems and give descriptive results.

Solve a word problem and explore related facts.

Solve a word problem:

Related examples.

• Our Mission

3 Simple Strategies to Improve Students’ Problem-Solving Skills

These strategies are designed to make sure students have a good understanding of problems before attempting to solve them.

Research provides a striking revelation about problem solvers. The best problem solvers approach problems much differently than novices. For instance, one meta-study showed that when experts evaluate graphs , they tend to spend less time on tasks and answer choices and more time on evaluating the axes’ labels and the relationships of variables within the graphs. In other words, they spend more time up front making sense of the data before moving to addressing the task.

While slower in solving problems, experts use this additional up-front time to more efficiently and effectively solve the problem. In one study, researchers found that experts were much better at “information extraction” or pulling the information they needed to solve the problem later in the problem than novices. This was due to the fact that they started a problem-solving process by evaluating specific assumptions within problems, asking predictive questions, and then comparing and contrasting their predictions with results. For example, expert problem solvers look at the problem context and ask a number of questions:

• What do we know about the context of the problem?
• What assumptions are underlying the problem? What’s the story here?
• What qualitative and quantitative information is pertinent?
• What might the problem context be telling us? What questions arise from the information we are reading or reviewing?
• What are important trends and patterns?

As such, expert problem solvers don’t jump to the presented problem or rush to solutions. They invest the time necessary to make sense of the problem.

Now, think about your own students: Do they immediately jump to the question, or do they take time to understand the problem context? Do they identify the relevant variables, look for patterns, and then focus on the specific tasks?

If your students are struggling to develop the habit of sense-making in a problem- solving context, this is a perfect time to incorporate a few short and sharp strategies to support them.

3 Ways to Improve Student Problem-Solving

1. Slow reveal graphs: The brilliant strategy crafted by K–8 math specialist Jenna Laib and her colleagues provides teachers with an opportunity to gradually display complex graphical information and build students’ questioning, sense-making, and evaluating predictions.

For instance, in one third-grade class, students are given a bar graph without any labels or identifying information except for bars emerging from a horizontal line on the bottom of the slide. Over time, students learn about the categories on the x -axis (types of animals) and the quantities specified on the y -axis (number of baby teeth).

The graphs and the topics range in complexity from studying the standard deviation of temperatures in Antarctica to the use of scatterplots to compare working hours across OECD (Organization for Economic Cooperation and Development) countries. The website offers a number of graphs on Google Slides and suggests questions that teachers may ask students. Furthermore, this site allows teachers to search by type of graph (e.g., scatterplot) or topic (e.g., social justice).

2. Three reads: The three-reads strategy tasks students with evaluating a word problem in three different ways . First, students encounter a problem without having access to the question—for instance, “There are 20 kangaroos on the grassland. Three hop away.” Students are expected to discuss the context of the problem without emphasizing the quantities. For instance, a student may say, “We know that there are a total amount of kangaroos, and the total shrinks because some kangaroos hop away.”

Next, students discuss the important quantities and what questions may be generated. Finally, students receive and address the actual problem. Here they can both evaluate how close their predicted questions were from the actual questions and solve the actual problem.

To get started, consider using the numberless word problems on educator Brian Bushart’s site . For those teaching high school, consider using your own textbook word problems for this activity. Simply create three slides to present to students that include context (e.g., on the first slide state, “A salesman sold twice as much pears in the afternoon as in the morning”). The second slide would include quantities (e.g., “He sold 360 kilograms of pears”), and the third slide would include the actual question (e.g., “How many kilograms did he sell in the morning and how many in the afternoon?”). One additional suggestion for teams to consider is to have students solve the questions they generated before revealing the actual question.

3. Three-Act Tasks: Originally created by Dan Meyer, three-act tasks follow the three acts of a story . The first act is typically called the “setup,” followed by the “confrontation” and then the “resolution.”

This storyline process can be used in mathematics in which students encounter a contextual problem (e.g., a pool is being filled with soda). Here students work to identify the important aspects of the problem. During the second act, students build knowledge and skill to solve the problem (e.g., they learn how to calculate the volume of particular spaces). Finally, students solve the problem and evaluate their answers (e.g., how close were their calculations to the actual specifications of the pool and the amount of liquid that filled it).

Often, teachers add a fourth act (i.e., “the sequel”), in which students encounter a similar problem but in a different context (e.g., they have to estimate the volume of a lava lamp). There are also a number of elementary examples that have been developed by math teachers including GFletchy , which offers pre-kindergarten to middle school activities including counting squares , peas in a pod , and shark bait .

Students need to learn how to slow down and think through a problem context. The aforementioned strategies are quick ways teachers can begin to support students in developing the habits needed to effectively and efficiently tackle complex problem-solving.

A Blog About Parenting: Coping Skills, Behavior Management and Special Needs

25 Fun Problem Solving Activities for Kids

Problem-solving activities for kids : Explore 24 fun problem-solving games and activities, and learn effective tips and strategies to teach kids problem-solving skills. If you want to explore problem-solving strategies more in-depth, you can also grab our workbook “ Problem-Solving for Kids ” (printable resource).

Problem-solving is the cognitive process of finding solutions to challenges or complex situations.

A systematic approach to problem-solving tends to include defining the problem, gathering information and data, generating potential solutions, evaluating the pros and cons of each solution, making a decision, and implementing the chosen solution.

Effective problem-solving often requires critical thinking, a good dose of creativity, and the ability to consider multiple perspectives. It may also involve identifying patterns, breaking down a problem into manageable chunks, and applying our logic to develop solutions.

Problem-solving is present in everyday situations and across all fields: business, science, personal life, and education. There is not one single aspect in our lives where we don’t need to apply our problem-solving skills.

Table of Contents

• Problem-solving steps
• Development of problem-solving in childhood
• Benefits of developing problem-solving skills
• 10 Tips to teach kids problem-solving skills
• 10 Examples of problem-solving strategies
• 25 Problem-solving activities and games for kids

Problem-Solving Steps

Some key components of problem-solving include:

• Identifying the problem Recognizing and defining the issue or challenge that needs to be addressed.
• Analyzing the problem Investigating and understanding the underlying causes, factors, and relationships related to the problem.
• Generating solutions Generating potential solutions or strategies to address the problem.
• Evaluating all possible solutions (Pros and Cons Analysis) Assessing the feasibility, effectiveness, and potential consequences of each solution. Considering the positive and negative aspects of each solution.
• Decision-making Selecting the best solution based on our analysis and judgment.
• Implementing the best solution Actioning our chosen solution
• Monitoring progress and results
• Reflecting on the outcomes Reviewing and evaluating the outcomes of the implemented solution, learning from the experience, and making adjustments if necessary.

Development of Problem-Solving Skills in Childhood

Children begin to develop problem-solving skills from a very early age, and these skills continue to develop and refine throughout childhood and adolescence.

Babies soon learn about action and reaction. And, as early as eight months, they begin to acquire an understanding of cause and effect (they shake a rattle, it makes a sound; they push a toy, it falls)

Between 13 and 24 months, they start solving simple problems through trial and error and engage in symbolic play using their imagination.

As children progress into middle childhood (ages 7-11), they develop more advanced problem-solving skills. They become capable of understanding multiple perspectives and can consider multiple factors when solving problems. They start using logic and reasoning to solve increasingly complex problems.

During adolescence (ages 12 and up), problem-solving skills continue to develop. Teenagers can generate and test hypotheses and use deductive and inductive reasoning to arrive at solutions.

Each child will develop their problem-solving skills at their own pace. Some children may show advanced problem-solving abilities at an earlier age. Others may require more time and experience to develop these skills fully.

Benefits of Developing Problem-Solving Skills in Children

Problem-solving skills in children are crucial for children’s cognitive, social, and emotional development. It equips them to approach challenges, think critically, make informed decisions, and find creative solutions. 

The benefits of good problem-solving skills in children include:

• Positive impact on self-esteem and confidence Identifying, analyzing, and solving their problems contributes to our kids’ sense of competence .
• Fosters Independence and Autonomy When our kids are able to problem-solve on their own, they take one more step toward independence
• Academic Success Problem-solving skills contribute to academic achievement, as they help students analyze and solve complex problems across various subjects.
• Cognitive Development Problem-solving fosters cognitive skills such as logical reasoning, analytical thinking, and abstract reasoning.
• Critical Thinking Problem-solving enhances critical thinking abilities, enabling children to evaluate information, identify biases, and make informed judgments.
• Creativity Problem-solving promotes creativity by encouraging children to think outside the box, generate innovative ideas, and explore multiple solutions.
• Emotional Resilience Problem-solving skills enhance emotional resilience by enabling children to manage and cope with challenges effectively, reducing stress and promoting well-being.
• Improved Social Interactions/Relationships Problem-solving abilities contribute to better social interactions, conflict resolution , and peer collaboration, promoting healthy relationships.
• Future career success Problem-solving skills are highly valued in the workplace and can positively influence future career success.

10+ Helpful Tips to Teach Kids Problem-Solving Skills

Teaching problem-solving skills to kids is an important part of their cognitive development. It helps them develop critical thinking, creativity, and resilience.

But how can we help our kids and students to develop this essential skill?

We can help our kids and students develop and improve their problem-solving skills in many ways.  These are some helpful tips that you could consider:

• Model problem-solving behavior When you see yourself in a problem-solving situation, verbalize your thought process: “I wonder how I should address this issue. I guess my alternatives could be… They all have positives and negatives….”
• Let them participate in the problem-solving situation “Could you help me solve this puzzle?”
• Provide real-life problem-solving situations Real-life scenarios make problem-solving more meaningful for kids. For example, discuss how to resolve a conflict with a sibling or how to make the morning routine smoother.
• Teach them how to break down problems Show them how to break down complex problems into manageable sub-problems.
• Practice brainstorming Create brainstorming situations where all the family (or the classroom) can contribute to solving a problem
• Teach the value of perseverance Sometimes, we must stick to a situation and persevere before finding a solution. Encourage kids to persevere through challenges and setbacks, emphasizing that mistakes and failures are opportunities for learning.
• Encourage critical thinking Encourage kids to analyze situations, consider different perspectives, and evaluate possible outcomes.
• How could we make your school lunch healthier but still yummy?
• How could we reuse/recycle all this paper?
• What could we do to help you remember all the steps in your night routine?
• Encourage reflection When they can find a solution for a problem, don’t jump to solve it for them. Encourage them to reflect on the problem and find and evaluate alternatives. And after a problem is solved, think about the whole process and the learnings. “How did this work?” “What did you learn” “Do you need to change anything?”
• Foster creativity Provide them with opportunities for imaginative play, creative projects, and brainstorming sessions.
• Teach the value of teamwork Teach kids the importance of working together to solve problems. Engage them in group activities or projects that require teamwork and collaboration. This helps kids learn the value of different perspectives and work together towards an objective while they practice their communication skills.
• Teach decision-making skills Teach kids how to approach problems systematically by going through the steps we have mentioned in our first section.
• Encourage both structured and free play. Structured play can help you create good problem-solving situations, while free play will foster creativity.

Developing problem-solving skills is an ongoing process that will also continue in adulthood. Provide your kids with guidance and support, and celebrate their efforts and achievements along the way.

10 Examples of Problem-Solving Strategies

There are different strategies that can help us solve a wide range of problems. Here are some commonly recognized problem-solving strategies:

1 . Trial and Error : This is the first problem strategy that we ever learn. We start using trial and error strategies in infancy, and it continues serving its purpose in many situations. This strategy involves trying different solutions or approaches and learning from the errors or failures until a successful solution is found.

2. Algorithm: An algorithm is a step-by-step procedure or a set of rules that guarantees a solution to a specific problem. It is a systematic approach to problem-solving that follows a predetermined set of instructions.

3. Heuristics: Heuristics are mental shortcuts or rules of thumb that help simplify problem-solving by providing quick and efficient strategies. While heuristics can be effective in many situations, they may also lead to biases and errors.

4. Divide and Conquer: This strategy involves breaking down a complex problem into smaller, more manageable chunks or steps that make the overall problem easier to tackle.

5. Working Backwards: This strategy involves starting from the desired outcome and working backward to determine the steps or actions needed to reach that outcome. We often use this problem-solving strategy when we set goals.

6. Analogical Reasoning: Analogical reasoning involves drawing parallels between the current problem and a similar problem that has been solved in the past. By applying the solution from the previous problem to the current one, individuals can find a solution more efficiently.

7. Brainstorming: Brainstorming gets lots of brains working on the same problem. It is a great collaborative problem-solving strategy that can bring different perspectives and experiences to the table and may result in lots of creative ideas and solutions. 

8. Decision Matrix: A decision matrix is a systematic approach to evaluating and comparing different options or solutions. It involves creating a matrix that lists alternatives and the criteria for evaluation. It assigns weights or scores to each criterion to come up with the optimal alternative.

9. Root Cause Analysis: Sometimes, we need to understand what is causing a problem before we can attempt to solve it, as different causes may require different approaches (for example, when you are sick, your doctor may need to understand what is causing the problem before prescribing a medicine)

10. Simulation and Modeling: Simulation involves creating a simplified representation or model of a problem situation to gain insights and test different scenarios.

Our choice of strategy will depend on the problem, available resources, and our own personal preferences and circumstances. We may also need to combine strategies or apply different ones to different aspects of a complex problem.

(Disclosure: We are a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for us to earn fees by linking to Amazon.com and affiliated sites. You can also read our Disclosure & Disclaimer policy  here )

Best Problem-Solving Activities for Kids

Play-based activities are centered around play and are designed to engage children in active learning and exploration. And fun problem-solving activities are a great way to develop children’s critical thinking, creativity, and decision-making skills.

In this section, we will review some problem-solving games and activities that will engage your kids’ critical-thinking skills and creativity.

1. Puzzle Games Puzzles are a fun activity for children of all ages. Young children will enjoy simple puzzles, while older children (and adults!) can have fun with more complex ones. Encourage them to use logical thinking and problem-solving strategies to complete the puzzles.

2. Crosswords A crossword is another fun type of puzzle and a good source of mental stimulation.

3. Sudoku Sudoku is a popular logic-based puzzle that involves filling a grid with numbers.

It can be extremely easy or very challenging, adaptable even for young learners.

Let’s go now for a couple of building challenges!

4. Build the Tallest Tower Give the child a set of materials (Legos, building blocks, wooden blocks, or other construction materials) and ask them to build the tallest tower they can. This simple game will encourage them to problem-solve as they build and figure out how to make the tower stable.

5. Build Towers with Different Materials Ask your child to build three different towers with different materials. Then assess how stable they are and how much weight they can hold. Analyze the pros and cons of using each type of material.

6. Treasure Hunt Set up a treasure hunt with clues leading to hidden objects or rewards. Children will have to follow the clues and solve puzzles to find the ultimate prize. This activity encourages problem-solving, critical thinking, and teamwork.

7. Scavenger Hunt Playing Scavenger Hunt can be a fun way for our kids to put their creative problem-solving skills to good use. Provide them with clues and puzzles that they must solve in order to find the next clue.

8. Mystery Bag Fill a bag with random objects and ask children to come up with creative uses for each item. Encourage them to think outside the box and find innovative solutions.

9. Memory Game While memory games primarily focus on memory retention and recall, they can indirectly contribute to problem-solving skills by developing cognitive abilities such as attention, information processing, and adjusting their strategies.

10. Role-Playing Scenarios Create role-playing scenarios where children have to solve a problem or make decisions. For example, pretend to be stranded on a desert island and ask them to decide what items they will take and how they will survive.

11. Role-Play Social Situations Work in developing social skills with social problem-solving situations.

12. Brainstorming Sessions Choose a topic or problem and hold brainstorming sessions where children can generate as many ideas as possible. Encourage them not to limit themselves (even if alternatives feel unfeasible!)

13. Team Building Activities and Games Engage children in team-building games like building a balloon tower. Each team member will need to collaborate, communicate, and problem-solve together to complete the project.

14. Escape Rooms An escape room is a super fun team problem-solving activity.

In an escape room, participants are locked inside a themed room and must work together to solve puzzles, find clues, and accomplish tasks within a given time limit in order to “escape” from the room.

15. Science Experiments Conduct simple science experiments that involve problem-solving. For example, in the classic “sink or float” experiment, children predict and test which objects will sink or float in water.

Problem-Solving Board Games

There are many board games that will test our kids problems solving activities. These are just a few examples:

16. Cluedo Players must solve a murder mystery by deducing the murderer, the weapon used, and the location of the crime. Players collect and examine clues to eliminate possibilities and make logical deductions.

17. Codenames Another classic game where players are split into two teams and must guess words based on clues from their teammates.

There are many codenames games available, including themes like Disney or Harry Potter.

18. Mastermind Game In this strategy game players take turns setting and solving secret codes

19. Scrabble Scrabble is a classic word game where players form words on a game board using letter tiles.

Kids must use their problem-solving skills to analyze the available letters, consider the best word combination and strategically place those words to score the highest points.

Learning Problem-Solving with Card Games

Card games provide opportunities for kids to develop problem-solving skills such as strategy, memory, pattern recognition, decision-making, and observation.

Just a couple of examples:

20. Uno Uno is a classic card game where kids match cards based on color or number. They need to assess their cards, strategize and make decisions about which cards to play to get rid of their cards while also considering the cards in their opponents’ hands.

21. Go Fish Go Fish is a classic card game where players try to collect sets of cards by asking other players if they have specific cards. Players need to remember which cards they have and make decisions about who to ask and what sets to pursue.

22. Coding Challenges Introduce children to coding activities using platforms like Scratch (or ScratchJr for younger kids), Code.org, or Tynker. Coding involves problem-solving and logical thinking, and children can create interactive stories, games, or animations.

23. Outdoor Problem Solving Take children outside and present them with challenges that require problem-solving, such as building a shelter using natural materials or finding their way through an obstacle course.

24. Problem-Solving Worksheets Help your child follow a systematic approach to problem-solving with these helpful worksheets

25. Goal-Setting Activities for Kids Learning to set goals and make plans to achieve them is also a problem-solving activity. I have several resources to teach kids about goal-setting that I will list below:

• Goal-Setting Activities for Kids
• SMART Goals for Kids
• Goal Tracker Thermometer

Remember to provide guidance and support during these activities while encouraging children to think independently and come up with their own solutions.

Problem-Solving Worksheets

Looking for kid-friendly examples of problem-solving strategies ?

This workbook explores the following  problem-solving strategies  (with child-friendly examples and activities):

• Trial and Error
• Heuristics (Clever shortcuts)
• Divide and Conquer
• Working Backwards
• Brainstorming
• Decision Matrix
• Root Cause Analysis
• Systematic problem-solving

One Comment

I always look forward to your articles with active interventions. Thank you!

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *