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Problem-solving.

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out of harm's way

in a position that is safe from harm or from which harm cannot be done

Trial, judge, and jury: talking about what happens when a criminal is caught

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5 Effective Problem-Solving Strategies

Got a problem you’re trying to solve? Strategies like trial and error, gut instincts, and “working backward” can help. We look at some examples and how to use them.

We all face problems daily. Some are simple, like deciding what to eat for dinner. Others are more complex, like resolving a conflict with a loved one or figuring out how to overcome barriers to your goals.

No matter what problem you’re facing, these five problem-solving strategies can help you develop an effective solution.

What are problem-solving strategies?

To effectively solve a problem, you need a problem-solving strategy .

If you’ve had to make a hard decision before then you know that simply ruminating on the problem isn’t likely to get you anywhere. You need an effective strategy — or a plan of action — to find a solution.

In general, effective problem-solving strategies include the following steps:

• Define the problem.
• Come up with alternative solutions.
• Decide on a solution.
• Implement the solution.

Problem-solving strategies don’t guarantee a solution, but they do help guide you through the process of finding a resolution.

Using problem-solving strategies also has other benefits . For example, having a strategy you can turn to can help you overcome anxiety and distress when you’re first faced with a problem or difficult decision.

The key is to find a problem-solving strategy that works for your specific situation, as well as your personality. One strategy may work well for one type of problem but not another. In addition, some people may prefer certain strategies over others; for example, creative people may prefer to depend on their insights than use algorithms.

It’s important to be equipped with several problem-solving strategies so you use the one that’s most effective for your current situation.

1. Trial and error

One of the most common problem-solving strategies is trial and error. In other words, you try different solutions until you find one that works.

For example, say the problem is that your Wi-Fi isn’t working. You might try different things until it starts working again, like restarting your modem or your devices until you find or resolve the problem. When one solution isn’t successful, you try another until you find what works.

Trial and error can also work for interpersonal problems . For example, if your child always stays up past their bedtime, you might try different solutions — a visual clock to remind them of the time, a reward system, or gentle punishments — to find a solution that works.

2. Heuristics

Sometimes, it’s more effective to solve a problem based on a formula than to try different solutions blindly.

Heuristics are problem-solving strategies or frameworks people use to quickly find an approximate solution. It may not be the optimal solution, but it’s faster than finding the perfect resolution, and it’s “good enough.”

Algorithms or equations are examples of heuristics.

An algorithm is a step-by-step problem-solving strategy based on a formula guaranteed to give you positive results. For example, you might use an algorithm to determine how much food is needed to feed people at a large party.

However, many life problems have no formulaic solution; for example, you may not be able to come up with an algorithm to solve the problem of making amends with your spouse after a fight.

3. Gut instincts (insight problem-solving)

While algorithm-based problem-solving is formulaic, insight problem-solving is the opposite.

When we use insight as a problem-solving strategy we depend on our “gut instincts” or what we know and feel about a situation to come up with a solution. People might describe insight-based solutions to problems as an “aha moment.”

For example, you might face the problem of whether or not to stay in a relationship. The solution to this problem may come as a sudden insight that you need to leave. In insight problem-solving, the cognitive processes that help you solve a problem happen outside your conscious awareness.

4. Working backward

Working backward is a problem-solving approach often taught to help students solve problems in mathematics. However, it’s useful for real-world problems as well.

Working backward is when you start with the solution and “work backward” to figure out how you got to the solution. For example, if you know you need to be at a party by 8 p.m., you might work backward to problem-solve when you must leave the house, when you need to start getting ready, and so on.

5. Means-end analysis

Means-end analysis is a problem-solving strategy that, to put it simply, helps you get from “point A” to “point B” by examining and coming up with solutions to obstacles.

When using means-end analysis you define the current state or situation (where you are now) and the intended goal. Then, you come up with solutions to get from where you are now to where you need to be.

For example, a student might be faced with the problem of how to successfully get through finals season . They haven’t started studying, but their end goal is to pass all of their finals. Using means-end analysis, the student can examine the obstacles that stand between their current state and their end goal (passing their finals).

They could see, for example, that one obstacle is that they get distracted from studying by their friends. They could devise a solution to this obstacle by putting their phone on “do not disturb” mode while studying.

Let’s recap

Whether they’re simple or complex, we’re faced with problems every day. To successfully solve these problems we need an effective strategy. There are many different problem-solving strategies to choose from.

Although problem-solving strategies don’t guarantee a solution, they can help you feel less anxious about problems and make it more likely that you come up with an answer.

8 sources collapsed

• Chu Y, et al. (2011). Human performance on insight problem-solving: A review. https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1094&context=jps
• Dumper K, et al. (n.d.) Chapter 7.3: Problem-solving in introductory psychology. https://opentext.wsu.edu/psych105/chapter/7-4-problem-solving/
• Foulds LR. (2017). The heuristic problem-solving approach. https://www.tandfonline.com/doi/abs/10.1057/jors.1983.205
• Gick ML. (1986). Problem-solving strategies. https://www.tandfonline.com/doi/abs/10.1080/00461520.1986.9653026
• Montgomery ME. (2015). Problem solving using means-end analysis. https://sites.psu.edu/psych256sp15/2015/04/19/problem-solving-using-means-end-analysis/
• Posamentier A, et al. (2015). Problem-solving strategies in mathematics. Chapter 3: Working backwards. https://www.worldscientific.com/doi/10.1142/9789814651646_0003
• Sarathy V. (2018). Real world problem-solving. https://www.frontiersin.org/articles/10.3389/fnhum.2018.00261/full
• Woods D. (2000). An evidence-based strategy for problem solving. https://www.researchgate.net/publication/245332888_An_Evidence-Based_Strategy_for_Problem_Solving

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problem-solving

Definition of problem-solving

Examples of problem-solving in a sentence.

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'problem-solving.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

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Cite this entry.

“Problem-solving.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/problem-solving. Accessed 24 Aug. 2024.

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Overview of the Problem-Solving Mental Process

• 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.

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You can become a better problem solving by:

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

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

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

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

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

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

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

40 problem-solving techniques and processes

All teams and organizations encounter challenges. Approaching those challenges without a structured problem solving process can end up making things worse.

Proven problem solving techniques such as those outlined below can guide your group through a process of identifying problems and challenges , ideating on possible solutions , and then evaluating and implementing the most suitable .

In this post, you'll find problem-solving tools you can use to develop effective solutions. You'll also find some tips for facilitating the problem solving process and solving complex problems.

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What is problem solving?

Problem solving is a process of finding and implementing a solution to a challenge or obstacle. In most contexts, this means going through a problem solving process that begins with identifying the issue, exploring its root causes, ideating and refining possible solutions before implementing and measuring the impact of that solution.

For simple or small problems, it can be tempting to skip straight to implementing what you believe is the right solution. The danger with this approach is that without exploring the true causes of the issue, it might just occur again or your chosen solution may cause other issues.

Particularly in the world of work, good problem solving means using data to back up each step of the process, bringing in new perspectives and effectively measuring the impact of your solution.

Effective problem solving can help ensure that your team or organization is well positioned to overcome challenges, be resilient to change and create innovation. In my experience, problem solving is a combination of skillset, mindset and process, and it’s especially vital for leaders to cultivate this skill.

What is the seven step problem solving process?

A problem solving process is a step-by-step framework from going from discovering a problem all the way through to implementing a solution.

With practice, this framework can become intuitive, and innovative companies tend to have a consistent and ongoing ability to discover and tackle challenges when they come up.

You might see everything from a four step problem solving process through to seven steps. While all these processes cover roughly the same ground, I’ve found a seven step problem solving process is helpful for making all key steps legible.

We’ll outline that process here and then follow with techniques you can use to explore and work on that step of the problem solving process with a group.

The seven-step problem solving process is:

1. Problem identification 

The first stage of any problem solving process is to identify the problem(s) you need to solve. This often looks like using group discussions and activities to help a group surface and effectively articulate the challenges they’re facing and wish to resolve.

Be sure to align with your team on the exact definition and nature of the problem you’re solving. An effective process is one where everyone is pulling in the same direction – ensure clarity and alignment now to help avoid misunderstandings later.

2. Problem analysis and refinement

The process of problem analysis means ensuring that the problem you are seeking to solve is  the   right problem . Choosing the right problem to solve means you are on the right path to creating the right solution.

At this stage, you may look deeper at the problem you identified to try and discover the root cause at the level of people or process. You may also spend some time sourcing data, consulting relevant parties and creating and refining a problem statement.

Problem refinement means adjusting scope or focus of the problem you will be aiming to solve based on what comes up during your analysis. As you analyze data sources, you might discover that the root cause means you need to adjust your problem statement. Alternatively, you might find that your original problem statement is too big to be meaningful approached within your current project.

Remember that the goal of any problem refinement is to help set the stage for effective solution development and deployment. Set the right focus and get buy-in from your team here and you’ll be well positioned to move forward with confidence.

3. Solution generation

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

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

4. Solution development

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

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

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

5. Decision making and planning

Nearly there! Once you’ve got a set of possible, you’ll need to make a decision on which to implement. This can be a consensus-based group decision or it might be for a leader or major stakeholder to decide. You’ll find a set of effective decision making methods below.

Once your group has reached consensus and selected a solution, there are some additional actions that also need to be decided upon. You’ll want to work on allocating ownership of the project, figure out who will do what, how the success of the solution will be measured and decide the next course of action.

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

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

6. Solution implementation 

This is what we were waiting for! All problem solving processes have the end goal of implementing an effective and impactful solution that your group has confidence in.

Project management and communication skills are key here – your solution may need to adjust when out in the wild or you might discover new challenges along the way. For some solutions, you might also implement a test with a small group and monitor results before rolling it out to an entire company.

You should have a clear owner for your solution who will oversee the plans you made together and help ensure they’re put into place. This person will often coordinate the implementation team and set-up processes to measure the efficacy of your solution too.

7. Solution evaluation 

So you and your team developed a great solution to a problem and have a gut feeling it’s been solved. Work done, right? Wrong. All problem solving strategies benefit from evaluation, consideration, and feedback.

You might find that the solution does not work for everyone, might create new problems, or is potentially so successful that you will want to roll it out to larger teams or as part of other initiatives. 

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

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

It’s also worth underlining how important record keeping is throughout the problem solving process. If a solution didn’t work, you need to have the data and records to see why that was the case. If you go back to the drawing board, notes from the previous workshop can help save time.

What does an effective problem solving process look like?

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

The format of a workshop ensures that you can get buy-in from your group, encourage free-thinking and solution exploration before making a decision on what to implement following the session.

This Design Sprint 2.0 template is an effective problem solving process from top agency AJ&Smart. It’s a great format for the entire problem solving process, with four-days of workshops designed to surface issues, explore solutions and even test a solution.

Check it for an example of how you might structure and run a problem solving process and feel free to copy and adjust it your needs!

For a shorter process you can run in a single afternoon, this remote problem solving agenda will guide you effectively in just a couple of hours.

Whatever the length of your workshop, by using 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!

Complete problem-solving methods

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

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.

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

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   It doesn’t matter where you work and what your job role is, if you work with other people together as a team, you will always encounter the same challenges: Unclear goals and miscommunication that cause busy work and overtime Unstructured meetings that leave attendants tired, confused and without clear outcomes. Frustration builds up because internal challenges to productivity are not addressed Sudden changes in priorities lead to a loss of focus and momentum Muddled compromise takes the place of clear decision- making, leaving everybody to come up with their own interpretation. In short, a lack of structure leads to a waste of time and effort, projects that drag on for too long and frustrated, burnt out teams. AJ&Smart has worked with some of the most innovative, productive companies in the world. What sets their teams apart from others is not better tools, bigger talent or more beautiful offices. The secret sauce to becoming a more productive, more creative and happier team is simple: Replace all open discussion or brainstorming with a structured process that leads to more ideas, clearer decisions and better outcomes. When a good process provides guardrails and a clear path to follow, it becomes easier to come up with ideas, make decisions and solve problems. This is why AJ&Smart created Lightning Decision Jam (LDJ). It’s a simple and short, but powerful group exercise that can be run either in-person, in the same room, or remotely with distributed teams.

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.

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.

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.

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.

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.

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!

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.

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.

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.

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.

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.

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.

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.

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.

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!

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 brainstorming solutions

Now you have the context and background of the problem you are trying to solving, now comes the time to start ideating and thinking about how you’ll solve the issue.

Here, you’ll want to encourage creative, free thinking and speed. Get as many ideas out as possible and explore different perspectives so you have the raw material for the next step.

Looking at a problem from a new angle can be one of the most effective ways of creating an effective solution. TRIZ is a problem-solving tool that asks the group to consider what they must not do in order to solve a challenge.

By reversing the discussion, new topics and taboo subjects often emerge, allowing the group to think more deeply and create ideas that confront the status quo in a safe and meaningful way. If you’re working on a problem that you’ve tried to solve before, TRIZ is a great problem-solving method to help your team get unblocked.

Making Space with TRIZ   #issue analysis   #liberating structures   #issue resolution   You can clear space for innovation by helping a group let go of what it knows (but rarely admits) limits its success and by inviting creative destruction. TRIZ makes it possible to challenge sacred cows safely and encourages heretical thinking. The question “What must we stop doing to make progress on our deepest purpose?” induces seriously fun yet very courageous conversations. Since laughter often erupts, issues that are otherwise taboo get a chance to be aired and confronted. With creative destruction come opportunities for renewal as local action and innovation rush in to fill the vacuum. Whoosh!

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.

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.

Idea and Concept Development

Brainstorming without structure can quickly become chaotic or frustrating. In a problem-solving context, having an ideation framework to follow can help ensure your team is both creative and disciplined.

In this method, you’ll find an idea generation process that encourages your group to brainstorm effectively before developing their ideas and begin clustering them together. By using concepts such as Yes and…, more is more and postponing judgement, you can create the ideal conditions for brainstorming with ease.

Idea & Concept Development   #hyperisland   #innovation   #idea generation   Ideation and Concept Development is a process for groups to work creatively and collaboratively to generate creative ideas. It’s a general approach that can be adapted and customized to suit many different scenarios. It includes basic principles for idea generation and several steps for groups to work with. It also includes steps for idea selection and development.

Problem-solving techniques for developing and refining 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 develop and refine your ideas in order to bring them closer to a solution that actually solves the problem.

Use these problem-solving techniques when you want to help your team think through their ideas and refine them as part of your problem solving process.

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.

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

Ensuring that everyone in a group is able to contribute to a discussion is vital during any problem solving process. Not only does this ensure all bases are covered, but its then easier to get buy-in and accountability when people have been able to contribute to the process.

1-2-4-All is a tried and tested facilitation technique where participants are asked to first brainstorm on a topic on their own. Next, they discuss and share ideas in a pair before moving into a small group. Those groups are then asked to present the best idea from their discussion to the rest of the team.

This method can be used in many different contexts effectively, though I find it particularly shines in the idea development stage of the process. Giving each participant time to concretize their ideas and develop them in progressively larger groups can create a great space for both innovation and psychological safety.

1-2-4-All   #idea generation   #liberating structures   #issue analysis   With this facilitation technique you can immediately include everyone regardless of how large the group is. You can generate better ideas and more of them faster than ever before. You can tap the know-how and imagination that is distributed widely in places not known in advance. Open, generative conversation unfolds. Ideas and solutions are sifted in rapid fashion. Most importantly, participants own the ideas, so follow-up and implementation is simplified. No buy-in strategies needed! Simple and elegant!

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.

Problem-solving techniques for making decisions and planning

After your group is happy with the possible solutions you’ve developed, now comes the time to choose which to implement. There’s more than one way to make a decision and the best option is often dependant on the needs and set-up of your group.

Sometimes, it’s the case that you’ll want to vote as a group on what is likely to be the most impactful solution. Other times, it might be down to a decision maker or major stakeholder to make the final decision. Whatever your process, here’s some techniques you can use to help you make a decision during your problem solving process.

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.

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.

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.

Straddling the gap between decision making and planning, MoSCoW is a simple and effective method that allows a group team to easily prioritize a set of possible options.

Use this method in a problem solving process by collecting and summarizing all your possible solutions and then categorize them into 4 sections: “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”.

This method is particularly useful when its less about choosing one possible solution and more about prioritorizing which to do first and which may not fit in the scope of your project. In my experience, complex challenges often require multiple small fixes, and this method can be a great way to move from a pile of things you’d all like to do to a structured plan.

MoSCoW   #define intentions   #create   #design   #action   #remote-friendly   MoSCoW is a method that allows the team to prioritize the different features that they will work on. Features are then categorized into “Must have”, “Should have”, “Could have”, or “Would like but won‘t get”. To be used at the beginning of a timeslot (for example during Sprint planning) and when planning is needed.

When it comes to managing the rollout of a solution, clarity and accountability are key factors in ensuring the success of the project. The RAACI chart is a simple but effective model for setting roles and responsibilities as part of a planning session.

Start by listing each person involved in the project and put them into the following groups in order to make it clear who is responsible for what during the rollout of your solution.

• Responsibility  (Which person and/or team will be taking action?)
• Authority  (At what “point” must the responsible person check in before going further?)
• Accountability  (Who must the responsible person check in with?)
• Consultation  (Who must be consulted by the responsible person before decisions are made?)
• Information  (Who must be informed of decisions, once made?)

Ensure this information is easily accessible and use it to inform who does what and who is looped into discussions and kept up to date.

RAACI   #roles and responsibility   #teamwork   #project management   Clarifying roles and responsibilities, levels of autonomy/latitude in decision making, and levels of engagement among diverse stakeholders.

Problem-solving warm-up activities

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

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.

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.

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.

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.

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.

Closing activities for a problem-solving process

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

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.

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.

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.

Tips for 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.

Create psychologically safe spaces for discussion

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 tough for people to stand up and contribute if the problems or challenges are emotive or personal in nature. Try and create a psychologically safe space for these kinds of discussions and where possible, create regular opportunities for challenges to be brought up organically.

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!

Save time and effort creating an effective problem solving process

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 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! 

James Smart is Head of Content at SessionLab. He’s also a creative facilitator who has run workshops and designed courses for establishments like the National Centre for Writing, UK. He especially enjoys working with young people and empowering others in their creative practice.

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

Your list of techniques for problem solving can be helpfully extended by adding TRIZ to the list of techniques. TRIZ has 40 problem solving techniques derived from methods inventros and patent holders used to get new patents. About 10-12 are general approaches. many organization sponsor classes in TRIZ that are used to solve business problems or general organiztational problems. You can take a look at TRIZ and dwonload a free internet booklet to see if you feel it shound be included per your selection process.

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120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

• 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 . ( See our entire list of back to school resources for teachers here .)

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.

Try Prodigy

There's no cost to you or your students and Prodigy is fully aligned with state standards for grades 1-8 math.

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7 Problem Solving Skills That Aren’t Just Buzzwords (+ Resume Example)

• Júlia Mlčúchova , 
• Updated April 8, 2024 9 min read

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

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

Sounds good, right? Curious to learn more? 

In this article we’ll show you:

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

Table of Contents

Click on a section to skip

What are problem solving skills?

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

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

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

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

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

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

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

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

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

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

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

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

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

Wondering how good is your resume?

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

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

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

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

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

• Analytical skills
• Research skills
• Critical thinking 
• Decision-making
• Collaboration
• Having a growth mindset

Let's have a look at each of them in greater detail!

#1 Analytical skills

Firstly, to truly understand complex problems, you need to break them down into more manageable parts . Then, you observe them closely and ask yourself: “ Which parts work and which don't,” How do these parts contribute to the problem as a whole,” and "What exactly needs to be fixed?” In other words, you gather data , you study it, and compare it - all to pinpoint the cause of the issue as closely as possible.

#2 Research skills

Another priceless tool is your research skills (sometimes relying on just one source of information isn't enough). Besides, to make a truly informed decision , you'll have to dig a little deeper. Being a good researcher means looking for potential solutions to a problem in a wider context. For example: going through team reports, customer feedback, quarterly sales or current market trends.  

#3 Critical thinking

Every employer wants to hire people who can think critically. Yet, the ability to evaluate situations objectively and from different perspectives , is actually pretty hard to come by. But as long as you stay open-minded, inquisitive, and with a healthy dose of skepticism, you'll be able to assess situations based on facts and evidence more successfully. Plus, critical thinking comes in especially handy when you need to examine your own actions and processes. 

 #4 Creativity

Instead of following the old established processes that don't work anymore, you should feel comfortable thinking outside the box. The thing is, problems have a nasty habit of popping up unexpectedly and rapidly. And sometimes, you have to get creative in order to solve them fast. Especially those that have no precedence. But this requires a blend of intuition, industry knowledge, and quick thinking - a truly rare combination. 

#5 Decision-making

The analysis, research, and brainstorming are done. Now, you need to look at the possible solutions, and make the final decision (informed, of course). And not only that, you also have to stand by it ! Because once the train gets moving, there's no room for second guessing. Also, keep in mind that you need to be prepared to take responsibility for all decisions you make. That's no small feat! 

#6 Collaboration

Not every problem you encounter can be solved by yourself alone. And this is especially true when it comes to complex projects. So, being able to actively listen to your colleagues, take their ideas into account, and being respectful of their opinions enables you to solve problems together. Because every individual can offer a unique perspective and skill set. Yes, democracy is hard, but at the end of the day, it's teamwork that makes the corporate world go round. 

#7 Having a growth mindset

Let's be honest, no one wants their work to be riddled with problems. But facing constant challenges and changes is inevitable. And that can be scary! However, when you're able to see these situations as opportunities to grow instead of issues that hold you back, your problem solving skills reach new heights. And the employers know that too!

Now that we've shown you the value problem-solving skills can add to your resume, let's ask the all-important question: “How can I learn them?”

Well…you can't. At least not in the traditional sense of the word. 

Let us explain: Since problem-solving skills fall under the umbrella of soft skills , they can't be taught through formal education, unlike computer skills for example. There's no university course that you can take and graduate as a professional problem solver. 

But, just like other interpersonal skills, they can be nurtured and refined over time through practice and experience. 

Unfortunately, there's no one-size-fits-all approach, but the following tips can offer you inspiration on how to improve your problem solving skills:

• Cultivate a growth mindset. Remember what we've said before? Your attitude towards obstacles is the first step to unlocking your problem-solving potential. 
• Gain further knowledge in your specialized field. Secondly, it's a good idea to delve a little deeper into your chosen profession. Because the more you read on a subject, the easier it becomes to spot certain patterns and relations.  
• Start with small steps. Don't attack the big questions straight away — you'll only set yourself up for failure. Instead, start with more straightforward tasks and work your way up to more complex problems. 
• Break problems down into more digestible pieces. Complex issues are made up of smaller problems. And those can be further divided into even smaller problems, and so on. Until you're left with only the basics. 
• Don't settle for a single solution. Instead, keep on exploring other possible answers.
• Accept failure as a part of the learning process. Finally, don't let your failures discourage you. After all, you're bound to misstep a couple of times before you find your footing. Just keep on practicing. 

How to improve problem solving skills with online courses

While it’s true that formal education won’t turn you into a master problem solver, you can still hone your skills with courses and certifications offered by online learning platforms :

• Analytical skills. You can sharpen your analytical skills with Data Analytics Basics for Everyone from IBM provided by edX (Free); or Decision Making and Analytical Thinking: Fortune 500 provided by Udemy (＄21,74).
• Creativity. And, to unlock your inner creative mind, you can try Creative Thinking: Techniques and Tools for Success from the Imperial College London provided by Coursera (Free).
• Critical thinking. Try Introduction to Logic and Critical Thinking Specialization from Duke University provided by Coursera (Free); or Logical and Critical Thinking offered by The University of Auckland via FutureLearn.  
• Decision-making. Or, you can learn how to become more confident when it's time to make a decision with Decision-Making Strategies and Executive Decision-Making both offered by LinkedIn Learning (1 month free trial).
• Communication skills . Lastly, to improve your collaborative skills, check out Communicating for Influence and Impact online at University of Cambridge. 

The fact that everybody and their grandmothers put “ problem-solving skills ” on their CVs has turned the phrase into a cliche. 

But there's a way to incorporate these skills into your resume without sounding pretentious and empty. Below, we've prepared a mock-up resume that manages to do just that.

FYI, if you like this design, you can use the template to create your very own resume. Just click the red button and fill in your information (or let the AI do it for you).

Problem solving skills on resume example

This resume was written by our experienced resume writers specifically for this profession.

Why this example works?

• Firstly, the job description itself is neatly organized into bullet points .  
• Instead of simply listing soft skills in a skills section , you can incorporate them into the description of your work experience entry.  
• Also, the language here isn't vague . This resume puts each problem-solving skill into a real-life context by detailing specific situations and obstacles. 
• And, to highlight the impact of each skill on your previous job position, we recommend quantifying your results whenever possible. 
• Finally, starting each bullet point with an action verb (in bold) makes you look more dynamic and proactive.

To sum it all up, problem-solving skills continue gaining popularity among employers and employees alike. And for a good reason!

Because of them, you can overcome any obstacles that stand in the way of your professional life more efficiently and systematically. 

In essence, problem-solving skills refer to the ability to recognize a challenge, identify its root cause, think of possible solutions , and then implement the most effective one. 

Believing that these skills are all the same would be a serious misconception. In reality, this term encompasses a variety of different abilities , including:

In short, understanding, developing, and showcasing these skills, can greatly boost your chances at getting noticed by the hiring managers. So, don't hesitate and start working on your problem-solving skills right now!

Julia has recently joined Kickresume as a career writer. From helping people with their English to get admitted to the uni of their dreams to advising them on how to succeed in the job market. It would seem that her career is on a steadfast trajectory. Julia holds a degree in Anglophone studies from Metropolitan University in Prague, where she also resides. Apart from creative writing and languages, she takes a keen interest in literature and theatre.

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“Problem-Solving” Or “Problem Solving”? Learn If It Is Hyphenated

Is it problem-solving or problem solving? Hyphenation rules seem to be a little confusing when you’re first picking up a language. Don’t worry, though. They’re not nearly as complicated as the language may have led you to believe!

Problem-Solving Or Problem Solving – Hyphenated Or Not?

When we discuss the problem-solving hyphen rule, we learn that problem-solving is hyphenated when used to modify a noun or object in a sentence. We keep the two words separated when using them as their own noun and not modifying anything else in the sentence.

Examples Of When To Use “Problem-Solving”

Now that we’re into the whole debate of problem-solving vs problem solving, let’s look through some examples of how we can use “problem-solving” with a hyphen. As stated above, we use “problem-solving” when modifying a noun or object in a sentence. It’s the most common way to write “problem-solving.” Even the spelling without a hyphen is slowly being pushed out of common language use!

• This is a problem-solving class.
• I hold a problem-solving position at my workplace.
• My manager put me in charge of the problem-solving accounts.
• They say I have a problem-solving mind.
• We’re known as problem-solving children.

Examples Of When To Use “Problem Solving”

Though much less common to be seen written as a phrase noun, it is still worth mentioning. It’s grammatically correct to use “problem solving” at the end of a sentence or clause without a hyphen. However, as we stated above, many people are beginning to prefer the ease of sticking to the hyphenated spelling, meaning that it’s slowly phasing out of existence even in this form.

• I’m good at problem solving.
• This requires a lot of problem solving.
• We are all trained in problem solving.
• My job asks for problem solving.
• Did you say you were good at problem solving?

Is Problem-Solving Hyphenated AP Style?

Have you had a look through the rules in the AP stylebook before? Even if you haven’t, there’s a good explanation for hyphens there. As we stated above, we use hyphens when linking close words that modify a noun or object in a sentence. They’re used to help a reader better understand what is going on through the modification of the clause.

Should I Capitalize “Solving” In The Word “Problem-Solving”?

The question of “is problem-solving hyphenated” was answered, but now we’ve got a new question. What happens to capitalization rules when we add a hyphen to a title. It depends on your own title choices, so let’s look a little further into the three potential options. The first option capitalizes only the first word and any proper nouns in a title. In this case, neither word in “problem-solving” is capitalized.

The second option capitalizes all words except for short conjunctions, short prepositions, and articles. In this case, you will always capitalize “problem” but always leave “solving” uncapitalized. The final option capitalizes every single word in a title. No matter what, you’ll capitalize both words in “problem-solving” when using this style to write your titles.

Does The Rule Also Apply To “Problem Solver” Vs “Problem-Solver”?

The same rule does apply when we use “problem solver” instead of “problem solving.” However, it’s not often that we’ll see a “problem-solver” modifying a noun or object (unless it’s a problem-solver robot or something). So, it’s most likely you’ll write “problem solver.”

Alternatives To “Problem-Solving”

If you’re still struggling with the hyphen rule of whether it’s problem solving or problem-solving, there’s one last thing we can help you with. We can give you some alternatives that have the same meanings but don’t require a hyphen. This way, you can be safe in your own knowledge without having to worry about getting the rules wrong.

• interpretive

Quiz – Problem-Solving Or Problem Solving?

We’ll finish with a quiz to see how much you’ve learned from this article. The answers are all multiple choice, so you should have a blast with them! We’ll include the answers at the end to reference as well.

• I’ve been told that I’m good at (A. problem-solving / B. problem solving).
• I hold my (A. problem-solving / B. problem solving) skills close to my heart.
• We aren’t great at (A. problem-solving / B. problem solving).
• These are all the best (A. problem-solving / B. problem solving) subjects.
• Can we have a go at a (A. problem-solving / B. problem solving) puzzle?

Quiz Answers

Martin holds a Master’s degree in Finance and International Business. He has six years of experience in professional communication with clients, executives, and colleagues. Furthermore, he has teaching experience from Aarhus University. Martin has been featured as an expert in communication and teaching on Forbes and Shopify. Read more about Martin here .

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• “On-Time” Or “On Time”? Learn If “On Time” Is Hyphenated
• Year round or Year-round? (Hyphen Rule Explained)

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• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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• Resume and Cover Letter
• 7 Best Problem-Solving Skills...

7 Best Problem-Solving Skills for Your Resume + Examples

11 min read · Updated on April 17, 2024

If you're a strong problem solver, your resume needs to prove it!

Imagine this scenario: a supplier delivers the wrong piece of equipment, your deadline is tomorrow, and your logistics person is out sick. What would you do if you were the one who had to respond?

All businesses encounter problems at one time or another. That's why companies need high-quality employees on hand who can solve problems like shifting deadlines, equipment failure, and changing client needs. Those problem-solving skills can mean the difference between success and failure. 

That's why today's employers are actively seeking candidates who possess these critical problem-solving skills. 

But what are problem-solving skills? 

How do you identify which ones you might have or which ones a hiring manager might be looking for? 

Most importantly, how can you present problem-solving on your resume to land that interview?

In this post, we'll help you learn to identify, define, and present problem-solving skills in your resume.

What are problem-solving skills?

Put simply, problem-solving skills help you overcome challenges and obstacles. They enable you to identify the core issue, propose solutions, choose the best option, and implement it.

When employers talk about problem-solving skills, they're usually referring to the ability to deal with challenging, complex, or unexpected situations. While they enable someone to assess and solve problems calmly, these skills can also be useful for relationship building and routine decision-making.

Why do companies need employees with problem-solving skills?

All companies experience challenges that can impact their operations and effectiveness. Those businesses will always need people to help them to find solutions to their problems. In fact, according to the National Association of Colleges and Employers' Job Outlook, 86% of employers look for problem-solving skills on student resumes.

Employers like to see good problem-solving skills because it also shows them you have a range of other talents, like logic, creativity, resilience, imagination, and lateral thinking.

Looking for problem-solving skills in a job description

Sometimes, a job description will plainly state the problem-solving skills that the job requires. More often, however, problem-solving is one of those skill sets that don't necessarily appear in the “requirements” section of a job post. Employers simply expect candidates to demonstrate an analytical mind. So, instead, they will describe those desired skills using other phrases.

In those instances, you can look for keywords to identify the skills the employer is seeking. When you find any relevant keywords in the job description, you'll be able to tell what skills you should highlight in the resume you send in.

How to include problem-solving skills on a resume

It should be easy to highlight these skills during an interview, where you can describe a specific problem and paint a picture of how you successfully solved it. But it's also easy to find ways to illustrate your problem-solving on your resume.

Problem-solving skills sound like they're self-explanatory, but they can be difficult to describe without good storytelling. Unlike conceptual skills like abstract thinking and ideation, problem-solving skills are all about developing and implementing an action plan. That's why the best strategy to demonstrate your problem-solving skills is to tell a story: find specific examples of challenging scenarios and explain the plan you implemented and the results you achieved. 

Related post : How to Create an Effective STAR Method Resume (With Examples)

Many resumes will use terms like “critical thinker” or “problem-solver.” Instead, get specific by showing how you've used a skill in a way that has solved a problem at work. 

Give examples of scenarios where those skills lead to a solution

Describe a specific process you employed

List major accomplishments enabled by your solution

Add specific training related to problem-solving skills

Use various keywords to avoid repeating “problem-solving”

Let's look at 4 places on a resume where you can describe your problem-solving skills. 

Where to include problem-solving skills on your resume

The summary.

The summary is a great place to present a core skill that has benefitted you and your employers. If you've been responsible for finding out-of-the-box solutions to unexpected problems or been a team leader known for adjusting to personnel or process challenges, this is the place to introduce those talents.

Solutions-driven sales specialist with 10 years of experience managing sales teams, analyzing markets, expanding market reach, and solving logistics issues. Extensive experience with rolling out new products and reinventing campaigns. Transformed market by 40% despite a period of intense market fluctuation.

In the work experience section

The work experience section is the ideal place to list problem-solving skills that have contributed to proven solutions. When detailing past job roles, you can use details like percentages, dollar amounts, and specific scenarios to show how your ability to analyze issues, find options, and communicate action plans has solved problems. 

Mention a time when you took the initiative to troubleshoot key areas

Explain your habit of collecting new data regularly

Give examples of instances when you assumed a leadership role in process optimization

Look at the following resume example. It shows how this candidate's ability to design solutions, optimize testing processes, and adjust the process to the client helped to optimize process efficiency and save the client money. 

In addition, the candidate highlights his communication skills by showing that he can collaborate with clients to adapt processes to their needs. 

Solar Engineer, Acme Corp, 2010 - 2020

Developed solution designs in collaboration with Software Architects that improved process efficiency by 150% and reduced costs by $300K

Supported testing on 3 large-scale projects to refine solutions and ensure they were fit for purpose and matched the customer's needs, resulting in $1M savings for the client

The skills section

If problem-solving skills are needed for a particular role, the hiring manager will be looking for them in the skills section. The key, however, is to only list skills that specifically relate to the job posting. 

Remember, it's crucial to tailor each resume to a specific job advertisement, including the skills section. This is obviously easier if the job post explicitly lists desired skills. If it doesn't, look for keywords in the bullet points of the requirements part of the job description to find specific problem-solving skills to include in your resume.

Is it a management position looking for a “proven leader?” Communication skills are a must-have talent.

Is it a logistics position that requires experience with scaling? Then, troubleshooting and negotiation skills will be paramount.

There are both soft skills and hard skills that can be defined as problem-solving skills. “Test development” can be trained, but “troubleshooting” improves with experience. When considering which skills you possess, look at both categories.

Data analysis / Process analysis / Project design / Solution design / Test development / Benchmark development / Troubleshooting / Collaboration

A notable achievements section

A notable achievements section isn't always necessary, but some resumes can benefit from including one. If, for example, you're using a functional resume format for a career change resume or you're a senior executive looking to emphasize career highlights, an accomplishments section can really highlight those skills in action. 

If you're using this section to focus on your problem-solving skills, describe accomplishments with demonstrable results.

ACCOMPLISHMENTS AND ACHIEVEMENTS

• Re-designed and upgraded front-end on 20+ sites with jQuery, AJAX, and Handlebars.js
• Oversaw process improvements, which reduced expenses by $225,000 per quarter
• Restructured the supply chain team following vendor flow issues

Related post : Seven Key Resume Sections and How to Organize Them

7 Important problem-solving skills for your resume

Problem-solving skills can range from detail-oriented diagnostics to team leadership. Here's a list of skills involved in various stages of the problem-solving process. When crafting your resume, look to these examples to see what problem-solving skills you might have.

1. Research

Research skills are an essential component of the problem-solving skill set, enabling you to identify and understand the root cause of an issue. Research involves gathering data and information, consulting with more experienced colleagues, acquiring knowledge online or from external sources, and collating newfound data for dissemination. This skill is about the ability to find and use the right resources, extract the data you need, and brainstorm with the right group of people. This means:

Studying specific cases without generalizing

Aiming at variables that make the desired differences

Reporting findings in understandable terms

2. Analysis

The first step in finding a solution is an effective analysis of the problem.  To solve a problem, you must be able to analyze it from every angle. Your analytical skills will also help you identify and propose solutions that can resolve the problem.

Analytical skills allow you to assess data and processes to find solutions to a company's challenges. These include:

Forecasting

Data analysis

Interpretation of data and metrics

Deductive reasoning

Inductive reasoning 

Diagnostics

3. Critical-thinking

Critical thinking is the ability to process details with a particular flow and draw connections between concepts and facts. In other words, it's “thinking about thinking” – or finding and fixing flaws in the way we think.

The ability to think critically is the foundation of problem solving. Unless you can see the big picture, you won't be able to identify the pros and cons of different action plans. 

Critical thinking includes:

Interpretation

Open-mindedness

4. Decision making

Decision-making is the ability to choose solutions to problems. Simply stated, it's taking the relevant collected data, considering multiple viewpoints, and making an informed choice.

Once the choices are narrowed down, you'll need to pull the trigger – knowing you'll be held accountable for the decision. At times, you may need to make these decisions quickly, even if the wrong decision might make the problem worse. The ability to make proper use of your research and analysis to select the best action plan is a valuable skill. Components of this skill include:

Emotional Intelligence

Organization

5. Creativity

Sometimes, the best solution is only found by thinking outside the box. That demands creativity. 

Creativity is the ability to approach a task or a challenge in a different way. In other words, it's possessing the imagination to generate new ideas and find interesting approaches and unique perspectives. Creativity is often described as

Divergent thinking

Inspirational thinking

Outside-the-box thinking

Experimental thinking

6. Communication

Strong communication skills are vital during all phases of problem solving:

While identifying and analyzing the problem, you'll need to know how to communicate the core issues to others.

When researching the background of the issue, you'll need to know what communication channels are appropriate when seeking guidance.

When brainstorming possible solutions, you will need to know how to guide a team through positive and effective discussions.

Then, once you find a solution, communicating the action plan with clarity and precision is key to avoiding confusion and achieving proper implementation. 

No problem would ever be solved without good communication skills at work. 

Communication skills, however, include a much broader array of abilities beyond just speaking clearly. They also encompass listening in ways that make your colleagues feel heard, body language that puts your audience at ease, and vocal pitch adjustments to make your point land better. Here are a few common communication skills:

Active listening

Giving constructive feedback

Presentation / visual communication

Nonverbal communication

Written communication

Oral communication

Voice modulation

Rapport building 

7. Collaboration

In the business world, most problems are solved by teams of dedicated personnel, working in collaboration with one another. When highlighting this skill, you need to show how you've worked effectively as part of a team to generate and implement solutions.

Collaboration, by definition, means working with one or more individuals to complete a task. In the workplace, collaboration can be brainstorming ideas, delegating tasks to individual strengths, layering pieces of a process, or bringing together the team to understand the bigger picture.

When people work together, they're more effective at problem solving than when attempting to go it alone. Successful collaboration with your coworkers also increases their motivation and engagement at work, making them feel like they're an important part of the team. 

Collaboration includes:

Long-term thinking

Adaptability

Positive debate

Emotional intelligence

The bottom line

In an increasingly complex business environment, the ability to solve problems is more important than ever before. As a result, including these high-value problem-solving skills on your resume can help to ensure that employers recognize your full value proposition as a prospective new hire. That, in turn, can help to separate you from your competition and increase your odds of landing an interview and job offer.

If you want to make sure that the problem-solving skills in your resume are making the right impression on employers, take a few moments to get your free resume review from our team of experts today!

Related reading:

9 Soft Skills Employers Are Looking for in 2022

11 Steps to Writing the Perfect Resume

Standout Skills for a Resume: How to Make your Resume Great  

Related Articles:

Guide to Writing a Great Resume with No Work Experience

Higher Order Thinking Explained

How to Describe Organizational Skills When Applying for a Job

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Our math problem solver that lets you input a wide variety of math math problems and it will provide a step by step answer. This math solver excels at math word problems as well as a wide range of math subjects.

• Math Word Problems
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Here are example math problems within each subject that can be input into the calculator and solved. This list is constanstly growing as functionality is added to the calculator.

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Math Word Problem Solutions

Math word problems require interpreting what is being asked and simplifying that into a basic math equation. Once you have the equation you can then enter that into the problem solver as a basic math or algebra question to be correctly solved. Below are math word problem examples and their simplified forms.

Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 �� b}

Word Problem: if there are 40 cookies all together and Angela takes 10 and Brett takes 5 how many are left?

Simplified: 40 - 10 - 5

Pre-Algebra Solutions

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• Variables, Expressions, and Integers
• Simplifying and Evaluating Expressions
• Solving Equations
• Multi-Step Equations and Inequalities
• Ratios, Proportions, and Percents
• Linear Equations and Inequalities

Algebra Solutions

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• Algebra Concepts and Expressions
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Trigonometry Solutions

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• Algebra Concepts and Expressions Review
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Precalculus Solutions

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Calculus Solutions

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Finite Math Solutions

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Linear Algebra Solutions

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• Introduction to Matrices
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Chemistry Solutions

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Physics Solutions

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Geometry Graphing Solutions

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Strategies for Solving Word Problems – Math

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

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

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

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

1. read the entire word problem.

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

2. Think About the Word Problem

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

Here are the questions:

A. what exactly is the question.

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

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

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

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

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

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

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

C. What information do I already have?

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

3. Write on the Word Problem

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

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

4. Draw a Simple Picture and Label It

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

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

5. Estimate the Answer Before Solving

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

6. Check Your Work When Done

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

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

7. Practice Word Problems Often

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

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

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

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

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

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

CLICK HERE to take a look at 3rd grade:

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

CLICK HERE to see 4th grade:

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

CLICK HERE to take a look at 5th grade:

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

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

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

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Word Problems Activities

Teach your child all about word problems with amazing educational resources for children. These online word problems learning resources break down the topic into smaller parts for better conceptual understanding and grasp. Get started now to make word problems practice a smooth, easy and fun process for your child!

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Addition Word Problems

Adding One by Making a Model Game

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Adding Within 5 by Making a Model Game

Add more arrows to your child’s math quiver by adding within 5 by making a model.

Add within 5: Summer Word Problems Worksheet

Engaging summer-themed worksheet with word problems to enhance addition skills within 5.

Add within 5: Halloween Word Problems Worksheet

Spooky-themed worksheet for practicing addition within 5 through Halloween word problems.

Subtraction Word Problems

Solve Subtraction Scenarios Game

Apply your knowledge to solve subtraction scenarios.

Word Problems: Subtracting One Game

Sharpen your math skills with the 'Word Problems: Subtracting One' game.

Subtract within 5: Summer Word Problems Worksheet

A fun, summer-themed worksheet designed to enhance students' subtraction skills with problems up to 5.

Subtract within 5: Halloween Word Problems Worksheet

Spooky themed worksheet to master subtraction within 5 through fun Halloween word problems!

Multiplication Word Problems

Solve the Word Problems Related to Multiplication Game

Unearth the wisdom of mathematics by learning to solve word problems related to multiplication.

Solve Word Problems on Decimal Multiplication Game

Kids must solve word problems on decimal multiplication to practice decimals.

Complete the Word Problem for Equal Groups Worksheet

Help your child revise multiplication by solving word problems for equal groups.

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Learners must complete the word problems for arrays to enhance their math skills.

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Model and Add (Within 10) Game

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Subtract within 5: Christmas Word Problems Worksheet

Engaging Christmas-themed worksheet for students to master subtraction within 5 through word problems.

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Apply your knowledge to solve word problems on fraction-whole number multiplication.

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A summer-themed worksheet for students to practice dividing 2-digit numbers by 1-digit numbers.

Solve 'Add To' Scenarios Game

Add more arrows to your child’s math quiver by solving 'Add To' scenarios.

Solve 'Take Apart' Scenarios Game

Take the pressure off by simplifying subtraction by solving 'Take Apart' scenarios.

Word Problems on Adding Fractions & Mixed Numbers Worksheet

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Add within 5: Shopping Word Problems Worksheet

Engaging worksheet with a shopping theme to help students master addition within 5 through word problems.

Solve Comparison Word Problems Game

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Word Problems on Addition of Fractions Game

Use your fraction skills to solve word problems on addition of fractions.

Subtract within 5: Shopping Word Problems Worksheet

Engaging subtraction worksheet with a shopping theme, helping students solve problems within 5.

Make a Model to Multiply Worksheet

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Take a look at subtraction scenarios with this game.

Divide 2-digit Numbers by 1-digit Numbers: Halloween Word Problems Worksheet

Halloween-themed worksheet to enhance skills in dividing 2-digit numbers by 1-digit numbers.

Adding Fractions & Mixed Numbers Word Problems Worksheet

Help your child solve word problems on adding fractions & mixed numbers.

Find the Number of Groups Game

Find the number of groups to practice division.

Word Problems on Subtraction of Fractions Game

Have your own math-themed party by learning how to solve word problems on subtraction of fractions.

Add within 5: Travel Word Problems Worksheet

This worksheet combines fun travel-themed scenarios with math problems, requiring students to add numbers within 5.

Subtract within 5: Travel Word Problems Worksheet

Travel-themed worksheet to enhance students' subtraction skills within 5 through word problems.

Solve 'Add To' Word Problems Game

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Take Away Scenario Game

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Multiply by Making a Model Worksheet

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Divide 2-digit Numbers by 1-digit Numbers: Christmas Word Problems Worksheet

Christmas-themed worksheet to practice dividing 2-digit numbers by 1-digit numbers through word problems.

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Problem Solving Words

Words related to problem solving.

Below is a massive list of problem solving words - that is, words related to problem solving. The top 4 are: mathematics , artificial intelligence , computer science and thinking . You can get the definition(s) of a word in the list below by tapping the question-mark icon next to it. The words at the top of the list are the ones most associated with problem solving, and as you go down the relatedness becomes more slight. By default, the words are sorted by relevance/relatedness, but you can also get the most common problem solving terms by using the menu below, and there's also the option to sort the words alphabetically so you can get problem solving words starting with a particular letter. You can also filter the word list so it only shows words that are also related to another word of your choosing. So for example, you could enter "mathematics" and click "filter", and it'd give you words that are related to problem solving and mathematics.

You can highlight the terms by the frequency with which they occur in the written English language using the menu below. The frequency data is extracted from the English Wikipedia corpus, and updated regularly. If you just care about the words' direct semantic similarity to problem solving, then there's probably no need for this.

There are already a bunch of websites on the net that help you find synonyms for various words, but only a handful that help you find related , or even loosely associated words. So although you might see some synonyms of problem solving in the list below, many of the words below will have other relationships with problem solving - you could see a word with the exact opposite meaning in the word list, for example. So it's the sort of list that would be useful for helping you build a problem solving vocabulary list, or just a general problem solving word list for whatever purpose, but it's not necessarily going to be useful if you're looking for words that mean the same thing as problem solving (though it still might be handy for that).

If you're looking for names related to problem solving (e.g. business names, or pet names), this page might help you come up with ideas. The results below obviously aren't all going to be applicable for the actual name of your pet/blog/startup/etc., but hopefully they get your mind working and help you see the links between various concepts. If your pet/blog/etc. has something to do with problem solving, then it's obviously a good idea to use concepts or words to do with problem solving.

If you don't find what you're looking for in the list below, or if there's some sort of bug and it's not displaying problem solving related words, please send me feedback using this page. Thanks for using the site - I hope it is useful to you! 🐛

• mathematics
• artificial intelligence
• computer science
• intelligence
• collaborative
• engineering
• cognitive psychology
• gestalt psychology
• calculation
• inspiration
• problematic
• computation
• abstraction
• implication
• complicated
• cerebration
• intellection
• understanding
• difficulties
• interpersonal
• memorization
• comprehension
• organizational
• experiential
• attentional
• socialization
• interdisciplinary
• competencies
• communicative
• brainstorming
• participatory
• computational
• communication
• variational
• associative
• conversational
• disciplines
• combinatorics
• possibility
• implications
• possibilities
• fundamental
• questioningly
• unquestioned
• differences
• consequences
• interrogatively
• interrogative
• interrogate
• interrogatory
• complexities
• unquestionably
• determining
• perspective
• psychologist
• interrogation
• interrogator
• introspection
• behaviorism
• systemizing
• adaptiveness
• grantsmanship
• interactional
• kinesthetic
• kinaesthetic
• verbalization
• sensorimotor
• memorisation
• proficiencies
• brainteasers
• psychophysics
• elicitation
• perseveration
• insightfulness
• cooperativeness
• participative
• individualizes
• centredness
• systematizing
• psychometrics
• counterquestion
• questionable
• catechetically
• interrogatingly
• catechetics
• interpellate
• unanswerable
• neuropsychology
• thought process
• convergent thinking
• inquisitiveness
• incontrovertible
• herbert a. simon
• inquisition
• irresponsible
• unanswering
• indisputable
• answeringly
• problem finding
• uncertainty
• problem shaping
• catechismal
• invitational
• perplexedly
• questionnaire
• inquisitive
• decomposition
• unsolicited
• unquestionable
• deliberative
• mathematical problem
• deductive reasoning
• simultaneous equations
• problem solver
• nonverbal communication
• socratic method
• inductive reasoning
• operant conditioning
• behavior modification
• rote learning
• counterchallenge
• inconvenience
• yes no question
• investigative
• expert system
• embarrassment
• controvertible
• cross question
• lead question
• counterblast
• troubleshoot
• rechallenge
• greek language
• invitingness
• question question
• procatalepsis
• challengeable
• gordian knot
• unrequested
• petitionary
• respondence
• dumb insolence
• spanish inquisition
• answerphone
• postulation
• computer modeling
• question mark
• answer back
• pick someone's brain
• marriage proposal
• can of worm
• fill in blank
• press conference
• karl duncker
• optimal solution
• get back to
• tower of hanoi
• cross purpose
• dorothy dixer
• urim and thummim
• crossword puzzle
• traffic congestion
• cognitive process
• president bush
• allen newell
• cross examination
• word problem
• weight of world
• re examination
• cross examine
• fly in ointment
• jigsaw puzzle
• data deduplication
• root cause analysis
• failure mode and effects analysis
• dietrich dörner
• failure analysis
• forensic engineering
• donald broadbent
• cognitive sciences
• scientific method
• knowledge domain
• functional fixedness
• peter cathcart wason
• abraham s. luchins
• confirmation bias
• norman maier

That's about all the problem solving related words we've got! I hope this list of problem solving terms was useful to you in some way or another. The words down here at the bottom of the list will be in some way associated with problem solving, but perhaps tenuously (if you've currenly got it sorted by relevance, that is). If you have any feedback for the site, please share it here , but please note this is only a hobby project, so I may not be able to make regular updates to the site. Have a nice day! 🐊

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7 Problem-Solving Skills That Can Help You Be a More Successful Manager

Discover what problem-solving is and why it's important for managers. Explore the steps of the process and learn about seven problem-solving skills.

Managers regularly use problem-solving skills to oversee the day-to-day operations of a particular department and sometimes a whole company. Managers with good problem-solving skills can help ensure companies run smoothly and prosper.

If you're a current manager or are striving to become one, read this guide to discover what problem-solving skills are and why it's important for managers to have them. Learn the steps of the problem-solving process, and explore seven skills that can help make problem-solving easier and more effective.

What is problem-solving?

Problem-solving is both an ability and a process. As an ability, problem-solving can help resolve issues in different environments, such as home, school, abroad, and social situations. As a process, problem-solving involves a series of steps for finding solutions to questions or concerns that arise throughout life.

The importance of problem-solving for managers

Managers deal with problems regularly, whether supervising a staff of two or 100. Workplaces can benefit in several ways when people solve problems quickly and effectively. These include:

Greater creativity

Higher productivity

Increased job fulfillment

Satisfied clients or customers

Better cooperation and cohesion

Improved environments for employees and customers

7 skills that make problem-solving easier

Companies depend on managers who can solve problems adeptly. Although problem-solving is a skill in its own right, a subset of seven skills can help make it easier. These include analysis, communication, emotional intelligence, resilience, creativity, adaptability, and teamwork.

1. Analysis

As a manager, you'll solve each problem by assessing the situation first. Then, you’ll use analytical skills to distinguish between ineffective and effective solutions.

2. Communication

Effective communication plays a significant role in problem-solving, particularly when others are involved. Some skills that can help enhance communication at work include active listening, speaking with an even tone and volume, and supporting verbal information with written communication.

3. Emotional intelligence

Emotional intelligence is the ability to recognise and manage emotions in any situation. People with emotional intelligence usually solve problems calmly and systematically, which often yields better results.

4. Resilience

Emotional intelligence and resilience are closely related traits. Resiliency is the ability to cope quickly and bounce back from difficult situations. Those who possess resilience can often accurately interpret people and situations, which can be incredibly advantageous when difficulties arise.

5. Creativity 

When brainstorming solutions to problems, creativity can help you to think outside the box. Problem-solving strategies can be enhanced with the application of creative techniques. You can use creativity to:

Approach problems from different angles

Improve your problem-solving process

Spark creativity in your employees and peers

6. Adaptability

Adaptability is the capacity to adjust to change. When a particular solution doesn't work, an adaptable person can revisit the concern to think up another one without getting frustrated.

7. Teamwork

Finding a solution to a problem regularly involves working in a team. Good teamwork requires being comfortable working with others and collaborating with them, which can result in better problem-solving overall.

Steps of the problem-solving process

Effective problem-solving involves five essential steps. One way to remember them is through the IDEAL model, created in 1984 by psychology professors John D. Bransford and Barry S. Stein. The steps to solving problems in this model include identifying a problem, defining the goals you hope to achieve, exploring potential solutions, choosing and acting on it, and looking at (or evaluating) the outcome [ 1 ].

1. Identify the problem and root out its cause.

To solve a problem, you must first admit that one exists to find its root cause. Finding the cause of the problem may involve asking questions like:

Can the problem be solved?

How big of a problem is it?

Why do I think the problem is occurring?

What are some things I know about the situation?

What are some things I don't know about the situation?

Are there any people who contributed to the problem?

Are there materials or processes that contributed to the problem?

Are there any patterns I can identify?

2. Define the goals you hope to achieve.

Every problem is different. The goals you hope to achieve when problem-solving depends on the scope of the problem. Some examples of goals you might set include:

Gather as much factual information as possible.

Brainstorm many different strategies to come up with the best one.

Be flexible when considering other viewpoints.

Articulate clearly and encourage questions so everyone involved is on the same page.

Be open to other strategies if the chosen strategy doesn't work.

Stay positive throughout the process.

3. Explore potential solutions.

Once you've defined the goals you hope to achieve when problem-solving, it's time to start the process. This involves steps that often include fact-finding, brainstorming, prioritising solutions, and assessing the cost of top solutions in terms of time, labour, and money.

4. Choose a solution and act on it.

Evaluate the pros and cons of each potential solution and choose the one most likely to solve the problem within your given budget, abilities, and resources. Once you choose a solution, it's important to commit to it and see it through. Draw up a plan of action for implementation and share it clearly and effectively, both verbally and in writing, with all involved parties. Make sure everyone understands their role for a successful conclusion.

5. Look at (or evaluate) the outcome.

Evaluation offers insights into your current situation and future problem-solving. When evaluating the outcome, ask yourself questions like:

Did the solution work?

Will this solution work for other problems?

What changes would you have made?

Would another solution have worked better?

Improve your problem-solving skills.

Problem-solving is an important skill for managers, and it involves analysing the situation, communicating effectively, and coming up with creative solutions. As a current or future manager looking to build your problem-solving skills, it is often helpful to take a professional course. Consider Improving Communication Skills offered by the University of Pennsylvania on Coursera. You'll learn how to boost your ability to persuade, ask questions, negotiate, apologise, and more. 

You might also consider taking Emotional Intelligence: Cultivating Immensely Human Interactions , offered by the University of Michigan on Coursera. You'll explore the interpersonal and intrapersonal skills common to people with emotional intelligence and learn how emotional intelligence is connected to team success and leadership.

Article sources

Indian Institute of Public Administration. “ Problem-Solving , https://www.iipa.org.in/cms/public/training_course/59.” Accessed 20 August 2024. 

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Synonyms for Problem solver

570 other terms for problem solver - words and phrases with similar meaning.

Master Algebra: How to Solve Word Problems in Algebra with Ease

How to solve word problems in algebra..

If you’ve ever found yourself scratching your head over a word problem in algebra, you’re not alone. Many students struggle with translating words into equations and solving them. But fear not, because I’m here to break it down for you and show you how to tackle those tricky word problems like a pro.

The first step in solving word problems in algebra is to carefully read the problem and identify the key information. Look for keywords like “sum,” “difference,” “product,” and “quotient” that indicate what operation you need to perform. Pay attention to any numbers or variables mentioned in the problem, as well as any relationships between them.

Next, you’ll need to translate the words into algebraic expressions or equations. This is where many students get tripped up, but it’s not as hard as it seems. Start by defining your variables – for example, let x represent the unknown quantity you’re trying to find. Then, use the information given in the problem to set up an equation that represents the relationships between the variables.

Once you have your equation, it’s time to solve for the unknown variable. Depending on the problem, this may involve combining like terms, distributing, factoring, or using the quadratic formula. Don’t be afraid to try different approaches and see what works best for the problem at hand.

If you’re still feeling stuck, don’t hesitate to ask for help. Your teacher, classmates, or online resources can provide valuable insight and guidance. Sometimes all it takes is a fresh perspective to help you see the solution more clearly.

Practice makes perfect when it comes to solving word problems in algebra. The more you work through different types of problems, the more comfortable you’ll become with the process. Challenge yourself with a variety of problems, from simple one-step equations to complex multi-step equations, to build your problem-solving skills.

In conclusion, solving word problems in algebra doesn’t have to be daunting. By breaking down the problem, translating it into algebraic equations, and working through the steps methodically, you can conquer even the most challenging word problems. Remember to stay patient, persistent, and open to seeking help when needed. With practice and determination, you’ll be a word problem-solving whiz in no time.

How Can I Identify the Problem?

When faced with a word problem in algebra, the first step is to identify the problem at hand. Take your time to read the problem carefully and understand what it is asking you to find. Look for keywords and phrases that indicate what operation or formula you need to use to solve the problem. Sources like Mathway can provide examples and step-by-step solutions to help you understand how to identify the problem.

How Can I Translate Words into Equations?

Once you have identified the problem, the next step is to translate the words into algebraic equations. This involves assigning variables to unknown quantities and setting up equations based on the information given in the problem. For example, if the problem asks you to find the sum of two numbers, you can let x represent the first number and y represent the second number. Then, you can set up an equation like x + y = sum. Websites like Khan Academy offer tutorials on how to translate words into equations.

How Can I Solve the Equations?

Once you have translated the words into equations, the next step is to solve the equations to find the unknown quantities. Depending on the complexity of the problem, you may need to use different algebraic techniques such as simplifying, factoring, or solving for a specific variable. Online resources like Wolfram Alpha can help you solve equations step-by-step and provide explanations on each step of the process.

How Can I Check My Answer?

After you have solved the equations and found the solution to the word problem, it is essential to check your answer to ensure its accuracy. One way to check your answer is by plugging the solution back into the original problem and seeing if it satisfies all the conditions given. Another method is to use a calculator or online tool to verify your answer. Websites like Symbolab offer algebra calculators that can help you check your answers.

How Can I Practice Solving Word Problems?

Practice is key to mastering algebra word problems. The more you practice solving different types of word problems, the more familiar you will become with the techniques and strategies needed to solve them. You can find plenty of practice problems and worksheets online on websites like IXL and Math-Drills . Additionally, textbooks and workbooks dedicated to algebra word problems can provide you with ample opportunities to practice and improve your skills.

In conclusion, solving word problems in algebra may seem daunting at first, but with practice and the right strategies, you can tackle them with confidence. By following the steps outlined in this article and utilizing online resources and tools, you can improve your algebra skills and become proficient at solving word problems. Remember to take your time, read the problem carefully, and break it down into manageable steps. With persistence and dedication, you can overcome any algebra word problem that comes your way.

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More From Forbes

Today’s ‘wordle’ #1161 hints, clues and answer for friday, august 23rd.

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How to solve today's Wordle.

Looking for Thursday’s Wordle hints, clues and answer? You can find them here:

It’s 2XP Friday for Competitive Wordle players, which means that every point you gain or lose when competing is doubled, for better or worse. You can see the Competitive Wordle rules for scoring below. I play against the Wordle Bot, but you can play against anybody—your spouse, the Bot, me, very intelligent apes.

In any case, it’s basically the weekend and we’re entering the final week of August, which has been a pretty solid month as far as 2024 goes. I’m hoping September will be even better. Let’s do this Wordle!

How To Solve Today’s Wordle

The Hint: A creature used in ancient medicine.

The Clue: This Wordle has a double letter in it.

Okay, spoilers below!

The Answer:

Today's Wordle

Wordle Analysis

Every day I check Wordle Bot to help analyze my guessing game. You can check your Wordles with Wordle Bot right here .

I’m a little surprised at how poorly STORE did as my opening guess. With just 1 yellow box, I learned later I had 266 remaining solutions. Ouch. CHAIN slashed that down to just 3, but all I knew at the time was I had three yellow boxes and absolutely no clue what the answer was. I tried BELCH to no avail, but at this point there was only one possible solution remaining and I finally came up with it: LEECH for the win!

Competitive Wordle Score

Naturally, I guessed in four which gives me 0 points and I tied the Bot so another 0. 2 x 0 (for 2XP Friday) results in a big fat 0 as well. Zeroes all around . . . .

How To Play Competitive Wordle

• Guessing in 1 is worth 3 points; guessing in 2 is worth 2 points; guessing in 3 is worth 1 point; guessing in 4 is worth 0 points; guessing in 5 is -1 points; guessing in 6 is -2 points and missing the Wordle is -3 points.
• If you beat your opponent you get 1 point. If you tie, you get 0 points. And if you lose to your opponent, you get -1 point. Add it up to get your score. Keep a daily running score or just play for a new score each day.
• Fridays are 2XP, meaning you double your points—positive or negative.
• You can keep a running tally or just play day-by-day. Enjoy!

Today’s Wordle Etymology

The word "leech" has an interesting etymology, originating from Old English. Here’s a breakdown:

• Old English : The word "lǣce" referred to a physician or healer. This usage was common in Old English and persisted for several centuries. The connection to healing comes from the historical practice of using leeches in medicine, particularly for bloodletting.
• Proto-Germanic : "Lǣce" is derived from the Proto-Germanic word "*lēkijaz," which also meant a healer or physician.
• Old High German : A similar word existed in Old High German, "lāhhi," which also referred to a physician.
• Use in Medicine : The term "leech" became associated with the bloodsucking creature due to its frequent use in medical treatments for bloodletting. Over time, as the practice became more widespread and the creature's use in medicine became prominent, the term "leech" transitioned to specifically refer to the bloodsucking worm.
• Modern Usage : Today, "leech" is primarily used to describe the parasitic worm, but it also retains a metaphorical meaning, describing a person who exploits others.

Pair this with yesterday’s BRUTE and we’ve got the makings of a real cast of vagabonds! Maybe tomorrow’s word will be KNAVE.

Be sure to check out my blog for my daily Wordle and Strands guides as well as all my other writing about TV shows, streaming guides, movie reviews, video game coverage and much more. Thanks for stopping by!

Oh, and I’ve started a book-themed Instagram page that’s just getting off the ground if anyone wants to follow me there.

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How Math Word Problem Solving Tools Can Boost Your Grades

• August 20, 2024 2:06 PM / Updated: August 20, 2024 2:06 PM

If you have difficulty with math word problems, you are not the only one. Some students find them challenging because they require math and reading comprehension. However, here is the great news: There are some excellent tools that can boost your grades by making the process less stressful and more manageable. Let’s discuss how these tools work and how they can help you succeed in your math classes.

Understanding the Challenge of Math Word Problems

Math word problems can be tricky because they involve more than just numbers. You need to read and understand the problem, figure out what math operation to use, and solve it. This can be overwhelming, especially if you’re not confident in your math skills or find the wording of the problem confusing.

For example, a problem might say, “A has three times as many apples as B. If B has five apples, how many apples does A have?” To solve this, you must understand the relationship between A and B’s apples, recognize that multiplication is involved, and then calculate the answer.

How Math Word Problem Solving Tools Work

Math word problem-solving tools are designed to help you break down and understand word problems step by step. Here’s how they typically work:

• Input the Problem: You type the word problem into the tool. Some tools even allow you to photograph the problem using your phone.
• Analyze the Problem: The tool scans the problem for important details, such as numbers, keywords (like “times” for multiplication), and relationships between the elements.
• Suggest a Solution: Based on its analysis, the tool suggests the best mathematical operation (addition, subtraction, multiplication, or division) to solve the problem.
• Provide the Answer: Finally, the tool gives you the correct answer.

What are the Benefits of Using Math Word Problem Solving Tools

Now that you know how these tools work, let’s discuss the benefits and how they can help improve your grades.

• Builds Confidence: When you struggle with math problems, it can be easy to feel defeated. They help to build confidence by guiding you through the solution process.
• Saves Time: If you’re stuck on a problem, you might spend a lot of time figuring it out. A math word problem-solving tool can save you time by quickly breaking down the problem and showing you how to solve it.
• Reduces Stress: Math word problems can be stressful and lead to depression, especially when you’re pressured to get good grades.
• Provides Instant Feedback: One of the great things about these tools is that they provide instant feedback. You don’t have to wait for your teacher to grade your work to know if you got the answer right.

When to Use Math Word Problem Solving Tools

While these tools are incredibly helpful, it is important to use them wisely. They are best used as learning aids, not as shortcuts.

• Test Preparation: Before a test, you can use these tools to practice solving word problems.
• Learning New Concepts: If you’re learning a new math concept that involves word problems, these tools can help you understand how to apply the concept in different scenarios.
• Reviewing Mistakes: If you made mistakes on a homework assignment or test, you can use these tools to review the problems and learn from your errors.

Choosing the Right Tool for You

There are many math word problem-solving tools available, so how do you choose the right one? Here are a few things to consider:

• User-Friendly Interface: Choose a tool that is easy to use and has a clear, simple interface. You don’t want to waste time figuring out how the tool works.
• Availability: Some tools are available as apps that you can download on your phone, while others are web-based. Choose one that you can easily access whenever you need it.
• Cost: While many tools are free, some offer additional features for a fee. Consider what you need and whether it’s worth paying for extra features.

Final Thoughts

Math word problem-solving tools can help students struggling with math. They break problems down into steps and give instant feedback, which can build confidence, save time, and help you understand math concepts. Whether you are studying for an exam or need help completing your homework, these tools can help you overcome it. So why not give them a try? You might find that with a little help, math word problems aren’t so tough after all.

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3 Math Tasks You Already Use That Can Foster Collaboration

Elementary teachers can turn common activities into opportunities for students to work and learn together.

Picture a “traditional” math class and then a “21st-century” math class. One of the most obvious differences is probably how students are interacting: No longer silently sitting in rows of desks, students are talking to each other. They are collaborating. 

Collaborative learning promotes higher-level reasoning, self-esteem, and positive relationships at school . To unlock the benefits of collaborative learning for young mathematicians, teachers can plan accessible tasks. When students don’t have to devote as much “brain space” to understanding the directions for a task, they can focus instead on collaborating on the math itself. This supports all students, including multilingual students and students with disabilities.

Start with tasks that are engaging, but not content-heavy , so that you can prioritize laying the groundwork for collaboration. Even a task as simple as taking turns drawing a picture can be productive for discussing expectations around sharing work and communicating. From there, you can use the warm-ups, word problems, and manipulatives that you and your students are already familiar with to generate accessible and meaningful collaborative tasks.

1. Collaborate Using Your Warm-Ups

Routines like warm-ups, number sense routines, or number talks invite students to reason and discuss, typically in a whole group setting. However, these can be done collaboratively as well. 

Selecting warm-ups for collaboration: Look for routines that have many possible “right” answers, so that all group members will be able to contribute meaningfully. This doesn’t have to be multiple numerical answers; it could also be many ways to get to a solution—for example, different ways to see a total in a dot talk . When you do this routine as a whole group, you may find yourself saying to students, “Wow, I hadn’t thought of that!” Those activities lend themselves well to collaboration.

Preparing warm-ups for collaboration: In a whole group discussion, you use your learning objectives to steer the conversation as it happens. For example, if we were discussing “Ways to Make 1/8” as a whole class and students were only talking about shapes, I might ask the class to think about a number line. If this discussion were to happen in collaborative groups, that steering needs to be built into the task. One way to do this is with a checklist. For example, when my third graders did “Ways to Make 1/8” as a collaborative task, each group got this checklist:

• 2 ways to make 1/8 of a square
• 2 ways to make 1/8 of a rectangle
• 1 way to make 1/8 of a circle
• 1 way to make 1/8 on a number line
• 2 ways to make 1/8 of numbers (example: 1/8 of 16 is 2)

The checklist makes it obvious to students how they should be contributing, and even though I might not be part of every conversation, I know that key points are surfacing throughout the room.

2. Collaborate Using Your Word Problems

Whether writing word problems yourself or using the ones in a curriculum, word problems are a feature of every math class.

Selecting word problems for collaboration: Make sure the context of the chosen word problem is accessible, or plan for making the context accessible. You might use images or videos to make sure students understand the vocabulary and can make connections to background knowledge. If the word problems in your curriculum have instructions like “Use an array model to solve,” leave those parts out. Groups should solve in ways that make sense to them, and diversity in strategies both within groups and between groups will lead to important mathematical discussions.

Preparing word problems for collaboration: You can turn one word problem into an extended collaborative task by planning a series of increasingly challenging number sets to fit into the story. For example, “Allison filled up 8 baskets of peaches, with 10 peaches in each basket. How many peaches is that?” followed by 18 baskets of 10, then 18 baskets of 25. If groups are working at vertical surfaces like whiteboards, they can look around the room after finishing one number set to see what number set to work on next, as described by Peter Liljedahl in Building Thinking Classrooms . This promotes knowledge mobility and frees the teacher to discuss with groups as needed. 

3. Collaborate Using Your Manipulatives

Counting collections is a rich collaborative task for students across elementary grades. You might be surprised by how excited students are to count even the most familiar math manipulatives. 

Preparing counting collections: Students will need “right-sized” collections, tools for organizing, and space to record. Don’t be afraid to offer big collections. Collections of, say, 45 for kindergartners or 845 for fourth graders can be meaningful opportunities for developing place value understanding. Tools like cups, plates, paper trays from the cafeteria, and your number lines or hundred charts should be available for students to take up as they need. Finally, think about how you want students to record their collections: on paper , on whiteboards, and/or digitally on a platform like Seesaw.

To grow your collection of collections beyond your classroom manipulatives and supplies, invite students to bring in collections from home, or round up unwanted items around your school. I have many beautiful collections of transparent manipulatives left over from the overhead projector days.

If At First You Don’t Succeed…

Collaboration is tricky. Even with extensive planning and coaching , students and groups will struggle at times. But if collaboration is hard for your class , that means they need to practice it more, not less. More collaboration doesn’t have to mean planning more tasks from scratch; you can and should use the resources you already have and turn those into revisit-able routines. Having familiar routines for collaboration means that students can dive straight into the learning, while continuing to develop their identities as good group-mates who know how to support each other and work together.