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How to Strengthen Problem-Solving Skills in Everyday Life

Problem-solving is an essential skill that we rely on in both personal and professional settings. From minor inconveniences to complex challenges, we are constantly presented with situations that require us to find effective solutions. Strengthening your problem-solving abilities can improve decision-making, reduce stress, and lead to more successful outcomes.

Whether you’re facing a difficult task at work, managing personal relationships, or navigating everyday life, honing your problem-solving skills is key. By cultivating a strategic mindset, staying mentally sharp, and using the right techniques, you can become more effective at identifying solutions to problems. Some individuals also use brain supplements like nootropics to support mental clarity, focus, and cognitive performance, making problem-solving easier and more efficient.

Ask the Right Questions

The benefits of a step-by-step approach, techniques to foster creativity, stress management techniques for problem-solving, embrace a growth mindset, daily practices to sharpen problem-solving skills, define the problem clearly.

The first step to solving any problem is understanding exactly what the problem is. Many people jump into problem-solving mode without fully analyzing the situation, which can lead to incomplete solutions or overlooked details. Taking the time to clearly define the problem will help you identify the best approach and ensure that you are solving the right issue.

To clearly define a problem, start by asking questions that help you get to the root of the issue. For example, what is the real challenge here? What are the contributing factors? Who is affected by this problem, and why? By breaking the problem down and examining all of its aspects, you can gain a deeper understanding of what needs to be addressed.

In both personal and professional settings, it’s important to differentiate between symptoms and root causes. While it’s tempting to address surface-level symptoms, solving the root cause will prevent the problem from reoccurring. Taking time to ask the right questions and fully define the problem sets the stage for more effective solutions.

Break the Problem into Manageable Steps

Large, complex problems can feel overwhelming, leading to procrastination or poor decision-making. Breaking a problem into smaller, manageable steps makes it easier to approach systematically and keeps you focused on the next actionable task. This step-by-step approach not only simplifies the problem but also helps reduce stress and mental fatigue.

Breaking a problem down into smaller parts allows you to tackle each aspect one at a time. This reduces overwhelm and helps you stay organized throughout the process. For example, if you’re working on a challenging project at work, break it down into research, planning, execution, and review stages. Focus on completing one stage before moving to the next, allowing for greater clarity and concentration.

• Identify Sub-Problems: Break the larger problem into smaller sub-problems that can be addressed independently. This makes the overall challenge more manageable and gives you a clear starting point.
• Create Actionable Steps: Turn each sub-problem into a specific action step that you can take to move forward. Having a clear plan of action keeps you focused and reduces the chances of becoming overwhelmed.

For individuals seeking enhanced cognitive performance during problem-solving, some find that using nootropics supports mental clarity and sustained focus, making it easier to work through each step without losing momentum.

Use Creative Problem-Solving Techniques

Creative problem-solving involves looking beyond traditional solutions and thinking outside the box to find new, innovative approaches. This technique is particularly useful when facing complex challenges or when conventional methods aren’t working. Cultivating creativity in problem-solving can lead to unexpected breakthroughs and more effective solutions.

One popular creative problem-solving method is brainstorming. During a brainstorming session, you generate as many ideas as possible without immediately judging or discarding them. This helps you explore a wide range of possibilities before narrowing down your options. Another effective technique is mind mapping, which involves visually organizing ideas and solutions in a diagram, helping you see connections that might not be immediately obvious.

• Brainstorming: Write down every idea, no matter how unconventional, and explore each one before deciding on the best solution. You might be surprised by the creative insights that emerge.
• Mind Mapping: Draw a visual representation of the problem, with the central issue in the middle and branches representing possible solutions. This helps you see relationships and generate new ideas.

Creative problem-solving requires mental flexibility and the ability to see beyond traditional approaches. Many individuals use brain supplements like nootropics to enhance cognitive flexibility, supporting innovative thinking and creativity during the problem-solving process.

Stay Calm and Manage Stress

Problem-solving is much more difficult when you’re feeling stressed or overwhelmed. High stress levels can cloud judgment, reduce cognitive function, and make it harder to think clearly. Learning how to manage stress effectively is essential for maintaining mental sharpness and approaching problems with a clear, focused mindset.

One of the best ways to reduce stress while problem-solving is to practice mindfulness. Mindfulness helps you stay present and focused on the task at hand, rather than becoming distracted by anxiety or worry about the outcome. Taking regular breaks to breathe deeply, meditate, or step away from the problem for a few minutes can also help you reset and return to the issue with fresh energy.

Physical activity, such as going for a walk or engaging in light exercise, can reduce stress and boost mental clarity, helping you approach problems with a clearer perspective. Staying calm under pressure allows you to think more rationally, helping you find more effective solutions to the challenges you face.

For those looking for additional support in managing stress and maintaining focus, some turn to brain supplements like nootropics to enhance cognitive resilience. These supplements may help reduce mental fatigue, promote calmness, and support better decision-making during stressful situations.

Learn from Mistakes and Adapt

Not every solution will work perfectly the first time. Learning from mistakes and remaining adaptable is a key part of strengthening your problem-solving skills. When a solution doesn’t lead to the desired outcome, it’s important to analyze what went wrong and adjust your approach accordingly.

A growth mindset—the belief that skills and abilities can be developed through effort and learning—helps you view challenges as opportunities for growth. Rather than becoming discouraged by setbacks, see them as valuable learning experiences. Each mistake brings you closer to understanding the problem more deeply and finding the right solution.

Take time to reflect on what went wrong, whether it was a flaw in the solution itself or in the approach you used. This reflection helps you adapt your problem-solving techniques and develop more effective strategies for the future. By staying flexible and open to learning, you strengthen your overall problem-solving abilities.

Adaptability and a willingness to learn from mistakes are essential for long-term success. Many individuals find that using nootropics helps improve cognitive flexibility, making it easier to adjust their strategies and think critically about what changes need to be made.

Practice Problem-Solving Regularly

Like any skill, problem-solving improves with practice. The more you challenge your brain to find solutions, the sharper and more effective your problem-solving skills become. Incorporating problem-solving exercises into your daily routine helps keep your mind sharp and better prepared to tackle challenges as they arise.

One way to practice problem-solving regularly is to engage in puzzles, logic games, or brainteasers. These exercises challenge your brain to think critically and explore different approaches to finding solutions. Additionally, applying problem-solving techniques to everyday challenges, such as organizing your schedule or resolving a conflict, provides valuable real-world practice.

Another effective practice is to reflect on recent challenges you’ve faced and analyze how you approached them. Consider what worked, what didn’t, and how you could improve your approach in the future. By making problem-solving a regular part of your daily routine, you strengthen your mental agility and become more confident in handling any issues that arise.

Some individuals use brain supplements like nootropics to support cognitive performance and problem-solving skills, helping them stay sharp and focused even during complex challenges. Nootropics can provide an additional mental boost, enhancing clarity, focus, and creativity while solving problems.

10 Everyday uses for Problem Solving Skills

• Problem Solving & Decision Making Real world training delivers real world results. Learn More

Many employers are recognizing the value and placing significant investments in developing the problem solving skills of their employees.  While we often think about these skills in the work context, problem solving isn’t just helpful in the workplace.  Here are 10 everyday uses for problem solving skills that can you may not have thought about

1. Stuck in traffic and late for work, again

With busy schedules and competing demands for your time, getting where you need to be on time can be a real challenge.  When traffic backs up, problem solving skills can help you figure out alternatives to avoid congestion, resolve the immediate situation and develop a solution to avoid encountering the situation in the future.

2. What is that stain on the living room carpet?

Parents, pet owners and spouses face this situation all the time.  The living room carpet was clean yesterday but somehow a mysterious stain has appeared and nobody is claiming it.  In order to clean it effectively, first you need to figure out what it is.  Problem solving can help you track down the culprit, diagnose the cause of the stain and develop an action plan to get your home clean and fresh again.

3. What is that smell coming from my garden shed?

Drawing from past experiences, the seasoned problem solver in you suspects that the source of the peculiar odor likely lurks somewhere within the depths of the shed. Your challenge now lies in uncovering the origin of this scent, managing its effects, and formulating a practical plan to prevent such occurrences in the future.

4. I don’t think the car is supposed to make that thumping noise

As with many problems in the workplace, this may be a situation to bring in problem solving experts in the form of your trusted mechanic.  If that isn’t an option, problem solving skills can be helpful to diagnose and assess the impact of the situation to ensure you can get where you need to be.

5. Creating a budget

Tap into your problem-solving prowess as you embark on the journey of budgeting. Begin by determining what expenses to include in your budget, and strategize how to account for unexpected financial surprises. The challenge lies in crafting a comprehensive budget that not only covers your known expenses but also prepares you for the uncertainties that may arise.

6. My daughter has a science project – due tomorrow

Sometimes the challenge isn’t impact, its urgency.  Problem solving skills can help you quickly assess the situation and develop an action plan to get that science project done and turned in on time.

7. What should I get my spouse for his/her birthday?

As with many problems, this one may not have a “right answer” or apparent solution.  Its time to apply those problem solving skills to evaluate the effects of past decisions combined with current environmental signals and available resources to select the perfect gift to put a smile on your significant other’s face.

8. The office printer suddenly stopped working, and there are important documents that need to be printed urgently.

Uh oh, time to think quickly.  There is an urgent situation that must be addressed to get things back to normal, a cause to be identified (what’s causing the printer issue), and an action plan to resolve it.  Problem solving skills can help you avoid stress and ensure that your documents are printed on time.

9. I’m torn between two cars! Which one should I choose?

In a world brimming with countless choices, employ decision analysis as your trusty tool to navigate the sea of options. Whether you’re selecting a car (or any other product), the challenge is to methodically identify and evaluate the best choices that align with your unique needs and preferences.

10. What’s for dinner?

Whether you are planning to eat alone, with family or entertaining friends and colleagues, meal planning can be a cause of daily stress.  Applying problem solving skills can put the dinner dilemma into perspective and help get the food on the table and keep everyone happy.

Problem Solving skills aren’t just for the workplace – they can be applied in your everyday life.  Kepner-Tregoe can help you and your team develop your problem solving skills through a combination of training and consulting with our problem solving experts.

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

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

What Is Problem Solving?

Definition and importance.

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

Problem-Solving Steps

The problem-solving process typically includes the following steps:

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

Defining the Problem

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

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

Generating Solutions

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

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

Evaluating and Selecting Solutions

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

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

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

Implementing and Monitoring the Solution

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

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

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

Problem-Solving Techniques

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

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

Brainstorming

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

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

When brainstorming, remember to:

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

Root Cause Analysis

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

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

SWOT Analysis

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

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

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

Mind Mapping

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

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

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

Examples of Problem Solving in Various Contexts

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

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

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

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

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

• Overcoming a personal obstacle, such as improving your fitness level, by establishing achievable goals, measuring progress, and adjusting your approach accordingly
• Navigating a new environment or city by researching your surroundings, asking for directions, or using technology like GPS to guide you
• Dealing with a sudden change, like a change in your work schedule, by assessing the situation, identifying potential impacts, and adapting your plans to accommodate the change.
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5 Examples of Problem Solving Scenarios + ROLE PLAY SCRIPTS

Problem-solving is an essential skill in our daily lives. It enables us to analyze situations, identify challenges, and find suitable solutions. In this article, we’ll explore five real-life problem-solving scenarios from various areas, including business, education, and personal growth. By understanding these examples, you can develop your problem-solving abilities and effectively tackle challenges in your life.

Examples of Problem Solving Scenarios

Improving Customer Service Scenario:

Solution : The store manager assembles a team to analyze customer feedback, identify key issues, and propose solutions. They implement a new training program focused on customer service skills, streamline the checkout process, and introduce an incentive system to motivate employees. As a result, customer satisfaction improves, and the store’s reputation is restored.

Enhancing Learning Outcomes Scenario:

A high school teacher notices that her students struggle with understanding complex concepts in her science class, leading to poor performance on tests.

Overcoming Procrastination Scenario:

An individual consistently procrastinates, leading to increased stress and reduced productivity.

Solution : The person identifies the root cause of their procrastination, such as fear of failure or lack of motivation. They establish clear goals and deadlines, break tasks into manageable steps, and use time management tools, like the Pomodoro Technique , to stay focused. By consistently applying these strategies, they successfully overcome procrastination and enhance their productivity.

Reducing Patient Wait Times Scenario:

Solution : The clinic’s management team conducts a thorough analysis of the appointment scheduling process and identifies bottlenecks. They implement a new appointment system, hire additional staff, and optimize the workflow to reduce wait times. As a result, patient satisfaction increases, and staff stress levels decrease.

Reducing Plastic Waste Scenario:

Solution : Community leaders organize a task force to address the issue. They implement a recycling program, educate residents about the environmental impact of plastic waste, and collaborate with local businesses to promote the use of eco-friendly packaging alternatives. These actions lead to a significant reduction in plastic waste and a cleaner, healthier community.

Conclusion : These five examples of problem-solving scenarios demonstrate how effective problem-solving strategies can lead to successful outcomes in various aspects of life. By learning from these scenarios, you can develop your problem-solving skills and become better equipped to face challenges in your personal and professional life. Remember to analyze situations carefully, identify the root causes, and implement solutions that address these issues for optimal results.

Role Play: Improving Customer Service in a Retail Store

Scenario : A retail store is experiencing a decline in customer satisfaction, with clients complaining about slow service and unhelpful staff.

Role Play Script:

Assistant Manager : I agree. We could also implement a new training program for our staff, focusing on customer service skills and techniques.

Sales Associate : (Smiling) Of course! I’d be happy to help. What product are you looking for?

Sales Associate : Let me check our inventory system to see if we have it in stock. (Checks inventory) I’m sorry, but it seems we’re currently out of stock. However, we’re expecting a new shipment within two days. I can take your contact information and let you know as soon as it arrives.

Customer : That would be great! Thank you for your help.

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Problem-Solving Strategies and Obstacles

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• Application
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From deciding what to eat for dinner to considering whether it's the right time to buy a house, problem-solving is a large part of our daily lives. Learn some of the problem-solving strategies that exist and how to use them in real life, along with ways to overcome obstacles that are making it harder to resolve the issues you face.

What Is Problem-Solving?

In cognitive psychology , the term 'problem-solving' refers to the mental process that people go through to discover, analyze, and solve problems.

A problem exists when there is a goal that we want to achieve but the process by which we will achieve it is not obvious to us. Put another way, there is something that we want to occur in our life, yet we are not immediately certain how to make it happen.

Maybe you want a better relationship with your spouse or another family member but you're not sure how to improve it. Or you want to start a business but are unsure what steps to take. Problem-solving helps you figure out how to achieve these desires.

The problem-solving process involves:

• Discovery of the problem
• Deciding to tackle the issue
• Seeking to understand the problem more fully
• Researching available options or solutions
• Taking action to resolve the issue

Before problem-solving can occur, it is important to first understand the exact nature of the problem itself. If your understanding of the issue is faulty, your attempts to resolve it will also be incorrect or flawed.

Problem-Solving Mental Processes

Several mental processes are at work during problem-solving. Among them are:

• Perceptually recognizing the problem
• Representing the problem in memory
• Considering relevant information that applies to the problem
• Identifying different aspects of the problem
• Labeling and describing the problem

Problem-Solving Strategies

There are many ways to go about solving a problem. Some of these strategies might be used on their own, or you may decide to employ multiple approaches when working to figure out and fix a problem.

An algorithm is a step-by-step procedure that, by following certain "rules" produces a solution. Algorithms are commonly used in mathematics to solve division or multiplication problems. But they can be used in other fields as well.

In psychology, algorithms can be used to help identify individuals with a greater risk of mental health issues. For instance, research suggests that certain algorithms might help us recognize children with an elevated risk of suicide or self-harm.

One benefit of algorithms is that they guarantee an accurate answer. However, they aren't always the best approach to problem-solving, in part because detecting patterns can be incredibly time-consuming.

There are also concerns when machine learning is involved—also known as artificial intelligence (AI)—such as whether they can accurately predict human behaviors.

Heuristics are shortcut strategies that people can use to solve a problem at hand. These "rule of thumb" approaches allow you to simplify complex problems, reducing the total number of possible solutions to a more manageable set.

If you find yourself sitting in a traffic jam, for example, you may quickly consider other routes, taking one to get moving once again. When shopping for a new car, you might think back to a prior experience when negotiating got you a lower price, then employ the same tactics.

While heuristics may be helpful when facing smaller issues, major decisions shouldn't necessarily be made using a shortcut approach. Heuristics also don't guarantee an effective solution, such as when trying to drive around a traffic jam only to find yourself on an equally crowded route.

Trial and Error

A trial-and-error approach to problem-solving involves trying a number of potential solutions to a particular issue, then ruling out those that do not work. If you're not sure whether to buy a shirt in blue or green, for instance, you may try on each before deciding which one to purchase.

This can be a good strategy to use if you have a limited number of solutions available. But if there are many different choices available, narrowing down the possible options using another problem-solving technique can be helpful before attempting trial and error.

In some cases, the solution to a problem can appear as a sudden insight. You are facing an issue in a relationship or your career when, out of nowhere, the solution appears in your mind and you know exactly what to do.

Insight can occur when the problem in front of you is similar to an issue that you've dealt with in the past. Although, you may not recognize what is occurring since the underlying mental processes that lead to insight often happen outside of conscious awareness .

Research indicates that insight is most likely to occur during times when you are alone—such as when going on a walk by yourself, when you're in the shower, or when lying in bed after waking up.

How to Apply Problem-Solving Strategies in Real Life

If you're facing a problem, you can implement one or more of these strategies to find a potential solution. Here's how to use them in real life:

• Create a flow chart . If you have time, you can take advantage of the algorithm approach to problem-solving by sitting down and making a flow chart of each potential solution, its consequences, and what happens next.
• Recall your past experiences . When a problem needs to be solved fairly quickly, heuristics may be a better approach. Think back to when you faced a similar issue, then use your knowledge and experience to choose the best option possible.
• Start trying potential solutions . If your options are limited, start trying them one by one to see which solution is best for achieving your desired goal. If a particular solution doesn't work, move on to the next.
• Take some time alone . Since insight is often achieved when you're alone, carve out time to be by yourself for a while. The answer to your problem may come to you, seemingly out of the blue, if you spend some time away from others.

Obstacles to Problem-Solving

Problem-solving is not a flawless process as there are a number of obstacles that can interfere with our ability to solve a problem quickly and efficiently. These obstacles include:

• Assumptions: When dealing with a problem, people can make assumptions about the constraints and obstacles that prevent certain solutions. Thus, they may not even try some potential options.
• Functional fixedness : This term refers to the tendency to view problems only in their customary manner. Functional fixedness prevents people from fully seeing all of the different options that might be available to find a solution.
• Irrelevant or misleading information: When trying to solve a problem, it's important to distinguish between information that is relevant to the issue and irrelevant data that can lead to faulty solutions. The more complex the problem, the easier it is to focus on misleading or irrelevant information.
• Mental set: A mental set is a tendency to only use solutions that have worked in the past rather than looking for alternative ideas. A mental set can work as a heuristic, making it a useful problem-solving tool. However, mental sets can also lead to inflexibility, making it more difficult to find effective solutions.

How to Improve Your Problem-Solving Skills

In the end, if your goal is to become a better problem-solver, it's helpful to remember that this is a process. Thus, if you want to improve your problem-solving skills, following these steps can help lead you to your solution:

• Recognize that a problem exists . If you are facing a problem, there are generally signs. For instance, if you have a mental illness , you may experience excessive fear or sadness, mood changes, and changes in sleeping or eating habits. Recognizing these signs can help you realize that an issue exists.
• Decide to solve the problem . Make a conscious decision to solve the issue at hand. Commit to yourself that you will go through the steps necessary to find a solution.
• Seek to fully understand the issue . Analyze the problem you face, looking at it from all sides. If your problem is relationship-related, for instance, ask yourself how the other person may be interpreting the issue. You might also consider how your actions might be contributing to the situation.
• Research potential options . Using the problem-solving strategies mentioned, research potential solutions. Make a list of options, then consider each one individually. What are some pros and cons of taking the available routes? What would you need to do to make them happen?
• Take action . Select the best solution possible and take action. Action is one of the steps required for change . So, go through the motions needed to resolve the issue.
• Try another option, if needed . If the solution you chose didn't work, don't give up. Either go through the problem-solving process again or simply try another option.

You can find a way to solve your problems as long as you keep working toward this goal—even if the best solution is simply to let go because no other good solution exists.

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

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10 Problem-solving strategies to turn challenges on their head

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What is an example of problem-solving?

What are the 5 steps to problem-solving, 10 effective problem-solving strategies, what skills do efficient problem solvers have, how to improve your problem-solving skills.

Problems come in all shapes and sizes — from workplace conflict to budget cuts.

Creative problem-solving is one of the most in-demand skills in all roles and industries. It can boost an organization’s human capital and give it a competitive edge. 

Problem-solving strategies are ways of approaching problems that can help you look beyond the obvious answers and find the best solution to your problem . 

Let’s take a look at a five-step problem-solving process and how to combine it with proven problem-solving strategies. This will give you the tools and skills to solve even your most complex problems.

Good problem-solving is an essential part of the decision-making process . To see what a problem-solving process might look like in real life, let’s take a common problem for SaaS brands — decreasing customer churn rates.

To solve this problem, the company must first identify it. In this case, the problem is that the churn rate is too high. 

Next, they need to identify the root causes of the problem. This could be anything from their customer service experience to their email marketing campaigns. If there are several problems, they will need a separate problem-solving process for each one. 

Let’s say the problem is with email marketing — they’re not nurturing existing customers. Now that they’ve identified the problem, they can start using problem-solving strategies to look for solutions. 

This might look like coming up with special offers, discounts, or bonuses for existing customers. They need to find ways to remind them to use their products and services while providing added value. This will encourage customers to keep paying their monthly subscriptions.

They might also want to add incentives, such as access to a premium service at no extra cost after 12 months of membership. They could publish blog posts that help their customers solve common problems and share them as an email newsletter.

The company should set targets and a time frame in which to achieve them. This will allow leaders to measure progress and identify which actions yield the best results.

Perhaps you’ve got a problem you need to tackle. Or maybe you want to be prepared the next time one arises. Either way, it’s a good idea to get familiar with the five steps of problem-solving. 

Use this step-by-step problem-solving method with the strategies in the following section to find possible solutions to your problem.

1. Identify the problem

The first step is to know which problem you need to solve. Then, you need to find the root cause of the problem. 

The best course of action is to gather as much data as possible, speak to the people involved, and separate facts from opinions. 

Once this is done, formulate a statement that describes the problem. Use rational persuasion to make sure your team agrees .

2. Break the problem down 

Identifying the problem allows you to see which steps need to be taken to solve it. 

First, break the problem down into achievable blocks. Then, use strategic planning to set a time frame in which to solve the problem and establish a timeline for the completion of each stage.

3. Generate potential solutions

At this stage, the aim isn’t to evaluate possible solutions but to generate as many ideas as possible. 

Encourage your team to use creative thinking and be patient — the best solution may not be the first or most obvious one.

Use one or more of the different strategies in the following section to help come up with solutions — the more creative, the better.

4. Evaluate the possible solutions

Once you’ve generated potential solutions, narrow them down to a shortlist. Then, evaluate the options on your shortlist. 

There are usually many factors to consider. So when evaluating a solution, ask yourself the following questions:

• Will my team be on board with the proposition?
• Does the solution align with organizational goals ?
• Is the solution likely to achieve the desired outcomes?
• Is the solution realistic and possible with current resources and constraints?
• Will the solution solve the problem without causing additional unintended problems?

5. Implement and monitor the solutions

Once you’ve identified your solution and got buy-in from your team, it’s time to implement it. 

But the work doesn’t stop there. You need to monitor your solution to see whether it actually solves your problem. 

Request regular feedback from the team members involved and have a monitoring and evaluation plan in place to measure progress.

If the solution doesn’t achieve your desired results, start this step-by-step process again.

There are many different ways to approach problem-solving. Each is suitable for different types of problems. 

The most appropriate problem-solving techniques will depend on your specific problem. You may need to experiment with several strategies before you find a workable solution.

Here are 10 effective problem-solving strategies for you to try:

• Use a solution that worked before
• Brainstorming
• Work backward
• Use the Kipling method
• Draw the problem
• Use trial and error
• Sleep on it
• Get advice from your peers
• Use the Pareto principle
• Add successful solutions to your toolkit

Let’s break each of these down.

1. Use a solution that worked before

It might seem obvious, but if you’ve faced similar problems in the past, look back to what worked then. See if any of the solutions could apply to your current situation and, if so, replicate them.

2. Brainstorming

The more people you enlist to help solve the problem, the more potential solutions you can come up with.

Use different brainstorming techniques to workshop potential solutions with your team. They’ll likely bring something you haven’t thought of to the table.

3. Work backward

Working backward is a way to reverse engineer your problem. Imagine your problem has been solved, and make that the starting point.

Then, retrace your steps back to where you are now. This can help you see which course of action may be most effective.

4. Use the Kipling method

This is a method that poses six questions based on Rudyard Kipling’s poem, “ I Keep Six Honest Serving Men .” 

• What is the problem?
• Why is the problem important?
• When did the problem arise, and when does it need to be solved?
• How did the problem happen?
• Where is the problem occurring?
• Who does the problem affect?

Answering these questions can help you identify possible solutions.

5. Draw the problem

Sometimes it can be difficult to visualize all the components and moving parts of a problem and its solution. Drawing a diagram can help.

This technique is particularly helpful for solving process-related problems. For example, a product development team might want to decrease the time they take to fix bugs and create new iterations. Drawing the processes involved can help you see where improvements can be made.

6. Use trial-and-error

A trial-and-error approach can be useful when you have several possible solutions and want to test them to see which one works best.

7. Sleep on it

Finding the best solution to a problem is a process. Remember to take breaks and get enough rest . Sometimes, a walk around the block can bring inspiration, but you should sleep on it if possible.

A good night’s sleep helps us find creative solutions to problems. This is because when you sleep, your brain sorts through the day’s events and stores them as memories. This enables you to process your ideas at a subconscious level. 

If possible, give yourself a few days to develop and analyze possible solutions. You may find you have greater clarity after sleeping on it. Your mind will also be fresh, so you’ll be able to make better decisions.

8. Get advice from your peers

Getting input from a group of people can help you find solutions you may not have thought of on your own. 

For solo entrepreneurs or freelancers, this might look like hiring a coach or mentor or joining a mastermind group. 

For leaders , it might be consulting other members of the leadership team or working with a business coach .

It’s important to recognize you might not have all the skills, experience, or knowledge necessary to find a solution alone. 

9. Use the Pareto principle

The Pareto principle — also known as the 80/20 rule — can help you identify possible root causes and potential solutions for your problems.

Although it’s not a mathematical law, it’s a principle found throughout many aspects of business and life. For example, 20% of the sales reps in a company might close 80% of the sales. 

You may be able to narrow down the causes of your problem by applying the Pareto principle. This can also help you identify the most appropriate solutions.

10. Add successful solutions to your toolkit

Every situation is different, and the same solutions might not always work. But by keeping a record of successful problem-solving strategies, you can build up a solutions toolkit. 

These solutions may be applicable to future problems. Even if not, they may save you some of the time and work needed to come up with a new solution.

Improving problem-solving skills is essential for professional development — both yours and your team’s. Here are some of the key skills of effective problem solvers:

• Critical thinking and analytical skills
• Communication skills , including active listening
• Decision-making
• Planning and prioritization
• Emotional intelligence , including empathy and emotional regulation
• Time management
• Data analysis
• Research skills
• Project management

And they see problems as opportunities. Everyone is born with problem-solving skills. But accessing these abilities depends on how we view problems. Effective problem-solvers see problems as opportunities to learn and improve.

Ready to work on your problem-solving abilities? Get started with these seven tips.

1. Build your problem-solving skills

One of the best ways to improve your problem-solving skills is to learn from experts. Consider enrolling in organizational training , shadowing a mentor , or working with a coach .

2. Practice

Practice using your new problem-solving skills by applying them to smaller problems you might encounter in your daily life. 

Alternatively, imagine problematic scenarios that might arise at work and use problem-solving strategies to find hypothetical solutions.

3. Don’t try to find a solution right away

Often, the first solution you think of to solve a problem isn’t the most appropriate or effective.

Instead of thinking on the spot, give yourself time and use one or more of the problem-solving strategies above to activate your creative thinking. 

4. Ask for feedback

Receiving feedback is always important for learning and growth. Your perception of your problem-solving skills may be different from that of your colleagues. They can provide insights that help you improve. 

5. Learn new approaches and methodologies

There are entire books written about problem-solving methodologies if you want to take a deep dive into the subject. 

We recommend starting with “ Fixed — How to Perfect the Fine Art of Problem Solving ” by Amy E. Herman. 

6. Experiment

Tried-and-tested problem-solving techniques can be useful. However, they don’t teach you how to innovate and develop your own problem-solving approaches. 

Sometimes, an unconventional approach can lead to the development of a brilliant new idea or strategy. So don’t be afraid to suggest your most “out there” ideas.

7. Analyze the success of your competitors

Do you have competitors who have already solved the problem you’re facing? Look at what they did, and work backward to solve your own problem. 

For example, Netflix started in the 1990s as a DVD mail-rental company. Its main competitor at the time was Blockbuster. 

But when streaming became the norm in the early 2000s, both companies faced a crisis. Netflix innovated, unveiling its streaming service in 2007. 

If Blockbuster had followed Netflix’s example, it might have survived. Instead, it declared bankruptcy in 2010.

Use problem-solving strategies to uplevel your business

When facing a problem, it’s worth taking the time to find the right solution. 

Otherwise, we risk either running away from our problems or headlong into solutions. When we do this, we might miss out on other, better options.

Use the problem-solving strategies outlined above to find innovative solutions to your business’ most perplexing problems.

If you’re ready to take problem-solving to the next level, request a demo with BetterUp . Our expert coaches specialize in helping teams develop and implement strategies that work.

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Elizabeth Perry, ACC

Elizabeth Perry is a Coach Community Manager at BetterUp. She uses strategic engagement strategies to cultivate a learning community across a global network of Coaches through in-person and virtual experiences, technology-enabled platforms, and strategic coaching industry partnerships. With over 3 years of coaching experience and a certification in transformative leadership and life coaching from Sofia University, Elizabeth leverages transpersonal psychology expertise to help coaches and clients gain awareness of their behavioral and thought patterns, discover their purpose and passions, and elevate their potential. She is a lifelong student of psychology, personal growth, and human potential as well as an ICF-certified ACC transpersonal life and leadership Coach.

8 creative solutions to your most challenging problems

5 problem-solving questions to prepare you for your next interview, 31 examples of problem solving performance review phrases, what are metacognitive skills examples in everyday life, what is lateral thinking 7 techniques to encourage creative ideas, leadership activities that encourage employee engagement, learn what process mapping is and how to create one (+ examples), how much do distractions cost 8 effects of lack of focus, 10 organizational skills that will put you a step ahead, the pareto principle: how the 80/20 rule can help you do more with less, thinking outside the box: 8 ways to become a creative problem solver, 3 problem statement examples and steps to write your own, 10 examples of principles that can guide your approach to work, contingency planning: 4 steps to prepare for the unexpected, stay connected with betterup, get our newsletter, event invites, plus product insights and research..

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How to Solve Daily Life Problems

Everyone has problems in life. For the most part, we are able to quickly solve them without much trouble. We either come up with a quick solution or use a strategy that worked in the past. For example, if you overslept in the morning and are going to be late for work, you might decide to call work and explain your situation while getting dressed and ready in half the usual time.

Problems become more difficult when there is no obvious solution and strategies that you have tried in the past don’t work. These types of problems cause a great deal of stress and anxiety and require new and different strategies.

The Steps to Solving Daily Life Problems

Step 1: is there a problem.

As a first step, it is important to realize that there is a problem. Because problems can cause anxiety, many people will try to avoid, ignore or procrastinate when dealing with difficult issues in their lives.

Unfortunately, avoiding your problems usually causes them to come back, and a small problem can become a big problem over time. So, how can you recognize a problem early on?

• Make a list. Get in the habit of writing out a list of the problems in your life. It is easier to work on a problem if you have written it down. This approach will also help you to see how certain problems seem to come up again and again.

Hint : Write it down. When a problem causes you anxiety, it is best to use a pen and paper and to work it out in written form. You are more likely to deal with a problem when it is written down in front of you.

• Use your feelings. We often make the mistake of thinking our negative emotions are the problem. This is false. For example, you might think, “the problem is that I am always stressed at work.” Where as it is more accurate to say there is a problem at work (such as difficulties with coworkers or a huge workload), which is making you feel stressed. Use your negative emotions to guide you: when you are feeling anxious, stressed, frustrated, or annoyed in a particular situation, try to find the problem that is making you feel that way.
• Find the challenge. A huge obstacle for most people is the negative way that they look at problems: if you think that problems are completely threatening, or that having them is a sign of weakness or failure, and you see yourself as a bad problem solver, you won’t solve the problem! That is, even if you are good at solving problems, you won’t try to deal with them if you don’t think you can and you don’t see any benefit to it. If you can find some benefit or opportunity in a problem, you are more likely to work on it. For example, if your problem is not getting along with coworkers, the opportunity might be that it is a chance to improve your communication skills and possibly resolve some arguments with your coworkers.

Key Point: There is always a benefit to solving problems. Remember that if you solve a problem, even a difficult one, it is one less thing to worry about, and one less problem on your problem list!

Step 2: What is the problem?

Before trying to solve a problem, you first need to define it. Here are some tips on how to properly define what your problem is:

• What is the situation? (e.g. my boss gives me too much work)
• What would I like the situation to be? (e.g. I would like my boss to give me less work)
• What is the obstacle that is keeping me from my desired situation? (e.g. I’m unsure how to talk to my boss about my work obligations)

You can then put your problem into a sentence. For example, the problem is that my boss gives me too much work; I would like to have less work, but I’m not sure how to ask him to reduce my workload.

• Just the facts: Be careful to avoid putting opinions or assumptions into your definition. For example, thinking that your work problem is that “my boss is a jerk” is an opinion. Besides, it makes the problem almost impossible to solve.
• Be specific and concrete: If you are too vague when defining your problem, it will be difficult to know how to even begin solving it. For example, thinking that, “my problem is my work” is not specific or concrete; what is it about your work that is a problem? How will you even start fixing this kind of problem?

Step 3: What are my goals for this problem?

In order to know whether you have solved your problems, it is important to know ahead of time what a solved problem would look like. Here are some tips for setting goals:

• Be realistic: Make sure that your goals are achievable; if they are unrealistic, you will probably not reach them and you will feel badly. For example, with the work problem, if your goal is to only do your work when you feel like it, you will likely not solve your problem.
• Be specific: If your goals are vague, you won’t know when you have reached them. For example, if you think, “my goal is to be happy at work”, what does that mean? Do you want to be happy all the time? How happy? When will you know when you have reached your “happy” goal?
• Start with short-term goals: If you set goals that can be reached relatively quickly, you are more likely to work on your problem. You can set long-term goals too, but make sure to have short-terms goals as well so you know whether the problem is solved. With the work problem, a long-term goal might be to get another job while a short-term goal might be to reduce your workload.

Step 4: Thinking up solutions

The biggest mistake that we tend to make when finding solutions for our problems is to think about the same old solutions. However, if those old solutions worked, the problem would not still be around. In order to come up with new solutions, you can follow the rules of brainstorming:

• Devise lots of solutions: You are more likely to come up with a good solution if you have a lot of solutions to choose from. Try to come up with at least 10 possible solutions to your problem.
• Don’t judge your solutions: Remember that you aren’t choosing a solution yet, you are just trying to think of as many options as you can; so don’t judge them. Even silly, strange or extreme solutions are good ones at this stage. For the work problem, you might think about solutions like “quit my job” or “organize a strike”. Write them down! You will never come up with new solutions if you aren’t willing to even think about silly ones.
• Have a variety of solutions: Make sure that your solutions are different from each other. For example, with the work problem, there is not much variety if your solutions are to “ask the boss to have lunch with me”, “ask the boss to have coffee with me”, or “ask the boss to come out to dinner”. Although these are 3 solutions, they are basically all the same solution: ask the boss to do something social with you.

REMEMBER : When it comes to difficult problems, the first idea that comes to your mind is not always the best. Take the time to come up with new possibilities.

Some other tips for thinking up lots of different solutions are:

• Be specific:  Make sure that your solutions involve specific behaviours, and not general strategies. For example, the solution, “give the boss a list of all the work I am doing now” is very specific, compared to the solution, “be more assertive with my boss”. If you picked the latter solution, you would have a new problem — figuring out how to be more assertive.
• Ask for help:  If you are having a hard time coming up with new and different solutions to your problem, ask friends, family or coworkers for advice. Other people might have ideas that you have not even thought of.

Step 5: Deciding on a solution

If you struggle with anxiety, actually picking a solution to your problem can often seem quite difficult. However, it is important to remember that not solving a problem can lead to more anxiety than trying to solve it, no matter how anxious you feel. The following are some guidelines that can help you find the best solution to your problem.

REMEMBER : The goal is to find the best solution to your problem, NOT the perfect solution. If there was a “perfect” solution, you would have already found it.

• Will this solution fix my problem and help me reach my goals?  This guideline might seem obvious, however, it is important to make sure that your solution will help you reach your goals. For example, “work harder” as a solution to the work problem will not help you reach your goal of having less work to do in a day.
• How much time and effort does this solution involve?  You can expect that any solution will require some time and effort but the amount involved needs to be related to your needs. “Quitting my job” as a solution to the work problem might involve a great deal of effort, since you would have to start looking for a new job.
• How will I feel if I pick this solution?  If you think that a solution will make you feel bad, guilty or too anxious, it might not be the best solution. For example, “lie to the boss about how much work I actually did” might make you feel bad.
• You right now and in the future
• Other people in your life right now and in the future

REMEMBER : There is no perfect solution, so when you are judging each potential solution it is unlikely that it will meet all four criteria. That is, it probably won’t solve the problem with no time or effort, make you feel happy while doing it, and have no costs and only benefits. You are looking for a solution that BEST meets the criteria, not perfectly.

STEP 6: Carrying out the solution

This is often the most difficult step because you now have to actually start carrying out the solution you chose. Most people are afraid that they might have picked the wrong solution, or that perhaps there is a better solution if they just think about the problem more. This is not helpful thinking: it is better to act than to do nothing at all.

To help you carry out your solution, you can make an action plan. If you know how you are going to carry out your solution, you are more likely to follow through.

Your plan should include all the steps that you will need to take to carry out the solution, and it should be as specific and concrete as possible. For example, if my solution is to “get a new job”, some of the steps involved in that solution might be:

• Make a list of the types of jobs I would like to have
• Buy a newspaper every day and check the “help wanted” ads
• Contact all the employers who advertise a job that I would like to have
• Rearrange my work schedule so I can go to interviews, if necessary

STEP 7: Checking in on your problem

Now that you have carried out your solution, you need to make sure that it is working. Sometimes the best-laid plans don’t always turn out perfectly, so it is a good idea to have markers that let you know whether you are on the right track. For example, with the work problem, you might use your workload as a marker for tracking your solution. If you notice that your workload is going down, then your solution is probably working.

What do I do if my solution isn’t working?

Because the unexpected happens in life, sometimes even the best solutions don’t work out well, which is unfortunate but normal. The best thing to do is to recycle through the different steps and ask yourself the following questions:

• Did I define the problem properly?
• Were my goals realistic?
• Are there other possible solutions?
• Is there a better solution that I could have picked?
• Did I carry it out as planned?

If you work through these steps, you might find that you went wrong somewhere, and then you can fix it and try again.

TIP : Solving the difficult problems in life is hard work, so make sure to reward yourself afterward for a job well done.

Here is a helpful resource for more information on problem solving:

Solving Life’s Problems: A 5-Step Guide to Enhanced Well-Being  by A.M. Nezu, C.M. Nezu, and T.J. D’Zurilla. Springer Publishing.

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Improve Your Problem-Solving Skills – Steps, Processes & Technique

When you are faced with a problem, how do you go about solving it? Do you let it overwhelm you, or do you flex your problem-solving muscles and figure out the best possible solution?

People who allow themselves to be overwhelmed or ignore complex problems often become frantic and confused. They usually take a haphazard approach to thinking, and then they are dismayed when they find themselves floundering and making no progress.

Luckily, there is a much better way.

I’d like to introduce you to a problem-solving process that can help you face and tackle any type of challenge. With these 10 problem-solving strategies, you will strengthen your ability to always find a solution while enabling yourself to see real progress.

Once you begin to execute these problem-solving  techniques, you will feel confident to face a problem right away.

What Are Problem-Solving Skills?

Problem-solving skills involve identifying a problem, coming up with possible solutions, choosing an appropriate solution, and then implementing it.

Often, there is more than one correct solution to a problem. But frequently, you are looking for the best solution that applies to your particular circumstance.

For instance, possible solutions to losing weight include eating less, adding healthier foods to your diet, walking 30 minutes a day, swimming three times a week, training for a 5K race, drinking more water, and many other effective solutions.

Your job is to find the solution that will work best for you and give you the most success.

Good problem-solving skills are essential in all areas of your life because we encounter problems to solve in one form or another nearly every day, from small things like getting stuck in traffic to major events like being diagnosed with a chronic illness.

A problem can be defined in one of two ways:

“Any question or matter involving doubt, uncertainty, or difficulty; a question proposed for solution or discussion.”

The Encyclopedia of the Sciences of Learning explains that a problem:

“…is generally considered to be a task, a situation, or person which is difficult to deal with or control due to complexity and transparency. In everyday language, a problem is a question proposed for a solution, a matter stated for examination or proof.”

In short, a problem is something that’s hard to deal with and needs to be solved.

Examples of common problems in the workplace might include:

• Lack of motivation or boredom
• Discrimination
• Conflict with a boss or coworkers
• Performance issues
• Burnout or stress
• Bad working conditions

Or maybe you’re dealing with problems in your personal life. For example:

• A strained marriage or divorce
• Financial worries
• Health issues
• Grief over the death of loved ones
• Issues your children are experiencing
• A decision to move, change jobs, or get an education

No matter what you’re facing, it’s important to actively cultivate your creative thinking and learn problem-solving techniques. 

When you’re able to solve problems effectively, you will enjoy greater satisfaction in life. Your relational skills will improve, and your problem-solving abilities will make you highly valuable in the workplace.

The Importance of Solving Problems

We solve problems daily in all aspects of life. People who are good problem solvers are more likely to be successful in getting around obstacles and achieving their desired end result.

What’s more, solving complex problems doesn’t only help change your external circumstances. You’ll also feel happier and more confident in yourself, knowing you can solve future problems.  

Problem-solving allows you to:

• Fix things that are broken
• Address risk
• Improve performance
• Seize opportunity
• Lower stress and anxiety
• Prevent more serious consequences

Having a problem-solving strategy will make you more attractive to hiring managers. In many cases, you might be asked in a job interview about your problem-solving skills. 

It’s smart to think of an example ahead of time–a problem that came up at your last job and how you solved it–so you’ll be prepared. You can also mention the soft skills listed above: 

“My communication skills, flexibility, and ability to think outside the box help me deal with problems in a timely manner.”

The more you practice effective problem-solving techniques, the better you will get at solving problems and the more reliable and trustworthy you will become in your field as well as in your personal life.

Understanding the Problem-Solving Process

When you’re setting out to solve a problem, what should you do first?

While there is no one-size-fits-all approach to problem-solving, there is a general framework that you can use to help solve problems.

The problem-solving process is often broken down into seven steps:

• Identify the issue and its root cause
• Understand every angle of the problem
• List possible solutions
• Evaluate the options
• Choose an option
• Evaluate the results

I’ll explain this process and each of these steps, plus a few bonus steps. I’ll also share some further problem-solving strategies so you are well-equipped with solution-finding techniques that you can apply to various situations.

The important thing to understand now, though, is that you can use a structured process to improve problem-solving skills. You don’t have to shoot in the dark–simply follow the steps listed in this process.

Problem-Solving Skills

What kind of skills should you cultivate to become a better problem-solver?

You can also work on things like your communication skills, analytical skills, and other key skills in life that will make you a better problem solver. These soft skills go hand in hand with being able to come up with solutions quickly.

Focus on the following:

Brainstorming

This is a method of free-thinking used to generate ideas that involve thinking of a long list of possible solutions without making an initial judgment about how effective they might be. You can brainstorm with a group of people or on your own.

Data gathering

Collecting information related to the issue is a vital problem-solving tool as the more information you have about the root cause and contributing factors to a problem, the easier it will be to find solutions that work. Fact-finding can come from interviewing people involved, researching related problems, reading documents, analyzing data, and more.

Creative thinking

When you’re a creative thinker, you’re able to look at a complex problem or an everyday problem and think of unique, original solutions. Your ability to come up with creative solutions will make you more marketable as well as more successful in meeting complex problems head-on.

Communication

Having communication skills is essential to work with others to solve problems. You need to not only be able to express your thoughts clearly and concisely without causing offense or contention, but you also need to be able to listen to others as they express their views until everyone is on the same page.

Like communication skills, teamwork involves being able to work collectively with others to apply problem-solving strategies. Often, two heads are better than one, and the wisdom you gain from collective intelligence will make identifying underlying causes and finding solutions much easier.

Analyzing involves being able to break up a complex problem into smaller parts so you can examine and evaluate it to understand the problem better. 

You may find the root cause of the problem as well as contributing factors. Ill-defined problems are difficult to solve, so it is important to be able to apply problem analysis to any issue you are dealing with.

Time management

Time-management skills help you avoid procrastination and spending time on unnecessary tasks. 

You can develop good time management skills by setting goals, making daily to-do lists, prioritizing your tasks, and reducing or eliminating distractions.

Troubleshooting

Troubleshooting is applying a step-by-step process to find the cause of a problem and then working your way to different solutions. 

Common, well-defined problems, such as those that occur in the computer science field or automotive industry, may have a preset list of troubleshooting steps to follow. 

Other problems will require you to develop a troubleshooting process as you go. Troubleshooting skills make you a valuable asset to any team.

When you take initiative, you do not wait for others to tell you what to do. You see a need and seek to fill that need. Often, by taking initiative, you can address an issue before a problem occurs. 

One example in the workplace would be to sign up for training that will keep you up to date on the newest developments in your industry.

Flexibility

Being flexible is an important tool you will use to solve problems. It’s an essential skill in all aspects of your life. When you are too rigid, you often are not able to see creative solutions and different strategies that can help make your life easier. 

There is often more than one good way to solve the same problem, and being open-minded will help you move from your existing beliefs to other effective ways of solving problems.

I know this is a long list, but you don’t have to do everything at once.

Even more, chances are you’ve already picked up some of these skills in your daily life without even realizing it. Keeping these skills in mind as you practice solving problems will help you become better at not only solution-finding but at everything you do.

10 Steps to Solving a Problem

In this 10-step problem-solving process, I’ll walk you through how to identify and implement the right solution to the problem at hand. In learning these steps, you will develop your critical thinking and elevate your problem-solving skills.

1. Take a Positive Approach

When a problem arises, it’s easy to enter panic mode or envision worst-case scenarios. Before you let your mind go there, take a step back and address every problem as simply another situation.

It is a challenge that you can handle, with the right approach. Part of that approach is thinking positively and creatively about the situation.

When figuring out ways to use creative thinking for problem-solving, I like to explore  how geniuses solve challenges . They think outside the box, keep an open mind, and take a systematic approach.

It all starts with thinking positively about the problem.

One problem-solving strategy I like to use is to think of it as a situation, not a problem.

Problems are a fact of life; you can’t control when or how they occur, but you can control your attitude. The more positive your language and mental process are, the more confident and optimistic you will be when approaching any complication.

How can you develop a more positive outlook on life? This mindset shift can take some time. 

You can’t snap your fingers and instantly become a more positive person overnight. However, there are actionable steps you can take to be more positive.

Start by focusing on the good things in your life. Yes, you have problems, but you have good things too. If you’re struggling to come up with anything that makes you smile, consider keeping a gratitude journal where you make an entry every day.

I also recommend positive affirmations and self-talk. Repeat phrases to yourself such as “There are good things in my life,” “I can come up with creative solutions,” or “I have good problem-solving skills.”

And of course, it’s important to surround yourself with people who are equally as positive and upbeat as you’re trying to be. The same applies to all aspects of your life. Read positive books, articles, and social media posts. Listen to uplifting music, and watch videos and movies that leave you feeling positive and optimistic.

Remember that every problem comes with a solution already custom-made for it. You just need to find it, and you can by maintaining a calm, positive attitude and steadily progressing through the different stages of the problem-solving process.

2. Define The Problem

Problem identification is a vital step in problem-solving processes so that you know exactly what you are dealing with. What might seem to be the root cause of your situation may be something entirely different.

Also, defining the problem will help you gather data, analyze the issues surrounding it, and find a potential solution.

What exactly is the challenge you are facing? What about this particular situation is causing you stress and anxiety? You must clearly define the problem to resolve it.

Not only should you clarify what the problem is, but you should also see what caused the problem. If you can’t conclude the cause of the problem, you may need to meet with other parties involved to determine the root before moving forward.

Sometimes a clear root cause cannot be determined, or there may be several factors that are causing the problem. In these cases, you can still move forward in finding solutions by defining what is currently hard to deal with and what needs to be changed or solved.

If you are working with a group, it’s important to write and rewrite the problem until everyone agrees that the problem is clearly and correctly defined. Each person will bring a unique perspective that will help clarify what the situation is.

Identify important details that define that problem, and weed out information that is extraneous or useless so that it doesn’t distract you from your ability to solve it or waste your time.

It can help to ask the following questions:

• Who is involved in the problem?
• What exactly is happening that is preventing forward progress?
• When did the problem occur and how often?
• Why is the problem happening?
• How is it affecting workflow or people?

Write out the problem so that it is easy for you and everyone else to see exactly what it is. It may help to draw a picture, diagram, or graph to fully visualize the problem.

When the issue is clearly defined, the solution may be obvious. But you may never find the solution at all if the problem isn’t defined.

3. Use Creative Thinking

As I mentioned in the first step, geniuses solve issues with out-of-the-box thinking. So you need to see the problem from every angle before you begin moving down solution paths.

You should think: Are there other problems that are affecting this obstacle? If so, you need to address it first.

It can be easy to have tunnel vision when you’re problem-solving, but there are usually multiple things at play with any dilemma. Zoom out from the situation at hand and see all contributing factors to the issue and listen to everyone’s point of view.

Meeting with others who may be involved in the process can offer you more brainpower to shed light on the problem. That’s why teamwork is so important. You can work together to look at what the issue is affecting, what is affecting it, and how to solve it.

It might feel as if you can work faster on your own. But when you collaborate with others, you’ll be able to come up with higher-quality solutions.

In fact, statistics show that 86% of employees and executives say lack of collaboration or ineffective communication causes workplace failures.

Don’t be afraid to sit down with people involved in the problem to work things out. People outside the problem can also offer a valuable third-party opinion. Their advice and ideas may actually be more helpful because they don’t have a personal stake in the issue.

When discussing the problem with others, replace “No, but” with “Yes, and.” For example, if someone says, “I think part of the problem stems from a lack of communication within the team.” Respond with, “Yes, and it can also come from people arriving late to meetings.”

This approach validates what the other person is saying so that all input is accepted as valuable and ideas are not negated. It also gives you an equal opportunity to add your ideas and input.

Think creatively by looking outside of your industry or situation for solutions. While it is helpful to analyze how others within your field or circumstances have solved a similar problem, you might find helpful insight in looking at how companies or individuals in other walks of life that have seemingly non-matching characteristics have approached related problems.

Ask “what if” questions. This can often help you think outside the box when solving problems creatively. As you look at potential solutions, ask,

“Why not?”

“What assumptions can we get rid of?”

“What can we add beyond the expected solutions?” and similar questions to take a broader view of the problem and possible solutions.

State the opposite of the problem to get a different perspective on it. For example, instead of asking, “How can we encourage our existing customers to buy more products?” ask, “How can we discourage our existing customers from buying more products.” This process can lead to surprisingly effective solutions.

4. Brainstorm Possible Solutions

Part of addressing the situation from different directions is to come up with not just one but several solutions. There are likely to be multiple solutions to any single problem.

The first conclusion that comes to mind may not be the best one, but the more you focus, the more solutions you will find. That’s why brainstorming all possible resolutions is an essential step to  problem-solving .

If you’re brainstorming together with a group of others, make sure to define a clear goal for the brainstorming session before you begin. Allow people time before the meeting to reflect on the problem. This will allow them to come prepared with ideas.

Throughout the session, record any suggestions that come up. You can write them on a physical whiteboard so that everyone can see them, or simply jot them down in a digital folder. Share these notes with attendees post-meeting and assign any follow-up tasks.

Reserve judgment until after your brainstorming session is complete. Some ideas may seem ridiculous or impractical, but say them and record them anyway. The goal is to move beyond existing ideas and look at the problem and possible solutions from every angle. Sometimes, an idea that seems far-flung can begin a conversation and flow of ideas that lead to the best solution.

Defining your end goal will help inspire unique ways you can get there. It can also help to pose the problem as a question and come up with conclusions to that question. Use the examples offered earlier of who, what, when, where, and how questions to get you started.

5. Find The Best Solution 

Now, not all possible solutions you outlined will be a good fit. You should be able to narrow down each method and see which is the most effective for your issue.

After brainstorming all potential solutions, ask yourself, “What solution will likely produce the best outcome?”

Do this by comparing each of the results with the one you believe to be the most ideal. Which one is the best under the current circumstances? What will successfully solve the problem? Which one will lead to a better outcome in the future? What will prevent further problems? Is there more than one solution that we should apply for the best results?

It might take some time to work through each of your potential solutions. Some will quickly weed themselves out. In other cases, though, don’t be afraid to spend some time thinking about how a given solution would work.

Identify the pros and cons or benefits and costs of each solution to help you determine which one or more is best.

After looking in-depth at the various approaches, decide on the best solution for the situation.

6. Expect the Best and Prepare for the Worst

Before you jump at the chance to solve your problem with the best-fit solution, consider the repercussions of the solution. 

Now is the time to jump to worst-case scenarios. What will happen if the solution fails? Knowing the answer to this will allow you to prepare if it doesn’t resolve your dilemma.

Even if at first you don’t succeed, you will learn something in the end. Don’t take it as a failure but as a learning opportunity.

Accept that it didn’t work and try something new. Determine what didn’t work and why to come up with additional possible strategies. Thankfully, you already have a list of alternative solutions that can help you find the right one.

Preparing for the worst is not about thinking negatively. Remember, the power of positive thinking will allow you to uncover more solutions. If you can train your mind to think this way, the more solution-oriented you will become.

Instead, thinking through worst-case scenarios is simply being realistic. This allows you to create a Plan B. 

If one solution doesn’t work, which solution will you try next? Come up with a backup plan. You might move on to the next solution on your shortlist, or you might tweak things and continue working with your #1 idea.

Preparing for the worst allows you to end up with the best possible solution.

7. Set a Deadline

The next of my 10 problem-solving strategies is to create a timeframe for your solution. Determine:

• When to implement the solution
• How long it will take to complete
• When you expect to see results

What actions are necessary to meet this deadline, and who will be accomplishing it? List out the tasks needed and assign each one to an appropriate person.

It’s important to not only set a deadline, but also place standards on how you will measure its success. How will you know that you’re making progress, or in other words, what will be your key performance indicators (KPIs)? How will you compare the success of this solution against the success of another?

Determine what key performance indicators will allow you to measure the success of your outcomes and set a series of short-term deadlines to report. Clearly communicate these benchmarks with everyone involved.

Make sure people understand how you’re choosing to measure success so they can be successful by your standards.

8. Take Responsibility

Now that you’ve found the solution to the problem that you want to implement, consider how it will impact the situation if it works or if it doesn’t.

If your outcome doesn’t work, that’s okay, but it is your job to accept responsibility. Be ready to admit any mistakes and continue working to make things right.

Some of the most creative ideas never transpire because no one is assigned the authority to carry out the decision.

Taking responsibility for your decision doesn’t necessarily mean you need to be the one to implement it. There may be various people involved in the problem and different jobs required to accomplish the solution.

By taking responsibility for the decision you make, you’ll ensure that everyone involved knows what job they need to do, when they need to do it, and how the successful or unsuccessful completion of that job is defined.

9. Solve the Problem

Now, it’s finally time to take action.

Execute your solution so you can reach your defined goals and learn what works best. Continue communicating with everyone on board as you all work together to solve the problem.

However, not every problem will be solved easily.

You may encounter additional obstacles as you attempt to solve the initial problem. You can overcome any drawback by tapping into your creative mind and taking action consistently and persistently until you reach your goal.

As you work hard, you can develop your capacity to achieve more in the future. Every time you successfully solve a problem, you are developing your analytical skills, communication skills, and problem-solving abilities. You’re also increasing your confidence.

Next time you need to solve a problem, you can look back on the successful jobs you’ve done before.

10. Track Your Results

The final step of my  problem-solving process is to track the results. Using the deadlines, KPIs, and scheduled reports you set in step seven will let you know immediately if you’re on track or falling behind.

When you reach your deadline, ask yourself if you met the goals you set out to achieve.

What worked and what didn’t work? Did you solve the problem? Did you solve it with the approach and timeframe you expected?

Answering these questions will allow you to understand if you need to take further action and help you improve your problem-solving methods for the future.

The best way to learn to problem solve is to simply do it. Jump in with both feet and start coming up with potential solutions to issues that need fixing. Over time, you’ll learn about problem-solving without even realizing it.

However, in addition to learning “on the job,” you can also take courses to help boost your skills. 

Studying subjects like project management or data analysis is a good way to help you succeed in identifying problems, thinking of better solutions, and leading others with good communication as you work together to put your solutions in place.

Bonus: Further Problem-Solving Strategies

More good news: The process outlined above isn’t the only way to solve complex problems. In fact, there are many strategies you can implement for solving a problem.

Here are summaries of a few more problem-solving methods that you can learn more about:

The IDEAL process of solving a problem can help you look at situations objectively and remove the emotional aspects that can arise when a problem occurs. It works especially well for problems that may not seem to have a clear cause or may need more than one solution. The steps involve:

• Identifying the problem
• Defining what the problem is and the desired outcome
• Exploring possible solutions
• Acting on a solution
• Looking back to evaluate the effectiveness of the solution

Root Cause Analysis

Root cause analysis is actually a set of various problem-solving processes that aim to identify the main cause of a problem so that you can find appropriate solutions. The purpose of root cause analysis is to get to the root of a problem and prevent further difficulties instead of treating the symptoms of a problem.

At the same time, this approach to solving complex problems recognizes that there is value in treating symptoms for short-term relief while the larger problem-finding process is going on.

It also assumes that there can be more than one root cause and focuses on how and why a problem occurs instead of who causes it.

This method provides a structured approach to solving a complex problem, especially those that do not have a clear solution. Simplex problem-solving involves eight steps:

• Problem finding: Identifying what the problem is
• Fact-finding: Collecting information and data about the problem
• Problem definition: Clearly define the complex problem so you know what you are solving
• Idea finding: Generating possible solutions to the problem
• Evaluation and Selection: Choosing the solution that seems to like it will best address the complex problem
• Planning: Deciding how you will implement the solution
• Sell the idea: Get stakeholders on board with implementing the solution
• Action: Carrying out the solution

Appreciative Inquiry

Appreciative inquiry looks at a problem from a different angle, or not at all. It focuses on what is going right instead of what is going wrong. It is often best applied when a change is needed within an organization or individual. This approach leans heavily on cognitive science and positive thinking.

It involves five steps:

• Define the desired outcome
• Discover what our strengths are
• Dream of what would work well in the future
• Design a plan to make it happen
• Deploy the action

Six Thinking Hats

This approach to solving a complex problem focuses on approaching solutions in a balanced way. Using the six thinking hats approach, you will ask yourself a series of questions based on six principles or divide your team into six different groups:

• The white hat will focus on facts and logic (objective)
• The red hat will focus on emotion and instinct (intuitive)
• The black hat will focus on predicting negative outcomes (cautious)
• The yellow hat will look for positive outcomes (optimistic)
• The green hat will focus on reducing criticism and increasing ideas (creative)
• The blue hat will focus on management and organization (control)

The 5 whys is an example of a root cause analysis tool. The purpose of using this problem-solving technique is to find the exact reason a problem is occurring by asking a series of “why” questions. After asking why five times, the cause of the problem and its accompanying solution should be clear.

Start Implementing Solutions to Problems Today

You don’t need to feel overwhelmed and confused when a problem arises anymore. Stress and unhappiness are simply byproducts of how you respond to those situations. Instead, you can look at each problem or difficulty by asking, “What is the opportunity in this?”

When you enhance your problem-solving skills, you will experience determination and a sense of calmness when the next difficult situation arises.

While you may not know how to resolve most issues right away, you will know the problem-solving steps to take to uncover the best response: Define the problem, determine the cause, discover the best problem-solving technique, take action, and analyze the outcome.

Follow this process over and over again and you will creatively solve your problems. After all, an effective way to solve problems is a skill that you can develop with practice.

To help you enhance your success, download my free  SMART Goals Template . This resource is a good fit for someone who wants to achieve their goals and optimize their success. I walk you through how to set goals and plan ahead the right way. As you advance your problem-solving skills, you will experience more success in your daily life—for big-picture items and small ones alike.

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About Brian Tracy — Brian is recognized as the top sales training and personal success authority in the world today. He has authored more than 60 books and has produced more than 500 audio and video learning programs on sales, management, business success and personal development, including worldwide bestseller The Psychology of Achievement. Brian's goal is to help you achieve your personal and business goals faster and easier than you ever imagined. You can follow him on Twitter , Facebook , Pinterest , Linkedin and Youtube .

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ROCK thru real life challenges

How to solve life problems: 10 real-life examples.

• By Lee Havenga |
• April 8, 2021

A friend of mine, who has been following ROCK thru since the beginning, recently asked me how ROCK thru can really be applied to everyday life. She understood each of the four principles, R espect, O wnership, C onnection, and K indness, and they sounded great in theory. But, she wanted to know how to solve life problems using ROCK principles. To explain how the ROCK principles can be applied to help you through life’s challenges, big and small, below are ten scenarios of life problems and how to ROCK thru them.

Before you dive into the examples here are a few things to keep in mind. 

Applying the Principles to Life Problems

Life problems are unique.

These examples are meant to provide a better understanding of how to ROCK thru a challenging situation. There is a good chance that none of these examples will perfectly fit your unique lens of life. But hopefully, there will be a few moments, maybe even pieced together from different scenarios, that you can relate to. When you read through the examples, you may sense some repetitiveness, and that’s the point. As you apply the principles to your own life, you begin to see that they are consistently applicable, no matter the challenge.

Life problems are unpredictable

Most life problem solutions rely on interactions with other people in our interdependent culture, and people are unpredictable. This is why I don’t play out the scenarios to the final solution. I don’t want to paint the picture of applying these principles and living “happily ever after.” Instead, the scenarios are intended to show the intentional process, mind shift, and approach when applying these principles. As Patrick M. Regan said, “…remind yourself that the only thing you can truly control is you – and your reaction to what the world throws at you.” The scenarios give you an idea of how to use the ROCK principles to control your reactions to life problems, not anyone else’s.

It can be difficult to solve life problems

ROCK thru is an approach to life, not a quick fix for substantial challenges. These principles aren’t magic, and applying them takes some diligence. It also takes a fair amount of courage and self-awareness to pull off. But I’ve found that although difficult, working through a problem in this way gets me to a better solution, faster. I’m sharing this not to overwhelm you but to be forthright. Also, without this context, some of the scenarios will seem grossly oversimplified. We live in a complex world with complex problems that don’t usually have simple answers. But ROCK thru provides a framework to apply love, through Respect, Ownership, Connection, and Kindness, to help get through those difficult times and solve life problems.

Solving life problems can be messy

In the beginning, when the four principles (Respect, Ownership, Connection, and Kindness) began to emerge, I was frustrated when they didn’t fit neatly into their own categories. After a while, I began to realize that way the principles converge is part of their beauty. They naturally flow into one another, combining into one thing, love.

How to apply R.O.C.K. to Solve Life Problems

There is a visual summary infographic at the bottom of this page if you want a simple overview and reference of how to apply Respect, Ownership, Connection, and Kindness to solve life problems. 

Apply Respect to Solve a Life Problem

Name all of the people in the situation and what aspects of Respect you can give. Always include yourself since you can’t truly offer Respect to others if you don’t grant it to yourself first. Also, even if you feel resentful towards another person, dig deep to find an aspect of their character that you can honor. This will be an essential foundation so that you can ROCK thru the situation.

Apply Ownership (and the three A’s) to Solve a Life Problem

Intentionally become A ware and A ccept the Truths of the Situation:

Be sure that you look at the situation from multiple perspectives, especially those of other people who may have a different outlook. This is where you search and layout all the truths; the good, the bad, and the ugly. Ownership and Connection often overlap here because you may need to reach out to others to have a well-rounded understanding.

Take A ction on the Truths:

This step can be overwhelming, so when dealing with a complex issue, it is best to write down the actions you plan to take. Break down the actions that you plan to take into manageable steps. I find it best when they are “SMART” (Specific, Measurable, Achievable, Relevant, and Time-bound) actions so that your plan is realistic and doable.

An example of a higher-level SMART action is: “Eliminate all of my credit card debt, $3,419.27, in six months.”

An example of a lower-level task action (a step towards the larger goal) is: “Cancel current credit cards so that no more debt can be accumulated.”

Of course, writing the steps down is only the first step to taking action. Next, you will need to work through the actions you have listed. If you get stuck or overwhelmed, go back to the other principles. Remind yourself of the Respect you have for yourself and others involved in the situation. This reminds you of an important aspect of why you are working to solve the problem in the first place. Make Connections with those in your support system and/or get professional help. And as you are taking action, impart Kindness on yourself. Working through to a solution is not easy so give yourself a break along the way. Most times it is fear that holds us back from taking action. That’s too much to unpack here but to gain a better understanding go to this post about overcoming fear and finding courage . 

Apply Connection to Solve a Life Problem

When using the ROCK principles to problem solve, Connection can be the most difficult of the four. We are often not comfortable with sharing our issues with others for fear of judgment. We are also not accustomed to reaching out for help or support. However, this principle adds the vital support, accountability, and perspective needed to quickly reach a solution. Be brave, find someone you trust or a professional and start making progress.

Apply Kindness to Solve a Life Problem

Although you are reading the principles in the order that spells out the ROCK acronym (Respect, Ownership, Connection, and Kindness), the pillars are meant to overlap and be integrated as you work through to your solution. When generous consideration is given to others, solutions come more easily and quickly. We can disagree and be kind to each other at the same time.  

Although being kind sounds nice, the truth is that it’s not easy. It takes conscious effort and practice to do so. Especially when it comes to being kind to ourselves. Kindness to others begins with being kind to yourself. Make learning about and developing self-love activities a priority. 

10 Examples of how to ROCK thru to solve life problems

These ten examples are written in the first person, the “I” perspective, so the life problem and solution can be relatable. Think of these questions and responses as if you are having a conversation with yourself. Applying the ROCK thru principles is much like that anyway. They are meant to put you in a specific frame of mind so that you can approach and move through your challenges with thoughts and actions of love at the forefront. 

Here are links to each of the 10 scenarios so you can jump to and begin with the one that may be most applicable to you and begin to solve life problems.

Life Problem 1: Feeling Stuck

Life problem 2: relationship challenges.

• Life Problem 3: Chronic Illness
• Life Problem 4: Loss and Grief

Life Problem 5: Negativity

Life problem 6: financial debt.

• Life Problem 7: Expectations and Pressure

Life Problem 8: Parenting Decisions

Life problem 9: workplace conflict, life problem 10: overwhelmed and exhausted.

I’ve been in my current role at work for several years and can’t seem to make career advancements within my company. I feel stuck and not sure what to do next.

I honor myself and the vision that I have for my career.

I honor my leaders at work, knowing that they too have a vision for our team and department.

Ownership (and the three A’s)

I like my current role and the company I work for.

I have a vision for how I’d like my career to progress.

I don’t have a good understanding of how my leaders see my career progressing.

I would move to another company to advance my career.

There is one specific leader who doesn’t seem to recognize my skills.

My natural tendency is to try to be content with the job I have. Still, it feels disingenuous to ignore my aspirations.

I write out a reasonable career trajectory noting both benefits to my company and me.

I share with my leaders to get input and advice on what steps to take to make it happen.

I put an action plan and timeline together for these steps. 

I schedule check-ins with my leaders to assess the progress.

I check in with myself to put together a clear vision and steps to achieve the goals.

I talk with my leaders to assess and get input on the vision and steps.

I seek out a mentor for a perspective outside of my company. 

I connect with other professionals on LinkedIn who currently have the next role that I would like to gain a better understanding of the skills needed.

I give myself the love, support, and encouragement as I work towards my professional goals. I show Kindness to others within my company to balance my passion for people and my professional aspirations.

I’m in a relationship with a guy that I hang out with all the time. Ryan and I go to dinner, watch movies, text every day, and are physically intimate. We have fun and have a lot in common. But, he doesn’t want to be “a couple.”

I honor myself and know I am enough, just as I am. 

Since I Respect Ryan in so many ways, I honor his perspective even though I don’t understand it or agree with it.

I don’t understand why he doesn’t want to be an “official” couple.

I really like spending time with Ryan.

I’m afraid that if I push too hard on this topic, he’ll distance himself.

I want to be authentic to myself and what I want in my life. 

I want to be intimate with someone who wants me to be their girlfriend. 

I think through the steps I want to take next.

I have three actions that I want to take; all of them fall into the Connection principle. 

I share my truths with others, a trusted girlfriend, and my brother to get well-rounded input.

I adjust my truths based on the points each of them makes that resonate with me.

Then, I share all of my truths with Ryan so he can fully understand my perspective.

I show myself Kindness by bravely approaching this topic. 

I take action so that I can be authentic to myself, the ultimate demonstration of self-Kindness.

Life Problem 3: Chronic Illness 

I have MS, a progressive, incurable disease that affects me in significant ways that aren’t always apparent to other people. How do I get through this and help those who love me better understand when I’m not feeling well?

I honor myself and know I am more than this disease. 

I honor others and know that they want to support me.

I don’t want MS, but it’s my reality.

I’m afraid of the progressive nature of the disease.

My natural tendency is to be in denial, although I know that will not help.

The more I know about the disease, the better I can cope.

My family wants to help; they just don’t understand the disease.

MS is complex and affects people in different ways.  

Utilize the resources at the MS Society website.

I talk to family members and tell them how the disease is affecting me and what I need.

I accept the help and support that others want to give.

I recognize that I need a support system. 

I join a local chapter of the MS Society or an online forum.  

I leverage the experiences and solutions of others who also have MS. 

I keep those closest to me updated on how the disease affects me because that is the only way they can support me.

MS is not kind to me, so I need to be extra kind to myself.  

I generously give myself; body, mind, and soul, what it needs.

Life Problem 4: Loss and Grief 

My closest friend just moved away, and she is starting a new and exciting life without me. I feel so alone. 

I honor myself and my feelings, knowing that it’s okay to miss my friend.

I honor my friend and the dreams that she wants to achieve in her new location.

Intentionally become Aware and Accept the Truths of the Situation:

I miss my friend. We used to have so much fun doing things, especially mountain biking. 

I’m afraid that she’ll forget me.

I’m afraid that I won’t find another friend to do similar activities with.

My natural tendency in situations like this is to shut down, although I know that will not help.

I know the reality is that I can make new friends, but I’m missing her so much that I don’t feel like being social.

Take Action on the Truths:

I talk with my friend and am honest about how I am feeling.

I reach out to my sister, and we plan a mountain biking trip together.

I research mountain biking clubs in my area.

I research mountain biking tours in a country I’ve always wanted to visit.

I connect with myself, knowing that situations like this have sent me into a downward spiral in the past. Being connected to myself during this difficult time is essential. 

I connect with my friend, being honest about my feelings. I wish her well, but I miss how much fun we had together. I suggest that I come to visit her when she gets settled. 

I start to research excellent mountain biking trails in her area. 

Although it’s difficult for me, I put myself out there. 

I join a mountain biking club to connect with others with similar interests.

I work on expanding my friend circle so that I can more easily adapt in the future. 

I send her a care package with a few things for her new apartment. (After all, although I’m having a rough go of it, I still want my friend to be happy.)

I generously give myself what I need.

I give my friend what she needs and support her in her new life adventure. 

My head is filled with negative narratives all day long. I know that this causes me to transfer that negativity to parts of my life that I value, like my relationships and career. 

I honor myself and my relationships that are impacted by my negativity. Even negative emotions need to be validated and understood. It’s not the emotions that are the problem, it’s how I allow the negativity to seep into my actions.

I don’t really know why I have such a negative lens on life. 

I know that the negativity is hurting personal and professional relationships.

I am willing to put in the work to solve the problem.

I really don’t know the steps that I need to take. 

I seek out resources to learn more about negativity and get ideas on how to overcome it.

I find a therapist to help me understand why I feel this way. 

I spend more time around the most positive people in my life.

I begin a daily gratitude journal to force myself to recognize just three things a day that I can be grateful for.

I seek professional guidance and reach out to a therapist. 

I share my goals with a few people that I trust so they can know that I am trying to resolve the problem and that I may be going through some emotional difficulties. 

I recognize that this is a difficult journey. 

I also give myself grace when I “mess up” along the way. I remind myself that it is a process.

I have credit card debt that I can’t seem to pay down, and it continues to get larger. 

I honor myself and that I am an evolving person that can learn from my mistakes.

I honor the financial decisions I have made in the past.

I have spent more than I have earned.

 I feel good, even if it’s for just a short time, when I buy things.

When I buy things or activities similar to my friends, I feel more part of the group.

I know that with the interest rate I am paying, each item purchased ends up costing a lot more.

Emotionally, it feels almost like an addiction. Sometimes I really can’t resist the temptation to buy something.

Logically, I know that I need to stop spending and pay off my credit card debt.

I seek out guidance from several financial experts to compare options to solve this problem.

I research ways to get out of debt. 

I set a “SMART” ( S pecific, M easurable, A chievable, R elevant, and T ime-bound) goal to use for focus. Example: “I will eliminate all of my credit card debt, $3,419.27, in six months.”

I put one or two strategies into place to begin to meet the goal. 

I research and seek resources at Spenders Anonymous.

I cancel current credit cards so that no more debt can be accumulated.

I add additional strategies after I master the first few.

I share the plan with a close friend or family member who can help me be accountable.

I spend more time with friends who I feel more comfortable with even when I don’t overspend.

I gently support myself through this challenging transition to more responsible spending. 

I lovingly encourage myself.

When I overspend, I don’t beat myself up. I remind myself that it takes time to change and allow myself some mistakes. 

Life Problem 7: Expectations and Pressure 

My parents, both doctors, want me to follow in their footsteps and become a physician. I know that is not the career path I want to take. If I don’t go to MD school, they won’t pay for college.

I honor my parents and their vision for me even though it is different than mine. 

I have no interest in becoming a physician. 

I’m afraid that if I do, I will be caught in a career that makes me miserable. 

I understand why my parents have this dream for me. 

Social work, the profession that I’d like to pursue, requires a degre e wh ich I don’t have the money to fund

I know that my parents genuinely want the best for me. 

If my parents don’t pay for my college, I will accumulate a lot of loan debt earning my degree.

I make a list of how becoming a social worker aligns with who I am and the life I’d like to lead.

I address my parents’ concerns so they know that I have taken their experience into consideration. 

I ask my parents to meet with me so we can talk.

I reach out to a few social workers to better understand the pros and cons of being a social worker. I adjust my truths where needed.

I listen intently to myself as I make the list of why the profession is meaningful to me. 

I meet with my parents to share my perspective.

I mentally prepare myself and commit to go into the conversation with my parents with Respect and Kindness. I generously listen and do my best to not lash out if my parents are still not supportive. 

My ten-year-old wants an iPhone. I decided that 12 years old would be an appropriate time to have a phone. But, now, I’m wavering because so many of her friends have smartphones.

I honor myself and know that I have good reasons for my decision. 

I love my daughter and want to keep her safe.

I know the data on the unfortunate effects of access to a smartphone, especially at a young age.

My daughter wants an iPhone but doesn’t need one.

There is other technology that she can access to meet some of her needs and wants.

I am the parent, and my job is to do what I think is best for her, even if that is different from what my daughter or other parents believe.

I do some more research to see if there are any new data that may change my point of view.

I ask my daughter for specific reasons why he wants a phone to be aware of his perspective. 

I talk to a few other parents to talk through my rationale and get their perspective. 

I talk to my daughter. I share the reasoning with her.

When I talk with my daughter, I do so by also generously listening to his perspective. I know that I can make her feel validated by listening and acknowledging her feelings. 

A colleague threw me under the bus in a meeting by inferring that my recent maternity leave was disruptive to a project.

I honor my family and where they fit into my value system.

I honor my colleague enough to address this situation. 

My family is important to me.

My career is important to me.  

I know I can successfully have both.

I took a reasonable amount of maternity leave that was supported by my boss.

Before I left for maternity leave, all details were shared with the point-person aligned to my projects.

I connect with my colleague to share how his behavior made me feel and more clearly share his concerns.

Although it is difficult, I meet with my colleague so that this incident doesn’t have a long-term impact on our relationship and work productivity. 

I give myself extra doses of self-Kindness and assurance that there is nothing wrong with growing my family and balancing it with a career. 

I approached the conversation with my colleague with Kindness, knowing that challenges were likely beneath the comment. I seek understanding and give her attention during the conversation as he shares his perspective. 

I am a working single mom of three. I am constantly on the go, and I am simply exhausted.

I honor myself and know I am enough and that I am doing the best that I can. 

I honor the difficulty of my situation.

I work hard to make ends meet.

I love my kids.

Taking a break or relaxing is a luxury that I feel I can’t afford.

I am willing to sacrifice myself for my kids’ well-being but know that it is detrimental to my health.

I am always tired. As a result, I can get pretty crabby with my kids. 

I know I can’t go on like this, but I don’t feel like I have any options. 

I take an evening and research “relaxation techniques for busy moms.”

I find a few options that feel doable.

I ask my neighbor if she is interested in taking one another’s kids once a week to each have a break. 

I ask a few other moms what they do to keep sane and healthy.

I share my challenge with my friend who has been in a similar situation. I ask for her support and some ideas that helped her when she was feeling overwhelmed. 

I show myself Kindness and give myself 10-20 minutes a day of permission to enjoy something small like a foot bath, a podcast episode, or quiet time with my cat. This helps me avoid resentfulness and shows my kids how they can give themselves Kindness too.

I hope these examples help you better understand and know how to apply the ROCK principles to your everyday, real-life problems to find real-life solutions. Let’s talk more about using Respect, Ownership, Connection, and Kindness to find answers. Leave questions or thoughts in the comments below, and together*, we’ll ROCK thru to solve life problems! XO ~ Lee

*Please keep in mind that I’m not a professional therapist. This article is about using the four principles to solve problems, but if you need support unpacking emotions and getting suggestions for your specific issue, I highly recommend that you connect with a therapist. Here’s a great article that gives 9 Tips for Finding the Right Therapist.

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20 Examples of Algebra in Everyday Life We Can All Relate To

One of the most common questions I get as a high school math teacher is “where exactly will I use algebra in the real world?” Fortunately, there are plenty of examples of algebra in everyday life!

Many students find it helpful to know just where they can apply math in their everyday life. After all, if it isn’t useful, is there a point to learning it at all?

Now, I will be the first to admit that we don’t all use abstract algebra to make our lunches or drive to school or work. But, I can guarantee that you will be surprised by just how much material and real-life examples of algebra you can apply to your real life. 

I am excited to share my personal top 20 answers that I give to my own students who ask me this question! How many of these uses of algebra can you relate to?

What is Algebra?

Considered the father of algebra, Muhammad ibn Musa al-Khwarizmi was a Persian mathematician famous for using the Arabic word  al jabr . Originally used to describe  completion  or  rejoining,  we now know algebra as a tool to determine unknown variables and unknown values.

Depending where in the world you study, the concepts of algebra will vary quite extensively. But in general, algebra involves using an algebraic expression to represent real-life situations so that we can determine the value of an unknown quantity. In practice, this often involves moving terms between two sides of the equation in order to solve the equation .

20 Examples of Algebra in Everyday Life

Whether you realize it or not, your basic knowledge of algebra helps you complete many of the daily tasks that you are responsible for in your everyday life! Even if mathematics is not related to your chosen career path, there are still examples of algebra in everyday life that you can relate to! Let’s dig into this list so that you can develop a new appreciation for this beautiful subject!

1. Calculating Gas Mileage

One of the best real-life applications of algebra is the ability to figure out how far you can drive with a specific number of gallons of gas. One of my biggest fears is being stuck on a freeway as my car’s gas tank is slowly depleting. But, with some knowledge of your vehicle’s mileage, you can figure out how much gas you need to get from point A to B.

2. Calculating the Length of a Trip

Okay so you know how far you are going to get on a gallon of gas. But how long will it take you to get there? If you know how fast you are travelling, and you know how far away your destination is, you can determine the amount of time it will take! This is a simple use of algebraic operations that can help pass the time on a long road trip!

3. Financial Planning

I credit my own financial literacy to my understanding of algebra and mathematics in general. Understanding algebra helped my family build our bank account, stay out of debt, and ensure that we always have enough money for our purchases before we make them.

There are so many problems that students solve in the finance area in studies of algebra. Calculating how much money is required, or the total amount of money after some amount of time are very valuable skills that are transferable to real-life problems that involve money. So pay attention!

4. Budgeting

Another important part of being financially literate is understanding how to set up a budget that balances your monthly expenses and income. Being able to set goals and calculate how much money is needed to work toward them is something that algebraic thinking helps make possible!

5. Comparing Cell Phone Plans

Cell phone companies all offer different plans with specific numbers to entice you to sign up for their service. It might seem like common sense to choose the cheapest option, but having good problem solving skills can help you get the best plan for your own needs without spending too much money!

6. Calculating Exchange Rates

Going on a trip overseas? Did you bring enough money? Knowing how to use simple algebraic concepts and exchange rates can help you calculate how much money is required for your trip.

7. Field of Art

Many people are surprised to hear about the application of algebra in the arts. While many people view the field of art and mathematics as separate, they are more closely related than you might think! Sure, artists aren’t sitting down solving complex algebraic equations and math problems. However, they do use ratios and proportions alongside  the principles of art  to create patterns, balance, contrast, and more.

8. Time Management

One of the most difficult problems people face in the real world is management of time. Do you ever feel like you are always spending too much time on the wrong thing? Whether it is planning your morning routine or figuring out how much time a task will take, time management is an essential life skill.

The words we use to describe our units of time all have deep roots in algebra and our understanding of fractions! Understanding exactly how much time half of one hour is goes a long way!

One of the most common examples of algebra in everyday life happens every time you cook or bake! Recipes are designed to help you bake a specific amount of food or dessert. But what if you want half of that amount? Or double? If you couldn’t use algebra, you could end up with WAY too much cake (not that that is a bad thing…).

10. Grocery Shopping

Next time you find yourself at the grocery store, pay attention to how often you are required to think about algebra. You will be shocked!

There are discounts from the original price everywhere you look. And it seems that every product has two size options to choose from. Understanding basic math and use of algebraic operations is the best way to keep the total cost of your grocery bill as low as possible!

11. Logical Thinking

You will not apply every mathematical problem you solve to the real world. However, constant exposure to complex problems helps develop logical thinking and problem solving skills. This is a simple example of how this invaluable skill will help you solve real-life problems in your daily life and in the workplace.

12. Chemical Sciences

You’ve probably seen the word problem that asks how much of each chemical is required to form some sort of solution, right? Setting up two linear equations and solving the system is something that many chemists do to ensure they have the correct proportions in their solutions.

13. Mental Algebra

One of the most practical applications of algebra is being able to perform quick mental algebra. There are too many aspects of daily life to list, but a great example is if you are working as a part time cashier. Sure, the cash register will tell you how much change to give, but basic math is helpful if there is ever an argument. The customer is always right, after all!

14. In Video Games?

If you have been around  Math By The Pixel  before, you’ll know that a big part of my story is that I am a huge fan of retro gaming. But do I actually use algebra while playing video games? 

Well, yes and no. As a math teacher, my knowledge of quadratic equations has helped me understand the impact that gravity has on a video game character. This helps me make insane jumps that many people just can’t make.

15. Doing Your Taxes

One of the most common complaints I get from students is that our math courses don’t teach them useful skills like doing their taxes. And taxes truly are one of the examples of algebra in everyday life that can help you out in this finance area! All of the skills you gain when working with percentages and solving for unknown values are actually quite applicable to filing your taxes. But I agree with the students on this one – we need a course on this useful life skill!

16. Construction

Whether you are calculating the area of a rectangle to find the square footage on a floor plan, or building a deck that will support some number of people, the use of algebraic operations is essential in so many construction jobs and trades .

17. A Mathematically Perfect Cup of Coffee

The perfect cup of coffee is essential to the start of any math teacher’s day. The best way to make the perfect cup is using a simple equation to determine the exact amount of water and coffee needed to make the perfect cup. Setting up a quick ratio and cross multiplying to solve for variable x is worth the effort. Trust me.

18. Computer Programming

As a math teacher turned web developer, I can’t tell you the number of times my knowledge of algebra concepts has come in handy. If you aren’t working in technology, this won’t be one of the examples of algebra in everyday life you can relate heavily to. But if you are, you will find knowledge of ratios, proportions, and percentages come in handy quite often!

19. Health and Fitness

Another one of the examples of algebra in everyday life that many people overlook is in exercising to maintain health. Whether it is working with your body mass index to optimize weight loss, or planning out caloric intake, you would be surprised how often a simple equation can come in handy!

20. Home Improvement

As a home owner, you will see examples of algebra in everyday life quite often. Whether you are looking to determine how much paint you need to cover a wall, or calculating the square footage of sod you need to cover your backyard, there are real-life examples of algebra in home improvement everywhere you turn.

My wife (who is also a math teacher) and I actually recently worked together to determine the most efficient use of materials while building our kids this outdoor mud kitchen! We were proud to say that our skillful application of algebra left us with only 6 inches of wasted wood by the end of the project!

Using Examples of Algebra in Everyday Life

Algebra is widely regarded as one of the most important branches of mathematics. While it isn’t always easy to see, there are examples of algebra in everyday life wherever you look. Even if you aren’t solving a traditional mathematical problem to determine unknown variables, or working with algebraic formulas , algebra is still everywhere in our daily lives. 

As a math teacher, I see the importance of algebra in a way that many don’t. Algebra is a sense that we all start to understand in the early stages of development in our lives as we learn basic problem solving skills. These skills only grow and develop over time as we learn to apply them to more and more complex scenarios.

I hope that you found something surprising on this list that you can apply in your own life! This is one of my favorite essential questions to discuss with my classes at the beginning of the year. I truly believe that understanding where you can find examples of algebra in everyday life enhances your appreciation for the subject!

Did you find this guide to examples of algebra in everyday life helpful? Share this post and subscribe to Math By The Pixel on YouTube for more helpful mathematics content!

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Examples Of Critical Thinking At The Workplace & In Real Life

Work from home (WFH) has created many problems for people such as long working hours, neck and back pain, and…

Work from home (WFH) has created many problems for people such as long working hours, neck and back pain, and even having multiple cups of coffee every day. Now that organizations are prioritizing fully remote or blended working models, such scenarios are impossible to ignore.

An extremely unhealthy habit that is a product of working at home is the high consumption of coffee. Studies suggest that several coffee aficionados use the beverage as a substitute for breakfast.  Drinking coffee may seem harmless but search the internet and you will find a long list of its disadvantages—from restlessness and insomnia to weight gain, anxiety and risk of heart attacks in young adults. But then you will find as many links listing the advantages of drinking coffee (if it’s within a certain limit).

Does that sound confusing? Which source should you trust then? By thinking critically, you can come to a conclusion that is logical.

This is just one of the examples of critical thinking in everyday life and its importance. We face many more small and big critical thinking examples in real life.

If you think it may not always be possible to apply critical thinking, you can follow the Ladder of Inference framework from Harappa Education’s Thinking Critically course. It is a four-step approach to understand how you can process information. The course covers several examples of critical thinking to explain it in detail.

To understand this better, let’s see some examples of critical thinking:

Critical thinking examples in the workplace.

Here are some common examples of critical thinking that will help you understand why it’s an essential skill in professional life:

Promoting a teamwork approach to problem-solving

As a team leader, the job of encouraging your team to work towards solving a problem falls on your shoulders. But every individual in a team may come up with different inputs and points of view.

You must logically analyze team members’ inputs. And then offer constructive criticism while sharing your own opinion on the situation. This is one of the common critical thinking examples in the workplace.

Self-evaluating your contributions

Imagine that your chief operating officer creates a new target for the organization. Now it’s your right and responsibility to use critical thinking skills examples and evaluate your contribution to reach the target.

Knowing how your contribution is important will help you discover ways to improve your performance. The result will show the impact your work has made, whether it’s solving a critical bug or coming up with a creative way to approach possible clients. Studying a few critical thinking skills examples will help you analyze your situation better.

This is among the most common critical thinker examples you can find and follow in every organization.

It’s evident from these examples of critical thinking that it’s a valuable skill every employee should strengthen. From efficient decision-making to navigating conflicts, thinking critically help you evaluate situations better instead of jumping to hasty and half-baked conclusions.

Examples of Critical Thinking in Real Life

Choosing a Career Path

Should I go for a full-time college or enroll in an online course? Which stream do I choose? Should I try to get a job in a private organization, work as a consultant, or move towards opening a start-up? We all face such dilemmas in our lives at some point or the other. But every option comes with its pros and cons and, therefore, it’s important to choose carefully.

Such critical thinking examples in everyday life highlight the importance of this process. Choosing the right career path certainly takes time. So as a critical thinker, you weigh the pros and cons of every option.

Also, consider the professional, financial and social context in the form of some critical thinking examples in real life. Know your interest and skill set. Answer questions such as “What is important for me?” and “Why is this important for me?”

Don’t go ahead right after making a choice. If you look at some critical thinker examples, you will understand the impact your chosen path will have in the next one, five and 10 years. Accordingly, you may like to rethink your career path. To be able to do this, some critical thinking will be required.

Evaluating Online Information

There are other examples of critical thinking in everyday life as well. There are hundreds of fake news items that we come across every day on the internet or social media. How do we find the truth among so much noise? Critical thinking can come to your aid.

We come across these and many more critical thinking skills examples in the digital world. With the exchange of information increasing by the minute, the need for critical thinking skills is only increasing.

But asking certain questions will help you process such information.

Who published the article?

What are their sources of information?

What are their intentions?

Are they representing themselves or someone else?

Don’t you think if most social media users ask themselves these questions, social media wars will reduce?

Critical thinker examples and applications can be found inside as well as outside classrooms and meeting rooms. So start working on your critical thinking skills now. Join Harappa Education’s Thinking Critically course, which explains the essential techniques with the help of a few great critical thinker examples. Empower yourself to make qualified decisions.

Explore topics such as Critical Thinking , How to Improve Critical Thinking & Ladder of Inference from our Harappa Diaries blog section and develop your strategic thinking skills .

Tackling Workplace Challenges: How to Improve Your Problem-Solving Skills

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Picture this: you’re in the middle of your workday, and suddenly, a problem arises. Maybe it’s a miscommunication between team members, a tight deadline that’s getting closer, or an unhappy customer you need to appease.

Sounds familiar, doesn’t it?

The thing is, facing challenges at work is pretty much inevitable. But what sets successful professionals apart is their knack for tackling these issues head-on with a problem-solving mindset.

You see, being a great problem solver is a game-changer in any work environment. It helps us navigate through obstacles, come up with creative solutions, and turn potential setbacks into opportunities for growth.

In this article, we will dive into some common workplace problems and explore real-life examples of problem-solving scenarios.

We’ll also share practical solutions and strategies that you can use to tackle these challenges, ultimately empowering you to become a more effective problem solver and team player.

Common Workplace Problems Businesses Experience

Before we dive into the nitty-gritty of problem-solving scenarios, let’s take a quick look at some of the most common workplace problems that almost every professional encounters at some point in their career.

By understanding these challenges, we’ll be better equipped to recognize and address them effectively.

Communication breakdowns

Miscommunications and misunderstandings can happen to the best of us. With team members working together, sometimes remotely or across different time zones, it’s not surprising that communication breakdowns can occur. These issues can lead to confusion, missed deadlines, and even strained relationships within the team if left unaddressed.

Some examples of communication breakdowns include:

• Unclear instructions
• Lack of updates on project progress
• Messages lost in a sea of emails

Fostering open communication channels and utilizing collaboration tools can help teams stay connected and informed.

Conflicting priorities and resource allocation

With limited resources and multiple projects competing for attention, it can be challenging to determine which tasks should take precedence. Juggling conflicting priorities and allocating resources efficiently is a common workplace problem that can result in decreased productivity and increased stress if not managed properly.

For example, two high-priority projects might be scheduled simultaneously, leaving team members stretched thin and struggling to meet deadlines. Developing a clear project prioritization framework and regularly reviewing priorities can help teams stay focused and manage their resources effectively.

Employee performance issues

It’s not unusual for team members to face performance-related challenges occasionally. Employee performance issues can affect team productivity and morale, whether it’s due to a lack of skills, motivation, or other factors. Identifying and addressing these concerns early on is crucial for maintaining a high-performing and engaged team.

For instance, employees may struggle to keep up with their workload due to a skills gap or personal issues. Providing coaching, training, and support can help employees overcome performance challenges and contribute positively to the team’s success.

Customer satisfaction challenges

Meeting customer expectations and delivering exceptional service are goals for most organizations. However, addressing customer satisfaction challenges can be tricky, especially when dealing with diverse customer needs, tight deadlines, or limited resources.

Ensuring a customer-centric approach to problem-solving can help overcome these obstacles and keep your customers happy.

For example, a product might not meet customer expectations, resulting in negative feedback and returns. By actively listening to customer concerns, involving them in the solution process, and implementing improvements, organizations can turn customer dissatisfaction into opportunities for growth and enhanced customer loyalty.

Adapting to change

Change is inevitable in the modern workplace, whether due to new technology, evolving market conditions, or organizational restructuring. Adapting to change can be difficult for some team members, leading to resistance or fear of the unknown.

Embracing a flexible mindset and developing strategies to cope with change is essential for maintaining a productive and resilient work environment.

For instance, a company might introduce new software that requires employees to learn new skills, causing anxiety and frustration. By providing training, resources, and support, leaders can help team members adapt to change more effectively and even become champions of new initiatives.

How to Identify Workplace Problems

A problem-free workplace doesn’t exist.

Even if you run a well-oiled machine with many happy employees, it’s still a good idea to proactively search for any problems.

The earlier you can get ahead of issues, the easier it will be to put things right and avoid any breakdowns in productivity. Here’s how you can go about that:

Recognizing the Signs of Potential Issues

Before diving into problem-solving strategies, it’s essential first to identify the workplace problems that need attention.

Look out for signs that could indicate potential issues, such as decreased productivity and efficiency, increased employee turnover or dissatisfaction, frequent miscommunications, and conflicts, or declining customer satisfaction and recurring complaints. These red flags might signal underlying problems that require your attention and resolution.

Proactive Problem Identification Strategies

To stay ahead of potential issues, it’s crucial to adopt a proactive approach to problem identification. Open communication channels with your team members and encourage them to share their concerns, ideas, and feedback.

Regular performance reviews and feedback sessions can also help identify areas for improvement or potential problems before they escalate.

Fostering a culture of transparency and trust within the organization makes it easier for employees to voice their concerns without fear of retribution. Additionally, utilizing data-driven analysis and performance metrics can help you spot trends or anomalies that may indicate underlying problems.

Seeking Input from Various Sources

When identifying workplace problems, gathering input from various sources is crucial to ensure you’re getting a comprehensive and accurate picture of the situation. Employee surveys and suggestion boxes can provide valuable insights into potential issues.

At the same time, team meetings and brainstorming sessions can stimulate open discussions and creative problem-solving.

Cross-departmental collaboration is another effective way to identify potential problems, enabling different teams to share their perspectives and experiences. In some cases, it might be helpful to seek external expert consultations or benchmark against industry standards to gain a broader understanding of potential issues and identify best practices for resolving them.

Problem-Solving Scenario Examples and Solutions

Let’s dive into some real-life problem-solving scenarios, exploring the challenges and their practical solutions. We’ll discuss communication issues, conflicting priorities, employee performance, customer satisfaction, and managing change.

Remember, every situation is unique; these examples are just a starting point to inspire your problem-solving process.

Scenario 1: Resolving communication issues within a team

• Identifying the root causes: Let’s say your team has been missing deadlines and experiencing confusion due to poor communication. The first step is identifying the root causes, such as ineffective communication tools, unclear instructions, or a lack of regular updates.
• Implementing effective communication strategies: Implement strategies to improve communication. For example, consider adopting collaboration tools like Slack or Microsoft Teams to streamline communication, establish clear channels for updates, and create guidelines for concise and transparent instructions.
• Encouraging a culture of openness and feedback: Cultivate a team culture that values openness and feedback. Encourage team members to voice concerns, ask questions, and share ideas. Regularly hold check-ins and retrospectives to discuss communication challenges and opportunities for improvement.

Scenario 2: Balancing conflicting priorities and resource constraints

• Evaluating project requirements and resources: In this scenario, you’re juggling two high-priority projects with limited resources. Start by evaluating each project’s requirements, resources, and potential impact on the organization.
• Prioritization techniques and delegation: Use prioritization techniques like the Eisenhower Matrix or MoSCoW method to rank tasks and allocate resources accordingly. Delegate tasks efficiently by matching team members’ skills and expertise with project requirements.
• Continuous monitoring and adjustment: Regularly monitor project progress and adjust priorities and resources as needed. Keep stakeholders informed about changes and maintain open lines of communication to ensure alignment and avoid surprises.

Scenario 3: Addressing employee performance concerns

• Identifying performance gaps: When an employee’s performance is below expectations, identify the specific areas that need improvement. Is it a skills gap, lack of motivation, or external factors like personal issues?
• Providing constructive feedback and support: Provide clear, constructive feedback to the employee, highlighting areas for improvement and offering support, such as training, coaching, or mentorship.
• Developing performance improvement plans: Collaborate with the employee to develop a performance improvement plan , outlining specific goals, timelines, and resources. Regularly review progress and adjust the plan as needed.

Scenario 4: Improving customer satisfaction

• Analyzing customer feedback and pain points: In this scenario, customers are dissatisfied with a product, resulting in negative feedback and returns. Analyze customer feedback to identify common pain points and areas for improvement.
• Implementing customer-centric solutions: Work with your team to develop and implement solutions that address customer concerns, such as enhancing product features or improving customer support.
• Monitoring progress and iterating for success: Regularly monitor customer satisfaction levels and gather feedback to assess the effectiveness of your solutions. Iterate and improve as needed to ensure continuous progress toward higher customer satisfaction.

Scenario 5: Managing change and uncertainty

• Assessing the impact of change on the organization: When faced with change, such as the introduction of new software, assess the potential impact on the organization, including the benefits, challenges, and required resources.
• Developing a change management plan: Create a comprehensive change management plan that includes communication strategies, training, and support resources to help team members adapt to the change.
• Fostering resilience and adaptability among team members: Encourage a culture of resilience and adaptability by providing ongoing support, celebrating small wins, and recognizing the efforts of team members who embrace and champion the change.

Scenario 6: Navigating team conflicts

• Identifying the sources of conflict: When conflicts arise within a team, it’s crucial to identify the underlying issues, such as personality clashes, competing interests, or poor communication.
• Facilitating open discussions and mediation: Arrange a meeting with the involved parties to discuss the conflict openly and objectively. Consider using a neutral third party to mediate the conversation, ensuring everyone’s perspective is heard and understood.
• Developing and implementing conflict resolution strategies: Work together to develop strategies for resolving the conflict, such as setting clear expectations, improving communication, or redefining roles and responsibilities. Monitor progress and adjust strategies as needed to ensure long-term resolution.

Scenario 7: Overcoming deadline pressure and time management challenges

• Assessing project progress and priorities: If a team is struggling to meet deadlines, assess project progress and review priorities. Identify tasks that are behind schedule, and determine if any can be reprioritized or delegated.
• Implementing time management techniques: Encourage the team to adopt effective time management techniques, such as the Pomodoro Technique or time blocking, to maximize productivity and stay focused on tasks.
• Adjusting project scope and resources as needed: In some cases, it may be necessary to adjust the project scope or allocate additional resources to ensure successful completion. Communicate any changes to stakeholders and maintain transparency throughout the process.

Scenario 8: Tackling low employee morale and engagement

• Identifying the causes of low morale: When faced with low employee morale, it’s essential to identify the contributing factors, such as lack of recognition, insufficient growth opportunities, or unrealistic expectations.
• Implementing targeted initiatives to boost morale: Develop and implement initiatives to address these factors, such as offering regular feedback and recognition, providing professional development opportunities, or reassessing workload and expectations.
• Monitoring and adjusting efforts to improve engagement: Regularly monitor employee morale and engagement through surveys or informal conversations. Adjust your initiatives to ensure continuous improvement and maintain a positive work environment.

Developing Problem-Solving Skills in the Workplace

As we’ve seen, problem-solving is a crucial skill for navigating the myriad challenges that can arise in the workplace. To become effective problem solvers, you must develop hard and soft skills that will allow you to tackle issues head-on and find the best solutions.

Let’s dive into these skills and discuss how to cultivate them in the workplace.

Soft Skills

Soft skills are non-technical, interpersonal abilities that help you interact effectively with others, navigate social situations, and perform well in the workplace. They are often referred to as “people skills” or “emotional intelligence” because they involve understanding and managing emotions and building relationships with colleagues, clients, and stakeholders.

Soft skills are typically learned through life experiences and personal development rather than formal education or training.

Examples of soft skills include:

• Critical thinking: Critical thinking is the ability to analyze a situation objectively, considering all relevant information before making a decision. To develop this skill, practice asking open-ended questions, challenging assumptions, and considering multiple perspectives when approaching a problem.
• Effective communication: Strong communication skills are vital for problem-solving, as they enable you to express your ideas clearly and listen actively to others. To improve your communication skills, focus on being concise, empathetic, and open to feedback. Remember that nonverbal communication, such as body language and tone, can be just as important as the words you choose.
• Collaboration and teamwork: Problem-solving often requires collaboration, as multiple minds can bring diverse perspectives and fresh ideas to the table. Foster a sense of teamwork by being open to others’ input, sharing knowledge, and recognizing the contributions of your colleagues.
• Emotional intelligence: The ability to recognize and manage your emotions, as well as empathize with others, can significantly impact your problem-solving abilities. To cultivate emotional intelligence, practice self-awareness, self-regulation, and empathy when dealing with challenges or conflicts.
• Adaptability and resilience: In a constantly changing work environment, the ability to adapt and bounce back from setbacks is essential. Develop your adaptability and resilience by embracing change, learning from failure, and maintaining a growth mindset.

Hard Skills

Hard skills, on the other hand, are specific, teachable abilities that can be acquired through formal education, training, or on-the-job experience. These skills are typically technical, industry-specific, or job-related and can be easily quantified and measured.

Hard skills are often necessary for performing specific tasks or operating specialized tools and equipment.

Examples of hard skills include:

• Project management: Effective problem-solving often involves managing resources, timelines, and tasks. Improve your project management skills by learning popular methodologies (e.g., Agile, Scrum, or Waterfall), setting clear goals, and monitoring progress.
• Data analysis and interpretation: Many problems require data analysis to identify trends, patterns, or insights that inform decision-making. Strengthen your data analysis skills by familiarizing yourself with relevant tools and software, such as Excel or Tableau, and practicing critical thinking when interpreting results.
• Technical proficiency: Depending on your industry, various technical skills may be crucial for problem-solving. Stay current with your field’s latest tools, technologies, and best practices by participating in workshops, online courses, or industry events.
• Decision-making: Strong decision-making skills are vital for problem-solving, as they enable you to evaluate options and choose the best course of action. Develop your decision-making abilities by learning about decision-making models (e.g., SWOT analysis, cost-benefit analysis, or decision trees) and applying them in real-life situations.

Both types of skills—soft and hard—play a crucial role in achieving success in the workplace, as they work together to create a well-rounded and highly effective employee. When combined, these skills enable individuals to excel in their roles and contribute significantly to their organization’s performance and productivity.

Boosting Your Problem-Solving Skills in the Workplace

Boosting your problem-solving skills in the workplace is essential for success, personal growth, and increased productivity.

To effectively improve these skills, consider the following strategies:

• Cultivate a growth mindset by embracing challenges as learning opportunities, being open to feedback, and believing in your ability to develop and improve.
• Enhance critical thinking and creativity by objectively analyzing information, considering multiple perspectives, and brainstorming innovative solutions.
• Develop effective communication skills, including active listening and clear articulation of your thoughts, to facilitate collaboration and problem-solving.
• Foster empathy and emotional intelligence to understand others’ emotions, perspectives, and needs, which can help you devise better solutions.
• Learn from experienced colleagues, study successful problem-solving strategies, and participate in professional development courses or workshops to gain new insights and techniques.
• Adopt a systematic approach to problem-solving by defining the problem, gathering and analyzing relevant information, generating and evaluating potential solutions, and implementing the chosen solution while monitoring its effectiveness.
• Stay organized and manage your time effectively by prioritizing tasks based on urgency and importance and breaking complex problems into smaller, more manageable parts.
• Embrace change, be resilient and adaptable, and learn from failures and setbacks to stay flexible and open to new ideas.

By dedicating time and effort to improving these aspects of your problem-solving skills, you can become a more effective problem-solver, contributing positively to your workplace and enhancing your career prospects.

Problems in the workplace will continuously develop and evolve over time if left unaddressed. Proactively dealing with these issues is the most effective method to ensure a positive and productive work environment.

By honing your problem-solving skills, embracing a growth mindset, and fostering open communication, you can tackle challenges head-on and prevent minor issues from escalating into significant obstacles.

Remember, staying proactive, adaptable, and continuously refining your problem-solving strategies is crucial for professional success and personal growth in the ever-changing world of work.

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32 Examples of Real-World Math Problems

• • Published: April 23, 2024
• • Last update: June 14, 2024
• • Grades: All grades

Introduction

8th grade algebra problem:

Farmer Alfred has three times as many chickens as cows. In total, there are 60 legs in the barn. How many cows does Farmer Alfred have? [1]

Does this sound like a real-world math problem to you? We’ve got chickens, cows, and Farmer Alfred – it’s a scenario straight out of everyday life, isn’t it?

But before you answer, let me ask you something: If you wanted to figure out the number of cows, would you:

• Count their legs, or
• Simply count their heads ( or even just ask Farmer Alfred, “Hey Alfred, how many cows do you have?” )

Chances are, most people would go with option B.

So, why do our math books contain so many “real-world math problems” like the one above?

In this article, we’ll dive into what truly makes a math problem a real-world challenge.

Understanding 'Problems' in Daily Life and Mathematics

The word “problem” carries different meanings in everyday life and in the realm of mathematics, which can sometimes lead to confusion. In our daily lives, when we say “ I have a problem ,” we typically mean that something undesirable has occurred – something challenging to resolve or with potential negative consequences.

For instance:

• “I have a problem because I’ve lost my wallet.”
• “I have a problem because I forgot my keys at home, and I won’t be able to get into the house when I return from school.”
• “I have a problem because I was sick and missed a few weeks of school, which means I’ll likely fail my math test.”

These are examples of everyday problems we encounter. However, once the problem is solved, it often ceases to be a problem:

• “I don’t have a problem getting into my house anymore because my mom gave me her keys.”

In mathematics, the term “problem” takes on a different meaning. According to the Cambridge dictionary [2], it’s defined as “ a question in mathematics that needs an answer. “

Here are a few examples:

• If x + 2 = 4, what is the value of x?
• How do you find the common denominator for fractions 1/3 and 1/4?
• What is the length of the hypotenuse in a right triangle if two legs are 3 and 4 feet long?

These are all examples of math problems.

It’s important to note that in mathematics, a problem remains a problem even after it’s solved. Math problems are universal, regardless of who encounters them [3]. For instance, both John and Emma could face the same math problem, such as “ If x + 2 = 4, then what is x? ” After they solve it, it still remains a math problem that a teacher could give to somebody else.

Understanding Real-World Math Problems

So, what exactly is a “real-world math problem”? We’ve established that in our daily lives, we refer to a situation as a “problem” when it could lead to unpleasant consequences. In mathematics, a “problem” refers to a mathematical question that requires a mathematical solution.

With that in mind, we can define a real-world math problem as:

A situation that could have negative consequences in real life and that requires a mathematical solution (i.e. mathematical solution is preferred over other solutions).

Consider this example:

Could miscalculating the flour amount lead to less-than-ideal results? Absolutely. Messing up the flour proportion could result in a less tasty cake – certainly an unpleasant consequence.

Now, let’s explore the methods for solving this. While traditional methods, like visually dividing the flour or measuring multiple times, have their place, they may not be suitable for larger-scale events, such as catering for a wedding with 250 guests. In such cases, a mathematical solution is not only preferred but also more practical.

By setting up a simple proportion – 1 1/2 cups of flour for 8 people equals x cups for 20 people – we can quickly find the precise amount needed: 3 3/4 cups of flour. In larger events, like the wedding, the mathematical approach provides even more value, yielding a requirement of nearly 47 cups of flour.

This illustrates why a mathematical solution is faster, more accurate, and less error-prone, making it the preferred method. Coupled with the potential negative consequences of inaccuracies, this makes the problem a real-world one, showcasing the practical application of math in everyday scenarios.

Identifying Non-Real-World Math Problems

Let’s revisit the example from the beginning of this article:

Farmer Alfred has three times as many chickens as cows. In total, there are 60 legs in the barn. How many cows does Farmer Alfred have?

3rd grade basic arithmetic problem:

Noah has $56, and Olivia has 8 times less. How much money does Olivia have?

Once more, in our daily routines, do we handle money calculations this way? Why would one prefer to use mathematical solution ($56 : 8 =$7). More often than not, we’d simply ask Olivia how much money she has. While the problem can theoretically be solved mathematically, it’s much more practical, efficient, and reliable to resolve it by directly asking Olivia.

Examples like these are frequently found in math textbooks because they aid in developing mathematical thinking. However, the scenarios they describe are uncommon in real life and fail to explicitly demonstrate the usefulness of math. In essence, they don’t showcase what math can actually be used for. Therefore, there are two crucial aspects of true real-world math problems: they must be commonplace in real life, and they must explicitly illustrate the utility of math.

To summarize:

Word problems that are uncommon in real life and fail to convincingly demonstrate the usefulness of math are not real-world math problems.

Real-World Math Problems Across Professions

Many professions entail encountering real-world math problems on a regular basis. Consider the following examples:

Nurses often need to calculate accurate drug dosage amounts using proportions, a task solved through mathematical methods. Incorrect dosage calculations can pose serious risks to patient health, leading to potentially harmful consequences.

Construction engineers frequently need to determine whether a foundation will be sturdy enough to support a building, employing mathematical solving techniques and specialized formulas. Errors in these calculations can result in structural issues such as cracks in walls due to foundation deformation, leading to undesirable outcomes.

Marketers often rely on statistical analysis to assess the performance of online advertisements, including metrics like click-through rates and the geographical distribution of website visitors. Mathematical analysis guides decision-making in this area. Inaccurate analyses may lead to inefficient allocation of advertisement budgets, resulting in less-than-optimal outcomes.

These examples illustrate real-world math problems encountered in various professions. While there are numerous instances of such problems, they are often overlooked in educational settings. At DARTEF, we aim to bridge this gap by compiling a comprehensive list of real-world math problems, which we’ll explore in the following section.

32 Genuine Real-World Math Problems

In this section, we present 32 authentic real-world math problems from diverse fields such as safety and security, microbiology, architecture, engineering, nanotechnology, archaeology, creativity, and more. Each of these problems meets the criteria we’ve outlined previously. Specifically, a problem can be classified as a real-world math problem if:

• It is commonly encountered in real-life scenarios.
• It has the potential for undesirable consequences.
• A mathematical solution is preferable over alternative methods.
• It effectively illustrates the practical utility of mathematics.

All these problems stem from actual on-the-job situations, showcasing the application of middle and high school math in various professions.

Math Problems in Biology

Real-world math problems in biology often involve performing measurements or making predictions. Mathematics helps us understand various biological phenomena, such as the growth of bacterial populations, the spread of diseases, and even the reconstruction of ancient human appearances. Here are a couple of specific examples:

1. Reconstructing Human Faces Using Parallel and Perpendicular Lines:

Archeologists and forensic specialists often reconstruct human faces based on skeletal remains. They utilize parallel and perpendicular lines to create symmetry lines on the face, aiding in the recovery of facial features and proportions. Our article, “ Parallel and Perpendicular Lines: A Real-Life Example (From Forensics and Archaeology) ,” provides a comprehensive explanation and illustrates how the shape of the nose can be reconstructed using parallel and perpendicular lines, line segments, tangent lines, and symmetry lines.

2. Measuring Bacteria Size Using Circumference and Area Formulas:

Microbiology specialists routinely measure bacteria size to monitor and document their growth rates. Since bacterial shapes often resemble geometric shapes studied in school, mathematical methods such as calculating circumference or area of a circle are convenient for measuring bacteria size. Our article, “ Circumference: A Real-Life Example (from Microbiology) ,” delves into this process in detail.

Math Problems in Construction and Architecture

Real-world math problems are abundant in architecture and construction projects, where mathematics plays a crucial role in ensuring safety, efficiency, and sustainability. Here are some specific case studies that illustrate the application of math in these domains:

3. Calculating Central Angles for Safe Roadways:​

Central angle calculations are a fundamental aspect of roadway engineering, particularly in designing curved roads. Civil engineers use these calculations to determine the degree of road curvature, which significantly impacts road safety and compliance with regulations. Mathematical concepts such as radius, degrees, arc length, and proportions are commonly employed by civil engineers in their daily tasks. Our article, “ How to Find a Central Angle: A Real-Life Example (from Civil Engineering) ,” provides further explanation and demonstrates the calculation of central angles using a real road segment as an example.

4. Designing Efficient Roof Overhang Using Trigonometry

Trigonometry is a powerful tool in architecture and construction, providing a simple yet effective way to calculate the sizes of building elements, including roof overhangs. For example, the tangent function is used to design the optimal length of a roof overhang that blocks the high summer sun while allowing the lower winter sun to enter . Our article, “ Tangent (Trigonometry): A Real-Life Example (From Architecture and Construction) ,” provides a detailed use case with two methods of calculation and also includes a worksheet.

5. Designing Efficient Roofs for Solar Panels Using Angle Geometry:

Mathematics plays a crucial role in architecture, aiding architects and construction engineers in designing energy-efficient building structures. For example, when considering the installation of solar panels on a building’s roof, understanding geometric properties such as adjacent and alternate angles is essential for maximizing energy efficiency . By utilizing mathematical calculations, architects can determine the optimal angle for positioning solar panels and reflectors to capture maximum sunlight. Our article, “ A Real-Life Example of How Angles are Used in Architecture ,” provides explanations and illustrations, including animations.

6. Precision Drilling of Oil Wells Using Trigonometry:

Petroleum engineers rely on trigonometric principles such as sines, cosines, tangents, and right-angle triangles to drill oil wells accurately. Trigonometry enables engineers to calculate precise angles and distances necessary for drilling vertical, inclined, and even horizontal wells. For instance, when drilling at an inclination of 30°, engineers can use trigonometry to calculate the vertical depth corresponding to each foot drilled horizontally. Our article, “ CosX: A Real-Life Example (from Petroleum Engineering) ,” provides examples, drawings of right triangle models, and necessary calculations.

7. Calculating Water Flow Rate Using Composite Figures:

Water supply specialists frequently encounter the task of calculating water flow rates in water canals, which involves determining the area of composite figures representing canal cross-sections . Many canal cross-sections consist of composite shapes, such as rectangles and triangles. By calculating the areas of these individual components and summing them, specialists can determine the total cross-sectional area and subsequently calculate the flow rate of water. Our article, “ Area of Composite Figures: A Real-Life Example (from Water Supply) ,” presents necessary figures, cross-sections, and an example calculation.

Math Problems in Business and Marketing

Mathematics plays a crucial role not only in finance and banking but also in making informed decisions across various aspects of business development, marketing analysis, growth strategies, and more. Here are some real-world math problems commonly encountered in business and marketing:

8. Analyzing Webpage Position in Google Using Polynomials and Polynomial Graphs:

Polynomials and polynomial graphs are essential tools for data analysis. They are useful for a wide variety of people, not only data analysts, but literally everyone who ever uses Excel or Google Sheets. Our article, “ Graphing Polynomials: A Real-World Example (from Data Analysis) ,” describes this and provides an authentic case study. The case study demonstrates how polynomials, polynomial functions of varying degrees, and polynomial graphs are used in internet technologies to analyze the visibility of webpages in Google and other search engines.”

9. Making Informed Business Development Decisions Using Percentages:

In business development, math problems often revolve around analyzing growth and making strategic decisions. Understanding percentages is essential, particularly when launching new products or services. For example, determining whether a startup should target desktop computer, smartphone, or tablet users for an app requires analyzing installation percentages among user groups to gain insights into consumer behavior. Math helps optimize marketing efforts, enhance customer engagement, and drive growth in competitive markets. Check out our article “ A Real-Life Example of Percent Problems in Business ” for a detailed description of this example.

10. Analyzing Customer Preferences Using Polynomials:

Marketing involves not only creative advertising but also thorough analysis of customer preferences and marketing campaigns. Marketing specialists often use simple polynomials for such analysis, as they help analyze multiple aspects of customer behavior simultaneously. For instance, marketers may use polynomials to determine whether low price or service quality is more important to hotel visitors. Smart analysis using polynomials enables businesses to make informed decisions. If you’re interested in learning more, our article “ Polynomials: A Real Life Example (from Marketing) ” provides a real-world example from the hotel industry.

11. Avoiding Statistical Mistakes Using Simpson’s Paradox:

Data gathering and trend analysis are essential in marketing, but a good understanding of mathematical statistics helps avoid intuitive mistakes . For example, consider an advertising campaign targeting Android and iOS users. Initial data may suggest that iOS users are more responsive. However, a careful statistical analysis, as described in our article “ Simpson’s Paradox: A Real-Life Example (from Marketing) ,” may reveal that Android users, particularly tablet users, actually click on ads more frequently. This contradiction highlights the importance of accurate statistical interpretation and the careful use of mathematics in decision-making.

Math Problems in Digital Agriculture

In the modern era, agriculture is becoming increasingly digitalized, with sensors and artificial intelligence playing vital roles in farm management. Mathematics is integral to this digital transformation, aiding in data analysis, weather prediction, soil parameter measurement, irrigation scheduling, and more. Here’s an example of a real-world math problem in digital agriculture:

12. Combatting Pests with Negative Numbers:

Negative numbers are utilized in agriculture to determine the direction of movement, similar to how they’re used on a temperature scale where a plus sign indicates an increase and a minus sign indicates a decrease. In agricultural sensors, plus and minus signs may indicate whether pests are moving towards or away from plants. For instance, a plus sign could signify movement towards plants, while a minus sign indicates movement away from plants. Understanding these directional movements helps farmers combat pests effectively. Our article, “ Negative Numbers: A Real-Life Example (from Agriculture) ,” provides detailed explanations and examples of how negative numbers are applied in agriculture.

Math Problems in DIY Projects

In do-it-yourself (DIY) projects, mathematics plays a crucial role in measurements, calculations, and problem-solving. Whether you’re designing furniture, planning home renovations, crafting handmade gifts, or landscaping your garden, math provides essential tools for precise measurements, material estimations, and budget management. Here’s an example of a real-world math problem in DIY:

13. Checking Construction Parts for Right Angles Using the Pythagorean Theorem:

The converse of the Pythagorean theorem allows you to check whether various elements – such as foundations, corners of rooms, garage walls, or sides of vegetable patches – form right angles. This can be done quickly using Pythagorean triples like 3-4-5 or 6-8-10, or by calculating with square roots. This method ensures the creation of right angles or verifies if an angle is indeed right. Our article, “ Pythagorean Theorem Converse: A Real-Life Example (from DIY) ,” explains this concept and provides an example of how to build a perfect 90° foundation using the converse of the Pythagorean theorem.

Math Problems in Entertainment and Creativity

Mathematics plays a surprisingly significant role in the creative industries, including music composition, visual effects creation, and computer graphic design. Understanding and applying mathematical concepts is essential for producing engaging and attractive creative works. Here’s an example of a real-world math problem in entertainment:

14. Controlling Stage Lamps with Linear Functions:

Linear and quadratic functions are essential components of the daily work of lighting specialists in theaters and event productions. These professionals utilize specialized software and controllers that rely on algorithms based on mathematical functions. Linear functions, in particular, are commonly used to control stage lamps, ensuring precise and coordinated lighting effects during performances. Our article, “ Linear Function: A Real-Life Example (from Entertainment) ,” delves into this topic in detail, complete with animations that illustrate how these functions are applied in practice.

Math Problems in Healthcare

Mathematics plays a crucial role in solving numerous real-world problems in healthcare, ranging from patient care to the design of advanced medical devices. Here are several examples of real-world math problems in healthcare:

15. Calculating Dosage by Converting Time Units:

Nurses frequently convert between hours, minutes, and seconds to accurately administer medications and fluids to patients. For example, if a patient requires 300mL of fluid over 2.5 hours, nurses must convert hours to minutes to calculate the appropriate drip rate for an IV bag. Understanding mathematical conversions and solving proportions are essential skills in nursing. Check out our article, “ Converting Hours to Minutes: A Real-Life Example (from Nursing) ,” for further explanation.

16. Predicting Healthcare Needs Using Quadratic Functions:

Mathematical functions, including quadratic functions, are used to make predictions in public health. These predictions are vital for estimating the need for medical services, such as psychological support following traumatic events. Quadratic functions can model trends in stress symptoms over time, enabling healthcare systems to anticipate and prepare for increased demand. Our article, “ Parabola Equation: A Real-Life Example (from Public Health) ,” provides further insights and examples.

17. Predicting Healthcare Needs Using Piecewise Linear Functions:

Piecewise linear functions are useful for describing real-world trends that cannot be accurately represented by other functions. For instance, if stress symptoms fluctuate irregularly over time, piecewise linear functions can define periods of increased and decreased stress levels. Our article, “ Piecewise Linear Function: A Real-Life Example (From Public Health) ,” offers an example of how these functions are applied.

18. Designing Medical Prostheses Using the Pythagorean Theorem:

The Pythagorean theorem is applied in the design of medical devices , particularly prostheses for traumatic recovery. Components of these devices often resemble right triangles, allowing engineers to calculate movement and placement for optimal patient comfort and stability during rehabilitation. For a detailed explanation and animations, see our article, “ The 3-4-5 Triangle: A Real-Life Example (from Mechatronics) .”

19. Illustrating Disease Survival Rates Using Cartesian Coordinate Plane:

In medicine, Cartesian coordinate planes are utilized for analyzing historical data, statistics, and predictions. They help visualize relationships between independent and dependent variables, such as survival rates and diagnostic timing in diseases like lung cancer. Our article, “ Coordinate Plane: A Real-Life Example (from Medicine) ,” offers a detailed exploration of this concept, including analyses for both non-smoking and smoking patients.

Math Problems in Industry

Mathematics plays a vital role in solving numerous real-world problems across various industries. From designing industrial robots to analyzing production quality and planning logistics, math is indispensable for optimizing processes and improving efficiency. Here are several examples of real-world math problems in industry:

20. Precise Movements of Industrial Robots Using Trigonometry:

Trigonometry is extensively utilized to direct and control the movements of industrial robots. Each section of an industrial robot can be likened to a leg or hypotenuse of a right triangle, allowing trigonometry to precisely control the position of the robot head. For instance, if the robot head needs to move 5 inches to the right, trigonometry enables calculations to ensure each section of the robot moves appropriately to achieve the desired position. For detailed examples and calculations, refer to our article, “ Find the Missing Side: A Real-life Example (from Robotics) .”

21. Measuring Nanoparticle Size via Cube Root Calculation:

Mathematics plays a crucial role in nanotechnology, particularly in measuring the size of nanoparticles. Cube roots are commonly employed to calculate the size of cube-shaped nanoparticles. As nanoparticles are extremely small and challenging to measure directly, methods in nanotechnology determine nanoparticle volume, allowing for the calculation of cube root to determine the size of the nanoparticle cube side. Check out our article, “ Cube Root: A Real-Life Example (from Nanotechnology) ,” for explanations, calculations, and insights into the connection between physics and math.

22. Understanding Human Emotions Using Number Codes for Robots:

Mathematics is employed to measure human emotions effectively, which is essential for building smart robots capable of recognizing and responding to human emotions. Each human emotion can be broken down into smaller features, such as facial expressions, which are assigned mathematical codes to create algorithms for robots to recognize and distinguish emotions. Explore our article, “ Psychology and Math: A Real-Life Example (from Smart Robots) ,” to understand this process and its connection to psychology.

23. Systems of Linear Equations in Self-Driving Cars:

In the automotive industry, mathematics is pivotal for ensuring the safety and efficiency of self-driving cars. Systems of linear equations are used to predict critical moments in road safety, such as when two cars are side by side during an overtaking maneuver. By solving systems of linear equations, self-driving car computers can assess the safety of overtaking situations. Our article, “ Systems of Linear Equations: A Real-Life Example (from Self-Driving Cars) ,” provides a comprehensive explanation, including animated illustrations and interactive simulations, demonstrating how linear functions and equations are synchronized with car motion.

Math Problems in Information Technology (IT)

Mathematics serves as a fundamental tool in the field of information technology (IT), underpinning various aspects of software development, cybersecurity, and technological advancements. Here are some real-world math problems encountered in IT:

24. Selecting the Right Word in Machine Translation Using Mathematical Probability:

Theoretical probability plays a crucial role in AI machine translation systems, such as Google Translate, by aiding in the selection of the most appropriate words. Words often have multiple translations, and theoretical probability helps analyze the frequency of word appearances in texts to propose the most probable translation. Dive deeper into this topic in our article, “ Theoretical Probability: A Real-Life Example (from Artificial Intelligence) .”

25. Creating User-Friendly Music Streaming Websites Using Mathematical Probability:

Probability is utilized in user experience (UX) design to enhance the usability of digital products , including music streaming websites. Recommendation algorithms calculate theoretical probability to suggest songs that users are likely to enjoy, improving their overall experience. Learn more about this application in our article, “ Theoretical Probability: A Real-Life Example (from Digital Design) .”

26. Developing Realistic Computer Games with Vectors:

Mathematics is essential in animating objects and simulating real-world factors in computer games. Vectors enable game developers to incorporate realistic elements like gravity and wind into the gaming environment. By applying vector addition, developers can accurately depict how external forces affect object trajectories, enhancing the gaming experience. Explore this concept further in our article, “ Parallelogram Law of Vector Addition: A Real-Life Example (from Game Development) .”

27. Detecting Malicious Bots in Social Media Using Linear Inequalities:

Mathematical inequalities are valuable tools in cybersecurity for identifying malicious activity on social media platforms. By analyzing behavioral differences between real users and bots—such as friend count, posting frequency, and device usage—cybersecurity experts can develop algorithms to detect and block suspicious accounts. Discover more about this application in our article, “ How to Write Inequalities: A Real-life Example (from Social Media) .”

28. Increasing Computational Efficiency Using Algebraic and Rational Expressions

Algebraic and rational expressions are crucial in computer technology for increasing computational efficiency . Every step in a computer program’s algorithm requires valuable time and energy for execution. This is especially important for programs used in various safety and security systems. Simplifying these expressions helps boost computational performance. Our article, “ Algebraic and Rational Expressions: A Real-Life Example (from Computer Technology) ,” explains this in detail.

Math Problems in Legal Issues

In legal proceedings, mathematics plays a crucial role in analyzing data and making informed decisions. Here’s a real-world math problem encountered in legal work:

29. Proving the Reliability of Technology in Court Using Percentages:

In certain court cases, particularly those involving new technologies like autonomous cars, lawyers may need to employ mathematical methods to justify evidence. Percentage analysis can be utilized to assess the reliability of technology in court. For instance, in cases related to self-driving cars, lawyers may compare the percentage of errors made by autonomous vehicles with those made by human drivers to determine the technology’s safety. Delve deeper into this topic in our article, “ Solving Percent Problems: A Real-Life Example (from Legal) .”

Math Problems in Safety and Security

In the realm of safety and security, mathematics plays a vital role in protecting people, nature, and assets. Real-world math problems in this field can involve reconstructing crime scenes, analyzing evidence, creating effective emergency response plans, and predicting and responding to natural disasters. Here are two examples:

30. Reconstructing a Crime Scene with Inverse Trigonometry:

Forensic specialists rely on mathematical methods, such as inverse trigonometry, to uncover details of crimes long after they’ve occurred. Inverse trigonometric functions like arcsin, arccos, and arctan enable forensic specialists to calculate precise shooting angles or the trajectory of blood drops at crime scenes. Dive into this topic in our article, “ Arctan: A Real-Life Example (from Criminology) .”

31. Responding to Wildfires with Mathematical Variables:

Variables in mathematical language are also prevalent in real-world scenarios like firefighting. For instance, when dealing with wildfires, independent variables like forest type, wind speed and direction, rainfall, and terrain slope influence fire spread speed (dependent variable) . By utilizing specialized formulas incorporating these variables, fire protection specialists can accurately predict fire paths and optimize firefighting efforts. Explore this practical application in our article, “ Dependent and Independent Variables: A Real-Life Example (from Fire Protection) .”

Math Problems in Weather and Climate

In the realm of weather and climate, mathematics is crucial for creating mathematical models of Earth’s atmosphere, making weather forecasts, predicting weather patterns, and assessing long-term climate trends. Here’s an example:

32. Forecasting Thunderstorms with Negative Numbers:

Negative numbers play a significant role in forecasting thunderstorms. The probability of thunderstorms is closely tied to the temperature differences between air masses in the atmosphere. By subtracting negative numbers (representing temperature values) and analyzing the results, meteorologists can forecast the likelihood of thunderstorms based on the temperature differentials. Dive deeper into this concept in our article, “ Subtracting Negative Numbers: A Real-Life Example (from Weather Forecast). “

Conclusions

Many students perceive math as disconnected from the real world, leading them to question its relevance. Admittedly, maintaining this relevance is no easy feat—it requires collective effort. Farmer Alfred can’t tackle this challenge alone. However, introducing more real-world math examples into the school curriculum is a crucial step. Numerous studies have demonstrated that such examples significantly enhance students’ motivation to learn math. Our own pilot tests confirm this, showing that a clear connection between real-world problems and math education profoundly influences how young people view their future careers.

Therefore, to increase the overall relevance of math education and motivate students, we must prioritize the integration of real-world examples into our teaching practices. At DARTEF, we are dedicated to this cause, striving to bring authenticity to mathematics education worldwide.

• Vos, Pauline. ““How real people really need mathematics in the real world”—Authenticity in mathematics education.” Education Sciences  8.4 (2018): 195.
• Cambridge dictionary, Meaning of problem in English.
• Reif, Frederick.  Applying cognitive science to education: Thinking and learning in scientific and other complex domains . MIT press, 2008.

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22 Examples of Mathematics in Everyday Life

Let’s read further to know the real-life situations where maths is applied.

1. Making Routine Budgets

How much should I spend today? When I will be able to buy a new car? Should I save more? How will I be able to pay my EMIs? Such thoughts usually come into our minds. The simple answer to such type of question is maths. We prepare budgets based on simple calculations with the help of simple mathematical concepts. So, we can’t say, I am not going to study maths ever! Everything which is going around us is somehow related to maths only.

Application: 

• Basic mathematical operations (addition, subtraction, multiplication, and division)
• Calculation of percentage
• Arithmetic calculations

2. Construction Purpose

You know what, maths is the basis of any construction work. A lot of calculations, preparations of budgets, setting targets, estimating the cost, etc., are all done based on maths. If you don’t believe it, ask any contractor or construction worker, and they will explain as to how important maths is for carrying out all the construction work.

Application:

• Preparing budgets
• Taking measurements
• Estimating the cost and profit
• Calculus and Statistics
• Trigonometry

3. Exercising and Training

I should reduce some body fat! Will I be able to achieve my dream body ever? How? When? Will I be able to gain muscles? Here, the simple concept that is followed is maths. Yes! based on simple mathematical concepts, we can answer to above-mentioned questions. We set our routine according to our workout schedule, count the number of repetitions while exercising, etc., just based on maths.

• Basic Mathematical Operations (additions, subtraction, multiplication, and division)
• Logical and Analogical Reasoning

4. Interior Designing

Interior designing seems to be a fun and interesting career but, do you know the exact reality? A lot of mathematical concepts, calculations, budgets, estimations, targets, etc., are to be followed to excel in this field. Interior designers plan the interiors based on area and volume calculations to calculate and estimate the proper layout of any room or building. Such concepts form an important part of maths.

• Ratios and Percentages
• Mathematical Operations

5. Fashion Designing

Just like interior design, maths is also an essential concept of fashion design. From taking measurements, estimating the quantity and quality of clothes, choosing the color theme, and estimating the cost and profit, to producing cloth according to the needs and tastes of the customers, maths is followed at every stage.

• Basic Mathematical Operations
• Rations and Percentages

6. Shopping at Grocery Stores and Supermarkets

The most obvious place where you would see the application of basic mathematical concepts is your neighborhood grocery store and supermarket. The schemes like ‘Flat 50% off, ‘Buy one get one free, etc., are seen in most of the stores. Customers visit the stores, see such schemes, estimate the quantity to be bought, the weight, the price per unit, discount calculations, and finally the total price of the product, and buy it. The calculations are done based on basic mathematical concepts. Thus, here also, maths forms an important part of our daily routine.

• Ratio and Percentage

7. Cooking and Baking

In your kitchen also, the maths is performed. For cooking or baking anything, a series of steps are followed, telling us how much of the quantity is to be used for cooking, the proportion of different ingredients, methods of cooking, the cookware to be used, and many more. Such are based on different mathematical concepts. Indulging children in the kitchen while cooking anything, is a fun way to explain maths as well as basic cooking methods.

• Mathematical Algorithm
• Ratios and Proportions

Maths improves the cognitive and decision-making skills of a person. Such skills are very important for a sportsperson because by this he can take the right decisions for his team. If a person lacks such abilities, he won’t be able to make correct estimations. So, maths also forms an important part of the sports field.

• Probability
• Mathematical Operations and Algorithm
• Logical Reasoning
• Game Theory

9.  Management of Time

Now managing time is one of the most difficult tasks which is faced by a lot of people. An individual wants to complete several assignments in a limited time. Not only the management, but some people also are not even able to read the timings on an analog clock. Such problems can be solved only by understanding the basic concepts of maths. Maths not only helps us to understand the management of time but also to value it.

10. Driving

‘Speed, Time, and Distance’ are all these three things that are studied in mathematical subjects, which are the basics of driving irrespective of any mode of transportation. Maths helps us to answer the following question;

• How much should be the speed to cover any particular distance?
• How much time would be taken?
• Whether to turn left or right?
• When to stop the car?
• When to increase or decrease the speed?
• Logical reasoning
• Numerical Reasoning

11. Automobiles Industry

The different car manufacturing companies produce cars based on the demands of the customers. Every company has its category of cars ranging from microcars to luxury SUVs. In such companies, basic mathematical operations are being applied to gain knowledge about the different demands of the customers.

12. Computer Applications

Ever wondered how a computer works? How easily it completes every task in a proper series of actions? The simple reason for this is the application of maths. The fields of mathematics and computing intersect both in computer science. The study of computer applications is next to impossible without maths. Concepts like computation, algorithms and many more forms the base for different computer applications like PowerPoint, word, excel, etc. are impossible to run without maths.

Applications:

• Computation
• Coding Methods
• Cryptography

13. Planning a Trip

We all are bored with our monotonous life and we wish to go on long vacations. For this, we have to plan things accordingly. We need to prepare the budget for the trip, the number of days, the destinations, and hotels adjust our other work accordingly, and many more. Here comes the role of maths. Basic mathematical concepts and operations are required to be followed to plan a successful trip.

14. Hospitals

Every Hospital has to make the schedule the timings of the doctors available, the systematic methods of conducting any major surgery, keeping the records of the patients, records of the success rate of surgeries, number of ambulances required, training for the use of medicines to nurses, prescriptions, and scheduling all tasks, etc. All these are done based on Mathematical concepts.

• Body Mass Index

15. Video Games

Playing video games is one of the most favorite entertainment activities done all over the world, irrespective of the fact that whether you are a kid or an adult. Students usually skip their maths classes to play video games. But, do you know here also they are learning maths? Here, they learn about the different steps and techniques to be followed to win any game. Not only while playing, but the engineers who introduce different games for people also follow the different mathematical concepts.

16. Weather Forecasting

The weather forecasting is all done based on the probability concept of maths. Through this, we get to know about the weather conditions like whether it’s going to be a sunny day or rainfall will come So, next time you plan your outing, don’t forget to see the weather forecasting.

Application:    

17. Base of Other Subjects

Though maths is itself a unique subject. But, you would be surprised to know that it forms the base for every subject. The subjects like physics, chemistry, economics, history, accountancy, and statistics every subject is based upon maths. So, next time you say, “I’m not going to study this maths subject ever!” remember, this subject will not going to leave you ever.

• Operations Research
• Linear Programming

18. Music and Dance

Listening to music and dancing is one of the most common hobbies of children. Here also, they learn maths while singing and learning different dance steps. Coordination in any dance can be gained by simple mathematical steps.

19. Manufacturing Industry

The part of maths called ‘Operations Research is an important concept that is being followed at every manufacturing unit. This concept of maths gives the manufacturer a simple idea of performing several tasks under the manufacturing unit like,

• What quantity is to be produced?
• What methods are to be followed?
• How to increase production?
• How the cost of production can be reduced?
• Removing unnecessary tasks.
• Following methods like target costing, ABC costing, cost-profit budgeting, and many more.
• Ratios and Probability

20. Planning of Cities

Urban planning includes the concepts of budgeting, planning, setting targets, and many more which all forms part of mathematics. No activity is possible without maths.

21. Problem-solving skills

Problem-solving skills are one of the most important skills which every individual should possess to be successful in life. Such skills help the individual in taking correct decisions in life, let it be professional or personal. This is all done when the person has the correct knowledge of basic mathematical concepts.

• Mathematical Reasoning

22. Marketing

The marketing agencies make the proper plans as to how to promote any product or service. The tasks like promoting a product online, use of social media platforms, following different methods of direct and indirect marketing, door-to-door sales, sending e-mails, making calls, and providing several schemes like ‘Buy one get one free, ‘Flat 50% off, offering discounts on special occasions, etc. are all done based on simple mathematical concepts. Thus, maths is present everywhere.

• Percentages
• Mathematical Operations  

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16 comments.

very good and rare found examples are here to be learned here.

Really informative and knowledgeable

I never realized how much math we use every day.

Example of cost

It nice and great! Idea

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Maths How To with Anita

7 Examples of Algebra in Everyday Life (Simplified Real-Life Applications)

Do you ever feel like algebra is just a bunch of meaningless equations and symbols? Well, think again! Algebra is actually all around us in everyday life. In this blog post, we will discuss seven examples of how algebra is used in the real world.

We will also provide real-life applications for each example. So whether you’re a student trying to understand why you’re learning this stuff or a teacher looking for ways to make it more relevant to your students, read on!

Examples of Algebra in everyday life

Whilst algebra has many applications in daily life, here are my favorite ways of using algebra to solve problems.

1. Calculating discounts at the store

You’re at the store and you see a shirt that’s on sale for 20% off. How much will it cost? This is a great opportunity to use some algebra!

Here’s how we can set this up:

Let x represent the original price of the shirt

Then, we know that:

x – 0.20x = the new price of the shirt

We can simplify x – 0.20x to 0.8x.

So then the new price of the shirt is 0.8x

If the original price of the shirt is $30,

then the new price of the shirt = 0.8 x 30 = $24

2. Are we there yet? Calculating how long it will take to get somewhere

Remember Bart Simpson asking ‘Are we there yet?’ on repeat.

Well, we can use algebra, specifically the formula linking distance, speed and time, to calculate how long it will take to arrive at your destination.

Say your car is traveling at 60 miles per hour, then the formula would be:

So instead of asking ‘Are we there yet?’, you could look out the window for a sign that shows how many miles to your destination then use the Distance-Speed-Time formula.

So the time to get to Las Vegas will be 72 divided by 60 which is just over 1. So it will be just over 1 hour to get there.

The distance – speed – time formula is a useful math formula to remember.

3. Figuring out how many pizzas to order

You’re having 7 friends over and you want pizza.

You each can eat at least 4 slices.

If there are 8 slices in a pizza, how many pizzas should you order?

You can use algebra to find how many pizzas you should order by writing an equation and solving it.

Let x represent the number of pizzas you should order.

So then you and 7 friends is 1 + 7, which is 8.

If each person eats 4 slices, the total number of slices is 8 x 4 = 32

Since each pizza has 8 slices, the number of slices in total will be 8x.

Here’s what it looks like as an algebraic equation:

So you will need to order at least 4 pizzas.

If your friend eat more than 4 slices each you need to order more pizzas.

If your mom and dad, brothers & sisters want pizza too, you will need to order more.

So we could write it as an algebraic inequality like this:

4. Calculating how many hours you need to work

Imagine there is a new pair of jeans you want that cost $75.

If your parents give you $25 towards them, how many hours of babysitting do you have to work in order to buy them?

Well you only need $50 right because $75 – $25 = $50

Let us say you earn $5 an hour for babysitting.

Then you will need to work for 10 hours.

Here’s what it looks like in algebra:

5. When adjusting amounts in a recipe when cooking

Let’s say you want to make some choc-chip cookies but the recipe requires 2 eggs and you only have 1 egg.

You will need to adjust the amounts of the rest of the ingredients.

This is a simple example where you can simply halve each ingredient.

Alternatively, you could use your knowledge of algebra to write an algebraic equation to calculate all the other quantities.

This is useful when its not a simple case of doubling or halving amounts.

For example if you wanted to make choc-chip cookies but you only have 2 cups of flour and you need 3 cups.

This means your recipe will be 2/3 of the original recipe.

So your formula will be:

new amount = 2/3 x recipe amount

6. Planning a budget and sticking to it

Budgeting is so important, whether you’re an individual, a family or a business. And algebra can help!

Let’s say you have $200 income in a month. You want to budget this out so that you don’t overspend and can even save money each month. Perhaps for an end-of-school holiday, a car or college.

List all your expenses, for example:

• $16 cell phone
• $30 monthly bus pass
• $50 going out with friends

Add up your expenses to find your monthly expenses.

16 + 30 +50 = 96

You should track your expenses in an app or spreadsheet to see what you are actually spending your money on. These days with apple pay and a cashless society it is very easy to spend money and not realize how much we are spending over. a month.

Subtract your total monthly expenses from your income to calculate the amount leftover that you can save (or invest).

Using algebra this could be done like this:

Let x represent your monthly expenditure.

Then we know that:

200-x = the amount we can save each month

Of course, this is just a simple example. In reality, you may use a spreadsheet (which is what I use). But you will need to understand the mathematics so you can enter a formula in your spreadsheet. This way when your expenses vary each month your savings will be automatically calculated.

So algebra can help you to create a budget, stick to it and even save or invest.

7. Comparing cell phone plans

The time will come when your parents stop paying your cell bill. In order to find the best value for money, you need to be able to compare different cell phone plans.

Algebra can help you do this!

Let’s say you’re looking at two different cell phone plans:

Plan A: $60/month with unlimited talk and text and 5GB data

Plan B: $20/month with unlimited talk and text and 1GB data plus $10/GB over this amount.

In order to compare cell phone plans, we need to find out how much data we use each month. You may need to look at past statements for this information.

Just say you use roughly 3GB of data each month.

On Plan A, the 3GB is included so your total bill would be $60

On Plan B, 3GB is over the 1GB of included data so you will need to pay extra. Each plan will have different costs.

The amount you will pay is calculated as follows:

# of GB over plan = 3GB minus 1GB = 2 GB

Cost for extra GB = 2 x $10/GB = $20

Total monthly cost = $20 + $20 = $40

So plan B ends up being $20 cheaper.

You could write this as a formula as:

Total monthly cost = 20 + (# GB used – 1GB) x 10

Since the amount of data used each month may vary, it Is called a variable.

Different plans may charge different excess data costs too.

You could set up a spreadsheet to calculate the different monthly costs for the varying amount of data used to help you decide which cell phone plan is best for your needs.

You can see that once you use over 5GB of data the monthly cost for plan B will be more than $60. This is when plan A is the best value.

So knowing how to write a formula can help you compare cell phone plans.

Wrapping up and my experience with using examples of Algebra in everyday life in the classroom.

There are countless other examples of how algebra is used in daily life. These are just a few of the ways that I use it on a regular basis to problem solve. I’m sure you can think of many more!

From my 14+ years of teaching high school mathematics to students of all abilities, I have observed that some students need to see the relevance of abstract concepts like Algebra in order to be interested.

Start the lesson with a hook or example of how they can use algebra in real life so they buy into the topic and are more engaged.

If you’re a teacher, try incorporating some real-life examples into your lessons. And if you’re a student, pay attention to the ways that you use algebra in your daily life. It will help you to better understand the concepts and make them more relevant to your own life.

I hope this article has helped you to see how algebra is used in everyday life.

Related posts:

‘How students can apply their learning to solve real-world problems’

Want to keep up with the latest education news and opinion? Follow  TES USA on Twitter  and like  TES USA on Facebook .

The application of knowledge and skills is called transfer by cognitive psychologists, and it is often considered a primary goal of education; and yet, it is extremely tricky to achieve. However, we want our students to be able to use their knowledge to solve problems in the “real world”.

Transfer can be conceptualized as a continuum. If you are applying information to something very similar, such as a question that asks about the same material but in a new and different way, we refer to that as near transfer. If instead we ask students to apply their information to solve a novel problem or explain a real-world scenario, that would be considered far transfer.

Transfer is an important topic in every discipline. In any class, we do not want students to only memorize the concepts and examples we use, but instead to be able to use them later in life. This is equally important in math and science as it is in history or psychology. How to Teach Transfer:

Even in controlled laboratory experiments, transfer is hard to achieve. There are essentially three basic rules that must be met in order for students to apply their knowledge (1) :

1) Students must be aware that something they have learned could be useful in this new situation.

Unfortunately, we do not know all of the situations that students will need to use the knowledge/skills we teach, but the best way to make them aware of transfer situations is to explicitly teach students when they can use the information. This will make them more likely to recognize situations in which they can apply their knowledge when they come up in the future.

For example, when teaching about the slope of a line in geometry, students could be taught about real world applications (far transfer), such as how to use slope when building a wheelchair ramp or to calculate the rate of return on investments. The more varied the examples, the more likely students are to recognize them in the future.

2) Students must be able to retrieve the information that could be useful.

In order to promote successful retrieval of information, you can use any evidence-based learning strategies. In our first TES post, I talked about five tips on how to study  that are all based on research. Any of these will promote better retrieval for transfer situations as well (as long as condition #1 above is met).

3) Students must be able to apply/use the information correctly in the new situation.

In order to learn how to appropriately apply information, students need to actually practice applying information. When teaching students about a situation in which prior knowledge might be useful, have them work in groups or alone to solve the problem of how to apply the information. In this way they get practice applying their knowledge, which also serves as retrieval practice. Double bonus! For the example above, students shouldn’t just be told about how to calculate their rate of return, they need to actually solve those problems using the concepts they are learning in class.

But Be Careful...

What is intuitive to us does not always match up with what works, so we must be careful in looking for evidence. In the case of transfer, a technique used by many teachers - quizzing some information in the hope that it will “trigger” other related information at test - doesn’t always work  (2) .

Instead, all three of the conditions above must be met and often the first condition is the trickiest. Students have to realize that there are situations in which they might need to apply the information from class. Giving them practice doing just that is the best way to promote transfer in the real world.

Further reading

(1) Barnett, S. M., & Ceci, S. J. (2002). When and where do we apply what we learn? A taxonomy for far transfer.  Psychological Bulletin, 128 , 612-637.

 (2) Wooldridge, C., Bugg, J., McDaniel, M., & Liu, Y. (2014). The testing effect with authentic educational materials: A cautionary note.  Journal of Applied Research in Memory and Cognition, 3 , 214-221.

Cindy Wooldridge ( @psydoccindy ) is a cognitive psychologist at Washburn University, Kansas, and a member of the Learning Scientists team.  Follow the Learning Scientists on Twitter at @AceThatTest .

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8 Examples of Integers in Real Life Situations

Math can sometimes seem like a puzzle. Terms like whole numbers, natural numbers, positive and negative numbers, and integers can all be confusing. To ease your confusion, let’s pick “integers” as the topic of discussion for today. You may be wondering, “What are integers anyway?” Well, integers are those unique numbers that don’t have any decimal or fractional parts. They are the whole numbers, both positive and negative (including zero), that help us count, compare, and understand the world around us.

But here’s the fun part – integers are all around us; all you need to do is look for them! From your pocket money to the temperature outside, they sneak into our daily life and make things measurable. So, let us explore integers and their significant presence in real-life situations. 

Why are integers important? 

Integers are like the backbone of mathematics, providing a solid foundation for countless mathematical operations and real-life applications. They are the building blocks that help a person attain mathematical fluency and make sense of the numerical complexities of our world.

Integers play a crucial role in understanding and representing quantities. The real-life examples of positive and negative numbers reflect so. They help us measure, make comparisons, and calculate a wide range of things, from financial transactions to temperature changes, population analysis, and more. They also allow us to make sense of the world around us and solve mathematical problems. 

By grasping and applying integers in multiple facets of life, we work on many valuable skills like critical thinking, problem-solving, and logical reasoning. You may be in school solving simple problems involving integers right now, but later, when you pursue a career in science, technology, engineering, mathematics, or any other field, a solid understanding of integers can help you grow professionally. 

Application of integers in real life: 8 relevant examples

1. world records.

World records are a fascinating real-life example of integers. From sports achievements to extraordinary human endeavors, world records capture the essence of pushing the boundaries of what we think is possible. Each record is a specific numerical value, an integer, representing the peak of human achievement in a particular category. Whether it’s the fastest sprint or the highest jump, these records serve as benchmarks that inspire individuals to strive for more. 

Suppose a runner completes a lap in 30 seconds. One person who fails to break the record could be at +5 seconds, whereas the other person who breaks the 30 seconds mark in 24 seconds is at -6 seconds. So you can see how these integers offer a universal language to quantify and compare human accomplishments and serve as a reminder that they are not merely a mathematical concept but also have the power to celebrate remarkable achievements.

2. AD and BC timeline

The concept of “BC” (Before Christ) and “AD” (Anno Domini) serves as real-life examples of integers in historical chronology. BC represents the years before the estimated birth of Jesus Christ, while AD denotes the years after his birth. Both BC and AD are used to create a linear timeline that provides a common reference point for dating events in human history. 

So if a person is born in 2023, it is +2023 AD, while those born 500 years before Christ can be said to be born in -500 BC. By assigning integers to specific years, BC and AD allow us to keep a record of historical events. They enable historians and researchers to establish connections, trace patterns, and gain insights into the progression of human civilization. 

3. Behavior points

Behavior points allow teachers to track and measure individual student behavior. These points are integers, which are used to incentivize or stop specific behaviors from occurring. Positive behavior points, for example, +10, may be awarded to students who display desirable actions, such as active participation, respectful behavior, or completing tasks on time. Negative behavior points, like -5, may be assigned to students who are disruptive and disobedient. 

By giving numerical values to these behaviors, a quantifiable system is established to track and assess the behavior patterns of students over time. These integers also help in the fair implementation of reward systems or consequences. It also helps promote self-awareness, encourages positive behavior, and provides a framework for individuals to reflect on their actions and strive for improvement. 

4. Price changes 

When prices of goods or services are adjusted, they are typically represented as integers that reflect the change. For example, if the original price of a product is $10 and it undergoes a price increase of +$2 (a positive), the new price would be $12. Conversely, if the price is adjusted by -$2 (a negative), it would result in a new price of $8. 

These integer values allow us to quantify price adjustments and let us make comparisons between different products. The integers used to represent price changes enable people to evaluate and analyze the impact of fluctuations, make purchasing decisions, and assess the affordability or value of goods and services. Plus, it also ensures transparency and consistency in the marketplace.

5. Calories gained/burned

Have you ever observed someone who is on a dieting spree? You will often see them counting their calories. Calories are integers or numerical values used to measure the energy content of food and energy expenditure through physical activity. When we consume food, we gain calories; when we exercise, we burn calories. Integers quantify these energy values and give us an idea of how well we meet our diet goals. 

For instance, if you eat a chocolate bar, you will be +200 calories closer to your daily caloric goal, but if you take a 30-minute jog, you may burn 300 calories and record it as -300 calories in your chart. By tracking calories gained and burned, one can manage their weight. Here integers serve as a means for individuals to meet their health and fitness goals and work towards a healthy lifestyle.

6. Business profit/loss

For any business to be successful, it is crucial to keep note of its profits and losses over a given period of time. Profit is a positive outcome, indicating that a business has earned more revenue than its expenses. At the same time, a loss represents a negative outcome, reflecting that the company’s expenses have exceeded the revenue generated. These financial figures are typically expressed as integers, which quantify the profit or loss incurred. 

So, if a company’s profit and loss statements reflect + $10,000, it means they have earned it as a profit. But if it shows a negative integer like -$5000, it would represent losses. So you can see how by using integers, businesses can measure and evaluate their financial performance and establish positive, negative, and zero correlations between different variables. This provides executives with crucial insights into a company’s financial health and helps identify improvement areas. 

7. pH values

In chemistry, pH is a measure of the acidity or alkalinity of a solution, typically ranging from 0 to 14. A pH of 7 is considered neutral; below 7 indicates acidity, while anything above 7 indicates alkalinity. As you can see, pH values are also integers. For instance, a solution with a pH of 3 is more acidic than another with a pH of 5. Usually, pH values are positive integers falling between 0 to 14. 

However, that does not mean a pH can never have a negative value. It may be hard to determine, but it is possible. Some environmental samples, like the Hot Springs near Ebeko Volcano in Russia, are reported to have a pH of -1.7. By utilizing integers to represent pH values, scientists and researchers can analyze the acidity or alkalinity levels of different solutions, thus, enabling them better understand their chemical characteristics. 

8. Game scores

Games with negative markings are yet another example of integers. Whether it’s an online or offline competition, game scores are represented mainly by numerical values. These integers measure the performance of a player within the game. Higher scores indicate greater achievement, while lower scores indicate lower success. 

The scores can be positive integers, or they can even be negative numbers if the player has received a negative marking Sometimes, it can even be zero! Integers depicting game scores provide a basis for rankings, records, and determining winners. It also encourages players to strive to achieve higher scores next time and facilitates friendly competition among players.

Summing up, 

Integers are the simplest and most fundamental component of mathematics. You need them for arithmetic operations, no matter how big or small. Maybe that’s why there are numerous quotes and sayings about the importance of numbers. By exploring examples of integers in real-life situations, we realize how relevant and powerful these numbers are in our everyday lives. Integers help us navigate financial transactions, analyze data, and make informed decisions.

They are not just confined to math textbooks but are needed to bring order and structure to our daily experiences. By recognizing and understanding integers, we gain mathematical fluency and valuable skills that extend far beyond the classroom. So, don’t get overwhelmed when you deal with integers. Use your knowledge to navigate and appreciate the numerical intricacies that appear in our everyday lives.

I am Priyanka Sonkushre, a writer and blogger. I am the person behind “ One Loving Mama ,” a mom blog. Equipped with a Bachelor’s degree along with an MBA, my healthcare background helps me deeply understand learning difficulties. I know how challenging it can be for parents to find the right resources to help their children excel in life. So, here I am to blend my healthcare expertise with my parenting experience to create valuable and helpful resources for parents and teachers supporting children with learning differences. If you wish, you can follow me on  Facebook  and  LinkedIn .

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Math Fluency Is All About Problem-Solving. Do We Teach It That Way?

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To learn math, students must build a mental toolbox of facts and procedures needed for different problems.

But students who can recall these foundational facts in isolation often struggle to use them flexibly to solve complex, real-world problems , known as procedural fluency.

“Mathematics is not just normalizing procedures and implementing them when somebody tells you to use that procedure. Mathematics is solving problems,” said Bethany Rittle-Johnson, a professor of psychology and human development at Peabody College in Vanderbilt University, who studies math instruction. “To solve problems, we have to figure out what strategy to use when—and that tends to get too little attention.”

In a series of ongoing experiments, Rittle-Johnson and her colleagues find students develop better procedural fluency when they get opportunities to compare and contrast problem-solving approaches and justify the approaches they use in different situations. While some students may develop this skill on their own, most need explicit instruction, she found.

Rittle-Johnson spoke with Education Week about how teachers can use such comparisons to help students develop a deeper understanding of math. This interview has been edited for space and clarity.

For more on the best research-based strategies on improving math instruction, see Education Week’s new math mini-course .

How often do teachers talk to students about multiple strategies, and how to select them, in math problem-solving?

Students in the [United States] are very rarely doing rich contextual problems. Even more rarely, they’re being asked to compare strategies to solve them. I don’t hear teachers talk about [using different strategies] a lot, and textbooks tend to do a pretty bad job of explaining it.

For example, in Algebra 1, solving systems of equations, there are many standard solutions strategies that are taught in separate chapters and textbooks, ... but I see shockingly little time spent having students think and compare and choose which strategy to use. In one study where teachers were trained [to compare math strategies], only about 20 percent did in the classroom—and only about 5 percent of teachers who [did not receive training.]

Sometimes I hear teachers say, “Well, multiple strategies, that’s great for my high-end learners, but I don’t want to show that to my struggling learners. … So maybe multiple strategies is the ideal, but I’m not going to get to it because I’m tight on time and my kids are behind.” But we hear from struggling learners that they really appreciate the multiple strategies and we see that it helps them, too, across the grade bands and across contexts.

How can teachers decide when to bring in and compare different strategies while introducing a new math concept?

We find comparisons can be useful in all different phases of instruction.

It can be helpful for kids to have had some time to think about one strategy before they think about multiple strategies, maybe at most a lesson. But the risk is in general, if you wait too long, kids just get attached to one strategy. You run the risk of kids becoming really attached to one strategy, and then they become more resistant to wanting to think about and use multiple strategies.

What does this sort of comparison look like in the classroom?

One best practice is to have the steps of the different strategies written out. It can be kids’ strategies that they wrote on the board. It can be projecting strategies from textbooks or your solutions, but one thing we know is: Make sure both strategies are visible so that kids don’t have to remember. Then we ask kids to think about similarities and differences and think about, when is each a good strategy?

Sometimes we have students compare correct and incorrect strategies and explain the concepts that make the correct strategy correct. Just because you teach kids correct ways of doing things, that doesn’t mean the incorrect strategies disappear. Students really need help thinking and reasoning through why those are wrong.

What are the more common struggles for teachers to teach multiple strategies?

The No. 1 barrier we face is time. Teachers just feel they’re under so much pressure to cover so much content that they feel like they can’t take the time to do this, and that they see the value and the payoff in it. It does pay off for what is assessed [in standardized math tests], but it’s not directly assessed, and so that makes teachers nervous.

Also, sometimes teachers really don’t like to say this way is better than this other way. Even though mathematicians would say, “yeah, this way is clearly better in this context, and this other way is clearly better in that context,” ... sometimes teachers feel uncomfortable that they’re making a value judgment.

But the evidence is really clear that it’s helpful to show correct and incorrect examples and talk through them.

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