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10 Best Problem-Solving Therapy Worksheets & Activities

Cognitive science tells us that we regularly face not only well-defined problems but, importantly, many that are ill defined (Eysenck & Keane, 2015).

Sometimes, we find ourselves unable to overcome our daily problems or the inevitable (though hopefully infrequent) life traumas we face.

Problem-Solving Therapy aims to reduce the incidence and impact of mental health disorders and improve wellbeing by helping clients face life’s difficulties (Dobson, 2011).

This article introduces Problem-Solving Therapy and offers techniques, activities, and worksheets that mental health professionals can use with clients.

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This Article Contains:

What is problem-solving therapy, 14 steps for problem-solving therapy, 3 best interventions and techniques, 7 activities and worksheets for your session, fascinating books on the topic, resources from positivepsychology.com, a take-home message.

Problem-Solving Therapy assumes that mental disorders arise in response to ineffective or maladaptive coping. By adopting a more realistic and optimistic view of coping, individuals can understand the role of emotions and develop actions to reduce distress and maintain mental wellbeing (Nezu & Nezu, 2009).

“Problem-solving therapy (PST) is a psychosocial intervention, generally considered to be under a cognitive-behavioral umbrella” (Nezu, Nezu, & D’Zurilla, 2013, p. ix). It aims to encourage the client to cope better with day-to-day problems and traumatic events and reduce their impact on mental and physical wellbeing.

Clinical research, counseling, and health psychology have shown PST to be highly effective in clients of all ages, ranging from children to the elderly, across multiple clinical settings, including schizophrenia, stress, and anxiety disorders (Dobson, 2011).

Can it help with depression?

PST appears particularly helpful in treating clients with depression. A recent analysis of 30 studies found that PST was an effective treatment with a similar degree of success as other successful therapies targeting depression (Cuijpers, Wit, Kleiboer, Karyotaki, & Ebert, 2020).

Other studies confirm the value of PST and its effectiveness at treating depression in multiple age groups and its capacity to combine with other therapies, including drug treatments (Dobson, 2011).

The major concepts

Effective coping varies depending on the situation, and treatment typically focuses on improving the environment and reducing emotional distress (Dobson, 2011).

PST is based on two overlapping models:

Social problem-solving model

This model focuses on solving the problem “as it occurs in the natural social environment,” combined with a general coping strategy and a method of self-control (Dobson, 2011, p. 198).

The model includes three central concepts:

• Social problem-solving
• The problem
• The solution

The model is a “self-directed cognitive-behavioral process by which an individual, couple, or group attempts to identify or discover effective solutions for specific problems encountered in everyday living” (Dobson, 2011, p. 199).

Relational problem-solving model

The theory of PST is underpinned by a relational problem-solving model, whereby stress is viewed in terms of the relationships between three factors:

• Stressful life events
• Emotional distress and wellbeing
• Problem-solving coping

Therefore, when a significant adverse life event occurs, it may require “sweeping readjustments in a person’s life” (Dobson, 2011, p. 202).

• Enhance positive problem orientation
• Decrease negative orientation
• Foster ability to apply rational problem-solving skills
• Reduce the tendency to avoid problem-solving
• Minimize the tendency to be careless and impulsive

D’Zurilla’s and Nezu’s model includes (modified from Dobson, 2011):

• Initial structuring Establish a positive therapeutic relationship that encourages optimism and explains the PST approach.
• Assessment Formally and informally assess areas of stress in the client’s life and their problem-solving strengths and weaknesses.
• Obstacles to effective problem-solving Explore typically human challenges to problem-solving, such as multitasking and the negative impact of stress. Introduce tools that can help, such as making lists, visualization, and breaking complex problems down.
• Problem orientation – fostering self-efficacy Introduce the importance of a positive problem orientation, adopting tools, such as visualization, to promote self-efficacy.
• Problem orientation – recognizing problems Help clients recognize issues as they occur and use problem checklists to ‘normalize’ the experience.
• Problem orientation – seeing problems as challenges Encourage clients to break free of harmful and restricted ways of thinking while learning how to argue from another point of view.
• Problem orientation – use and control emotions Help clients understand the role of emotions in problem-solving, including using feelings to inform the process and managing disruptive emotions (such as cognitive reframing and relaxation exercises).
• Problem orientation – stop and think Teach clients how to reduce impulsive and avoidance tendencies (visualizing a stop sign or traffic light).
• Problem definition and formulation Encourage an understanding of the nature of problems and set realistic goals and objectives.
• Generation of alternatives Work with clients to help them recognize the wide range of potential solutions to each problem (for example, brainstorming).
• Decision-making Encourage better decision-making through an improved understanding of the consequences of decisions and the value and likelihood of different outcomes.
• Solution implementation and verification Foster the client’s ability to carry out a solution plan, monitor its outcome, evaluate its effectiveness, and use self-reinforcement to increase the chance of success.
• Guided practice Encourage the application of problem-solving skills across multiple domains and future stressful problems.
• Rapid problem-solving Teach clients how to apply problem-solving questions and guidelines quickly in any given situation.

Success in PST depends on the effectiveness of its implementation; using the right approach is crucial (Dobson, 2011).

Problem-solving therapy – Baycrest

The following interventions and techniques are helpful when implementing more effective problem-solving approaches in client’s lives.

First, it is essential to consider if PST is the best approach for the client, based on the problems they present.

Is PPT appropriate?

It is vital to consider whether PST is appropriate for the client’s situation. Therapists new to the approach may require additional guidance (Nezu et al., 2013).

Therapists should consider the following questions before beginning PST with a client (modified from Nezu et al., 2013):

• Has PST proven effective in the past for the problem? For example, research has shown success with depression, generalized anxiety, back pain, Alzheimer’s disease, cancer, and supporting caregivers (Nezu et al., 2013).
• Is PST acceptable to the client?
• Is the individual experiencing a significant mental or physical health problem?

All affirmative answers suggest that PST would be a helpful technique to apply in this instance.

Five problem-solving steps

The following five steps are valuable when working with clients to help them cope with and manage their environment (modified from Dobson, 2011).

Ask the client to consider the following points (forming the acronym ADAPT) when confronted by a problem:

• Attitude Aim to adopt a positive, optimistic attitude to the problem and problem-solving process.
• Define Obtain all required facts and details of potential obstacles to define the problem.
• Alternatives Identify various alternative solutions and actions to overcome the obstacle and achieve the problem-solving goal.
• Predict Predict each alternative’s positive and negative outcomes and choose the one most likely to achieve the goal and maximize the benefits.
• Try out Once selected, try out the solution and monitor its effectiveness while engaging in self-reinforcement.

If the client is not satisfied with their solution, they can return to step ‘A’ and find a more appropriate solution.

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Positive self-statements

When dealing with clients facing negative self-beliefs, it can be helpful for them to use positive self-statements.

Use the following (or add new) self-statements to replace harmful, negative thinking (modified from Dobson, 2011):

• I can solve this problem; I’ve tackled similar ones before.
• I can cope with this.
• I just need to take a breath and relax.
• Once I start, it will be easier.
• It’s okay to look out for myself.
• I can get help if needed.
• Other people feel the same way I do.
• I’ll take one piece of the problem at a time.
• I can keep my fears in check.
• I don’t need to please everyone.

5 Worksheets and workbooks

Problem-solving self-monitoring form.

Answering the questions in the Problem-Solving Self-Monitoring Form provides the therapist with necessary information regarding the client’s overall and specific problem-solving approaches and reactions (Dobson, 2011).

Ask the client to complete the following:

• Describe the problem you are facing.
• What is your goal?
• What have you tried so far to solve the problem?
• What was the outcome?

Reactions to Stress

It can be helpful for the client to recognize their own experiences of stress. Do they react angrily, withdraw, or give up (Dobson, 2011)?

The Reactions to Stress worksheet can be given to the client as homework to capture stressful events and their reactions. By recording how they felt, behaved, and thought, they can recognize repeating patterns.

What Are Your Unique Triggers?

Helping clients capture triggers for their stressful reactions can encourage emotional regulation.

When clients can identify triggers that may lead to a negative response, they can stop the experience or slow down their emotional reaction (Dobson, 2011).

The What Are Your Unique Triggers ? worksheet helps the client identify their triggers (e.g., conflict, relationships, physical environment, etc.).

Problem-Solving worksheet

Imagining an existing or potential problem and working through how to resolve it can be a powerful exercise for the client.

Use the Problem-Solving worksheet to state a problem and goal and consider the obstacles in the way. Then explore options for achieving the goal, along with their pros and cons, to assess the best action plan.

Getting the Facts

Clients can become better equipped to tackle problems and choose the right course of action by recognizing facts versus assumptions and gathering all the necessary information (Dobson, 2011).

Use the Getting the Facts worksheet to answer the following questions clearly and unambiguously:

• Who is involved?
• What did or did not happen, and how did it bother you?
• Where did it happen?
• When did it happen?
• Why did it happen?
• How did you respond?

2 Helpful Group Activities

While therapists can use the worksheets above in group situations, the following two interventions work particularly well with more than one person.

Generating Alternative Solutions and Better Decision-Making

A group setting can provide an ideal opportunity to share a problem and identify potential solutions arising from multiple perspectives.

Use the Generating Alternative Solutions and Better Decision-Making worksheet and ask the client to explain the situation or problem to the group and the obstacles in the way.

Once the approaches are captured and reviewed, the individual can share their decision-making process with the group if they want further feedback.

Visualization

Visualization can be performed with individuals or in a group setting to help clients solve problems in multiple ways, including (Dobson, 2011):

• Clarifying the problem by looking at it from multiple perspectives
• Rehearsing a solution in the mind to improve and get more practice
• Visualizing a ‘safe place’ for relaxation, slowing down, and stress management

Guided imagery is particularly valuable for encouraging the group to take a ‘mental vacation’ and let go of stress.

Ask the group to begin with slow, deep breathing that fills the entire diaphragm. Then ask them to visualize a favorite scene (real or imagined) that makes them feel relaxed, perhaps beside a gently flowing river, a summer meadow, or at the beach.

The more the senses are engaged, the more real the experience. Ask the group to think about what they can hear, see, touch, smell, and even taste.

Encourage them to experience the situation as fully as possible, immersing themselves and enjoying their place of safety.

Such feelings of relaxation may be able to help clients fall asleep, relieve stress, and become more ready to solve problems.

We have included three of our favorite books on the subject of Problem-Solving Therapy below.

1. Problem-Solving Therapy: A Treatment Manual – Arthur Nezu, Christine Maguth Nezu, and Thomas D’Zurilla

This is an incredibly valuable book for anyone wishing to understand the principles and practice behind PST.

Written by the co-developers of PST, the manual provides powerful toolkits to overcome cognitive overload, emotional dysregulation, and the barriers to practical problem-solving.

Find the book on Amazon .

2. Emotion-Centered Problem-Solving Therapy: Treatment Guidelines – Arthur Nezu and Christine Maguth Nezu

Another, more recent, book from the creators of PST, this text includes important advances in neuroscience underpinning the role of emotion in behavioral treatment.

Along with clinical examples, the book also includes crucial toolkits that form part of a stepped model for the application of PST.

3. Handbook of Cognitive-Behavioral Therapies – Keith Dobson and David Dozois

This is the fourth edition of a hugely popular guide to Cognitive-Behavioral Therapies and includes a valuable and insightful section on Problem-Solving Therapy.

This is an important book for students and more experienced therapists wishing to form a high-level and in-depth understanding of the tools and techniques available to Cognitive-Behavioral Therapists.

For even more tools to help strengthen your clients’ problem-solving skills, check out the following free worksheets from our blog.

• Case Formulation Worksheet This worksheet presents a four-step framework to help therapists and their clients come to a shared understanding of the client’s presenting problem.
• Understanding Your Default Problem-Solving Approach This worksheet poses a series of questions helping clients reflect on their typical cognitive, emotional, and behavioral responses to problems.
• Social Problem Solving: Step by Step This worksheet presents a streamlined template to help clients define a problem, generate possible courses of action, and evaluate the effectiveness of an implemented solution.

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While we are born problem-solvers, facing an incredibly diverse set of challenges daily, we sometimes need support.

Problem-Solving Therapy aims to reduce stress and associated mental health disorders and improve wellbeing by improving our ability to cope. PST is valuable in diverse clinical settings, ranging from depression to schizophrenia, with research suggesting it as a highly effective treatment for teaching coping strategies and reducing emotional distress.

Many PST techniques are available to help improve clients’ positive outlook on obstacles while reducing avoidance of problem situations and the tendency to be careless and impulsive.

The PST model typically assesses the client’s strengths, weaknesses, and coping strategies when facing problems before encouraging a healthy experience of and relationship with problem-solving.

Why not use this article to explore the theory behind PST and try out some of our powerful tools and interventions with your clients to help them with their decision-making, coping, and problem-solving?

We hope you enjoyed reading this article. Don’t forget to download our three Positive Psychology Exercises for free .

• Cuijpers, P., Wit, L., Kleiboer, A., Karyotaki, E., & Ebert, D. (2020). Problem-solving therapy for adult depression: An updated meta-analysis. European P sychiatry ,  48 (1), 27–37.
• Dobson, K. S. (2011). Handbook of cognitive-behavioral therapies (3rd ed.). Guilford Press.
• Dobson, K. S., & Dozois, D. J. A. (2021). Handbook of cognitive-behavioral therapies  (4th ed.). Guilford Press.
• Eysenck, M. W., & Keane, M. T. (2015). Cognitive psychology: A student’s handbook . Psychology Press.
• Nezu, A. M., & Nezu, C. M. (2009). Problem-solving therapy DVD . Retrieved September 13, 2021, from https://www.apa.org/pubs/videos/4310852
• Nezu, A. M., & Nezu, C. M. (2018). Emotion-centered problem-solving therapy: Treatment guidelines. Springer.
• Nezu, A. M., Nezu, C. M., & D’Zurilla, T. J. (2013). Problem-solving therapy: A treatment manual . Springer.

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What is Problem Solving?

It is the cognitive process of identifying, analyzing, and finding solutions to challenges or issues. It involves using logical and creative thinking to address obstacles that occur, make decisions, and achieve goals. Consider the five problem-solving steps: identifying the problem, generating possible solutions, evaluating options, selecting the best solution, and implementing it. Understanding the steps is crucial for navigating complex challenges with clarity and efficiency.

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These worksheets are structured in such a way that encourages solution-based thinking. Engaging in interactive problem-solving activities can help develop critical thinking skills and creative approaches to overcoming obstacles. While these skills are used in a variety of aspects of life, our worksheets focus on problem solving in mathematics. Printable worksheets provide practice for any child who is learning to master new skills they are taught in class. They are perfect for any level, and can be applied to any type of mathematical problem or unit of study.

Why are They Important and How are They Best Used?

They are great for ensuring that students practice what they have yet to master, since they can be customized by the teacher to meet the class and individual needs. They can be used to practice all kinds of word problems involving addition, subtraction, multiplication, division, and so much more.

In a world where challenges are inevitable, the ability to tackle problems effectively is a valuable skill that can be applied across all subjects and age groups. Problem-solving skills are the generator of success. They empower individuals to navigate complex situations, identify triggers, and develop plans to overcome obstacles. From the classroom to the boardroom, these skills are in high demand.

Tailoring Problem-Solving Worksheets for Different Subjects

Mathematics.

Math problem-solving worksheets can be a playground for nurturing critical thinking. Through word problem worksheets, students not only practice calculations but also apply math concepts to real-world scenarios.

Scientific problem-solving worksheets ignite curiosity. They prompt students to hypothesize, design experiments, collect data, and draw conclusions, fostering a scientific mindset.

Language Arts

Language skills and critical thinking intertwine in language arts problem-solving worksheets. Analyzing literature, engaging in creative writing prompts, and correcting grammar offer a holistic approach.

Social Studies

History comes to life through problem-solving worksheets. Encourage students to ponder over historical dilemmas and global challenges, nurturing their ability to think beyond the surface.

Math Worksheet Activity Ideas

• "Math Detective" Challenge: Create a set of worksheets featuring a fictional mystery storyline. Each worksheet presents a clue that requires students to solve a math problem to unveil the next piece of the puzzle. This engaging activity encourages critical and sequential thinking.
• "Math Menu" Project: Design a menu-style worksheet with various math problems categorized by difficulty levels. Allow students to choose a certain number of problems from each category to complete, giving them autonomy and catering to their individual skill levels.
• "Design Your Dream House" Activity: Provide a worksheet that guides students through designing their dream house layout. They need to calculate room dimensions, total area, and even budget constraints. This hands-on activity integrates math into real-life scenarios.
• "Math Art Gallery" Exhibition: Assign each student a famous artwork and create a worksheet that involves geometric calculations related to the art's dimensions and shapes. Students can then present their findings in a "Math Art Gallery" exhibition.
• "Math in the News" Analysis: Collect recent news articles that involve math-related concepts, such as statistics, percentages, or data analysis. Provide worksheets that require students to analyze the math behind the news and discuss its implications.
• "Budgeting for Vacation" Project: Design a project-based worksheet where students plan a vacation, considering expenses like transportation, accommodations, and activities. They must budget and calculate costs while staying within a specified budget.
• "Math Around the World" Exploration: Create a worksheet that presents math problems related to different countries' cultures, currencies, and measurements. Students solve problems like converting currencies or calculating time zone differences.
• "Mathopoly" Board Game: Design a problem-solving board game where players move through spaces by solving math problems. This interactive approach adds an element of fun while reinforcing math skills.
• "Math Olympiad Simulation" Practice: Prepare a set of challenging math problems similar to those in Math Olympiad competitions. Have students work on these problems individually or in teams to sharpen their skills.
• "Math Interview" Project: Assign each student a famous mathematician or scientist and provide a worksheet that guides them to research and create interview-style questions. This encourages exploration of math history and its relevance.
• "Math Escape Room" Challenge: Develop a series of interconnected math problems that lead students through a virtual "escape room." They must solve each problem correctly to advance to the next step and eventually "escape."
• "Data Analysis Report" Assignment: Provide students with a dataset related to a topic of interest, such as sports statistics or environmental data. They must analyze the data, create graphs, and present their findings in a structured report.
• "Math and Music Fusion" Project: Combine math with music by providing a worksheet that explores concepts like rhythm, frequency, and ratios in music. Students can calculate beats per minute, analyze musical patterns, and even compose their own melodies.
• "Math Recipe Creation" Challenge: Ask students to create a new recipe by adjusting ingredient quantities based on serving sizes. They must calculate ratios, proportions, and conversions to ensure the recipe's success.

Designing Effective Problem-Solving Worksheets

Creating successful problem-solving worksheets involves careful planning. Here are some ideas to consider:

• Define the Learning Objective: Clarify the specific mathematical concept you want to reinforce with the worksheet. Outline the steps involved and determine how this worksheet will contribute to improving their skills.
• Select a Problem Type: Choose a math problem type that aligns with the learning objective. It could involve algebraic equations, geometry calculations, or even practical scenarios related to everyday life.
• Structure the Steps: Break down the problem-solving process into logical steps. Ensure that each step reflects the problem solving steps you want students to follow, such as understanding the problem, planning, solving, and verifying.
• Incorporate Interactive Elements: Integrate interactive elements like multiple-choice questions, fill-in-the-blanks, or even drawing areas to encourage problem solving exercises within the worksheet.
• Utilize Graphic Organizers: Introduce a visual problem solving graphic organizer to help students map out their thinking. This can include spaces for writing down given information, variables, and equations.
• Provide a Problem Solving Template: Offer a structured template that guides students through the problem-solving process. Include prompts and placeholders for each step to provide clear direction.
• Encourage Exploration: Inspire students to explore different types of techniques to arrive at solutions. Encourage them to think critically and try various strategies before settling on an approach.

By incorporating these elements, you can create a comprehensive problem solving worksheet for kids that not only teaches mathematical concepts but also equips them with transferable skills. Whether you're focusing on basic arithmetic or more advanced mathematical principles, this approach ensures an engaging and educational experience for young learners.

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Frequently Asked Questions About Problem Solving Worksheets

How can math problem-solving worksheets show students how to improve problem-solving skills.

They provide structured exercises that guide students through real-world scenarios. By actively engaging in these worksheets and activities, children can practice the problem solving process, enhancing their critical thinking and logical reasoning abilities.

What strategies can I use to teach problem-solving skills using math worksheets?

Incorporate helpful math problem solving worksheets for kids into your lessons. Support and encourage students to work through the problem-solving steps: understanding the problem, devising strategies, making calculations, and verifying their solutions. Provide examples, guidance, and feedback to nurture their problem-solving skills.

How can I ensure that students grasp the problem-solving process effectively?

Provide clear instructions in your math problem-solving worksheets that guide students through each step of the process. Offer examples and encourage them to discuss their approaches. By nurturing a supportive and collaborative environment, you can help both younger kids and older kids build confidence in their problem solving skills.

What are specific examples of how to teach problem-solving skills in math using pre-answered solution worksheets?

Teaching problem-solving skills in math using pre-answered solution worksheets can be exemplified through scenarios like quadratic equations. Present the class with a quadratic equation and a pre-answered solution that breaks down the steps of factoring or using the quadratic formula. This guides them to understand the process, identify key components, and apply appropriate methods. Similarly, for geometry, offer a challenging problem involving angles or area calculations, along with a pre-answered solution that demonstrates the application of relevant geometric principles. As students work through the problem and compare their reasoning with the pre-answered solution, they grasp problem-solving strategies, logical sequences, and the importance of meticulous calculations. In both cases, these worksheets instill confidence, reinforce systematic approaches, and enhance students' problem-solving skills while navigating mathematical complexities.

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Home » Blog » General » Free Problem Solving Worksheets: Practical Tools for Success

Free Problem Solving Worksheets: Practical Tools for Success

As a Speech Language Pathologist and Social Emotional Learning expert, I understand the importance of problem-solving skills in personal growth and success. Developing the ability to effectively solve problems not only enhances our cognitive abilities but also plays a crucial role in our social and emotional well-being. In this blog post, I will introduce you to the world of free problem solving worksheets, which are practical tools that can help you develop and strengthen your problem-solving skills.

Understanding Problem Solving

Before we dive into the world of problem solving worksheets, let’s first understand what problem solving entails. Problem solving is the process of identifying, analyzing, and finding solutions to challenges or obstacles that we encounter in our daily lives. It involves critical thinking, decision-making, and creativity.

Effective problem solving consists of several key components. Firstly, it requires the ability to define the problem clearly and understand its underlying causes. Secondly, it involves generating multiple possible solutions and evaluating their potential outcomes. Lastly, it requires implementing and evaluating the chosen solution to determine its effectiveness.

Developing problem-solving skills offers numerous benefits. It enhances our ability to think critically, make informed decisions, and adapt to new situations. It also boosts our self-confidence and resilience, as we become more equipped to handle challenges and overcome obstacles.

The Role of Worksheets in Problem Solving

Worksheets are valuable tools that can facilitate the problem-solving process. They provide structure and guidance, allowing us to break down complex problems into manageable steps. Free problem solving worksheets offer several advantages:

• Structured Approach: Worksheets provide a step-by-step framework for problem solving, ensuring that we cover all necessary aspects of the problem.
• Visual Representation: Worksheets often include visual elements such as diagrams or charts, which can help us visualize the problem and potential solutions.
• Practice and Reinforcement: Worksheets offer opportunities for practice and reinforcement of problem-solving skills, allowing us to apply what we have learned in a structured manner.

By incorporating worksheets into our problem-solving practice, we can enhance our social emotional learning. Social emotional learning (SEL) encompasses the development of self-awareness, self-management, social awareness, relationship skills, and responsible decision-making. Problem solving is a key component of responsible decision-making, as it involves considering the impact of our choices on ourselves and others.

Exploring Free Problem Solving Worksheets

Now that we understand the value of problem solving worksheets, let’s explore the different types of worksheets available:

• Step-by-step problem solving worksheets: These worksheets guide us through the problem-solving process, providing prompts and questions to help us analyze the problem, generate solutions, and evaluate their effectiveness.
• Decision-making worksheets: Decision-making is a crucial aspect of problem solving. These worksheets focus on helping us make informed decisions by considering the pros and cons of different options.
• Critical thinking worksheets: Critical thinking is an essential skill in problem solving. These worksheets encourage us to think deeply and critically about the problem, analyze information, and evaluate different perspectives.

There are several online resources where you can find free problem solving worksheets:

• Educational websites: Many educational websites offer free resources for problem solving and social emotional learning. Examples include EverydaySpeech, Education.com, and Teach-nology.
• Social emotional learning resources: SEL-focused websites and organizations often provide free problem solving worksheets as part of their curriculum. Look for websites like CASEL (Collaborative for Academic, Social, and Emotional Learning) and SEL for Prevention.
• Printable worksheet collections: Numerous websites offer collections of printable worksheets across various subjects, including problem solving. Websites like Super Teacher Worksheets and WorksheetWorks provide free options.

Tips for Effective Use of Problem Solving Worksheets

While using problem solving worksheets, it’s essential to keep a few tips in mind to maximize their effectiveness:

• Set clear goals and objectives: Before starting a worksheet, clearly define what you want to achieve and what specific problem you want to address.
• Provide guidance and support: If you’re using worksheets with children or students, offer guidance and support as they work through the problems. Encourage them to ask questions and provide explanations when needed.
• Encourage reflection and self-assessment: After completing a worksheet, encourage reflection on the problem-solving process. Ask questions like, “What did you learn from this exercise?” or “How could you apply these problem-solving skills in other situations?”

Incorporating Problem Solving Worksheets in Social Emotional Learning

Problem solving worksheets can be integrated into various aspects of social emotional learning:

• Integrating worksheets into SEL curriculum: Teachers and educators can incorporate problem solving worksheets into their SEL curriculum to enhance students’ problem-solving skills and promote responsible decision-making.
• Using worksheets in individual therapy sessions: Speech Language Pathologists and therapists can utilize problem solving worksheets in individual therapy sessions to help clients develop their problem-solving abilities and improve their social emotional well-being.
• Engaging students in group activities with worksheets: Group activities that involve problem solving worksheets can foster collaboration, communication, and teamwork among students, enhancing their social and emotional skills.

Problem solving skills are essential for personal growth and success. By developing these skills, we become better equipped to navigate challenges, make informed decisions, and achieve our goals. Free problem solving worksheets offer practical tools that can enhance our problem-solving abilities and promote social emotional learning.

So, why not start incorporating free problem solving worksheets into your daily practice? Start your EverydaySpeech Free trial today and explore a wide range of problem solving worksheets and other social emotional learning resources. Take the first step towards unlocking your problem-solving potential and embark on a journey of personal growth and success!

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Table of Contents

Problem Solving Worksheet 

The contents of this article are fact-based except otherwise stated within the article.

Dr Sabina Alispahic, PhD, is a psychologist and gestalt psychotherapist with expertise in clinical and health psychology. 

Dr Sabina Alispahic’s Highlights:

• Associate Professor at the University of Sarajevo for the past 12 years
• PhD in psychology at the University of Zagreb
• European Certificate of Psychotherapy

Professional experience

Dr Alispahic pioneered innovative teaching methods as an associate professor of clinical and health psychology, inspiring a new generation of mental health professionals while contributing to the field for over 12 years. Also, she empowered individuals across the globe as an online psychotherapist, delivering life-changing therapy and earning a reputation for compassionate care and exceptional results. She has demonstrated expertise in a range of therapeutic approaches (CBT, ACT, Gestalt, mindfulness, and family constellations).

Certifications

European Certificate of Psychotherapy (Education in Gestalt Psychotherapy Training of the Malta Institute)

Eight-week stress reduction mindfulness programme, Society of Psychologists in the Federation of Bosnia and Herzegovina

2009-2013 University of Zagreb, Faculty of Philosophy, Postgraduate Doctoral Studies in Psychology

2004-2008 University of Sarajevo, Faculty of Philosophy, Master Studies, Department of Psychology

Publications

Alispahic. S. (2021). Selected topics from psychotherapy Sarajevo: TDP.

Alispahic. S. (2020). Online psychotherapy. Handbook for psychotherapists and clients Sarajevo: TDP.

Alispahic, S., and Godinjak, A. (2018). (R)evolution of the doctor-patient relationship. Sarajevo: TDP.

Alispahic, S. (2016). The psychology of pain Sarajevo: Faculty of Philosophy (e-publication, Bosnian language): https://ebooks.ff.unsa.ba/index.php/ebooks_ffunsa/catalog/book/29

Book chapters

Alispahic, S. (2018). Psychological Theory and Therapy of Traumatic Memory In: A. Hamburger (ur.), Trauma, Trust, and Memory: Social Trauma and Reconciliation in Psychoanalysis, Psychotherapy, and Cultural Memory, 23-35. London and New York: Routledge, Taylor & Francis Group.

Link: https://www.taylorfrancis.com/chapters/edit/10.4324/9781003076247-4/psychological-theory-therapy-traumatic-memory-sabina-alispahić

Markovic Pavlovic, M., Alispahic, S., and Dautbegovic, A. (2015). Psychology of Nonkilling in Bosnia-Herzegovina. Knowledge and Attitudes of Students Towards Nonkilling Culture. In: R. Bahtijaragic i J. E. Pim (ur.), Nonkilling Balkans, 171-183. Honolulu: Centre for Global Nonkilling, and Sarajevo: Faculty of Philosophy.

Link: http://nonkilling.org/pdf/nkbalkans.pdf

Alispahic, S., & Alispahic, B. (2021). Definition of police psychology: The role of psychologists in the police. Technium Soc. Sci. J., 17 , 235-244.

Link: https://techniumscience.com/index.php/socialsciences/article/view/2678

Alispahic, S., Hasanbegovic-Anic, E., & Tuce, Đ. (2021). Big Five Personality Traits as Predictors of Mindfulness: A Study on a Bosnian Sample. Epiphany , 14 (1), 146-155.

Link: http://epiphany.ius.edu.ba/index.php/epiphany/article/view/357

Alispahic, S. & Hodžić Küreç, A. (2021). How does yoga affect health?  Yoga teachers’ experiences. International Scientific Journal of Kinesiology, Vol. 12 , 2, 135-140. 

Link: https://www.researchgate.net/profile/Sabina-Alispahic/publication/349140097_How_does_yoga_affect_health_Yoga_teachers_experiences/links/60226c87a6fdcc37a812def3/How-does-yoga-affect-health-Yoga-teachers-experiences.pdf

Hasanbegovic-Anic, E., Sandic, A., and Alispahic, S. (2018). Prevention of substance abuse in children and adolescents: an evidence-based practice approach. Epiphany , 11 (1), 11-30. 

Link: http://epiphany.ius.edu.ba/index.php/epiphany/article/view/280

Alispahic, S. and Hasanbegovic-Anic, E. (2017). Mindfulness: Age and Gender Differences in a Bosnian Sample. Psychological Thought, Vol. 10 (1), 155–166. 

Link: https://www.researchgate.net/publication/316560770_Mindfulness_Age_and_Gender_Differences_on_a_Bosnian_Sample

Hadziahmetovic, N., Alispahic, S., Tuce, Đ., i Hasanbegovic-Anic, E. (2016). Therapist interpersonal style and therapy benefit as determinants of client personality self-reports in Bosnia and Herzegovina. Vojnosanit Pregl, 73 (2): 135–145. 

Link: https://www.researchgate.net/publication/288178501_Therapist%27s_interpersonal_style_and_therapy_benefit_as_the_determinants_of_personality_self-reports_in_clients

Alispahic, S., Hasanbegovic-Anic, E., Tuce, Đ., Hadziahmetovic, N., Sandic, A. (2014). Characteristics of Patients Involved in Psychotherapy in Bosnia and Herzegovina. Journal of Health Sciences , 4 (1): 4-6. 

Link: https://www.jhsci.ba/ojs/index.php/jhsci/article/view/142

Alispahic, S. (2013). Motivational function of plans and goals. Psychological Thought, Vol. 6 (2), 96–203.

Link: https://www.researchgate.net/publication/258225796_Motivational_Function_of_Plans_and_Goals

Professional profiles

ResearchGate: https://www.researchgate.net/profile/Sabina-Alispahic

Google Scholar: https://scholar.google.com/citations?hl=hr&user=TnYiVK0AAAAJ

LinkedIn: https://www.linkedin.com/in/sabina-alispahić/

Reviewer bio

What is the theory behind this worksheet?

Problem-solving is the process of defining a problem, identifying its root cause, prioritizing and selecting potential solutions and implementing the chosen solution.

The underlying theories behind this worksheet include the principles of cognitive-behavioral theories and problem-solving theories. The relevant therapies may include:

• Cognitive behavioral therapy- is commonly used to address cognitive distortions and improve problem-solving abilities.
• Solution-focused brief therapy- focuses on the solutions rather than on problems and can be used to identify and work towards achievable goals.

How will this worksheet help you?

This worksheet is designed to help individuals to guide them through a structured process of identifying, analyzing, and resolving problems.

How should you use this worksheet?

Individuals can use this worksheet as a practical tool to enhance problem-solving skills and empower them to confidently approach challenges.

Was this helpful?

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Multi-Step Word Problems worksheets are an essential tool for teachers looking to challenge their students in the realm of Math. These worksheets provide a variety of Math Word Problems that require students to use critical thinking and problem-solving skills to find the solution. By incorporating multiple steps, these worksheets help students develop a deeper understanding of mathematical concepts and improve their ability to apply these concepts in real-world situations. Teachers can use these worksheets to create engaging and interactive lessons, allowing students to work individually or in groups to solve the problems. With a wide range of topics and difficulty levels, Multi-Step Word Problems worksheets cater to the diverse needs of students and can be easily adapted to suit different grade levels.

Quizizz is an excellent platform for teachers to access a vast library of worksheets, including Multi-Step Word Problems worksheets, and other valuable resources for teaching Math. With Quizizz, teachers can create customized quizzes and interactive lessons that incorporate Math Word Problems, allowing students to practice and improve their problem-solving skills. The platform also offers various features such as real-time feedback, progress tracking, and gamification elements, making learning Math more engaging and enjoyable for students. Teachers can easily integrate Quizizz into their lesson plans, ensuring that students receive a comprehensive and well-rounded education in Math. By utilizing Quizizz and its extensive collection of worksheets, teachers can effectively teach Math Word Problems and help their students excel in this crucial subject.

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Primary Grade Challenge Math by Edward Zaccaro

A good book on problem solving with very varied word problems and strategies on how to solve problems. Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division. Each chapter’s questions are broken down into four levels: easy, somewhat challenging, challenging, and very challenging.

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Team Building Exercises – Problem Solving and Decision Making

Fun ways to turn problems into opportunities.

By the Mind Tools Content Team

Whether there's a complex project looming or your team members just want to get better at dealing with day-to-day issues, your people can achieve much more when they solve problems and make decisions together.

By developing their problem-solving skills, you can improve their ability to get to the bottom of complex situations. And by refining their decision-making skills, you can help them work together maturely, use different thinking styles, and commit collectively to decisions.

In this article, we'll look at three team-building exercises that you can use to improve problem solving and decision making in a new or established team.

Exercises to Build Decision-Making and Problem-Solving Skills

Use the following exercises to help your team members solve problems and make decisions together more effectively.

Exercise 1: Lost at Sea*

In this activity, participants must pretend that they've been shipwrecked and are stranded in a lifeboat. Each team has a box of matches, and a number of items that they've salvaged from the sinking ship. Members must agree which items are most important for their survival.

Download and print our team-building exercises worksheet to help you with this exercise.

This activity builds problem-solving skills as team members analyze information, negotiate and cooperate with one another. It also encourages them to listen and to think about the way they make decisions.

What You'll Need

• Up to five people in each group.
• A large, private room.
• A "lost at sea" ranking chart for each team member. This should comprise six columns. The first simply lists each item (see below). The second is empty so that each team member can rank the items. The third is for group rankings. The fourth is for the "correct" rankings, which are revealed at the end of the exercise. And the fifth and sixth are for the team to enter the difference between their individual and correct score, and the team and correct rankings, respectively.
• The items to be ranked are: a mosquito net, a can of petrol, a water container, a shaving mirror, a sextant, emergency rations, a sea chart, a floating seat or cushion, a rope, some chocolate bars, a waterproof sheet, a fishing rod, shark repellent, a bottle of rum, and a VHF radio. These can be listed in the ranking chart or displayed on a whiteboard, or both.
• The experience can be made more fun by having some lost-at-sea props in the room.

Flexible, but normally between 25 and 40 minutes.

Instructions

• Divide participants into their teams, and provide everyone with a ranking sheet.
• Ask team members to take 10 minutes on their own to rank the items in order of importance. They should do this in the second column of their sheet.
• Give the teams a further 10 minutes to confer and decide on their group rankings. Once agreed, they should list them in the third column of their sheets.
• Ask each group to compare their individual rankings with their collective ones, and consider why any scores differ. Did anyone change their mind about their own rankings during the team discussions? How much were people influenced by the group conversation?
• Now read out the "correct" order, collated by the experts at the US Coast Guard (from most to least important): - Shaving mirror. (One of your most powerful tools, because you can use it to signal your location by reflecting the sun.) - Can of petrol. (Again, potentially vital for signaling as petrol floats on water and can be lit by your matches.) - Water container. (Essential for collecting water to restore your lost fluids.) -Emergency rations. (Valuable for basic food intake.) - Plastic sheet. (Could be used for shelter, or to collect rainwater.) -Chocolate bars. (A handy food supply.) - Fishing rod. (Potentially useful, but there is no guarantee that you're able to catch fish. Could also feasibly double as a tent pole.) - Rope. (Handy for tying equipment together, but not necessarily vital for survival.) - Floating seat or cushion. (Useful as a life preserver.) - Shark repellent. (Potentially important when in the water.) - Bottle of rum. (Could be useful as an antiseptic for treating injuries, but will only dehydrate you if you drink it.) - Radio. (Chances are that you're out of range of any signal, anyway.) - Sea chart. (Worthless without navigational equipment.) - Mosquito net. (Assuming that you've been shipwrecked in the Atlantic, where there are no mosquitoes, this is pretty much useless.) - Sextant. (Impractical without relevant tables or a chronometer.)

Advice for the Facilitator

The ideal scenario is for teams to arrive at a consensus decision where everyone's opinion is heard. However, that doesn't always happen naturally: assertive people tend to get the most attention. Less forthright team members can often feel intimidated and don't always speak up, particularly when their ideas are different from the popular view. Where discussions are one-sided, draw quieter people in so that everyone is involved, but explain why you're doing this, so that people learn from it.

You can use the Stepladder Technique when team discussion is unbalanced. Here, ask each team member to think about the problem individually and, one at a time, introduce new ideas to an appointed group leader – without knowing what ideas have already been discussed. After the first two people present their ideas, they discuss them together. Then the leader adds a third person, who presents his or her ideas before hearing the previous input. This cycle of presentation and discussion continues until the whole team has had a chance to voice their opinions.

After everyone has finished the exercise, invite your teams to evaluate the process to draw out their experiences. For example, ask them what the main differences between individual, team and official rankings were, and why. This will provoke discussion about how teams arrive at decisions, which will make people think about the skills they must use in future team scenarios, such as listening , negotiating and decision-making skills, as well as creativity skills for thinking "outside the box."

A common issue that arises in team decision making is groupthink . This can happen when a group places a desire for mutual harmony above a desire to reach the right decision, which prevents people from fully exploring alternative solutions.

If there are frequent unanimous decisions in any of your exercises, groupthink may be an issue. Suggest that teams investigate new ways to encourage members to discuss their views, or to share them anonymously.

Exercise 2: The Great Egg Drop*

In this classic (though sometimes messy!) game, teams must work together to build a container to protect an egg, which is dropped from a height. Before the egg drop, groups must deliver presentations on their solutions, how they arrived at them, and why they believe they will succeed.

This fun game develops problem-solving and decision-making skills. Team members have to choose the best course of action through negotiation and creative thinking.

• Ideally at least six people in each team.
• Raw eggs – one for each group, plus some reserves in case of accidents!
• Materials for creating the packaging, such as cardboard, tape, elastic bands, plastic bottles, plastic bags, straws, and scissors.
• Aprons to protect clothes, paper towels for cleaning up, and paper table cloths, if necessary.
• Somewhere – ideally outside – that you can drop the eggs from. (If there is nowhere appropriate, you could use a step ladder or equivalent.)
• Around 15 to 30 minutes to create the packages.
• Approximately 15 minutes to prepare a one-minute presentation.
• Enough time for the presentations and feedback (this will depend on the number of teams).
• Time to demonstrate the egg "flight."
• Put people into teams, and ask each to build a package that can protect an egg dropped from a specified height (say, two-and-a-half meters) with the provided materials.
• Each team must agree on a nominated speaker, or speakers, for their presentation.
• Once all teams have presented, they must drop their eggs, assess whether the eggs have survived intact, and discuss what they have learned.

When teams are making their decisions, the more good options they consider, the more effective their final decision is likely to be. Encourage your groups to look at the situation from different angles, so that they make the best decision possible. If people are struggling, get them to brainstorm – this is probably the most popular method of generating ideas within a team.

Ask the teams to explore how they arrived at their decisions, to get them thinking about how to improve this process in the future. You can ask them questions such as:

• Did the groups take a vote, or were members swayed by one dominant individual?
• How did the teams decide to divide up responsibilities? Was it based on people's expertise or experience?
• Did everyone do the job they volunteered for?
• Was there a person who assumed the role of "leader"?
• How did team members create and deliver the presentation, and was this an individual or group effort?

Exercise 3: Create Your Own*

In this exercise, teams must create their own, brand new, problem-solving activity.

This game encourages participants to think about the problem-solving process. It builds skills such as creativity, negotiation and decision making, as well as communication and time management. After the activity, teams should be better equipped to work together, and to think on their feet.

• Ideally four or five people in each team.
• Paper, pens and flip charts.

Around one hour.

• As the participants arrive, you announce that, rather than spending an hour on a problem-solving team-building activity, they must design an original one of their own.
• Divide participants into teams and tell them that they have to create a new problem-solving team-building activity that will work well in their organization. The activity must not be one that they have already participated in or heard of.
• After an hour, each team must present their new activity to everyone else, and outline its key benefits.

There are four basic steps in problem solving : defining the problem, generating solutions, evaluating and selecting solutions, and implementing solutions. Help your team to think creatively at each stage by getting them to consider a wide range of options. If ideas run dry, introduce an alternative brainstorming technique, such as brainwriting . This allows your people to develop one others' ideas, while everyone has an equal chance to contribute.

After the presentations, encourage teams to discuss the different decision-making processes they followed. You might ask them how they communicated and managed their time . Another question could be about how they kept their discussion focused. And to round up, you might ask them whether they would have changed their approach after hearing the other teams' presentations.

Successful decision making and problem solving are at the heart of all effective teams. While teams are ultimately led by their managers, the most effective ones foster these skills at all levels.

The exercises in this article show how you can encourage teams to develop their creative thinking, leadership , and communication skills , while building group cooperation and consensus.

* Original source unknown. Please let us know if you know the original source.

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Problem Solving Worksheets for Adults (7)

As a BetterHelp affiliate, we may receive compensation from BetterHelp if you purchase products or services through the links provided.

The Optimistminds editorial team is made up of psychologists, psychiatrists and mental health professionals. Each article is written by a team member with exposure to and experience in the subject matter.  The article then gets reviewed by a more senior editorial member. This is someone with extensive knowledge of the subject matter and highly cited published material.

This page provides you with problem-solving worksheets for adults. Problem-solving worksheets for adults aim to help adults identify and resolve their conflicts with effective problem-solving strategies.

These worksheets aid adults recognize different problem-solving skills and strategies to use them for dealing with unpleasant emotions and distressing events. 

Some of these problem-solving worksheets have been created by us while some of them have been curated from reputable third-party websites after reviewing relevant content in detail.

Problem Solving Worksheet for Adults- Identifying Problem-Solving Skills

Problem-solving is defined as the application of certain skills and strategies to resolve the problems.

It is the process of identifying solutions to specific problems either they are simple, difficult or complex. 

Problem-solving is done using problem-solving skills.

Problem-solving skills are the abilities and skills of an individual the enable him to resolve the conflicts efficiently and timely without any hindrance.

These skills help the individual to identify the problems, define them, think of all the possible solutions to the problem, selecting the most effective problem resolution strategy an implementing it to solve the problem efficiently. 

Some common problem-solving skills include research, decision-making, communication, analysis, dependability, coordination, understanding, active listening and so forth. 

The problem-solving process requires two types of mental skills. These are analytical and creative skills.

Analytical skills are based on logical thinking and include ordering, comparing, contrasting, evaluating and selecting.

On the other hand, creative skills refer to the ability to think of various ways of resolving a single problem.

Analytical skills are more beneficial and effective. 

Problem Solving Worksheet for Adults- Effective Problem Resolution Plan

Problem-solving is referred to as the process of identifying the problem, identifying the problem, finding alternative solutions to the problem, choosing the best and effective solution for the problem and implementing that strategy for resolving the problem efficiently.  

The effective problem-solving process consists of seven major steps.

The first step consists of identifying the problem, the second steps consist of analyzing the problem deeply to understand it and be able to define it, the third step involves enlisting all the possible solutions to the problem.

The fourth step refers to the evaluation of each solution on the basis of its feasibility, consequences, and effects.

The fifth step deals with selecting the best of all these solutions to the problem. The sixth step involves documentation or planning of how to resolve the problem using this particular solution.

The last step refers to the implementation of the solution or in other words that strategy to resolve the problem. 

These were the steps for resolving the conflict efficiently.

Now if we talk about problem-solving strategies, there are various ways of dealing with a single issue.

The five most common methods of resolving problems include trial and error method, difference reduction method, means-end analysis, working backward method and analogies.

Problem Solving Worksheet for Adults- Problem-Solving on the Basis of Outcomes

Problem-solving can be done in various ways. Before the individual works on resolving the problem, it is essential to understand the nature of the problem.

There are many kinds of problems.

Some common types of problems include constrained problems, ambiguous problems, predictable problems, known unknowns, unknown unknowns, political, technical, root cause analysis, strategy, tactics, decision-making, improvement, and reinvention.

Problems can be solved in a number of ways.

Some common problem-solving strategies include trial and error, using algorithms and using heuristics.

A simple problem can be solved easily but for the big, complex problems it is advisable to break the problem into smaller parts and them resolve those pasts one by one to solve the problem as a whole. 

Some effective problem-solving strategies include identifying the problem and understand it deeply to resolve it, breaking the probes into small parts and dealing with each art one by one, working on a timeline, using your own network or available solutions to the problem, avoid comparing your problems to other’s, taking a break if your feel exhausted, finding an effective solution, and keeping it and learning from every mistake.

Problem Solving Worksheet for Adults- Problem Solving Skills Worksheet

Problem-solving skills worksheet is a very brief, simple and easy to understand worksheet for enabling the individuals to effectively resolve their problems.

The problem-solving skills worksheet allows the individuals to identify the problem, understand the nature of the problem and analyze the problem deeply.

It enables individuals to determine the desired outcomes of the problem resolution.

Thee worksheet enables the individuals to think of some of the possible solutions to the problem and determine the effectiveness of each solution according to the outcomes each of them would produce.

Based on these outcomes, the individuals select the best resolution of the problem and work upon it to resolve their issue.

This worksheet is very simple and at the same time very effective.

You can download it in the form of pdf from here .

Problem Solving Worksheet for Adults- Problem Solving Packet

The problem-solving packet, offered by the therapistaid.com website, allows effective resolution of the problem.

This packet consists of five pages with each page covering one step to the problem-solving method.

The first page deals with defining the problem, the second page deals with finding solutions to the problem, the third page directs the individuals to select the best solution to the problem, the forth page enables the individuals to implement the solution to resolve their issue and the last page allows the individual to analyze the outcomes, effects, effectiveness, and efficiency of the solution they applied to resolve their issue.

These five pages of the problem-solving packet are amazing, detailed, effective and very helpful for the individual to help them improve their problem-solving abilities.

This worksheet is easily accessible on the internet.

You can download it in the form of pdf from here . 

Problem Solving Worksheet for Adults- Problem Solving Worksheet

The problem-solving worksheet is a very helpful worksheet that enables the individual to identify their problems, understand them and implement effective strategies for dealing with their problems.

This worksheet helps individuals resolve their problems in eight steps. Each step is complemented with a very detailed description of each step.

The individuals are directed to identify their problems, possible solutions of their problems, recognizing pros and cons of each possible solution, selection of the solution that produces desirable outcomes, making a framework to implement that solution, following the framework, reviewing the solution if it proved to be successful in resolving the problem or not and repeating the whole process again if the solution did not work out. 

This worksheet can be accessed from the internet easily.

To download it in the form of pdf, click here .

Problem Solving Worksheet for Adults- Problem Solving

The worksheet, problem-solving, consists of two pages. It is very engaging and at the same time an effective worksheet.

Thie worksheet allows individuals to successfully resolve their problems in five steps.

The worksheet enables the individuals to identify and define their problems in detail, considering the causes of problems and the goals related to resolving this problem.

Then the individuals are directed to think of all the possible solutions to their problem and select the preferred solutions on the basis of the feasibility of the solutions and other factors.

After this, the individuals are asked to identify the pros and cons of each solution followed by the selection and planning of the best solution.

Next, the individuals are directed to implement the solutions and review their effectiveness. 

To download this worksheet in the form of pdf, click here . 

This page provided you with some of the most effective problem-solving worksheets for adults .

These worksheets aimed to help adults identify the problems they are facing and enabled them to solve those problems mindfully, thoughtfully and effectively.

Some of these problems solving worksheets for adults were created by us while some of them were curated from reputable third-party websites after reviewing relevant content from various sites.

If you have any queries or questions regarding these worksheets, let us know through your comments, we will be glad to assist you. 

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Related posts, building resilience: psychological strategies for helping children cope with challenges, counseling compass: mapping your route to emotional well-being, how to deal with political anxiety in an election year.

10 Helpful Worksheet Ideas for Primary School Math Lessons

M athematics is a fundamental subject that shapes the way children think and analyze the world. At the primary school level, laying a strong foundation is crucial. While hands-on activities, digital tools, and interactive discussions play significant roles in learning, worksheets remain an essential tool for reinforcing concepts, practicing skills, and assessing understanding. Here’s a look at some helpful worksheets for primary school math lessons.

Comparison Chart Worksheets

Comparison charts provide a visual means for primary school students to grasp relationships between numbers or concepts. They are easy to make at www.storyboardthat.com/create/comparison-chart-template , and here is how they can be used:

• Quantity Comparison: Charts might display two sets, like apples vs. bananas, prompting students to determine which set is larger.
• Attribute Comparison: These compare attributes, such as different shapes detailing their number of sides and characteristics.
• Number Line Comparisons: These help students understand number magnitude by placing numbers on a line to visualize their relative sizes.
• Venn Diagrams: Introduced in later primary grades, these diagrams help students compare and contrast two sets of items or concepts.
• Weather Charts: By comparing weather on different days, students can learn about temperature fluctuations and patterns.

Number Recognition and Counting Worksheets

For young learners, recognizing numbers and counting is the first step into the world of mathematics. Worksheets can offer:

• Number Tracing: Allows students to familiarize themselves with how each number is formed.
• Count and Circle: Images are presented, and students have to count and circle the correct number.
• Missing Numbers: Sequences with missing numbers that students must fill in to practice counting forward and backward.

Basic Arithmetic Worksheets

Once students are familiar with numbers, they can start simple arithmetic. 

• Addition and Subtraction within 10 or 20: Using visual aids like number lines, counters, or pictures can be beneficial.
• Word Problems: Simple real-life scenarios can help students relate math to their daily lives.
• Skip Counting: Worksheets focused on counting by 2s, 5s, or 10s.

Geometry and Shape Worksheets

Geometry offers a wonderful opportunity to relate math to the tangible world.

• Shape Identification: Recognizing and naming basic shapes such as squares, circles, triangles, etc.
• Comparing Shapes: Worksheets that help students identify differences and similarities between shapes.
• Pattern Recognition: Repeating shapes in patterns and asking students to determine the next shape in the sequence.

Measurement Worksheets

Measurement is another area where real-life application and math converge.

• Length and Height: Comparing two or more objects and determining which is longer or shorter.
• Weight: Lighter vs. heavier worksheets using balancing scales as visuals.
• Time: Reading clocks, days of the week, and understanding the calendar.

Data Handling Worksheets

Even at a primary level, students can start to understand basic data representation.

• Tally Marks: Using tally marks to represent data and counting them.
• Simple Bar Graphs: Interpreting and drawing bar graphs based on given data.
• Pictographs: Using pictures to represent data, which can be both fun and informative.

Place Value Worksheets

Understanding the value of each digit in a number is fundamental in primary math.

• Identifying Place Values: Recognizing units, tens, hundreds, etc., in a given number.
• Expanding Numbers: Breaking down numbers into their place value components, such as understanding 243 as 200 + 40 + 3.
• Comparing Numbers: Using greater than, less than, or equal to symbols to compare two numbers based on their place values.

Fraction Worksheets

Simple fraction concepts can be introduced at the primary level.

• Identifying Fractions: Recognizing half, quarter, third, etc., of shapes or sets.
• Comparing Fractions: Using visual aids like pie charts or shaded drawings to compare fractions.
• Simple Fraction Addition: Adding fractions with the same denominator using visual aids.

Money and Real-Life Application Worksheets

Understanding money is both practical and a great way to apply arithmetic.

• Identifying Coins and Notes: Recognizing different denominations.
• Simple Transactions: Calculating change, adding up costs, or determining if there’s enough money to buy certain items.
• Word Problems with Money: Real-life scenarios involving buying, selling, and saving.

Logic and Problem-Solving Worksheets

Even young students can hone their problem-solving skills with appropriate challenges.

• Sequences and Patterns: Predicting the next item in a sequence or recognizing a pattern.
• Logical Reasoning: Simple puzzles or riddles that require students to think critically.
• Story Problems: Reading a short story and solving a math-related problem based on the context.

Worksheets allow students to practice at their own pace, offer teachers a tool for assessment, and provide parents with a glimpse into their child’s learning progression. While digital tools and interactive activities are gaining prominence in education, the significance of worksheets remains undiminished. They are versatile and accessible and, when designed creatively, can make math engaging and fun for young learners.

The post 10 Helpful Worksheet Ideas for Primary School Math Lessons appeared first on Mom and More .

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PEMDAS Problems Worksheets 5th Grade

Welcome to our PEMDAS Problems page. Here you will find our range of Math sheets which will help your child learn to use parentheses (brackets) and exponents (powers). There are also lots of sheets to help you practice and master PEMDAS.

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Using Parentheses and Exponents Worksheets

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PEMDAS Problems Online Quiz

Pemdas problems worksheets and help.

Here you will find a range of 5th grade math sheets which will help your child learn to use parentheses and exponents, and practice PEMDAS with a range of equations.

The sheets are arranged in order of difficulty with the easiest sheets first.

Using these sheets will help your child to:

• learn to use parentheses (brackets) and understand how they work;
• learn to use exponents (powers) and understand how they work.
• practice using PEMDAS to solve a range of different problems involving parentheses, exponents, as well as addition, subtraction, multiplication and division.

These pemdas problems are aimed at a 5th and 6th grade level.

PEMDAS (sometimes referred to as PEMDAS, BEDMAS or BODMAS) is a mathematical acronym to help you understand how calculations work.

The acronym refers to the order in which any calculation shold be done, and is typically introduced at around the 5th grade level.

The acronym stands for the following:

• P = Parentheses (Brackets)
• E = Exponents
• D = Division
• M = Multiplication
• A = Addition
• S = Subtraction

One popular way to remember the PEMDAS rule is the saying:

'Please Excuse My Dear Aunt Sally'.

However, the PEMDAS rule is not quite so straightforward as it seems.

If you would like help using this rule and looking at some worked examples, follow the link below.

• PEMDAS Rule Support Page

The sheets below do use the PEDMAS rule, but it is not necessary for you to be familiar with it in order to complete the worksheets.

The worksheets below gradually introduce parentheses and exponents in a simple way so that your child can (hopefully) quickly grasp these concepts before they start solving trickier pemdas problems.

Pemdas Problems - Using Parentheses (Brackets) Worksheets

• Using Parentheses Sheet 5:1
• PDF version
• Using Parentheses Sheet 5:2

Pemdas Problems - Using Exponents (Powers) Worksheets

• Using Exponents Sheet 5:1
• Using Exponents Sheet 5:2

Using Parentheses & Exponents Worksheets

• Using Parentheses & Exponents Sheet 5:1
• Using Parentheses & Exponents Sheet 5:2

Using Parentheses and Exponents Walkthrough Video

This short video walkthrough shows several problems from our Using Parentheses & Exponents Sheet 5:1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

PEMDAS Problems - Order of Operations Worksheets

The sheets below use PEMDAS to work out a range of calculations.

The first series of sheets are a great resource for students who are just learning the rule.

The second series of sheets are good for stretching and challenging more able students.

Pemdas Problems - Order of Operations worksheets

• Order of Operations Sheet 1
• Order of Operations Sheet 2
• Order of Operations Sheet 3

PEMDAS Challenges Worksheets

• PEMDAS Challenges Sheet 1
• PEMDAS Challenges Sheet 2
• PEMDAS Challenges Sheet 3

PEMDAS RULE GAME

The PEMDAS rule game is a game which involves using brackes, multiplication and addition or subtraction.

The aim of the game is to place digit cards in the pemdas game boards to get as close to the given target as possible.

PEMDAS GAME

Grade: 5th Grade + Number of players: any. Learning skills: learning PEMDAS and reasoning skills.

• Pemdas Game Board: addition and multiplication
• Pemdas Game Board: subtraction and multiplication
• Instructions
• Digit Cards 0-9 Sheet 1
• Digit Cards 0-9 Sheet 2

Looking for something harder?

The sheets in this section are at a harder level than those on this page.

• 6th Grade Order of Operations

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Fifth Grade Number Worksheets

Here you will find a range of Free Printable 5th Grade Number Worksheets.

• use place value with up to 3 decimal places;
• understand how to use exponents (powers) of a number;
• understand and use parentheses (brackets);
• understand and use multiples and factors;
• extend their knowledge of prime and composite (non-prime) numbers up to 100;
• know and be able to use the PEMDAS (or PEDMAS) rule.

All the Free 5th Grade Math Worksheets in this section are informed by the Elementary Math Benchmarks for 5th Grade.

• 5th Grade Place Value to 3dp
• Balancing Math Equations

Ordering Large Numbers and Decimals to 3dp

The sheets in this section involve ordering lists of decimals to 3 decimal places.

There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.

Each sheet is carefully graded and comes with an answer sheet provided.

• Ordering Large Numbers up to 100 million
• Ordering Decimals to 3dp

Fifth Grade Math Games

Here you will find a range of free printable 5th Grade Math games.

All children like to play Math games, and you will find a good range of Grade 5 Math Games here for your child to play and enjoy.

The following games involve different 5th Grade Math activities which you and your child can enjoy together.

• Math Games 5th Grade

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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at using PEMDAS to solve a range of math problems here.

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Free Problem Statement Templates: All Formats

By Kate Eby | March 4, 2024

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We've collected the top problem statement templates to help you identify and articulate challenges clearly and concisely in any business context. Download any of these free templates that align with your needs, and customize it for your organization.

On this page, you’ll find a  customer problem statement template , a  problem and solution slide template , a  problem statement document template , and more. You’ll also find information on different  types of problem statement templates and related  problem-solving tools .

5 Ws Problem Statement Template

Download a 5 Ws Problem Statement Template for

Microsoft Word | Adobe PDF | PowerPoint | Google Slides

When to Use This Template:  Use this 5 Ws problem statement template to create a methodical breakdown of issues at team meetings or brainstorming sessions. Ensure that nothing is overlooked by answering who, what, when, where, and why questions about a problem. By doing so, you can create a clear and concise problem statement.

Notable Template Features: Using five key questions to explore a problem fosters a comprehensive understanding of the issue while helping to narrow the focus of your final problem statement. Each segment of the template is color-coded and provides bullet points to delve into specifics, such as who is affected and the problem's scope and significance.

Customer Problem Statement Template

Download a Customer Problem Statement Template for

When to Use This Template:  This template provides a structured approach to translating client issues into an effective problem statement. It is especially useful for customer experience teams, marketing personnel, and product developers who are tasked with turning customer feedback into actionable insights.

Notable Template Features: This template takes you through the steps of clarifying customer issues and perspectives to help teams find customer-focused solutions. Download the template in PowerPoint or Google Slides  for presentations, or try the Microsoft Word or Adobe PDF versions to create a printable worksheet.

Three-Part Problem Statement Slide Template

Download a Three-Part Problem Statement Slide Template for

PowerPoint | Google Slides

When to Use This Template: Use this slide template to present key points to stakeholders in project reviews or strategic planning sessions. Teams can also use this template to facilitate problem-solving meetings.

Notable Template Features:  This template guides the audience from problem to solution to result, promoting a thorough understanding of the problem’s context. Each section includes bullet points to organize and present complex details in a simple yet engaging format.

Single-Problem Statement and Solution Slide Template

Download a Single-Problem Statement and Solution Slide Template for

When to Use This Template: This problem statement slide template allows you to clearly outline a problem and propose a viable solution in one visually dynamic slide, making it a perfect addition to business proposals, project pitches, and strategy meetings.

Notable Template Features:  This slide template separates the problem on the left from the solution on the right, using a clear layout and colorful symbols to grab the viewer's attention. This simple design ensures that the audience grasps the core issue quickly, facilitating a focused and efficient discussion.

For more slide template resources like this one, see this collection of free  PowerPoint problem statement templates .

Project Problem Statement Document Template

Download a Project Problem Statement Document Template for

Microsoft Word | Adobe PDF

When to Use This Template: Use this document template to draft a comprehensive problem statement report. The template is best for individuals or teams tasked with in-depth analysis and documentation of business issues, ensuring that they cover all relevant aspects of the problem.

Notable Template Features: This template features a structured outline with labeled sections for documenting the problem statement, background information, impact, and potential solutions. The outline takes readers through a logical progression — from identifying the problem to proposing solutions — for a clear and persuasive presentation.

Problem Statement Worksheet Template

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Excel | Microsoft Word | Adobe PDF

When to Use This Template:  Use this worksheet to create an effective problem statement when starting a new project. The template is particularly useful for project teams that need to align on the specifics of a problem, set measurable goals, and identify obstacles and solutions.

Notable Template Features:  This problem statement worksheet guides you through a step-by-step process to craft a concise and impactful problem statement. The template includes clear sections where you can provide details about the problem, the gap between the current state and the goal, and the people or processes affected. It includes space for setting SMART goals related to the problem, identifying barriers, and formulating a plan to overcome these challenges.

Problem Statement Matrix Template

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When to Use This Template:  This template helps teams and managers prioritize multiple problems. Teams can assess and sort problems based on urgency and potential impact to effectively guide strategic action plans. 

Notable Template Features:  This template organizes essential aspects of each problem into a simple matrix, including a problem statement, priority, visibility, impact, response timeframe, and proposed solutions. The matrix format is useful when you want an overview of problems with key details highlighted.

Types of Problem Statement Templates

Problem statements are used in business settings and academic research to clearly define a problem that needs to be solved. A well-written statement is concise, narrow in focus, and based on evidence. While all problem statements include similar elements, they will vary depending on the context and type of issue. There are many tools that can aid in this process. 

Here’s a closer look at the different types of problem statement templates for project and product management:

Customer Problem Statement Templates

Customer problem statement templates guide you through the process of viewing issues from the customer’s perspective. They provide a structured approach to mapping out the customer journey, pinpointing the underlying cause of problems, and understanding their emotional impacts on customers.

Customer problem statement templates typically organize information into five key elements:  

• I Am: Who is the customer? This could be as broad as a demographic group or as specific as a user persona. Clearly defining your customer sets the foundation for a more targeted analysis.
• I Am Trying To: What is the customer trying to achieve? Articulate the customer's goal or what they hope to accomplish with your product or service. This helps in aligning your solutions with customer needs.
• But: What is getting in their way? Identify the challenges that prevent the customer from achieving their goals. These could be related to product features, service limitations, or external factors.
• Because: What is the root of the issue? Analyze the internal and external factors that contribute to the problem to uncover the underlying causes.
• Which Makes Me Feel: What is the customer's emotional response to this issue? Emotions can affect how customers perceive your product or service. If they're feeling frustration, disappointment, or confusion, they might be less likely to engage positively with your brand or recommend your services to others. Knowing this helps convey the urgency of addressing the problem.

Using a customer problem statement template shifts the focus from internal perceptions of what the problem might be to a clearer understanding of the customer's experience. The process involves gathering and analyzing customer feedback, conducting market research, and possibly engaging directly with customers through interviews or surveys. 

Product Problem Statement Templates

Since having a customer-centric perspective is vital for developing successful products, there is overlap between product and customer problem statement templates. However, understanding customer issues is just one step in the development process. Product teams must consider whether the solutions they come up with will truly benefit the customer, what value a product will bring to the company, what steps are needed to solve the problem, and how to measure success. 

One common structure for product problem statement templates is the 5 Ws framework, which involves answering the following questions:  

• Who: Who is the problem affecting?
• What: What is the unmet need?
• When: When is the problem happening?
• Where: Where is the problem occurring?
• Why: Why is this worth solving?

Some templates might include a sixth question: How are you going to solve the problem?

These templates can help teams identify initial product opportunities, refine product concepts, and diagnose issues in existing products. They help in prioritizing features, making strategic adjustments, and communicating the product vision and challenges internally.

Project Problem Statement Templates

Similar to customer and product templates, project problem statement templates help teams articulate the core issue they aim to address with their project. They are often used at early planning stages to gain clarity and consensus among stakeholders on the project's direction.

A project problem statement template typically includes the following elements:  

• Problem: Clearly define the issue at hand with a precise description of the gap between the current state and the desired state.
• Background: Provide context for the problem by offering insights into its origins and scope. This helps stakeholders understand the complexity and nuances of the issue.
• Relevance: Highlight the significance of the problem, its potential impacts, and why addressing it matters to the organization or stakeholders.
• Objectives: Outline the objectives of the project with SMART goals that guide the project's direction and help in measuring its success.  

Some templates, such as a problem statement worksheet, are designed to help you craft an effective statement, while others are suitable for presentations or reports to stakeholders. For some helpful options, see this collection of free  problem statement slide templates .

Related Problem-Solving Templates

Fully understanding a problem and finding effective solutions requires in-depth analysis. Here is a list of problem-solving templates that can help with that process:

Fishbone Diagram Template

A  fishbone diagram template organizes the causes of a problem into categories, enabling teams to identify, analyze, and address root causes by branching out possible contributing factors from a central problem statement.

8D Report Template

An  8D report template guides teams through a structured eight-step process to identify, correct, and eliminate recurring problems. This problem-solving approach emphasizes root cause analysis and long-term solutions.

A3 Template

An  A3 template offers a concise framework for problem solving, encouraging teams to identify issues, find root causes, and develop solutions on a single A3-sized sheet of paper for clarity and efficiency.

Simple Root Cause Analysis Template

Use our  simple root cause analysis template to map out symptoms, effects, causes, and suggested solutions in a color-coded spreadsheet. Each section includes important details, such as urgency, risks, and success criteria for a systematic approach to analyzing problems.

DMAIC Root Cause Analysis Template

A  DMAIC analysis template outlines a structured, five-phase approach to problem solving

— define, measure, analyze, improve, control — guiding teams through a detailed process to identify problems, analyze causes, and improve processes.

For more problem-solving templates, see this collection of free  root cause analysis templates and  Lean Six Sigma templates .

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Python Practice for Beginners: 15 Hands-On Problems with Solutions

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Want to put your Python skills to the test? Challenge yourself with these 15 Python practice exercises taken directly from our Python courses!

There’s no denying that solving Python exercises is one of the best ways to practice and improve your Python skills . Hands-on engagement with the language is essential for effective learning. This is exactly what this article will help you with: we've curated a diverse set of Python practice exercises tailored specifically for beginners seeking to test their programming skills.

These Python practice exercises cover a spectrum of fundamental concepts, all of which are covered in our Python Data Structures in Practice and Built-in Algorithms in Python courses. Together, both courses add up to 39 hours of content. They contain over 180 exercises for you to hone your Python skills. In fact, the exercises in this article were taken directly from these courses!

In these Python practice exercises, we will use a variety of data structures, including lists, dictionaries, and sets. We’ll also practice basic programming features like functions, loops, and conditionals. Every exercise is followed by a solution and explanation. The proposed solution is not necessarily the only possible answer, so try to find your own alternative solutions. Let’s get right into it!

Python Practice Problem 1: Average Expenses for Each Semester

John has a list of his monthly expenses from last year:

He wants to know his average expenses for each semester. Using a for loop, calculate John’s average expenses for the first semester (January to June) and the second semester (July to December).

Explanation

We initialize two variables, first_semester_total and second_semester_total , to store the total expenses for each semester. Then, we iterate through the monthly_spending list using enumerate() , which provides both the index and the corresponding value in each iteration. If you have never heard of enumerate() before – or if you are unsure about how for loops in Python work – take a look at our article How to Write a for Loop in Python .

Within the loop, we check if the index is less than 6 (January to June); if so, we add the expense to first_semester_total . If the index is greater than 6, we add the expense to second_semester_total .

After iterating through all the months, we calculate the average expenses for each semester by dividing the total expenses by 6 (the number of months in each semester). Finally, we print out the average expenses for each semester.

Python Practice Problem 2: Who Spent More?

John has a friend, Sam, who also kept a list of his expenses from last year:

They want to find out how many months John spent more money than Sam. Use a for loop to compare their expenses for each month. Keep track of the number of months where John spent more money.

We initialize the variable months_john_spent_more with the value zero. Then we use a for loop with range(len()) to iterate over the indices of the john_monthly_spending list.

Within the loop, we compare John's expenses with Sam's expenses for the corresponding month using the index i . If John's expenses are greater than Sam's for a particular month, we increment the months_john_spent_more variable. Finally, we print out the total number of months where John spent more money than Sam.

Python Practice Problem 3: All of Our Friends

Paul and Tina each have a list of their respective friends:

Combine both lists into a single list that contains all of their friends. Don’t include duplicate entries in the resulting list.

There are a few different ways to solve this problem. One option is to use the + operator to concatenate Paul and Tina's friend lists ( paul_friends and tina_friends ). Afterwards, we convert the combined list to a set using set() , and then convert it back to a list using list() . Since sets cannot have duplicate entries, this process guarantees that the resulting list does not hold any duplicates. Finally, we print the resulting combined list of friends.

If you need a refresher on Python sets, check out our in-depth guide to working with sets in Python or find out the difference between Python sets, lists, and tuples .

Python Practice Problem 4: Find the Common Friends

Now, let’s try a different operation. We will start from the same lists of Paul’s and Tina’s friends:

In this exercise, we’ll use a for loop to get a list of their common friends.

For this problem, we use a for loop to iterate through each friend in Paul's list ( paul_friends ). Inside the loop, we check if the current friend is also present in Tina's list ( tina_friends ). If it is, it is added to the common_friends list. This approach guarantees that we test each one of Paul’s friends against each one of Tina’s friends. Finally, we print the resulting list of friends that are common to both Paul and Tina.

Python Practice Problem 5: Find the Basketball Players

You work at a sports club. The following sets contain the names of players registered to play different sports:

How can you obtain a set that includes the players that are only registered to play basketball (i.e. not registered for football or volleyball)?

This type of scenario is exactly where set operations shine. Don’t worry if you never heard about them: we have an article on Python set operations with examples to help get you up to speed.

First, we use the | (union) operator to combine the sets of football and volleyball players into a single set. In the same line, we use the - (difference) operator to subtract this combined set from the set of basketball players. The result is a set containing only the players registered for basketball and not for football or volleyball.

If you prefer, you can also reach the same answer using set methods instead of the operators:

It’s essentially the same operation, so use whichever you think is more readable.

Python Practice Problem 6: Count the Votes

Let’s try counting the number of occurrences in a list. The list below represent the results of a poll where students were asked for their favorite programming language:

Use a dictionary to tally up the votes in the poll.

In this exercise, we utilize a dictionary ( vote_tally ) to count the occurrences of each programming language in the poll results. We iterate through the poll_results list using a for loop; for each language, we check if it already is in the dictionary. If it is, we increment the count; otherwise, we add the language to the dictionary with a starting count of 1. This approach effectively tallies up the votes for each programming language.

If you want to learn more about other ways to work with dictionaries in Python, check out our article on 13 dictionary examples for beginners .

Python Practice Problem 7: Sum the Scores

Three friends are playing a game, where each player has three rounds to score. At the end, the player whose total score (i.e. the sum of each round) is the highest wins. Consider the scores below (formatted as a list of tuples):

Create a dictionary where each player is represented by the dictionary key and the corresponding total score is the dictionary value.

This solution is similar to the previous one. We use a dictionary ( total_scores ) to store the total scores for each player in the game. We iterate through the list of scores using a for loop, extracting the player's name and score from each tuple. For each player, we check if they already exist as a key in the dictionary. If they do, we add the current score to the existing total; otherwise, we create a new key in the dictionary with the initial score. At the end of the for loop, the total score of each player will be stored in the total_scores dictionary, which we at last print.

Python Practice Problem 8: Calculate the Statistics

Given any list of numbers in Python, such as …

 … write a function that returns a tuple containing the list’s maximum value, sum of values, and mean value.

We create a function called calculate_statistics to calculate the required statistics from a list of numbers. This function utilizes a combination of max() , sum() , and len() to obtain these statistics. The results are then returned as a tuple containing the maximum value, the sum of values, and the mean value.

The function is called with the provided list and the results are printed individually.

Python Practice Problem 9: Longest and Shortest Words

Given the list of words below ..

… find the longest and the shortest word in the list.

To find the longest and shortest word in the list, we initialize the variables longest_word and shortest_word as the first word in the list. Then we use a for loop to iterate through the word list. Within the loop, we compare the length of each word with the length of the current longest and shortest words. If a word is longer than the current longest word, it becomes the new longest word; on the other hand, if it's shorter than the current shortest word, it becomes the new shortest word. After iterating through the entire list, the variables longest_word and shortest_word will hold the corresponding words.

There’s a catch, though: what happens if two or more words are the shortest? In that case, since the logic used is to overwrite the shortest_word only if the current word is shorter – but not of equal length – then shortest_word is set to whichever shortest word appears first. The same logic applies to longest_word , too. If you want to set these variables to the shortest/longest word that appears last in the list, you only need to change the comparisons to <= (less or equal than) and >= (greater or equal than), respectively.

If you want to learn more about Python strings and what you can do with them, be sure to check out this overview on Python string methods .

Python Practice Problem 10: Filter a List by Frequency

Given a list of numbers …

… create a new list containing only the numbers that occur at least three times in the list.

Here, we use a for loop to iterate through the number_list . In the loop, we use the count() method to check if the current number occurs at least three times in the number_list . If the condition is met, the number is appended to the filtered_list .

After the loop, the filtered_list contains only numbers that appear three or more times in the original list.

Python Practice Problem 11: The Second-Best Score

You’re given a list of students’ scores in no particular order:

Find the second-highest score in the list.

This one is a breeze if we know about the sort() method for Python lists – we use it here to sort the list of exam results in ascending order. This way, the highest scores come last. Then we only need to access the second to last element in the list (using the index -2 ) to get the second-highest score.

Python Practice Problem 12: Check If a List Is Symmetrical

Given the lists of numbers below …

… create a function that returns whether a list is symmetrical. In this case, a symmetrical list is a list that remains the same after it is reversed – i.e. it’s the same backwards and forwards.

Reversing a list can be achieved by using the reverse() method. In this solution, this is done inside the is_symmetrical function.

To avoid modifying the original list, a copy is created using the copy() method before using reverse() . The reversed list is then compared with the original list to determine if it’s symmetrical.

The remaining code is responsible for passing each list to the is_symmetrical function and printing out the result.

Python Practice Problem 13: Sort By Number of Vowels

Given this list of strings …

… sort the list by the number of vowels in each word. Words with fewer vowels should come first.

Whenever we need to sort values in a custom order, the easiest approach is to create a helper function. In this approach, we pass the helper function to Python’s sorted() function using the key parameter. The sorting logic is defined in the helper function.

In the solution above, the custom function count_vowels uses a for loop to iterate through each character in the word, checking if it is a vowel in a case-insensitive manner. The loop increments the count variable for each vowel found and then returns it. We then simply pass the list of fruits to sorted() , along with the key=count_vowels argument.

Python Practice Problem 14: Sorting a Mixed List

Imagine you have a list with mixed data types: strings, integers, and floats:

Typically, you wouldn’t be able to sort this list, since Python cannot compare strings to numbers. However, writing a custom sorting function can help you sort this list.

Create a function that sorts the mixed list above using the following logic:

• If the element is a string, the length of the string is used for sorting.
• If the element is a number, the number itself is used.

As proposed in the exercise, a custom sorting function named custom_sort is defined to handle the sorting logic. The function checks whether each element is a string or a number using the isinstance() function. If the element is a string, it returns the length of the string for sorting; if it's a number (integer or float), it returns the number itself.

The sorted() function is then used to sort the mixed_list using the logic defined in the custom sorting function.

If you’re having a hard time wrapping your head around custom sort functions, check out this article that details how to write a custom sort function in Python .

Python Practice Problem 15: Filter and Reorder

Given another list of strings, such as the one below ..

.. create a function that does two things: filters out any words with three or fewer characters and sorts the resulting list alphabetically.

Here, we define filter_and_sort , a function that does both proposed tasks.

First, it uses a for loop to filter out words with three or fewer characters, creating a filtered_list . Then, it sorts the filtered list alphabetically using the sorted() function, producing the final sorted_list .

The function returns this sorted list, which we print out.

Want Even More Python Practice Problems?

We hope these exercises have given you a bit of a coding workout. If you’re after more Python practice content, head straight for our courses on Python Data Structures in Practice and Built-in Algorithms in Python , where you can work on exciting practice exercises similar to the ones in this article.

Additionally, you can check out our articles on Python loop practice exercises , Python list exercises , and Python dictionary exercises . Much like this article, they are all targeted towards beginners, so you should feel right at home!

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