problem solving strategies for writing

Collaboration, information literacy, writing process, problem-solving strategies for writers: a review of research.

Traditionally, in U.S. classrooms, the writing process is depicted as a series of linear steps (e.g., prewriting , writing , revising , and editing ). However, since the 1980s the writing process has also been depicted as a problem-solving process. This article traces the evolution of Linda Flower and John Hayes' problem-solving model of the writing process, and it provides you with an opportunity to illustrate your own writing process.

What are Problem Solving Strategies for Writers?

As an alternative to imagining the writing process to be a series of steps or stages that writers work through in linear manner or as a largely mysterious, creative processes informed by embodied knowledge , felt sense , and inner speech, Linda Flower and John Hayes suggested in 1977 that writing should be thought of as a “thinking problem,” a “problem-solving process,” or “cognitive problem solving process”:

“We frequently talk of writing as if it were a series of independent temporally bounded actions (e.g., pre-writing , writing , rewriting ). It is more accurate to see it as a hierarchical set of subproblems arranged under a goal or set of goals. The process then is an iterative one. For each subproblem along the way — whether it is making a logical connection between hazy ideas, or finding a persuasive tone — the writer may draw on a whole repertoire of procedures and heuristics” (Flower & Hayes, 1977, p. 460-461).

Examples of Problem-Solving Strategies

Rhetorical analysis , rhetorical reasoning
Engage in logical reasoning
Engaging in the information literacy perspectives and practices of educated, critical readers
Working with others during the writing process , such as brainstorming ideas together, collaborating on a draft , or writing as part of a team .
Sharing drafts with peers and giving each other constructive feedback . This can help writers see their work from different perspectives and identify areas for improvement that they might have overlooked.
Seeking guidance from more experienced writers or instructors, such as a teacher, tutor, or writing center consultant. This can involve discussing writing challenges, getting feedback on drafts , or learning new writing strategies .
Talking through ideas with others before and during the writing process . This can help writers clarify their thoughts, explore different viewpoints, and generate new ideas.
In group writing projects, members might need to negotiate on various aspects, like the division of tasks, the main argument or focus of the piece, or the style and tone of the writing .
Considering the needs, expectations, and perspectives of the intended readers. This can influence many aspects of the writing, from the overall structure and argument to the choice of language and examples.
Defining what one wants to achieve with a piece of writing, be it a specific grade, clarity of argument , or a certain word count.
Finding ways to stay motivated during the writing process, such as breaking the task into manageable pieces, rewarding oneself after reaching certain milestones, or focusing on the value and relevance of the task.
Managing feelings of frustration, anxiety, or boredom that may arise during the writing process. This might involve taking breaks, practicing mindfulness, or reframing negative thoughts.
Organizing one’s time effectively to meet deadlines and avoid last-minute stress. This might involve creating a writing schedule, setting aside specific times for writing, or using tools like timers or apps to stay focused.
Regularly reflecting on one’s writing process and progress, identifying strengths and areas for improvement, and making adjustments as necessary.
Critically reviewing one’s own writing to identify potential improvements, before getting feedback from others.
Thinking about one’s own thinking or writing process involves setting goals, self-monitoring one’s progress, and adjusting tactics as needed.

Review of Research

Initially, in 1977, the problem-solving model was fairly simple: it focused on the writer’s memory, the task environment (aka the rhetorical situation ), prewriting , and reviewing. By 2014, following multiple iterations, the model had become more sophisticated, adding layers of complexity, such as the writer’s motivation, their knowledge of design schemas (given the visual turn in writing ), their intrapersonal and intrapersonal competencies , and their access to production technologies (aka, new writing spaces).

In 1980 Hayes and Flower introduced their cognitive process model in “Identifying the Organization of Writing Processes.” Then, in 1981, they elaborated on that model in “A Cognitive Process Theory of Writing,” an article published in College Composition and Communication , a leading journal in writing studies .

As suggested by the above illustration, Flower and Hayes conceptualized the writing process to be composed of three major cognitive activities:

planning – Writers set goals and establish a plan for writing the document.
translating – Writers translate thought into words
reviewing – Writers detect and correct “weaknesses in the text with respect to language conventions and accuracy of meaning” (p. 12).

They also introduced the concept of a “monitor” to account for how writers switch between planning, translating, and reviewing based on the writer’s assessment of the text.

Later, in “Modeling and Remodeling Writing” (2012), provided a more robust, complex model of the writing process. In his revision, Hayes omitted the concept of the monitor and he suggested that composing occurs on three levels:

Control Level This level addresses (1) the writer’s motivation; (2) their ability to set goals (plan, write, revise); (3) their familiarity with writing schemas; (4) their current plan
Process Level This level focuses on (1) the task environment and (2) the writing process itself, detailing the interactions between the writer, the task, and the context in which writing occurs. Writing Processes: 1. The Evaluator (e.g., a teacher, boss, or client); 2. The Proposer; 3. The Translator; 4. The Transcriber. Task Environment: 1. Collaborators & Critics; 2. Transcribing Technology; 3. Task Materials, Written Plans; 4. Text Written So Far
working memory, which is responsible for temporarily storing and manipulating information during the writing process
long-term memory, which stores knowledge about language, genre conventions, and prior experiences with writing tasks
attention, which allows writers to focus on specific aspects of the task while filtering out irrelevant information
reading, which references the writer’s literary history, what they’ve read and how conversant they are with ongoing scholarly conversations about the topic.

Some key differences and improvements in the 2012 model include:

The 2012 model introduces additional cognitive components, such as working memory and motivation , which were not explicitly addressed in the original model.
The 2012 model endeavors to account for the social aspects of writing, including collaboration and communication with others during the writing process.
The original Hayes-Flower model presented the writing subprocesses (planning, translating, and reviewing) in a linear fashion. However, the 2012 model emphasizes that these processes are recursive and iterative, meaning that writers continually move back and forth between these stages as they write, revise, and refine their work.
The updated model aims to addresses the impact of digital technologies on the writing process, acknowledging that the use of computers, word processing software, and online resources can significantly influence how writers plan, compose, and revise their texts.

In 2014, Hayes, in collaboration with three other colleagues (Leijten et al. 2014), once again revised his model of the composing processes. Leijten et al. argue that writing processes have changed significantly since Hayes’ 2012 revision thanks to the development and adoption of new digital technologies. They were especially interested in online collaboration tools used in the work place.

As illustrated below, in the revised model, Leijten et al. added “design schemas” (e.g., graphics, drawings, photographs, and other visuals) to the control level. At the process level, they added graphics to the text the writer had produced thus far. They also included motivation management at the resource level to address the fatigue and conflicts that can set in during long projects involving many steps and people. Perhaps most importantly, they added a searcher to the writing process to account for how open the writer is to strategic searching or how open they are to new information that contradicts previous information .

A Fun Exercise

One of the takeaways from research on writer’s composing processes is that we’re all special snowflakes: we each have our unique processes for generating, research, and writing.

To gain some insight into your own writing processes, why not draw it?

Get your crayons out or whatever writing tools you use to draw.
Draft your own vision of the writing process.
Write a narrative that explains your drawing.

Hayes, J. R., & Flower, L. (1980). Identifying the Organization of Writing Processes. In L. W. Gregg, & E. R. Steinberg (Eds.), Cognitive Processes in Writing: An Interdisciplinary Approach (pp. 3-30). Hillsdale, NJ: Lawrence Erlbaum.

Hayes, J. R. (2012). Modeling and remodeling writing. Written Communication, 29(3), 369-388. https://doi: 10.1177/0741088312451260

Hayes, J. R., & Flower, L. S. (1986). Writing research and the writer. American Psychologist, 41(10), 1106-1113. https://doi.org/10.1037/0003-066X.41.10.1106

Leijten, Van Waes, L., Schriver, K., & Hayes, J. R. (2014). Writing in the workplace: Constructing documents using multiple digital sources. Journal of Writing Research, 5(3), 285–337. https://doi.org/10.17239/jowr-2014.05.03.3

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Effective problem statements have these 5 components

problem-statement-colleagues-gathered-talking-in-office

We’ve all encountered problems on the job. After all, that’s what a lot of work is about. Solving meaningful problems to help improve something.

Developing a problem statement that provides a brief description of an issue you want to solve is an important early step in problem-solving .

It sounds deceptively simple. But creating an effective problem statement isn’t that easy, even for a genius like Albert Einstein. Given one hour to work on a problem, he’d spend 55 minutes thinking about the problem and five minutes finding solutions. (Or so the story goes.)

Einstein was probably exaggerating to make a point. But considering his success in solving complex problems, we think he was on to something.

As humans, we’re wired to jump past the problem and go directly to the solution stage. In emergencies, this behavior can be lifesaving, as in leaping out of the way of a speeding car. But when dealing with longer-range issues in the workplace, this can lead to bad decisions or half-baked solutions.

That’s where problem statements come in handy. They help to meaningfully outline objectives to reach effective solutions. Knowing how to develop a great problem statement is also a valuable tool for honing your management skills .

But what exactly is a problem statement, when should you use one, and how do you go about writing one? In this article, we'll answer those questions and give you some tips for writing effective problem statements. Then you'll be ready to take on more challenges large and small.

What is a problem statement?

First, let’s start by defining a problem statement.

A problem statement is a short, clear explanation of an issue or challenge that sums up what you want to change. It helps you, team members, and other stakeholders to focus on the problem, why it’s important, and who it impacts.

A good problem statement should create awareness and stimulate creative thinking . It should not identify a solution or create a bias toward a specific strategy.

Taking time to work on a problem statement is a great way to short-circuit the tendency to rush to solutions. It helps to make sure you’re focusing on the right problem and have a well-informed understanding of the root causes. The process can also help you take a more proactive than reactive approach to problem-solving . This can help position you and your team to avoid getting stuck in constant fire-fighting mode. That way, you can take advantage of more growth opportunities.

When to use a problem statement

The best time to create a problem statement is before you start thinking of solutions. If you catch yourself or your team rushing to the solution stage when you’re first discussing a problem, hit the brakes. Go back and work on the statement of the problem to make sure everyone understands and agrees on what the real problem is.

Here are some common situations where writing problem statements might come in handy:

Writing an executive summary for a project proposal or research project
Collaborating on a cross-functional project with several team members
Defining the customer issue that a proposed product or service aims to solve
Using design thinking to improve user experience
Tackling a problem that previous actions failed to solve

problem-statement-colleagues-solving-at-laptop

How to identify a problem statement

Like the unseen body of an iceberg, the root cause of a specific problem isn’t always obvious. So when developing a problem statement, how do you go about identifying the true, underlying problem?

These two steps will help you uncover the root cause of a problem :

Collect information from the research and previous experience with the problem
Talk to multiple stakeholders who are impacted by the problem

People often perceive problems differently. Interviewing stakeholders will help you understand the problem from diverse points of view. It can also help you develop some case studies to illustrate the problem.

Combining these insights with research data will help you identify root causes more accurately. In turn, this methodology will help you craft a problem statement that will lead to more viable solutions.

What are problem statements used for?

You can use problem statements for a variety of purposes. For an organization, it might be solving customer and employee issues. For the government, it could be improving public health. For individuals, it can mean enhancing their own personal well-being . Generally, problem statements can be used to:

Identify opportunities for improvement
Focus on the right problems or issues to launch more successful initiatives – a common challenge in leadership
Help you communicate a problem to others who need to be involved in finding a solution
Serve as the basis for developing an action plan or goals that need to be accomplished to help solve the problem
Stimulate thinking outside the box and other types of creative brainstorming techniques

3 examples of problem statements

When you want to be sure you understand a concept or tool, it helps to see an example. There can also be some differences in opinion about what a problem statement should look like. For instance, some frameworks include a proposed solution as part of the problem statement. But if the goal is to stimulate fresh ideas, it’s better not to suggest a solution within the problem statement.

In our experience, an effective problem statement is brief, preferably one sentence. It’s also specific and descriptive without being prescriptive.

Here are three problem statement examples. While these examples represent three types of problems or goals, keep in mind that there can be many other types of problem statements.

Example Problem Statement 1: The Status Quo Problem Statement

Example:

The average customer service on-hold time for Example company exceeds five minutes during both its busy and slow seasons.

This can be used to describe a current pain point within an organization that may need to be addressed. Note that the statement specifies that the issue occurs during the company’s slow time as well as the busy season. This is helpful in performing the root cause analysis and determining how this problem can be solved.

The average customer service on-hold time for Example company exceeds five minutes during both its busy and slow seasons. The company is currently understaffed and customer service representatives are overwhelmed.

Background:

Example company is facing a significant challenge in managing their customer service on-hold times. In the past, the company had been known for its efficient and timely customer service, but due to a combination of factors, including understaffing and increased customer demand, the on-hold times have exceeded five minutes consistently. This has resulted in frustration and dissatisfaction among customers, negatively impacting the company's reputation and customer loyalty.

Reducing the on-hold times for customer service callers is crucial for Example company. Prolonged waiting times have a detrimental effect on customer satisfaction and loyalty, leading to potential customer churn and loss of revenue. Additionally, the company's declining reputation in terms of customer service can have a lasting impact on its competitive position in the market. Addressing this problem is of utmost importance to improve customer experience and maintain a positive brand image.

Objectives:

The primary objective of this project is to reduce the on-hold times for customer service callers at Example company. The specific objectives include:

Analyzing the current customer service workflow and identifying bottlenecks contributing to increased on-hold times.
Assessing the staffing levels and resource allocation to determine the extent of understaffing and its impact on customer service.
Developing strategies and implementing measures to optimize the customer service workflow and reduce on-hold times.
Monitoring and evaluating the effectiveness of the implemented measures through key performance indicators (KPIs) such as average on-hold time, customer satisfaction ratings, and customer feedback.
Establishing a sustainable approach to maintain reduced on-hold times, taking into account both busy and slow seasons, through proper resource planning, training, and process improvements.

Example Problem Statement 2: The Destination Problem Statement

Leaders at Example company want to increase net revenue for its premium product line of widgets by 5% for the next fiscal year.

This approach can be used to describe where an organization wants to be in the future. This type of problem statement is useful for launching initiatives to help an organization achieve its desired state.

Like creating SMART goals , you want to be as specific as possible. Note that the statement specifies “net revenue” instead of “gross revenue." This will help keep options open for potential actions. It also makes it clear that merely increasing sales is not an acceptable solution if higher marketing costs offset the net gains.

Leaders at Example company aim to increase net revenue for its premium product line of widgets by 5% for the next fiscal year. However, the company currently lacks the necessary teams to tackle this objective effectively. To achieve this growth target, the company needs to expand its marketing and PR teams, as well as its product development teams, to prepare for scaling.

Example company faces the challenge of generating a 5% increase in net revenue for its premium product line of widgets in the upcoming fiscal year. Currently, the company lacks the required workforce to drive this growth. Without adequate staff in the marketing, PR, and product development departments, the company's ability to effectively promote, position, and innovate its premium product line will be hindered. To achieve this kind of growth, it is essential that Example company expands teams, enhances capabilities, and strategically taps into the existing pool of loyal customers.

Increasing net revenue for the premium product line is crucial for Example company's overall business success. Failure to achieve the targeted growth rate can lead to missed revenue opportunities and stagnation in the market. By expanding the marketing and PR teams, Example company can strengthen its brand presence, effectively communicate the value proposition of its premium product line, and attract new customers.

Additionally, expanding the product development teams will enable the company to introduce new features and innovations, further enticing existing and potential customers. Therefore, addressing the workforce shortage and investing in the necessary resources are vital for achieving the revenue growth objective.

The primary objective of this project is to increase net revenue for Example company's premium product line of widgets by 5% in the next fiscal year. The specific objectives include:

Assessing the current workforce and identifying the gaps in the marketing, PR, and product development teams.
Expanding the marketing and PR teams by hiring skilled professionals who can effectively promote the premium product line and engage with the target audience.
Strengthening the product development teams by recruiting qualified individuals who can drive innovation, enhance product features, and meet customer demands.
Developing a comprehensive marketing and PR strategy to effectively communicate the value proposition of the premium product line and attract new customers.
Leveraging the existing base of loyal customers to increase repeat purchases, referrals, and brand advocacy.
Allocating sufficient resources, both time and manpower, to support the expansion and scaling efforts required to achieve the ambitious revenue growth target.
Monitoring and analyzing key performance indicators (KPIs) such as net revenue, customer acquisition, customer retention, and customer satisfaction to measure the success of the growth initiatives.
Establishing a sustainable plan to maintain the increased revenue growth beyond the next fiscal year by implementing strategies for continuous improvement and adaptation to market dynamics.

Example Problem Statement 3 The Stakeholder Problem Statement

In the last three quarterly employee engagement surveys , less than 30% of employees at Eample company stated that they feel valued by the company. This represents a 20% decline compared to the same period in the year prior.

This strategy can be used to describe how a specific stakeholder group views the organization. It can be useful for exploring issues and potential solutions that impact specific groups of people.

Note the statement makes it clear that the issue has been present in multiple surveys and it's significantly worse than the previous year. When researching root causes, the HR team will want to zero in on factors that changed since the previous year.

In the last three quarterly employee engagement surveys, less than 30% of employees at the Example company stated that they feel valued by the company. This indicates a significant decline of 20% compared to the same period in the previous year.

The company aspires to reduce this percentage further to under 10%. However, achieving this goal would require filling specialized roles and implementing substantial cultural changes within the organization.

Example company is facing a pressing issue regarding employee engagement and perceived value within the company. Over the past year, there has been a notable decline in the percentage of employees who feel valued. This decline is evident in the results of the quarterly employee engagement surveys, which consistently show less than 30% of employees reporting a sense of value by the company.

This decline of 20% compared to the previous year's data signifies a concerning trend. To address this problem effectively, Example company needs to undertake significant measures that go beyond superficial changes and necessitate filling specialized roles and transforming the company culture.

Employee engagement and a sense of value are crucial for organizational success. When employees feel valued, they tend to be more productive, committed, and motivated. Conversely, a lack of perceived value can lead to decreased morale, increased turnover rates, and diminished overall performance.

By addressing the decline in employees feeling valued, Example company can improve employee satisfaction, retention, and ultimately, overall productivity. Achieving the desired reduction to under 10% is essential to restore a positive work environment and build a culture of appreciation and respect.

The primary objective of this project is to increase the percentage of employees who feel valued by Example company, aiming to reduce it to under 10%. The specific objectives include:

Conducting a comprehensive analysis of the factors contributing to the decline in employees feeling valued, including organizational policies, communication practices, leadership styles, and cultural norms.
Identifying and filling specialized roles, such as employee engagement specialists or culture change agents, who can provide expertise and guidance in fostering a culture of value and appreciation.
Developing a holistic employee engagement strategy that encompasses various initiatives, including training programs, recognition programs, feedback mechanisms, and communication channels, to enhance employee value perception.
Implementing cultural changes within the organization that align with the values of appreciation, respect, and recognition, while fostering an environment where employees feel valued.
Communicating the importance of employee value and engagement throughout all levels of the organization, including leadership teams, managers, and supervisors, to ensure consistent messaging and support.
Monitoring progress through regular employee surveys, feedback sessions, and key performance indicators (KPIs) related to employee satisfaction, turnover rates, and overall engagement levels.
Providing ongoing support, resources, and training to managers and supervisors to enable them to effectively recognize and appreciate their teams and foster a culture of value within their respective departments.
Establishing a sustainable framework for maintaining high employee value perception in the long term, including regular evaluation and adaptation of employee engagement initiatives to address evolving needs and expectations.

problem-statement-man-with-arms-crossed-smiling

What are the 5 components of a problem statement?

In developing a problem statement, it helps to think like a journalist by focusing on the five Ws: who, what, when, where, and why or how. Keep in mind that every statement may not explicitly include each component. But asking these questions is a good way to make sure you’re covering the key elements:

Who: Who are the stakeholders that are affected by the problem?
What: What is the current state, desired state, or unmet need?
When: When is the issue occurring or what is the timeframe involved?
Where: Where is the problem occurring? For example, is it in a specific department, location, or region?
Why: Why is this important or worth solving? How is the problem impacting your customers, employees, other stakeholders, or the organization? What is the magnitude of the problem? How large is the gap between the current and desired state?

How do you write a problem statement?

There are many frameworks designed to help people write a problem statement. One example is outlined in the book, The Conclusion Trap: Four Steps to Better Decisions, ” by Daniel Markovitz. A faculty member at the Lean Enterprise Institute, the author uses many case studies from his work as a business consultant.

To simplify the process, we’ve broken it down into three steps:

1. Gather data and observe

Use data from research and reports, as well as facts from direct observation to answer the five Ws: who, what, when, where, and why.

Whenever possible, get out in the field and talk directly with stakeholders impacted by the problem. Get a firsthand look at the work environment and equipment. This may mean spending time on the production floor asking employees questions about their work and challenges. Or taking customer service calls to learn more about customer pain points and problems your employees may be grappling with.

2. Frame the problem properly

A well-framed problem will help you avoid cognitive bias and open avenues for discussion. It will also encourage the exploration of more options.

A good way to test a problem statement for bias is to ask questions like these:

3. Keep asking why (and check in on the progress)

When it comes to problem-solving, stay curious. Lean on your growth mindset to keep asking why — and check in on the progress.

Asking why until you’re satisfied that you’ve uncovered the root cause of the problem will help you avoid ineffective band-aid solutions.

Refining your problem statements

When solving any sort of problem, there’s likely a slew of questions that might arise for you. In order to holistically understand the root cause of the problem at hand, your workforce needs to stay curious.

An effective problem statement creates the space you and your team need to explore, gain insight, and get buy-in before taking action.

If you have embarked on a proposed solution, it’s also important to understand that solutions are malleable. There may be no single best solution. Solutions can change and adapt as external factors change, too. It’s more important than ever that organizations stay agile . This means that interactive check-ins are critical to solving tough problems. By keeping a good pulse on your course of action, you’ll be better equipped to pivot when the time comes to change.

BetterUp can help. With access to virtual coaching , your people can get personalized support to help solve tough problems of the future.

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Madeline Miles

Madeline is a writer, communicator, and storyteller who is passionate about using words to help drive positive change. She holds a bachelor's in English Creative Writing and Communication Studies and lives in Denver, Colorado. In her spare time, she's usually somewhere outside (preferably in the mountains) — and enjoys poetry and fiction.

Problem Solving Essays: Overview

Questions to consider:

How can determining the best approach to solve a problem help you generate solutions?
Why do thinkers create multiple solutions to problems?
How do writers translate these approaches and solutions into writing?

When we’re solving a problem, whether at work, school, or home, we are being asked to perform multiple, often complex, tasks. The most effective problem-solving approach includes some variation of the following steps:

Determine the issue(s)
Recognize other perspectives
Think of multiple possible results
Research and evaluate the possibilities
Select the best result(s)
Communicate your findings
Establish logical action items based on your analysis

Determining the best approach to any given problem and generating more than one possible solution to the problem constitutes the complicated process of problem-solving. People who are good at these skills are highly marketable because many jobs consist of a series of problems that need to be solved for production, services, goods, and sales to continue smoothly.

Think about what happens when a worker at your favorite coffee shop slips on a wet spot behind the counter, dropping several drinks she just prepared. One problem is the employee may be hurt, in need of attention, and probably embarrassed; another problem is that several customers do not have the drinks they were waiting for; and another problem is that stopping production of drinks (to care for the hurt worker, to clean up her spilled drinks, to make new drinks) causes the line at the cash register to back up. A good manager has to juggle all of these elements to resolve the situation as quickly and efficiently as possible. That resolution and return to standard operations doesn’t happen without a great deal of thinking: prioritizing needs, shifting other workers off one station onto another temporarily, and dealing with all the people involved, from the injured worker to the impatient patrons.

DETERMINING THE BEST APPROACH

Faced with a problem-solving opportunity, you must assess the skills you will need to create solutions. Problem-solving can involve many different types of thinking.

You may have to call on your creative, analytical, or critical thinking skills—or more frequently, a combination of several different types of thinking—to solve a problem satisfactorily.
When you approach a situation, how can you decide what is the best type of thinking to employ? Sometimes the answer is obvious; if you are working a scientific challenge, you likely will use analytical thinking; if you are a design student considering the atmosphere of a home, you may need to tap into creative thinking skills; and if you are an early childhood education major outlining the logistics involved in establishing a summer day camp for children, you may need a combination of critical, analytical, and creative thinking to solve this challenge.

What sort of thinking do you imagine initially helped in the following scenarios? How would the other types of thinking come into resolving these problems? Write a one- to two-sentence rationale on scrap paper or notepad that explains why you chose the answers to the questions below.

Analytical thinking
Creative thinking
Critical thinking

GENERATING MULTIPLE SOLUTIONS

Why do you think it is important to provide multiple solutions when you’re going through the steps to solve problems? Typically, you’ll end up only using one solution at a time, so why expend the extra energy to create alternatives? If you planned a wonderful trip to Europe and had all the sites you want to see planned out and reservations made, you would think that your problem-solving and organizational skills had quite a workout. But what if when you arrived, the country you’re visiting is enmeshed in a public transportation strike experts predict will last several weeks if not longer? A back-up plan would have helped you contemplate alternatives you could substitute for the original plans. You certainly cannot predict every possible contingency—sick children, weather delays, economic downfalls—but you can be prepared for unexpected issues to come up and adapt more easily if you plan for multiple solutions.Write out at least two possible solutions to these dilemmas:

Your significant other wants a birthday present—you have no cash.
You have three exams scheduled on a day when you also need to work.
Your car breaks down and requires an expensive repair and you need bus fare home—your cell phone is dead and you only have an ATM card with a max withdrawal limit of $200.
You have to pass a running test for your physical education class, but you’re out of shape.

Providing more than one solution to a problem gives people options. You may not need several options, but having more than one solution will allow you to feel more in control and part of the problem-solving process.

Writing Effective Problem Solving Essays

When someone’s purpose is to describe a problem and evaluate possible solutions, they will write a problem solving essay. In academic writing, the problem solving essay is very common and useful. For example, students would use it in a ecological class if they were asked to discuss solutions to the problem of endangered species. Students also can write this type of essay in an computer science class if they needed to suggest some ways to solve the inefficient performance of a system.

Once someone has decided to write a problem solving essay, there are several techniques should be pay attention. First, he/she should carefully investigate if a problem exists and describe the problem clearly. While describing a statement of problem, he/she should mentions why it is serious . Second, the solutions recommended for the problem should be convincing and effective. They must prove his viewpoint by supporting it with persuasive facts and evidences . Finally, the essay must be able to influence the readers that the proposed solutions are practical and valuable.

Introduction

Describe the problem and state why it is serious.
Write a thesis statement that identifies possible solutions.

Supporting Paragraphs

Discuss one solution in each supporting paragraph.
Provide details to support each solution.
Organize the paragraphs according to order of importance.
Summarize the solutions.
Draw a conclusion or make a prediction based on your suggestions.

Sources Used to Create this Chapter

The majority of the content for this section has been adapted from the following OER Material:

Strategic Information Literacy: Targeted Knowledge with Broad Application by Kristin Conlin and Allison Jennings-Roche, which was published under a CC-BY-NC-SA 4.0 license.

A Guide to Problem Solving Essays by Ken Lang, which was published under the CC-BY-NC-SA 4.0 International License.

Starting the Journey: An Intro to College Writing Copyright © by Leonard Owens III; Tim Bishop; and Scott Ortolano is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Problem-solving strategies for writing

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Problem-solving strategies for writing

ISBN-10 0155719831
ISBN-13 978-0155719835
Publisher Harcourt Brace Jovanovich
Publication date January 1, 1981
Language English
Print length 210 pages
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ISBN-10 ‏ : ‎ 0155719831
ISBN-13 ‏ : ‎ 978-0155719835
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35 problem-solving techniques and methods for solving complex problems

Design your next session with SessionLab

Join the 150,000+ facilitators  using SessionLab.

How do you identify problems?

How do you identify the right solution.

Tips for more effective problem-solving

Complete problem-solving methods

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

Problem-solving warm-up activities

Closing activities for a problem-solving process.

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

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

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

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

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

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

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

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

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

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

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

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

Tips for more effective problem solving

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

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

Clearly define the problem

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

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

Don’t jump to conclusions

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

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

Try different approaches

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

Don’t take it personally

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

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

Get the right people in the room

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

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

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

Document everything

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

Bring a facilitator

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

Develop your problem-solving skills

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

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

Design a great agenda

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

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

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

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

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

Design Sprint 2.0

Open Space Technology

1. Six Thinking Hats

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

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

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

2. Lightning Decision Jam

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

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

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

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

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

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

3. Problem Definition Process

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

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

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

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

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

4. The 5 Whys

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

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

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

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

5. World Cafe

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

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

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

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

6. Discovery & Action Dialogue (DAD)

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

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

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

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

7. Design Sprint 2.0

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

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

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

8. Open space technology

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

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

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

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

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

Techniques to identify and analyze problems

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

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

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

Let’s take a look!

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

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

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

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

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

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

10. The Creativity Dice

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

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

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

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

11. Fishbone Analysis

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

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

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

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

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

12. Problem Tree

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

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

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

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

13. SWOT Analysis

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

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

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

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

14. Agreement-Certainty Matrix

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

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

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

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

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

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

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

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

16. Speed Boat

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

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

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

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

17. The Journalistic Six

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

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

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

18. LEGO Challenge

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

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

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

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

19. What, So What, Now What?

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

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

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

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

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

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

20. Journalists

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

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

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

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

Problem-solving techniques for developing solutions

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

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

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

21. Mindspin

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

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

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

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

22. Improved Solutions

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

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

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

23. Four Step Sketch

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

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

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

24. 15% Solutions

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

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

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

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

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

25. How-Now-Wow Matrix

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

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

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

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

26. Impact and Effort Matrix

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

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

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

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

27. Dotmocracy

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

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

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

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

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

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

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

28. Check-in / Check-out

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

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

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

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

29. Doodling Together

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

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

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

30. Show and Tell

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

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

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

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

31. Constellations

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

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

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

32. Draw a Tree

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

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

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

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

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

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

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

One Breath Feedback
Who What When Matrix
Response Cards

How do I conclude a problem-solving process?

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

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

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

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

33. One Breath Feedback

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

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

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

34. Who What When Matrix

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

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

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

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

35. Response cards

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

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

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

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

Save time and effort discovering the right solutions

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

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

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

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

Over to you

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

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

thank you very much for these excellent techniques

Certainly wonderful article, very detailed. Shared!

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8 Effective Problem-Solving Strategies

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If you need to solve a problem, there are a number of different problem-solving strategies that can help you come up with an accurate decision. Sometimes the best choice is to use a step-by-step approach that leads to the right solution, but other problems may require a trial-and-error approach.

Some helpful problem-solving strategies include: Brainstorming Step-by-step algorithms Trial-and-error Working backward Heuristics Insight Writing it down Getting some sleep

Table of Contents

Why Use Problem-Solving Strategies

While you can always make a wild guess or pick at random, that certainly isn’t the most accurate way to come up with a solution. Using a more structured approach allows you to:

Understand the nature of the problem
Determine how you will solve it
Research different options
Take steps to solve the problem and resolve the issue

There are many tools and strategies that can be used to solve problems, and some problems may require more than one of these methods in order to come up with a solution.

Problem-Solving Strategies

The problem-solving strategy that works best depends on the nature of the problem and how much time you have available to make a choice. Here are eight different techniques that can help you solve whatever type of problem you might face.

Brainstorming

Coming up with a lot of potential solutions can be beneficial, particularly early on in the process. You might brainstorm on your own, or enlist the help of others to get input that you might not have otherwise considered.

Step-by-Step

Also known as an algorithm, this approach involves following a predetermined formula that is guaranteed to produce the correct result. While this can be useful in some situations—such as solving a math problem—it is not always practical in every situation.

On the plus side, algorithms can be very accurate and reliable. Unfortunately, they can also be time-consuming.

And in some situations, you cannot follow this approach because you simply don’t have access to all of the information you would need to do so.

Trial-and-Error

This problem-solving strategy involves trying a number of different solutions in order to figure out which one works best. This requires testing steps or more options to solve the problem or pick the right solution.

For example, if you are trying to perfect a recipe, you might have to experiment with varying amounts of a certain ingredient before you figure out which one you prefer.

On the plus side, trial-and-error can be a great problem-solving strategy in situations that require an individualized solution. However, this approach can be very time-consuming and costly.

Working Backward

This problem-solving strategy involves looking at the end result and working your way back through the chain of events. It can be a useful tool when you are trying to figure out what might have led to a particular outcome.

It can also be a beneficial way to play out how you will complete a task. For example, if you know you need to have a project done by a certain date, working backward can help you figure out the steps you’ll need to complete in order to successfully finish the project.

Heuristics are mental shortcuts that allow you to come up with solutions quite quickly. They are often based on past experiences that are then applied to other situations. They are, essentially, a handy rule of thumb.

For example, imagine a student is trying to pick classes for the next term. While they aren’t sure which classes they’ll enjoy the most, they know that they tend to prefer subjects that involve a lot of creativity. They utilize this heuristic to pick classes that involve art and creative writing.

The benefit of a heuristic is that it is a fast way to make fairly accurate decisions. The trade-off is that you give up some accuracy in order to gain speed and efficiency.

Sometimes, the solution to a problem seems to come out of nowhere. You might suddenly envision a solution after struggling with the problem for a while. Or you might abruptly recognize the correct solution that you hadn’t seen before.

No matter the source, insight-based problem-solving relies on following your gut instincts. While this may not be as objective or accurate as some other problem-solving strategies, it can be a great way to come up with creative, novel solutions.

Write It Down

Sometimes putting the problem and possible solutions down in paper can be a useful way to visualize solutions. Jot down whatever might help you envision your options. Draw a picture, create a mind map, or just write some notes to clarify your thoughts.

Get Some Sleep

If you’re facing a big problem or trying to make an important decision, try getting a good night’s sleep before making a choice. Sleep plays an essential role in memory consolidation, so getting some rest may help you access the information or insight you need to make the best choice.

Other Considerations

Even with an arsenal of problem-solving strategies at your disposal, coming up with solutions isn’t always easy. Certain challenges can make the process more difficult. A few issues that might emerge include:

Mental set : When people form a mental set, they only rely on things that have worked in the last. Sometimes this can be useful, but in other cases, it can severely hinder the problem-solving process.
Cognitive biases : Unconscious cognitive biases can make it difficult to see situations clearly and objectively. As a result, you may not consider all of your options or ignore relevant information.
Misinformation : Poorly sourced clues and irrelevant details can add more complications. Being able to sort out what’s relevant and what’s not is essential for solving problems accurately.
Functional fixedness : Functional fixedness happens when people only think of customary solutions to problems. It can hinder out-of-the-box thinking and prevents insightful, creative solutions.

Important Problem-Solving Skills

Becoming a good problem solver can be useful in a variety of domains, from school to work to interpersonal relationships. Important problem-solving skills encompass being able to identify problems, coming up with effective solutions, and then implementing these solutions.

According to a 2023 survey by the National Association of Colleges and Employers, 61.4% of employers look for problem-solving skills on applicant resumes.

Some essential problem-solving skills include:

Research skills
Analytical abilities
Decision-making skills
Critical thinking
Communication
Time management
Emotional intelligence

Solving a problem is complex and requires the ability to recognize the issue, collect and analyze relevant data, and make decisions about the best course of action. It can also involve asking others for input, communicating goals, and providing direction to others.

How to Become a Better Problem-Solver

If you’re ready to strengthen your problem-solving abilities, here are some steps you can take:

Identify the Problem

Before you can practice your problem-solving skills, you need to be able to recognize that there is a problem. When you spot a potential issue, ask questions about when it started and what caused it.

Do Your Research

Instead of jumping right in to finding solutions, do research to make sure you fully understand the problem and have all the background information you need. This helps ensure you don’t miss important details.

Hone Your Skills

Consider signing up for a class or workshop focused on problem-solving skill development. There are also books that focus on different methods and approaches.

The best way to strengthen problem-solving strategies is to give yourself plenty of opportunities to practice. Look for new challenges that allow you to think critically, analytically, and creatively.

Final Thoughts

If you have a problem to solve, there are plenty of strategies that can help you make the right choice. The key is to pick the right one, but also stay flexible and willing to shift gears.

In many cases, you might find that you need more than one strategy to make the choices that are right for your life.

Brunet, J. F., McNeil, J., Doucet, É., & Forest, G. (2020). The association between REM sleep and decision-making: Supporting evidences. Physiology & Behavior , 225, 113109. https://doi.org/10.1016/j.physbeh.2020.113109

Chrysikou, E. G, Motyka, K., Nigro, C., Yang, S. I. , & Thompson-Schill, S. L. (2016). Functional fixedness in creative thinking tasks depends on stimulus modality. Psychol Aesthet Creat Arts , 10(4):425‐435. https://doi.org/10.1037/aca0000050

Sarathy, V. (2018). Real world problem-solving. Front Hum Neurosci , 12:261. https://doi.org/10.3389/fnhum.2018.00261

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4.9: Strategies for Solving Applications and Equations

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Learning Objectives

By the end of this section, you will be able to:

Use a problem solving strategy for word problems
Solve number word problems
Solve percent applications
Solve simple interest applications

Before you get started, take this readiness quiz.

Translate “six less than twice x ” into an algebraic expression. If you missed this problem, review [link] .
Convert 4.5% to a decimal. If you missed this problem, review [link] .
Convert 0.6 to a percent. If you missed this problem, review [link] .

Have you ever had any negative experiences in the past with word problems? When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. Realize that your negative experiences with word problems are in your past. To move forward you need to calm your fears and change your negative feelings.

Start with a fresh slate and begin to think positive thoughts. Repeating some of the following statements may be helpful to turn your thoughts positive. Thinking positive thoughts is a first step towards success.

I think I can! I think I can!
While word problems were hard in the past, I think I can try them now.
I am better prepared now—I think I will begin to understand word problems.
I am able to solve equations because I practiced many problems and I got help when I needed it—I can try that with word problems.
It may take time, but I can begin to solve word problems.
You are now well prepared and you are ready to succeed. If you take control and believe you can be successful, you will be able to master word problems.

Use a Problem Solving Strategy for Word Problems

Now that we can solve equations, we are ready to apply our new skills to word problems. We will develop a strategy we can use to solve any word problem successfully.

EXAMPLE $\PageIndex{1}$

Normal yearly snowfall at the local ski resort is 12 inches more than twice the amount it received last season. The normal yearly snowfall is 62 inches. What was the snowfall last season at the ski resort?

EXAMPLE $\PageIndex{2}$

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was three more than twice the number of notebooks. He bought seven textbooks. How many notebooks did he buy?

He bought two notebooks

EXAMPLE $\PageIndex{3}$

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?

He did seven crosswords puzzles

We summarize an effective strategy for problem solving.

PROBLEM SOLVING STRATEGY FOR WORD PROBLEMS

Read the problem. Make sure all the words and ideas are understood.
Identify what you are looking for.
Name what you are looking for. Choose a variable to represent that quantity.
Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.
Solve the equation using proper algebra techniques.
Check the answer in the problem to make sure it makes sense.
Answer the question with a complete sentence.

Solve Number Word Problems

We will now apply the problem solving strategy to “number word problems.” Number word problems give some clues about one or more numbers and we use these clues to write an equation. Number word problems provide good practice for using the Problem Solving Strategy.

EXAMPLE $\PageIndex{4}$

The sum of seven times a number and eight is thirty-six. Find the number.

Did you notice that we left out some of the steps as we solved this equation? If you’re not yet ready to leave out these steps, write down as many as you need.

EXAMPLE $\PageIndex{5}$

The sum of four times a number and two is fourteen. Find the number.

EXAMPLE $\PageIndex{6}$

The sum of three times a number and seven is twenty-five. Find the number.

Some number word problems ask us to find two or more numbers. It may be tempting to name them all with different variables, but so far, we have only solved equations with one variable. In order to avoid using more than one variable, we will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.

EXAMPLE $\PageIndex{7}$

The sum of two numbers is negative fifteen. One number is nine less than the other. Find the numbers.

EXAMPLE $\PageIndex{8}$

The sum of two numbers is negative twenty-three. One number is seven less than the other. Find the numbers.

$−15,−8$

EXAMPLE $\PageIndex{9}$

The sum of two numbers is negative eighteen. One number is forty more than the other. Find the numbers.

$−29,11$

Consecutive Integers (optional)

Some number problems involve consecutive integers . Consecutive integers are integers that immediately follow each other. Examples of consecutive integers are:

\[\begin{array}{rrrr} 1, & 2, & 3, & 4 \\ −10, & −9, & −8, & −7\\ 150, & 151, & 152, & 153 \end{array}\]

Notice that each number is one more than the number preceding it. Therefore, if we define the first integer as n , the next consecutive integer is $n+1$. The one after that is one more than $n+1$, so it is $n+1+1$, which is $n+2$.

\[\begin{array}{ll} n & 1^{\text{st}} \text{integer} \\ n+1 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & 2^{\text{nd}}\text{consecutive integer} \\ n+2 & 3^{\text{rd}}\text{consecutive integer} \;\;\;\;\;\;\;\; \text{etc.} \end{array}\]

We will use this notation to represent consecutive integers in the next example.

EXAMPLE $\PageIndex{10}$

Find three consecutive integers whose sum is $−54$.

EXAMPLE $\PageIndex{11}$

Find three consecutive integers whose sum is $−96$.

$−33,−32,−31$

EXAMPLE $\PageIndex{12}$

Find three consecutive integers whose sum is $−36$.

$−13,−12,−11$

Now that we have worked with consecutive integers, we will expand our work to include consecutive even integers and consecutive odd integers . Consecutive even integers are even integers that immediately follow one another. Examples of consecutive even integers are:

\[24, 26, 28\]

\[−12,−10,−8\]

Notice each integer is two more than the number preceding it. If we call the first one n , then the next one is $n+2$. The one after that would be $n+2+2$ or $n+4$.

Consecutive odd integers are odd integers that immediately follow one another. Consider the consecutive odd integers 63, 65, and 67.

\[63, 65, 67\]

\[n,n+2,n+4\]

Does it seem strange to have to add two (an even number) to get the next odd number? Do we get an odd number or an even number when we add 2 to 3? to 11? to 47?

Whether the problem asks for consecutive even numbers or odd numbers, you do not have to do anything different. The pattern is still the same—to get to the next odd or the next even integer, add two.

EXAMPLE $\PageIndex{13}$

Find three consecutive even integers whose sum is $120$.

EXAMPLE $\PageIndex{14}$

Find three consecutive even integers whose sum is 102.

$32, 34, 36$

EXAMPLE $\PageIndex{15}$

Find three consecutive even integers whose sum is $−24$.

$−10,−8,−6$

When a number problem is in a real life context, we still use the same strategies that we used for the previous examples.

EXAMPLE $\PageIndex{16}$

A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?

According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,400. This was $1,600 less than six times the cost in 1975. What was the average cost of a car in 1975?

The average cost was $5,000.

EXAMPLE $\PageIndex{18}$

US Census data shows that the median price of new home in the U.S. in November 2014 was $280,900. This was $10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?

The median price was $19,300.

Solve Percent Applications

There are several methods to solve percent equations. In algebra, it is easiest if we just translate English sentences into algebraic equations and then solve the equations. Be sure to change the given percent to a decimal before you use it in the equation.

EXAMPLE $\PageIndex{19}$

Translate and solve:

What number is 45% of 84?
8.5% of what amount is $4.76?
168 is what percent of 112?
What number is 45% of 80?
7.5% of what amount is $1.95?
110 is what percent of 88?

EXAMPLE $\PageIndex{21}$

What number is 55% of 60?
8.5% of what amount is $3.06?
126 is what percent of 72?

ⓐ 33 ⓑ $36 ⓐ $175 \% $

Now that we have a problem solving strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we will solve involve everyday situations, you can rely on your own experience.

EXAMPLE $\PageIndex{22}$

The label on Audrey’s yogurt said that one serving provided 12 grams of protein, which is 24% of the recommended daily amount. What is the total recommended daily amount of protein?

EXAMPLE $\PageIndex{23}$

One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?

EXAMPLE $\PageIndex{24}$

One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?

Remember to put the answer in the form requested. In the next example we are looking for the percent.

EXAMPLE $\PageIndex{25}$

Veronica is planning to make muffins from a mix. The package says each muffin will be 240 calories and 60 calories will be from fat. What percent of the total calories is from fat?

EXAMPLE $\PageIndex{26}$

Mitzi received some gourmet brownies as a gift. The wrapper said each 28% brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat? Round the answer to the nearest whole percent.

EXAMPLE $\PageIndex{27}$

The mix Ricardo plans to use to make brownies says that each brownie will be 190 calories, and 76 calories are from fat. What percent of the total calories are from fat? Round the answer to the nearest whole percent.

It is often important in many fields—business, sciences, pop culture—to talk about how much an amount has increased or decreased over a certain period of time. This increase or decrease is generally expressed as a percent and called the percent change .

To find the percent change, first we find the amount of change, by finding the difference of the new amount and the original amount. Then we find what percent the amount of change is of the original amount.

FIND PERCENT CHANGE

\[\text{change}= \text{new amount}−\text{original amount}\]

change is what percent of the original amount?

EXAMPLE $\PageIndex{28}$

Recently, the California governor proposed raising community college fees from $36 a unit to $46 a unit. Find the percent change. (Round to the nearest tenth of a percent.)

EXAMPLE $\PageIndex{29}$

Find the percent change. (Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents.

$8.8 \% $

EXAMPLE $\PageIndex{30}$

Find the percent change. (Round to the nearest tenth of a percent.) In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was 2.25.

Applications of discount and mark-up are very common in retail settings.

When you buy an item on sale, the original price has been discounted by some dollar amount. The discount rate , usually given as a percent, is used to determine the amount of the discount . To determine the amount of discount, we multiply the discount rate by the original price.

The price a retailer pays for an item is called the original cost . The retailer then adds a mark-up to the original cost to get the list price , the price he sells the item for. The mark-up is usually calculated as a percent of the original cost. To determine the amount of mark-up, multiply the mark-up rate by the original cost.

\[ \begin{align} \text{amount of discount} &= \text{discount rate}· \text{original price} \\ \text{sale price} &= \text{original amount}– \text{discount price} \end{align}\]

The sale price should always be less than the original price.

\[\begin{align} \text{amount of mark-up} &= \text{mark-up rate}·\text{original price} \\ \text{list price} &= \text{original cost}–\text{mark-up} \end{align}\]

The list price should always be more than the original cost.

EXAMPLE $\PageIndex{31}$

Liam’s art gallery bought a painting at an original cost of $750. Liam marked the price up 40%. Find

the amount of mark-up and
the list price of the painting.

EXAMPLE $\PageIndex{32}$

Find ⓐ the amount of mark-up and ⓑ the list price: Jim’s music store bought a guitar at original cost $1,200. Jim marked the price up 50%.

ⓐ $600 ⓑ $1,800

EXAMPLE $\PageIndex{33}$

Find ⓐ the amount of mark-up and ⓑ the list price: The Auto Resale Store bought Pablo’s Toyota for $8,500. They marked the price up 35%.

ⓐ $2,975 ⓑ $11,475

Solve Simple Interest Applications

Interest is a part of our daily lives. From the interest earned on our savings to the interest we pay on a car loan or credit card debt, we all have some experience with interest in our lives.

The amount of money you initially deposit into a bank is called the principal , P , and the bank pays you interest, I. When you take out a loan, you pay interest on the amount you borrow, also called the principal.

In either case, the interest is computed as a certain percent of the principal, called the rate of interest , r . The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable t , (for time) represents the number of years the money is saved or borrowed.

Interest is calculated as simple interest or compound interest. Here we will use simple interest.

SIMPLE INTEREST

If an amount of money, P , called the principal, is invested or borrowed for a period of t years at an annual interest rate r , the amount of interest, I , earned or paid is

\[ \begin{array}{ll} I=Prt \; \; \; \; \; \; \; \; \; \; \; \; \text{where} & { \begin{align} I &= \text{interest} \\ P &= \text{principal} \\ r &= \text{rate} \\ t &= \text{time} \end{align}} \end{array}\]

Interest earned or paid according to this formula is called simple interest .

The formula we use to calculate interest is $I=Prt$. To use the formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information in a chart.

EXAMPLE $\PageIndex{34}$

Areli invested a principal of $950 in her bank account that earned simple interest at an interest rate of 3%. How much interest did she earn in five years?

$ \begin{aligned} I & = \; ? \\ P & = \; \$ 950 \\ r & = \; 3 \% \\ t & = \; 5 \text{ years} \end{aligned}$

$\begin{array}{ll} \text{Identify what you are asked to find, and choose a} & \text{What is the simple interest?} \\ \text{variable to represent it.} & \text{Let } I= \text{interest.} \\ \text{Write the formula.} & I=Prt \\ \text{Substitute in the given information.} & I=(950)(0.03)(5) \\ \text{Simplify.} & I=142.5 \\ \text{Check.} \\ \text{Is } \$142.50 \text{ a reasonable amount of interest on } \$ \text{ 950?} \; \;\;\;\;\; \;\;\;\;\;\; \\ \text{Yes.} \\ \text{Write a complete sentence.} & \text{The interest is } \$ \text{142.50.} \end{array}$

EXAMPLE $\PageIndex{35}$

Nathaly deposited $12,500 in her bank account where it will earn 4% simple interest. How much interest will Nathaly earn in five years?

He will earn $2,500.

EXAMPLE $\PageIndex{36}$

Susana invested a principal of $36,000 in her bank account that earned simple interest at an interest rate of 6.5%.6.5%. How much interest did she earn in three years?

She earned $7,020.

There may be times when we know the amount of interest earned on a given principal over a certain length of time, but we do not know the rate.

EXAMPLE $\PageIndex{37}$

Hang borrowed $7,500 from her parents to pay her tuition. In five years, she paid them $1,500 interest in addition to the $7,500 she borrowed. What was the rate of simple interest?

$ \begin{aligned} I & = \; \$ 1500 \\ P & = \; \$ 7500 \\ r & = \; ? \\ t & = \; 5 \text{ years} \end{aligned}$

Identify what you are asked to find, and choose What is the rate of simple interest? a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Change to percent form. Let r = rate of interest. I = P r t 1,500 = ( 7,500 ) r ( 5 ) 1,500 = 37,500 r 0.04 = r 4 % = r Check. I = P r t 1,500 = ? ( 7,500 ) ( 0.04 ) ( 5 ) 1,500 = 1,500 ✓ Write a complete sentence. The rate of interest was 4%. Identify what you are asked to find, and choose What is the rate of simple interest? a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Change to percent form. Let r = rate of interest. I = P r t 1 ,500 = ( 7,500 ) r ( 5 ) 1,500 = 37,500 r 0.04 = r 4 % = r Check. I = P r t 1 ,500 = ? ( 7,500 ) ( 0.04 ) ( 5 ) 1,500 = 1, 500 ✓ Write a complete sentence. The rate of interest was 4%.

EXAMPLE $\PageIndex{38}$

Jim lent his sister $5,000 to help her buy a house. In three years, she paid him the $5,000, plus $900 interest. What was the rate of simple interest?

The rate of simple interest was 6%.

EXAMPLE $\PageIndex{39}$

Loren lent his brother $3,000 to help him buy a car. In four years, his brother paid him back the $3,000 plus $660 in interest. What was the rate of simple interest?

The rate of simple interest was 5.5%.

In the next example, we are asked to find the principal—the amount borrowed.

EXAMPLE $\PageIndex{40}$

Sean’s new car loan statement said he would pay $4,866,25 in interest from a simple interest rate of 8.5% over five years. How much did he borrow to buy his new car?

$ \begin{aligned} I & = \; 4,866.25 \\ P & = \; ? \\ r & = \; 8.5 \% \\ t & = \; 5 \text{ years} \end{aligned}$

Identify what you are asked to find, What is the amount borrowed (the principal)? and choose a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Let P = principal borrowed. I = P r t 4,866.25 = P ( 0.085 ) ( 5 ) 4,866.25 = 0.425 P 11,450 = P Check. I = P r t 4,866.25 = ? ( 11,450 ) ( 0.085 ) ( 5 ) 4,866.25 = 4,866.25 ✓ Write a complete sentence. The principal was $11,450. Identify what you are asked to find, What is the amount borrowed (the principal)? and choose a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Let P = principal borrowed. I = P r t 4 ,866.25 = P ( 0.085 ) ( 5 ) 4,866.25 = 0.425 P 11,450 = P Check. I = P r t 4 ,866.25 = ? ( 11,450 ) ( 0.085 ) ( 5 ) 4,866.25 = 4,866.25 ✓ Write a complete sentence. The principal was $11,450.

EXAMPLE $\PageIndex{41}$

Eduardo noticed that his new car loan papers stated that with a 7.5% simple interest rate, he would pay $6,596.25 in interest over five years. How much did he borrow to pay for his car?

He paid $17,590.

EXAMPLE $\PageIndex{42}$

In five years, Gloria’s bank account earned $2,400 interest at 5% simple interest. How much had she deposited in the account?

She deposited $9,600.

Access this online resource for additional instruction and practice with using a problem solving strategy.

Begining Arithmetic Problems

Key Concepts

$\text{change}=\text{new amount}−\text{original amount}$

$\text{change is what percent of the original amount?}$

$ \begin{align} \text{amount of discount} &= \text{discount rate}· \text{original price} \\ \text{sale price} &= \text{original amount}– \text{discount price} \end{align}$
$\begin{align} \text{amount of mark-up} &= \text{mark-up rate}·\text{original price} \\ \text{list price} &= \text{original cost}–\text{mark-up} \end{align}$
If an amount of money, P , called the principal, is invested or borrowed for a period of t years at an annual interest rate r , the amount of interest, I , earned or paid is: \[\begin{aligned} &{} &{} &{I=interest} \nonumber\\ &{I=Prt} &{\text{where} \space} &{P=principal} \nonumber\\ &{} &{\space} &{r=rate} \nonumber\\ &{} &{\space} &{t=time} \nonumber \end{aligned}\]

Practice Makes Perfect

1. List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.

Answers will vary.

2. List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

3. There are $16$ girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.

4. There are $18$ Cub Scouts in Troop 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.

5. Huong is organizing paperback and hardback books for her club’s used book sale. The number of paperbacks is $12$ less than three times the number of hardbacks. Huong had $162$ paperbacks. How many hardback books were there?

58 hardback books

6. Jeff is lining up children’s and adult bicycles at the bike shop where he works. The number of children’s bicycles is nine less than three times the number of adult bicycles. There are $42$ adult bicycles. How many children’s bicycles are there?

In the following exercises, solve each number word problem.

7. The difference of a number and $12$ is three. Find the number.

8. The difference of a number and eight is four. Find the number.

9. The sum of three times a number and eight is $23$. Find the number.

10. The sum of twice a number and six is $14$. Find the number.

11 . The difference of twice a number and seven is $17$. Find the number.

12. The difference of four times a number and seven is $21$. Find the number.

13. Three times the sum of a number and nine is $12$. Find the number.

14. Six times the sum of a number and eight is $30$. Find the number.

15. One number is six more than the other. Their sum is $42$. Find the numbers.

$18, \;24$

16. One number is five more than the other. Their sum is $33$. Find the numbers.

17. The sum of two numbers is $20$. One number is four less than the other. Find the numbers.

$8, \;12$

18 . The sum of two numbers is $27$. One number is seven less than the other. Find the numbers.

19. One number is $14$ less than another. If their sum is increased by seven, the result is $85$. Find the numbers.

$32,\; 46$

20 . One number is $11$ less than another. If their sum is increased by eight, the result is $71$. Find the numbers.

21. The sum of two numbers is $14$. One number is two less than three times the other. Find the numbers.

$4,\; 10$

22. The sum of two numbers is zero. One number is nine less than twice the other. Find the numbers.

23. The sum of two consecutive integers is $77$. Find the integers.

$38,\; 39$

24. The sum of two consecutive integers is $89$. Find the integers.

25. The sum of three consecutive integers is $78$. Find the integers.

$25,\; 26,\; 27$

26. The sum of three consecutive integers is $60$. Find the integers.

27. Find three consecutive integers whose sum is $−36$.

$−11,\;−12,\;−13$

28. Find three consecutive integers whose sum is $−3$.

29. Find three consecutive even integers whose sum is $258$.

$84,\; 86,\; 88$

30. Find three consecutive even integers whose sum is $222$.

31. Find three consecutive odd integers whose sum is $−213$.

$−69,\;−71,\;−73$

32. Find three consecutive odd integers whose sum is $−267$.

33. Philip pays $$1,620$ in rent every month. This amount is $$120$ more than twice what his brother Paul pays for rent. How much does Paul pay for rent?

34. Marc just bought an SUV for $$54,000$. This is $$7,400$ less than twice what his wife paid for her car last year. How much did his wife pay for her car?

35. Laurie has $$46,000$ invested in stocks and bonds. The amount invested in stocks is $$8,000$ less than three times the amount invested in bonds. How much does Laurie have invested in bonds?

$$13,500$

36. Erica earned a total of $$50,450$ last year from her two jobs. The amount she earned from her job at the store was $$1,250$ more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?

In the following exercises, translate and solve.

37. a. What number is 45% of 120? b. 81 is 75% of what number? c. What percent of 260 is 78?

a. 54 b. 108 c. 30%

38. a. What number is 65% of 100? b. 93 is 75% of what number? c. What percent of 215 is 86?

39. a. 250% of 65 is what number? b. 8.2% of what amount is $2.87? c. 30 is what percent of 20?

a. 162.5 b. $35 c. 150%

40. a. 150% of 90 is what number? b. 6.4% of what amount is $2.88? c. 50 is what percent of 40?

In the following exercises, solve.

41. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16% of the total bill as a tip. How much should the tip be?

42. When Hiro and his co-workers had lunch at a restaurant near their work, the bill was $90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?

43. One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?

44. One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

45. A bacon cheeseburger at a popular fast food restaurant contains 2070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?

46. A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?

47. The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?

48. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?

49. Emma gets paid $3,000 per month. She pays $750 a month for rent. What percent of her monthly pay goes to rent?

50. Dimple gets paid $3,200 per month. She pays $960 a month for rent. What percent of her monthly pay goes to rent?

51. Tamanika received a raise in her hourly pay, from $15.50 to $17.36. Find the percent change.

52. Ayodele received a raise in her hourly pay, from $24.50 to $25.48. Find the percent change.

53. Annual student fees at the University of California rose from about $4,000 in 2000 to about $12,000 in 2010. Find the percent change.

54. The price of a share of one stock rose from $12.50 to $50. Find the percent change.

55. A grocery store reduced the price of a loaf of bread from $2.80 to $2.73. Find the percent change.

−2.5%

56. The price of a share of one stock fell from $8.75 to $8.54. Find the percent change.

57. Hernando’s salary was $49,500 last year. This year his salary was cut to $44,055. Find the percent change.

58. In ten years, the population of Detroit fell from 950,000 to about 712,500. Find the percent change.

In the following exercises, find a. the amount of discount and b. the sale price.

59. Janelle bought a beach chair on sale at 60% off. The original price was $44.95.

a. $26.97 b. $17.98

60. Errol bought a skateboard helmet on sale at 40% off. The original price was $49.95.

In the following exercises, find a. the amount of discount and b. the discount rate (Round to the nearest tenth of a percent if needed.)

61. Larry and Donna bought a sofa at the sale price of $1,344. The original price of the sofa was $1,920.

a. $576 b. 30%

62. Hiroshi bought a lawnmower at the sale price of $240. The original price of the lawnmower is $300.

In the following exercises, find a. the amount of the mark-up and b. the list price.

63. Daria bought a bracelet at original cost $16 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet?

a. $7.20 b. $23.20

64. Regina bought a handmade quilt at original cost $120 to sell in her quilt store. She marked the price up 55%. What was the list price of the quilt?

65. Tom paid $0.60 a pound for tomatoes to sell at his produce store. He added a 33% mark-up. What price did he charge his customers for the tomatoes?

a. $0.20 b. $0.80

66. Flora paid her supplier $0.74 a stem for roses to sell at her flower shop. She added an 85% mark-up. What price did she charge her customers for the roses?

67. Casey deposited $1,450 in a bank account that earned simple interest at an interest rate of 4%. How much interest was earned in two years?

68 . Terrence deposited $5,720 in a bank account that earned simple interest at an interest rate of 6%. How much interest was earned in four years?

69. Robin deposited $31,000 in a bank account that earned simple interest at an interest rate of 5.2%. How much interest was earned in three years?

70. Carleen deposited $16,400 in a bank account that earned simple interest at an interest rate of 3.9% How much interest was earned in eight years?

71. Hilaria borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000, plus $1,200 interest. What was the rate of simple interest?

72. Kenneth lent his niece $1,200 to buy a computer. Two years later, she paid him back the $1,200, plus $96 interest. What was the rate of simple interest?

73. Lebron lent his daughter $20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the $20,000, plus $3,000 interest. What was the rate of simple interest?

74. Pablo borrowed $50,000 to start a business. Three years later, he repaid the $50,000, plus $9,375 interest. What was the rate of simple interest?

75. In 10 years, a bank account that paid 5.25% simple interest earned $18,375 interest. What was the principal of the account?

76. In 25 years, a bond that paid 4.75% simple interest earned $2,375 interest. What was the principal of the bond?

77. Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Joshua borrow to buy the computer?

78. Margaret’s car loan statement said she would pay $7,683.20 in simple interest for a five-year loan at 9.8%. How much did Margaret borrow to buy the car?

Everyday Math

79 . Tipping At the campus coffee cart, a medium coffee costs $1.65. MaryAnne brings $2.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?

80 . Tipping Four friends went out to lunch and the bill came to $53.75 They decided to add enough tip to make a total of $64, so that they could easily split the bill evenly among themselves. What percent tip did they leave?

Writing Exercises

81. What has been your past experience solving word problems? Where do you see yourself moving forward?

82. Without solving the problem “44 is 80% of what number” think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.

83. After returning from vacation, Alex said he should have packed 50% fewer shorts and 200% more shirts. Explain what Alex meant.

84. Because of road construction in one city, commuters were advised to plan that their Monday morning commute would take 150% of their usual commuting time. Explain what this means.

a. After completing the exercises, use this checklist to evaluate your mastery of the objective of this section.

$This table has four columns and five rows. The first row is a header and it labels each column, “I can…”, “Confidently,” “With some help,” and “No-I don’t get it!” In row 2, the I can was use a problem-solving strategy for word problems. In row 3, the I can was solve number problems. In row 4, the I can was solve percent applications. In row 5, the I can was solve simple interest applications.$

b. After reviewing this checklist, what will you do to become confident for all objectives?

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COMMENTS

Problem-Solving Strategies for Writers: a Review of Research
What are Problem Solving Strategies for Writers? As an alternative to imagining the writing process to be a series of steps or stages that writers work through in linear manner or as a largely mysterious, creative processes informed by embodied knowledge, felt sense, and inner speech, Linda Flower and John Hayes suggested in 1977 that writing should be thought of as a "thinking problem," a ...
Problem-Solving Strategies for Writing
Problem-Solving Strategies for Writing. Paperback - January 1, 1993. A composition rhetoric with a strong process orientation. Flower's familiar cognitive approach is complemented in this edition by the new attention to the social factors that influence writers. Book recommendations, author interviews, editors' picks, and more.
Problem-solving strategies for writing : Flower, Linda : Free Download
Problem-solving strategies for writing by Flower, Linda. Publication date 1985 Topics English language, Report writing Publisher San Diego : Harcourt Brace Jovanovich Collection inlibrary; printdisabled; internetarchivebooks; americana Contributor Internet Archive Language English.
How to Write a Problem Statement (With 3 Examples)
Here are some common situations where writing problem statements might come in handy: Writing an executive summary for a project proposal or research project; ... 10 Problem-solving strategies to turn challenges on their head. Culture . Writing a value statement: your guide to keeping your team aligned.
Problem-solving Strategies for Writing
Problem-solving Strategies for Writing. Linda Flower. Harcourt Brace Jovanovich, 1985 - Language Arts & Disciplines - 256 pages. From inside the book . Contents. Preface . 1: ... talk techniques tell tence textbook thesis things tion topic sentence understand writ writer writer-based prose writer's block writing problem writing process ...
PDF 3 Writing and Problem Solving
3 Writing and Problem Solving ... Listing, brainstorming, and free writing are powerful strategies for getting ideas on paper, but students will need another kind of strategy to help them organize their thoughts so that a reader can grasp the relationships among their ideas. A tree diagram or flow chart of ideas
Problem Solving Strategies for Writing in College and Community
Linda Flower investigated the writing strategies of experienced and inexperienced writers, and came to the conclusion that the overall approach of good writers is that of treating writing as problem-solving. From this she derived nine steps for such an approach and almost thirty different sub-strategies.
Problem-solving Strategies for Writing
Problem-solving Strategies for Writing Linda Flower Snippet view - 1989. Common terms and phrases. analyze argument audience basic Brainstorming CALIFORNIA/SANTA CRUZ UNIVERSITY chapter code words Cognitive Psychology communication conclusion conflict create creative CRUZ The University cues Darwin define develop discussion draft editing ...
Problem Solving Essays: Overview
The most effective problem-solving approach includes some variation of the following steps: Determine the issue (s) Recognize other perspectives. Think of multiple possible results. Research and evaluate the possibilities. Select the best result (s) Communicate your findings. Establish logical action items based on your analysis.
Problem-Solving Strategies for Writing. Third Edition
Orders, Harcourt Brace Jovanovich, 7555 Caldwell Ave., Chicago, IL 60648 ($15.00). Reflecting new development in the field of rhetoric and composition, this textbook's third edition incorporates major changes which propose to turn theory into practical advice. These additions in the third edition draw on a new theoretical understanding of how ...
Problem-solving strategies for writing
1. Problem-solving strategies for writing. 1993, Harcourt Brace Jovanovich College Publishers. in English - 4th ed. 0155001701 9780155001701. zzzz. Not in Library. Libraries near you: WorldCat. 4.
Problem-solving strategies for writing
Comput. Sci. Educ. 1994. TLDR. Through a cross‐disciplinary approach, two researchers solved the problem of poorly written term papers in the computer science curriculum by using software engineering techniques and developing supplemental materials to help students create and then assess their work. Expand. 1 Excerpt.
Problem-Solving Strategies and the Writing Process
Problem-Solving Strategies and the Writing Process. IN THE MIDST of the composition renaissance, an odd fact stands out: our basic methods of teaching writing are the same ones English academics were using in the seventeenth century.'. We still undertake to teach people to write primarily by dissecting and describing a completed piece of writing.
7 Problem-Solving Skills That Can Help You Be a More ...
Problem-solving strategies can be enhanced with the application of creative techniques. You can use creativity to: ... both verbally and in writing. Make sure everyone understands their role for a successful conclusion. 5. Look at (or evaluate) the outcome. Evaluation offers insights into your current situation and future problem-solving. When ...
Problem-solving strategies for writing
Steps and strategies for the Composing Process including: Explore the Rhetorical Problem, Use Creative Thinking, Know the Needs of Your Reader and more. Read more Previous page
35 problem-solving techniques and methods for solving complex problems
Problem-solving strategies can live and die on whether people are onboard. Getting some quick wins is a great way of getting people behind the process. It can be extremely empowering for a team to realize that problem-solving techniques can be deployed quickly and easily and delineate between things they can positively impact and those things ...
Problem-solving Strategies for Writing. Linda Flower. New York
Problem-solving Strategies for Writing. Linda Flower. New York: Harcourt, Brace, Jovanovich Inc., 1981. Pp. xiii + 210. - Volume 6 Issue 3
Problem-Solution Essay
The first step to solving the problem of prescription drug addiction is to prevent the abuse of misuse of prescription drugs by children. ... This lesson has discussed three strategies for writing ...
Problem-Solving Strategies and the Writing Process
Problem-Solving Strategies and the Writing Process IN THE MIDST of the composition renaissance, an odd fact stands out: our basic methods of teaching writing are the same ones English academics were using in the seventeenth century.' We still undertake to teach people to write primarily by dissecting and describing a completed piece of writing.
Problem-Solving Strategies: Definition and 5 Techniques to Try
In general, effective problem-solving strategies include the following steps: Define the problem. Come up with alternative solutions. Decide on a solution. Implement the solution. Problem-solving ...
8 Effective Problem-Solving Strategies
Problem-solving strategies are ways of coming up with solutions to different types of problems. Learn more about different problem-solving strategies and skills. ... They utilize this heuristic to pick classes that involve art and creative writing. The benefit of a heuristic is that it is a fast way to make fairly accurate decisions. The trade ...
4.9: Strategies for Solving Applications and Equations
How To Use a Problem Solving Strategy for Word Problems. Read the problem. Make sure all the words and ideas are understood. Identify what you are looking for. Name what you are looking for. Choose a variable to represent that quantity. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important ...

Table of Contents

What are Problem Solving Strategies for Writers?

Examples of Problem-Solving Strategies

Review of Research

A Fun Exercise

Brevity - Say More with Less

Clarity (in Speech and Writing)

Coherence - How to Achieve Coherence in Writing

Flow - How to Create Flow in Writing

Inclusivity - Inclusive Language

The Elements of Style - The DNA of Powerful Writing

Suggested Edits

Other Topics:

Citation - Definition - Introduction to Citation in Academic & Professional Writing

Collaboration - What is the Role of Collaboration in Academic & Professional Writing?

Information Literacy - Discerning Quality Information from Noise

Rhetoric: Exploring Its Definition and Impact on Modern Communication

The Writing Process - Research on Composing

Writing Studies

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Academic Writing – How to Write for the Academic Community

Professional Writing – How to Write for the Professional World

Authority – How to Establish Credibility in Speech & Writing

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Effective problem statements have these 5 components

What is a problem statement?

When to use a problem statement

How to identify a problem statement

What are problem statements used for?

3 examples of problem statements

Example Problem Statement 1: The Status Quo Problem Statement

Example Problem Statement 2: The Destination Problem Statement

Example Problem Statement 3 The Stakeholder Problem Statement

What are the 5 components of a problem statement?

How do you write a problem statement?

1. Gather data and observe

2. Frame the problem properly

3. Keep asking why (and check in on the progress)

Refining your problem statements

Cultivate your creativity

Madeline Miles

Problem Solving Essays: Overview

DETERMINING THE BEST APPROACH

Writing Effective Problem Solving Essays

Introduction

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35 problem-solving techniques and methods for solving complex problems

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How do you identify problems?

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Clearly define the problem

Don’t jump to conclusions

Try different approaches

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