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Problem-Solving Strategies and Obstacles

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

Sean is a fact-checker and researcher with experience in sociology, field research, and data analytics.

JGI / Jamie Grill / Getty Images

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

What Is Problem-Solving?

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

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

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

The problem-solving process involves:

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

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

Problem-Solving Mental Processes

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

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

Problem-Solving Strategies

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

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

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

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

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

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

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

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

Trial and Error

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

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

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

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

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

How to Apply Problem-Solving Strategies in Real Life

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

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

Obstacles to Problem-Solving

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

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

How to Improve Your Problem-Solving Skills

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

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

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

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

Dunbar K. Problem solving . A Companion to Cognitive Science . 2017. doi:10.1002/9781405164535.ch20

Stewart SL, Celebre A, Hirdes JP, Poss JW. Risk of suicide and self-harm in kids: The development of an algorithm to identify high-risk individuals within the children's mental health system . Child Psychiat Human Develop . 2020;51:913-924. doi:10.1007/s10578-020-00968-9

Rosenbusch H, Soldner F, Evans AM, Zeelenberg M. Supervised machine learning methods in psychology: A practical introduction with annotated R code . Soc Personal Psychol Compass . 2021;15(2):e12579. doi:10.1111/spc3.12579

Mishra S. Decision-making under risk: Integrating perspectives from biology, economics, and psychology . Personal Soc Psychol Rev . 2014;18(3):280-307. doi:10.1177/1088868314530517

Csikszentmihalyi M, Sawyer K. Creative insight: The social dimension of a solitary moment . In: The Systems Model of Creativity . 2015:73-98. doi:10.1007/978-94-017-9085-7_7

Chrysikou EG, Motyka K, Nigro C, Yang SI, Thompson-Schill SL. Functional fixedness in creative thinking tasks depends on stimulus modality .  Psychol Aesthet Creat Arts . 2016;10(4):425‐435. doi:10.1037/aca0000050

Huang F, Tang S, Hu Z. Unconditional perseveration of the short-term mental set in chunk decomposition .  Front Psychol . 2018;9:2568. doi:10.3389/fpsyg.2018.02568

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

9.1 Use a Problem Solving Strategy

Learning objectives.

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

• Approach word problems with a positive attitude
• Use a problem solving strategy for word problems
• Solve number problems

Be Prepared 9.1

Before you get started, take this readiness quiz.

Translate “6 “6 less than twice x ” x ” into an algebraic expression. If you missed this problem, review Example 2.25 .

Be Prepared 9.2

Solve: 2 3 x = 24 . 2 3 x = 24 . If you missed this problem, review Example 8.16 .

Be Prepared 9.3

Solve: 3 x + 8 = 14 . 3 x + 8 = 14 . If you missed this problem, review Example 8.20 .

Approach Word Problems with a Positive Attitude

The world is full of word problems. How much money do I need to fill the car with gas? How much should I tip the server at a restaurant? How many socks should I pack for vacation? How big a turkey do I need to buy for Thanksgiving dinner, and what time do I need to put it in the oven? If my sister and I buy our mother a present, how much will each of us pay?

Now that we can solve equations, we are ready to apply our new skills to word problems. Do you know anyone who has had negative experiences in the past with word problems? Have you ever had thoughts like the student in Figure 9.2 ?

When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. We need to calm our fears and change our negative feelings.

Start with a fresh slate and begin to think positive thoughts like the student in Figure 9.3 . Read the positive thoughts and say them out loud.

If we take control and believe we can be successful, we will be able to master word problems.

Think of something that you can do now but couldn't do three years ago. Whether it's driving a car, snowboarding, cooking a gourmet meal, or speaking a new language, you have been able to learn and master a new skill. Word problems are no different. Even if you have struggled with word problems in the past, you have acquired many new math skills that will help you succeed now!

Use a Problem-solving Strategy for Word Problems

In earlier chapters, you translated word phrases into algebraic expressions, using some basic mathematical vocabulary and symbols. Since then you've increased your math vocabulary as you learned about more algebraic procedures, and you've had more practice translating from words into algebra.

You have also translated word sentences into algebraic equations and solved some word problems. The word problems applied math to everyday situations. You had to restate the situation in one sentence, assign a variable, and then write an equation to solve. This method works as long as the situation is familiar to you and the math is not too complicated.

Now we'll develop a strategy you can use to solve any word problem. This strategy will help you become successful with word problems. We'll demonstrate the strategy as we solve the following problem.

Example 9.1

Pete bought a shirt on sale for $18 , $18 , which is one-half the original price. What was the original price of the shirt?

Step 1. Read the problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the Internet.

• In this problem, do you understand what is being discussed? Do you understand every word?

Step 2. Identify what you are looking for. It's hard to find something if you are not sure what it is! Read the problem again and look for words that tell you what you are looking for!

• In this problem, the words “what was the original price of the shirt” tell you that what you are looking for: the original price of the shirt.

Step 3. Name what you are looking for. Choose a variable to represent that quantity. You can use any letter for the variable, but it may help to choose one that helps you remember what it represents.

• Let p = p = the original price of the shirt

Step 4. Translate into an equation. It may help to first restate the problem in one sentence, with all the important information. Then translate the sentence into an equation.

Step 5. Solve the equation using good algebra techniques. Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers.

Step 6. Check the answer in the problem and make sure it makes sense.

• We found that p = 36 , p = 36 , which means the original price was $36 . $36 . Does $36 $36 make sense in the problem? Yes, because 18 18 is one-half of 36 , 36 , and the shirt was on sale at half the original price.
• Step 7. Answer the question with a complete sentence.
• The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was $36 .” $36 .”

If this were a homework exercise, our work might look like this:

Joaquin bought a bookcase on sale for $120 , $120 , which was two-thirds the original price. What was the original price of the bookcase?

Two-fifths of the people in the senior center dining room are men. If there are 16 16 men, what is the total number of people in the dining room?

We list the steps we took to solve the previous example.

Problem-Solving Strategy

• Step 1. Read the word problem. Make sure you understand all the words and ideas. You may need to read the problem two or more times. If there are words you don't understand, look them up in a dictionary or on the internet.
• Step 2. Identify what you are looking for.
• Step 3. Name what you are looking for. Choose a variable to represent that quantity.
• Step 4. Translate into an equation. It may be helpful to first restate the problem in one sentence before translating.
• Step 5. Solve the equation using good algebra techniques.
• Step 6. Check the answer in the problem. Make sure it makes sense.

Let's use this approach with another example.

Example 9.2

Yash brought apples and bananas to a picnic. The number of apples was three more than twice the number of bananas. Yash brought 11 11 apples to the picnic. How many bananas did he bring?

Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was 3 3 more than the number of notebooks. He bought 5 5 textbooks. How many notebooks did he buy?

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is seven more than the number of crossword puzzles. He completed 14 14 Sudoku puzzles. How many crossword puzzles did he complete?

In Solve Sales Tax, Commission, and Discount Applications , we learned how to translate and solve basic percent equations and used them to solve sales tax and commission applications. In the next example, we will apply our Problem Solving Strategy to more applications of percent.

Example 9.3

Nga's car insurance premium increased by $60 , $60 , which was 8% 8% of the original cost. What was the original cost of the premium?

Pilar's rent increased by 4% . 4% . The increase was $38 . $38 . What was the original amount of Pilar's rent?

Steve saves 12% 12% of his paycheck each month. If he saved $504 $504 last month, how much was his paycheck?

Solve Number Problems

Now we will translate and solve number problems . In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don't usually arise on an everyday basis, but they provide a good introduction to practicing the Problem Solving Strategy . Remember to look for clue words such as difference , of , and and .

Example 9.4

The difference of a number and six is 13 . 13 . Find the number.

The difference of a number and eight is 17 . 17 . Find the number.

The difference of a number and eleven is −7 . −7 . Find the number.

Example 9.5

The sum of twice a number and seven is 15 . 15 . Find the number.

The sum of four times a number and two is 14 . 14 . Find the number.

Try It 9.10

The sum of three times a number and seven is 25 . 25 . Find the number.

Some number word problems ask you 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. 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 9.6

One number is five more than another. The sum of the numbers is twenty-one. Find the numbers.

Try It 9.11

One number is six more than another. The sum of the numbers is twenty-four. Find the numbers.

Try It 9.12

The sum of two numbers is fifty-eight. One number is four more than the other. Find the numbers.

Example 9.7

The sum of two numbers is negative fourteen. One number is four less than the other. Find the numbers.

Try It 9.13

The sum of two numbers is negative twenty-three. One number is 7 7 less than the other. Find the numbers.

Try It 9.14

The sum of two numbers is negative eighteen. One number is 40 40 more than the other. Find the numbers.

Example 9.8

One number is ten more than twice another. Their sum is one. Find the numbers.

Try It 9.15

One number is eight more than twice another. Their sum is negative four. Find the numbers.

Try It 9.16

One number is three more than three times another. Their sum is negative five. Find the numbers.

Consecutive integers are integers that immediately follow each other. Some examples of consecutive integers are:

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

Example 9.9

The sum of two consecutive integers is 47 . 47 . Find the numbers.

Try It 9.17

The sum of two consecutive integers is 95 . 95 . Find the numbers.

Try It 9.18

The sum of two consecutive integers is −31 . −31 . Find the numbers.

Example 9.10

Find three consecutive integers whose sum is 42 . 42 .

Try It 9.19

Find three consecutive integers whose sum is 96 . 96 .

Try It 9.20

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

Links To Literacy

Section 9.1 exercises, practice makes perfect.

In the following exercises, use the problem-solving strategy for word problems to solve. Answer in complete sentences.

Two-thirds of the children in the fourth-grade class are girls. If there are 20 20 girls, what is the total number of children in the class?

Three-fifths of the members of the school choir are women. If there are 24 24 women, what is the total number of choir members?

Zachary has 25 25 country music CDs, which is one-fifth of his CD collection. How many CDs does Zachary have?

One-fourth of the candies in a bag of are red. If there are 23 23 red candies, how many candies are in the bag?

There are 16 16 girls in a school club. The number of girls is 4 4 more than twice the number of boys. Find the number of boys in the club.

There are 18 18 Cub Scouts in Troop 645 . 645 . The number of scouts is 3 3 more than five times the number of adult leaders. Find the number of adult leaders.

Lee is emptying dishes and glasses from the dishwasher. The number of dishes is 8 8 less than the number of glasses. If there are 9 9 dishes, what is the number of glasses?

The number of puppies in the pet store window is twelve less than the number of dogs in the store. If there are 6 6 puppies in the window, what is the number of dogs in the store?

After 3 3 months on a diet, Lisa had lost 12% 12% of her original weight. She lost 21 21 pounds. What was Lisa's original weight?

Tricia got a 6% 6% raise on her weekly salary. The raise was $30 $30 per week. What was her original weekly salary?

Tim left a $9 $9 tip for a $50 $50 restaurant bill. What percent tip did he leave?

Rashid left a $15 $15 tip for a $75 $75 restaurant bill. What percent tip did he leave?

Yuki bought a dress on sale for $72 . $72 . The sale price was 60% 60% of the original price. What was the original price of the dress?

Kim bought a pair of shoes on sale for $40.50 . $40.50 . The sale price was 45% 45% of the original price. What was the original price of the shoes?

In the following exercises, solve each number word problem.

The sum of a number and eight is 12 . 12 . Find the number.

The sum of a number and nine is 17 . 17 . Find the number.

The difference of a number and twelve is 3 . 3 . Find the number.

The difference of a number and eight is 4 . 4 . Find the number.

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

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

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

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

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

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

One number is six more than the other. Their sum is forty-two. Find the numbers.

One number is five more than the other. Their sum is thirty-three. Find the numbers.

The sum of two numbers is twenty. One number is four less than the other. Find the numbers.

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

A number is one more than twice another number. Their sum is negative five. Find the numbers.

One number is six more than five times another. Their sum is six. Find the numbers.

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

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

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

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

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

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

The sum of two consecutive integers is −23 . −23 . Find the integers.

The sum of two consecutive integers is −37 . −37 . Find the integers.

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

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

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

Everyday Math

Shopping Patty paid $35 $35 for a purse on sale for $10 $10 off the original price. What was the original price of the purse?

Shopping Travis bought a pair of boots on sale for $25 $25 off the original price. He paid $60 $60 for the boots. What was the original price of the boots?

Shopping Minh spent $6.25 $6.25 on 5 5 sticker books to give his nephews. Find the cost of each sticker book.

Shopping Alicia bought a package of 8 8 peaches for $3.20 . $3.20 . Find the cost of each peach.

Shopping Tom paid $1,166.40 $1,166.40 for a new refrigerator, including $86.40 $86.40 tax. What was the price of the refrigerator before tax?

Shopping Kenji paid $2,279 $2,279 for a new living room set, including $129 $129 tax. What was the price of the living room set before tax?

Writing Exercises

Write a few sentences about your thoughts and opinions of word problems. Are these thoughts positive, negative, or neutral? If they are negative, how might you change your way of thinking in order to do better?

When you start to solve a word problem, how do you decide what to let the variable represent?

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

ⓑ If most of your checks were:

…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.

…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math, every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?

…no—I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.

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10 Problem-solving strategies to turn challenges on their head

Jump to section

What is an example of problem-solving?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

1. Identify the problem

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

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

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

2. Break the problem down 

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

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

3. Generate potential solutions

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

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

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

4. Evaluate the possible solutions

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

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

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

5. Implement and monitor the solutions

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

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

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

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

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

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

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

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

Let’s break each of these down.

1. Use a solution that worked before

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

2. Brainstorming

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

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

3. Work backward

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

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

4. Use the Kipling method

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

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

Answering these questions can help you identify possible solutions.

5. Draw the problem

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

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

6. Use trial-and-error

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

7. Sleep on it

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

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

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

8. Get advice from your peers

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

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

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

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

9. Use the Pareto principle

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

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

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

10. Add successful solutions to your toolkit

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

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

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

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

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

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

1. Build your problem-solving skills

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

2. Practice

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

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

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

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

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

4. Ask for feedback

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

5. Learn new approaches and methodologies

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

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

6. Experiment

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

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

7. Analyze the success of your competitors

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

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

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

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

Use problem-solving strategies to uplevel your business

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

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

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

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

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Maximize your time and productivity with strategies from our expert coaches.

Elizabeth Perry, ACC

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

8 creative solutions to your most challenging problems

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Problem Solving Strategies: Explore Concrete Examples

Nov 28, 2016

Welcome to Rithm’s series on problem-solving strategies. If you’re just joining us, you may want to start at the beginning. Here’s a list of the articles we’ve written:

• Understand the Problem
• Explore Concrete Examples
• Break It Down
• Solve a Simpler Problem
• Use Tools Strategically
• Look Back and Refactor

In How To Solve It , mathematician George Polya breaks the problem-solving process down into four pieces: understanding the problem, making a plan, executing the plan, and reflecting on the solution. We’ve already talked about understanding the problem, but the next parts of this process could benefit from a little unpacking.

Whether you’re building a new feature for an application with millions of users, or in the middle of a whiteboard interview, it’s essential that you have a plan before you start coding. But planning often requires forethought and insight that comes from experience. Because of this, beginners often feel trapped in a sort of catch-22: they need experience in order to formulate plans effectively, but they need to plan effectively in order to solve problems and gain experience!

Strategy #2: Explore Concrete Examples

When it comes to coding, one way to help formulate a plan is to explore concrete examples . Before starting to program a solution to your problem, make sure you have plenty of examples of how the solution should respond to different inputs. For larger features, these examples may be codified as user stories . For smaller pieces of functionality they may correspond to unit tests . In either case, having a clear understanding of the solution to the problem in many concrete cases can not only help develop your understanding of the problem, but also provides sanity checks that your eventual solution does what you initially thought it should do.

Imagine you’re in an interview and are asked to do the following:

Write a function which takes in a string and returns counts of each character in the string.

Once you feel like you understand the problem, a good check for your understanding is to propose a few different examples of the output that this function should produce for a given input. Here are some helpful things to keep in mind when formulating concrete examples:

• Progress to more complex examples . Once you’ve explored some simple concrete examples, ratchet up the difficulty and see if your understanding can keep pace. This process will often reveal other questions. In the problem above, for instance, what should the output be for an expression like charCount("Your PIN number is 1234!") ? Should the counter only return counts for letters, or for numbers too? What about non-alphanumeric characters? Should it distinguish between uppercase and lowercase letters? Being able to solve the problem in this specific case is critical to planning for a general solution.
• Explore examples with empty inputs . You should be sure to explore edge cases as well. Oftentimes edge cases will be specific to the problem at hand, but there are a couple of general principles. One is to explore what happens if you provide an absence of input into the problem. For example, what happens when you call charCount("") ? Should the output be an empty object? null ? An error?
• Explore examples with invalid inputs . Another helpful class of edge cases comes from considering what happens if you pass invalid data into problem. For example, what happens if you put something which is not a string into charCount ? What’s charCount(null) ? charCount({key: "value"}) ? Understanding these edge cases may not help you solve the core problem, but they will help you develop a more robust solution.

After you’ve explored several concrete examples, it’s time to tackle the problem in general. For that, you may want to make use of another problem-solving strategy. We’ll discuss this one next time.

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1.1: Introduction to Problem Solving

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• Page ID 9821

• Michelle Manes
• University of Hawaii

The Common Core State Standards for Mathematics ( http://www.corestandards.org/Math/Practice ) identify eight “Mathematical Practices” — the kinds of expertise that all teachers should try to foster in their students, but they go far beyond any particular piece of mathematics content. They describe what mathematics is really about, and why it is so valuable for students to master. The very first Mathematical Practice is:

Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

This chapter will help you develop these very important mathematical skills, so that you will be better prepared to help your future students develop them. Let’s start with solving a problem!

Draw curves connecting A to A, B to B, and C to C. Your curves cannot cross or even touch each other,they cannot cross through any of the lettered boxes, and they cannot go outside the large box or even touch it’s sides.

Think / Pair / Share

After you have worked on the problem on your own for a while, talk through your ideas with a partner (even if you have not solved it).

• What did you try?
• What makes this problem difficult?
• Can you change the problem slightly so that it would be easier to solve?

Problem Solving Strategy 1 (Wishful Thinking).

Do you wish something in the problem was different? Would it then be easier to solve the problem?

For example, what if ABC problem had a picture like this:

Can you solve this case and use it to help you solve the original case? Think about moving the boxes around once the lines are already drawn.

Here is one possible solution.

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McGraw Hill My Math Grade 1 Chapter 1 Lesson 6 Answer Key Problem-Solving Strategy: Write a Number Sentence

All the solutions provided in  McGraw Hill My Math Grade 1 Answer Key PDF Chapter 1 Lesson 6 Problem-Solving Strategy: Write a Number Sentence will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 1 Answer Key Chapter 1 Lesson 6 Problem-Solving Strategy: Write a Number Sentence

STRATEGY: Write a Number Sentence

Practice the Strategy

Apply the Strategy

Write an addition number sentence to solve.

Review the Strategies

Choose a strategy

• Write a number sentence.
• Make a table.
• Act it out.

Question 4. Jayla and Will each have 4 fish. How many total fish do Jayla and Will have? ______ fish Answer: 8 fish Explanation: Jayla and Will each have 4 fish. 4 + 4 = 8 8  fish that Jayla and Will had.

Question 5. Deon has 4 jump ropes. Karen has 3 jump ropes. How many jump ropes do they have in all? ____ jump ropes Answer: 7 jump ropes Explanation: Deon has 4 jump ropes. Karen has 3 jump ropes. 4 + 3 = 7 7 jump ropes that they have in all.

Question 6. There are 5 yellow beads and 4 red beads on a necklace. How many beads are on the necklace in all? _____ beads Answer: 9 beads Explanation: There are 5 yellow beads and 4 red beads on a necklace. 5 + 4 = 9 9 beads are on the necklace in all.

McGraw Hill My Math Grade 1 Chapter 1 Lesson 6 My Homework Answer Key

Problem Solving

Underline what you know. Circle what you need to find. Write an addition number sentence.

Math at Home Take advantage of problem-solving opportunities during daily routines such as riding in the car, bedtime, doing laundry, putting away groceries, planning schedules, and so on.

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