math problem solving flow chart

Problem-Solving Flowchart: A Visual Method to Find Perfect Solutions

Lucid Content

Reading time: about 7 min

“People ask me questions Lost in confusion Well, I tell them there's no problem Only solutions” —John Lennon, “Watching the Wheels”

Despite John Lennon’s lyrics, nobody is free from problems, and that’s especially true in business. Chances are that you encounter some kind of problem at work nearly every day, and maybe you’ve had to “put out a fire” before lunchtime once or twice in your career.

But perhaps what Lennon’s saying is that, no matter what comes our way, we can find solutions. How do you approach problems? Do you have a process in place to ensure that you and your co-workers come to the right solution?

In this article, we will give you some tips on how to find solutions visually through a problem-solving flowchart and other methods.

What is visual problem-solving?

If you are a literal thinker, you may think that visual problem-solving is something that your ophthalmologist does when your vision is blurry. For the rest of us, visual problem-solving involves executing the following steps in a visual way:

• Define the problem.
• Brainstorm solutions.
• Pick a solution.
• Implement solutions.
• Review the results.

How to make your problem-solving process more visual

Words pack a lot of power and are very important to how we communicate on a daily basis. Using words alone, you can brainstorm, organize data, identify problems, and come up with possible solutions. The way you write your ideas may make sense to you, but it may not be as easy for other team members to follow.

When you use flowcharts, diagrams, mind maps, and other visuals, the information is easier to digest. Your eyes dart around the page quickly gathering information, more fully engaging your brain to find patterns and make sense of the data.

Identify the problem with mind maps

So you know there is a problem that needs to be solved. Do you know what that problem is? Is there only one problem? Is the problem sum total of a bunch of smaller problems?

You need to ask these kinds of questions to be sure that you are working on the root of the issue. You don’t want to spend too much time and energy solving the wrong problem.

To help you identify the problem, use a mind map. Mind maps can help you visually brainstorm and collect ideas without a strict organization or structure. A mind map more closely aligns with the way a lot of our brains work—participants can bounce from one thought to the next defining the relationships as they go.

Mind mapping to solve a problem includes, but is not limited to, these relatively easy steps:

• In the center of the page, add your main idea or concept (in this case, the problem).
• Branch out from the center with possible root causes of the issue. Connect each cause to the central idea.
• Branch out from each of the subtopics with examples or additional details about the possible cause. As you add more information, make sure you are keeping the most important ideas closer to the main idea in the center.
• Use different colors, diagrams, and shapes to organize the different levels of thought.

Alternatively, you could use mind maps to brainstorm solutions once you discover the root cause. Search through Lucidchart’s mind maps template library or add the mind map shape library to quickly start your own mind map.

Create a problem-solving flowchart

A mind map is generally a good tool for non-linear thinkers. However, if you are a linear thinker—a person who thinks in terms of step-by-step progression making a flowchart may work better for your problem-solving strategy. A flowchart is a graphical representation of a workflow or process with various shapes connected by arrows representing each step.

Whether you are trying to solve a simple or complex problem, the steps you take to solve that problem with a flowchart are easy and straightforward. Using boxes and other shapes to represent steps, you connect the shapes with arrows that will take you down different paths until you find the logical solution at the end.

Flowcharts or decision trees are best used to solve problems or answer questions that are likely to come up multiple times. For example, Yoder Lumber , a family-owned hardwood manufacturer, built decision trees in Lucidchart to demonstrate what employees should do in the case of an injury.

To start your problem-solving flowchart, follow these steps:

• Draw a starting shape to state your problem.
• Draw a decision shape where you can ask questions that will give you yes-or-no answers.
• Based on the yes-or-no answers, draw arrows connecting the possible paths you can take to work through the steps and individual processes.
• Continue following paths and asking questions until you reach a logical solution to the stated problem.
• Try the solution. If it works, you’re done. If it doesn’t work, review the flowchart to analyze what may have gone wrong and rework the flowchart until you find the solution that works.

If your problem involves a process or workflow , you can also use flowcharts to visualize the current state of your process to find the bottleneck or problem that’s costing your company time and money.

Lucidchart has a large library of flowchart templates to help you analyze, design, and document problem-solving processes or any other type of procedure you can think of.

Draw a cause-and-effect diagram

A cause-and-effect diagram is used to analyze the relationship between an event or problem and the reason it happened. There is not always just one underlying cause of a problem, so this visual method can help you think through different potential causes and pinpoint the actual cause of a stated problem.

Cause-and-effect diagrams, created by Kaoru Ishikawa, are also known as Ishikawa diagrams, fishbone diagrams , or herringbone diagrams (because they resemble a fishbone when completed). By organizing causes and effects into smaller categories, these diagrams can be used to examine why things went wrong or might go wrong.

To perform a cause-and-effect analysis, follow these steps.

1. Start with a problem statement.

The problem statement is usually placed in a box or another shape at the far right of your page. Draw a horizontal line, called a “spine” or “backbone,” along the center of the page pointing to your problem statement.

2. Add the categories that represent possible causes.

For example, the category “Materials” may contain causes such as “poor quality,” “too expensive,” and “low inventory.” Draw angled lines (or “bones”) that branch out from the spine to these categories.

3. Add causes to each category.

Draw as many branches as you need to brainstorm the causes that belong in each category.

Like all visuals and diagrams, a cause-and-effect diagram can be as simple or as complex as you need it to be to help you analyze operations and other factors to identify causes related to undesired effects.

Collaborate with Lucidchart

You may have superior problem-solving skills, but that does not mean that you have to solve problems alone. The visual strategies above can help you engage the rest of your team. The more involved the team is in the creation of your visual problem-solving narrative, the more willing they will be to take ownership of the process and the more invested they will be in its outcome.

In Lucidchart, you can simply share the documents with the team members you want to be involved in the problem-solving process. It doesn’t matter where these people are located because Lucidchart documents can be accessed at any time from anywhere in the world.

Whatever method you decide to use to solve problems, work with Lucidchart to create the documents you need. Sign up for a free account today and start diagramming in minutes.

About Lucidchart

Lucidchart, a cloud-based intelligent diagramming application, is a core component of Lucid Software's Visual Collaboration Suite. This intuitive, cloud-based solution empowers teams to collaborate in real-time to build flowcharts, mockups, UML diagrams, customer journey maps, and more. Lucidchart propels teams forward to build the future faster. Lucid is proud to serve top businesses around the world, including customers such as Google, GE, and NBC Universal, and 99% of the Fortune 500. Lucid partners with industry leaders, including Google, Atlassian, and Microsoft. Since its founding, Lucid has received numerous awards for its products, business, and workplace culture. For more information, visit lucidchart.com.

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Sometimes you're faced with challenges that traditional problem solving can't fix. Creative problem solving encourages you to find new, creative ways of thinking that can help you overcome the issue at hand more quickly.

Dialogue mapping is a facilitation technique used to visualize critical thinking as a group. Learn how you and your team can start dialogue mapping today to solve problems and bridge gaps in knowledge and understanding (plus get a free template!).

Bring your bright ideas to life.

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Solving Equations Flowchart

More solving equations activities:

6 comments:

I absolutely love your ideas! Even a middle school student needs activities that they can color and display proudly! Thank you for making my job easier!

Yes, I agree! Even high schoolers like to color! I hope you have the best year!

I used the pennant activity above last year, and the kids LOVED it, (7th grade) they even wanted the harder 2 step equations !

Oh yay! That is great to hear! I do have a couple multi-step math pennants in my tpt store. One involves distribution and the other does not include this step. I hope you are having a great year! Thank you so much for taking time out of your day to comment. It means a lot!

Thank you! Loved the idea of just using index cards. :)

So happy I found this site. Keep up the good work. Great ideas and activities.

Problem solving - flowchart (6th grade math)

This is a multi-step math word problem. I make a flowchart for it, to show the solution steps. And then of course we solve the problem, with the help of a bar model. :)

Math Mammoth Grade 6 curriculum

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Blog Business What is a Problem-Solving Flowchart & How to Make One

What is a Problem-Solving Flowchart & How to Make One

Written by: Danesh Ramuthi Aug 10, 2023

Problem-Solving Flowcharts, contrary to what many believe aren’t just aesthetic wonders — they’re almost like magical blueprints for troubleshooting those pesky problems that many of us face.

Flowcharts take business challenges and turn them into a navigable pathway. In this post, I will guide you on key aspects of problem-solving flowcharts such as what it is, the advantages of problem-solving flowcharts, how to create one and more.

Besides, you’ll also discover how to create problem-solving flowcharts with the help of Venngage’s Flowchart Maker.

And for those of you thinking, “I’m no designer, how can I create one?” worry not! I’ve got you covered. Just hop on Venggage’s Flowchart Templates and you’ll be charting your way to problem-solving glory in no time.

Click to jump ahead:

What are problem-solving flowcharts?

When to use problem-solving flowcharts, what are the advantages of flowcharts in problem-solving, what are the 7 steps of problem-solving flowcharts.

• 5 different types of problem-solving flowcharts

Best practices for designing effective problem-solving flowcharts

How to make a flowchart using venngage , problem-solving flowcharts faqs.

• Final Thoughts

Problem-Solving Flowcharts is a graphical representation used to break down problem or process into smaller, manageable parts, identify the root causes and outline a step-by-step solution. 

It helps in visually organizing information and showing the relationships between various parts of the problem.

This type of flowcharts consists of different symbols and arrows, each representing different components or steps in the problem-solving process. 

By following the flow of the chart, individuals or teams can methodically approach problem, analyze different aspects of it and come to a well-informed solution.

Problem-Solving Flowcharts is a versatile tool that can be used in various scenarios. Here’s when to consider utilizing one:

• Complex Problems: When faced with a multifaceted issue that involves multiple steps or variables, flowcharts can help break down the complexity into digestible parts.
• Team Collaboration: If you’re working with a team and need a common understanding of problem and its potential solutions then a flowchart provides a visual that everyone can refer to.
• Analyzing Processes: In a situation where you need to understand a particular process, whether it’s within a project or a part of regular operations then mapping it out in a flowchart can offer clarity.
• Decision Making: When various paths or decisions might be taken, a flowchart can outline the potential outcomes of each aiding in making an informed choice.
• Training and Onboarding: Flowcharts can be used in training materials to help new employees understand complex processes or procedures which makes the learning curve smoother.
• Identifying Root Causes: If you’re looking to identify the underlying causes of problem then a flowchart can facilitate a systematic approach to reaching the root of the issue.

Related: How to Use Fishbone Diagrams to Solve Complex Problems

Problem-solving flowcharts can offer several benefits to the users who are looking to solve a particular problem. Few advantages of flowcharts in problem solving are: 

Visual Clarity

When you’re dealing with multifaceted problems or processes, words alone can make the situation seem even more tangled. Flowcharts distill these complexities into easily understandable visual elements. 

By mapping out each phase or component of problem, flowcharts offer a bird’s eye view enabling individuals to grasp the bigger picture and the finer details simultaneously.

Sequential Representation

Flowcharts excel in laying out the sequence of events or actions. By indicating a clear starting point and illustrating each subsequent step, they guide users through a process or solution path methodically. 

This linear representation ensures that no step is overlooked and each is executed in the right order.  

Collaboration

Problem-solving often requires team effort and flowcharts are instrumental in fostering collaborative environments. 

When a team is discussing potential solutions or trying to understand problem’s intricacies, a flowchart serves as a collective reference point. 

It aids in synchronizing everyone’s understanding, minimizing miscommunications and promoting constructive discussions. 

Read more about: Flowcharts Symbols and Meaning

1. Define the Problem  

Before anything else, it’s essential to articulate the problem or task you want to solve clearly and accurately. By understanding exactly what needs to be addressed you can ensure that subsequent steps align with the core issue.

2. Identify the Inputs and Outputs  

Determine what inputs (such as data, information or resources) will be required to solve the problem and what the desired outputs or outcomes are. Identifying these factors will guide you in structuring the steps needed to reach the end goal and ensure that all necessary resources are at hand.

3. Identify the Main Steps  

Break down the problem-solving process into its main steps or subtasks. This involves pinpointing the essential actions or stages necessary to reach the solution. Create a roadmap that helps in understanding how to approach the problem methodically.

4. Use Decision Symbols  

In problem-solving, decisions often lead to different paths or outcomes. Using standard symbols to represent these decision points in the flowcharts allows for a clear understanding of these critical junctures. It helps visually present various scenarios and their consequences.

5. Add Descriptions and Details  

A well-designed flowcharts is concise but clear in its labeling. Using arrows and short, descriptive phrases to explain what happens at each step or decision point ensures that the flowcharts communicates the process without unnecessary complexity. 

6. Revise and Refine  

Creating a flowcharts is not always a one-and-done process. It may require revisions to improve its clarity, accuracy or comprehensiveness. Necessary refinement ensures that the flowcharts precisely reflects the problem-solving process and is free from errors or ambiguities.

7. Use Flowchart Tool  

While it’s possible to draw a flowcharts manually, using a flowcharts tool like Venngage’s Flowchart Maker and Venngage’s Flowchart Templates can make the process more efficient and flexible. These tools come with pre-designed templates and intuitive interfaces that make it easy to create, modify and share flowcharts. 

5 different types of problem-solving flowcharts 

Let’s have a look at 5 most common types of flowcharts that individuals and organizations often use. 

1. Process Flowchart s

A process flowcharts is a visual representation of the sequence of steps and decisions involved in executing a particular process or procedure. 

It serves as a blueprint that showcases how different stages or functions are interconnected in a systematic flow and it highlights the direction of the process from its beginning to its end.

Process flowcharts are instrumental in training and onboarding, sales process , process optimization, documentation, recruitment and in any scenario where clear communication of a process is crucial.

2. Flowcharts Infographic 

A flowcharts infographic is a great way to showcase the process or a series of steps using a combination of graphics, icons, symbols and concise text. It aims to communicate complex information in a clear and easy-to-understand manner, making it a popular tool for conveying information, data and instructions in a visually engaging way.

For example, you can use this flowchart to illustrate a health insurance process that visually explains the steps involved from finding a provider to paying for your healthcare provider. 

3. Circular Flowcharts

A circular flowcharts is used to illustrate the flow of information, goods, services or money within a closed system or process. It gets its name from its circular shape, which emphasizes the continuous and cyclical nature of the flow. 

Circular flowcharts are widely used in various fields such as economics, business, engineering and process management to help visualize and understand complex systems.

In a circular flowcharts , elements are represented using various shapes and connected with arrows to indicate the direction of flow. The circular arrangement indicates that the process is ongoing and repeats itself over time.

4. Swimlane flowcharts

Swimlane flowcharts , also known as cross-functional flowcharts are a specific type of flowchart that organizes the process flow into lanes or “swimlanes.” 

Each lane represents a different participant or functional area involved in the process and the flowchart shows how activities or information move between these participants. 

Swimlane flowcharts are particularly useful for illustrating complex processes that involve multiple stakeholders or departments.

In a swimlane flowcharts, the process is divided horizontally into lanes and each lane is labeled with the name of the department, person or role responsible for that part of the process. Vertically, the flowchart displays the sequence of steps or actions taken in the process.

5. Decision Flowchart s

Decision flowcharts, also known as decision trees or flow diagrams are graphical representations that illustrate the process of making decisions or solving problems. 

They are widely used in various fields such as computer science, business mapping , engineering and problem-solving scenarios. 

Decision flowcharts help break down complex decision-making processes into simple, sequential steps, making it easier to understand and follow.

A decision tree is a specialized flowchart used to visually represent the process of decision-making. 

Businesses and other individuals can employ a decision tree analysis as a tool to aid in evaluating different options and the possible consequences associated with each choice.

Decision trees Infographics can be used to create a more nuanced type of flowchart that is more informative and visually appealing by combining a decision flowchart and the flowchart infographic. 

Decision flowcharts are valuable tools for visualizing decision-making processes, analyzing complex problems and communicating them effectively to others.

Designing effective problem-solving flowcharts involves careful consideration of various factors to ensure clarity, accuracy and usability. Here are some best practices to create efficient and useful problem-solving flowcharts:

• Understand the problem first & clearly define it
• Keep it simple
• Use standard & recognizable symbols
• Ensure that the flowchart follows a logical and sequential order
• Clearly label each decision point, action and outcome
• Verify the flowchart’s accuracy by testing it
• Clearly state the decision criteria that lead to different branches
• Provide context when the flowchart is part of a larger process or system
• Review and revise the flowchart

Creating problem-solving flowchart on Venngage is incredibly simple. All you have to do is:

• Start by Signing Up and Creating an Account with Venngage
• Choose a flowchart template that best suits your needs from our library.
• Start editing your flowchart by choosing the desired shapes, labels and colors.
• You can also enhance your flowchart by incorporating icons, illustrations or backgrounds all of which are readily available in our library.
• Once done, you will have 2 options to choose from, either sharing it online for free or downloading your flowchart to your desktop by subscribing to the Premium or Business Plan. 

Is flowchart the representation of problem solutions?

Flowcharts are not the representation of problem solutions per se; rather, they are a visual representation of processes, decision-making steps and actions taken to arrive at a solution to problem.

What are the 3 basic structures of flowcharts?

3 Basic Structures of Flowcharts are:

• Sequence: Simplify Complexity
• Selection (Decision): Embrace Choices
• Repetition (Loop): Emphasize Iteration

What are the elements of a good flowchart?

A good flowchart should exhibit clarity and simplicity, using consistent symbols and labels to depict a logical sequence of steps. It should be readable, with appropriate white space to avoid clutter while eliminating ambiguity through well-defined decision criteria and paths.

Can flowcharts be used for both simple and complex problem-solving?

Yes, flowcharts can be used for both simple and complex problem-solving scenarios. Flowcharts are versatile visual tools that can effectively represent various processes, decision-making steps and problem-solving approaches regardless of their complexity.

In both cases, flowcharts offer a systematic and visual means of organizing information, identifying potential problems and facilitating collaboration among team members.

Can problem-solving flowcharts be used in any industry or domain?

Problem-solving flowcharts can be used in virtually any industry or domain. The versatility and effectiveness of flowcharts make them applicable to a wide range of fields such as Business and Management, Software Development and IT, Healthcare, Education, Finance, Marketing & Sales and a lot more other industries. 

Final thoughts

Problem-solving flowcharts are a valuable and versatile tool that empowers individuals and teams to tackle complex problems with clarity and efficiency.

By visually representing the step-by-step process of identifying, analyzing and resolving issues, flowcharts serve as navigational guides simplifying intricate challenges into digestible parts.

With the aid of modern tools like Venngage’s Flowchart Maker and Venngage’s Flowchart Templates , designing impactful flowcharts becomes accessible to all while revolutionizing the way problems are approached and solved.

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Teaching Problem Solving in Math

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Every year my students can be fantastic at math…until they start to see math with words. For some reason, once math gets translated into reading, even my best readers start to panic. There is just something about word problems, or problem-solving, that causes children to think they don’t know how to complete them.

Every year in math, I start off by teaching my students problem-solving skills and strategies. Every year they moan and groan that they know them. Every year – paragraph one above. It was a vicious cycle. I needed something new.

I put together a problem-solving unit that would focus a bit more on strategies and steps in hopes that that would create problem-solving stars.

The Problem Solving Strategies

First, I wanted to make sure my students all learned the different strategies to solve problems, such as guess-and-check, using visuals (draw a picture, act it out, and modeling it), working backward, and organizational methods (tables, charts, and lists). In the past, I had used worksheet pages that would introduce one and provide the students with plenty of problems practicing that one strategy. I did like that because students could focus more on practicing the strategy itself, but I also wanted students to know when to use it, too, so I made sure they had both to practice.

I provided students with plenty of practice of the strategies, such as in this guess-and-check game.

There’s also this visuals strategy wheel practice.

I also provided them with paper dolls and a variety of clothing to create an organized list to determine just how many outfits their “friend” would have.

Then, as I said above, we practiced in a variety of ways to make sure we knew exactly when to use them. I really wanted to make sure they had this down!

Anyway, after I knew they had down the various strategies and when to use them, then we went into the actual problem-solving steps.

The Problem Solving Steps

I wanted students to understand that when they see a story problem, it isn’t scary. Really, it’s just the equation written out in words in a real-life situation. Then, I provided them with the “keys to success.”

S tep 1 – Understand the Problem.   To help students understand the problem, I provided them with sample problems, and together we did five important things:

• read the problem carefully
• restated the problem in our own words
• crossed out unimportant information
• circled any important information
• stated the goal or question to be solved

We did this over and over with example problems.

Once I felt the students had it down, we practiced it in a game of problem-solving relay. Students raced one another to see how quickly they could get down to the nitty-gritty of the word problems. We weren’t solving the problems – yet.

Then, we were on to Step 2 – Make a Plan . We talked about how this was where we were going to choose which strategy we were going to use. We also discussed how this was where we were going to figure out what operation to use. I taught the students Sheila Melton’s operation concept map.

We talked about how if you know the total and know if it is equal or not, that will determine what operation you are doing. So, we took an example problem, such as:

Sheldon wants to make a cupcake for each of his 28 classmates. He can make 7 cupcakes with one box of cupcake mix. How many boxes will he need to buy?

We started off by asking ourselves, “Do we know the total?” We know there are a total of 28 classmates. So, yes, we are separating. Then, we ask, “Is it equal?” Yes, he wants to make a cupcake for EACH of his classmates. So, we are dividing: 28 divided by 7 = 4. He will need to buy 4 boxes. (I actually went ahead and solved it here – which is the next step, too.)

Step 3 – Solving the problem . We talked about how solving the problem involves the following:

• taking our time
• working the problem out
• showing all our work
• estimating the answer
• using thinking strategies

We talked specifically about thinking strategies. Just like in reading, there are thinking strategies in math. I wanted students to be aware that sometimes when we are working on a problem, a particular strategy may not be working, and we may need to switch strategies. We also discussed that sometimes we may need to rethink the problem, to think of related content, or to even start over. We discussed these thinking strategies:

• switch strategies or try a different one
• rethink the problem
• think of related content
• decide if you need to make changes
• check your work
• but most important…don’t give up!

To make sure they were getting in practice utilizing these thinking strategies, I gave each group chart paper with a letter from a fellow “student” (not a real student), and they had to give advice on how to help them solve their problem using the thinking strategies above.

Finally, Step 4 – Check It.   This is the step that students often miss. I wanted to emphasize just how important it is! I went over it with them, discussing that when they check their problems, they should always look for these things:

• compare your answer to your estimate
• check for reasonableness
• check your calculations
• add the units
• restate the question in the answer
• explain how you solved the problem

Then, I gave students practice cards. I provided them with example cards of “students” who had completed their assignments already, and I wanted them to be the teacher. They needed to check the work and make sure it was completed correctly. If it wasn’t, then they needed to tell what they missed and correct it.

To demonstrate their understanding of the entire unit, we completed an adorable lap book (my first time ever putting together one or even creating one – I was surprised how well it turned out, actually). It was a great way to put everything we discussed in there.

Once we were all done, students were officially Problem Solving S.T.A.R.S. I just reminded students frequently of this acronym.

Stop – Don’t rush with any solution; just take your time and look everything over.

Think – Take your time to think about the problem and solution.

Act  – Act on a strategy and try it out.

Review – Look it over and see if you got all the parts.

Wow, you are a true trooper sticking it out in this lengthy post! To sum up the majority of what I have written here, I have some problem-solving bookmarks FREE to help you remember and to help your students!

You can grab these problem-solving bookmarks for FREE by clicking here .

You can do any of these ideas without having to purchase anything. However, if you are looking to save some time and energy, then they are all found in my Math Workshop Problem Solving Unit . The unit is for grade three, but it  may work for other grade levels. The practice problems are all for the early third-grade level.

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Q1. Add 10 and 20

To solve this problem we will take a variable sum and set it to zero. Then we will take the two numbers 10 and 20 as input. Next we will add both the numbers and save the result in the variable sum i.e., sum = 10 + 20. Finally, we will print the value stored in the variable sum.

Algorithm (in simple English)

• Initialize sum = 0 (PROCESS)
• Enter the numbers (I/O)
• Add them and store the result in sum (PROCESS)
• Print sum (I/O)

Q2. Find the sum of 5 numbers

In this question we are asked to find the sum of 5 numbers. So, we will take two variables - sum and count and set both of them to zero. The sum variable will store the result while the count variable will keep track of how many numbers we have read.

To solve this problem we will use the concept of loop. In loop or iterative operation, we execute some steps repeatedly as long as the given condition is TRUE. In this case we will keep reading the input till we have read 5 numbers.

So, we first initialize sum and count to zero. Then we will take the input and store it in a variable n. Next we will add the value stored in n to sum and save the answer in sum.

i.e., sum = sum + n

Then we will increment count by 1 and check if count is less than 5. If this condition is TRUE then we will take another input. If the condition is FALSE then we will print the value stored in variable sum.

• Initialize sum = 0 and count = 0 (PROCESS)
• Enter n (I/O)
• Find sum + n and assign it to sum and then increment count by 1 (PROCESS)
• Is count < 5 (DECISION)
• if YES go to step 2 else Print sum (I/O)

Q3. Print Hello World 10 times

This problem is also solved using the loop concept. We take a variable count and set it to zero. Then we print "Hello World" and increment count by 1.

i.e., count = count + 1

Next we check if count is less than 10. If this is TRUE then we again print "Hello World" and increment the variable count. On the other hand if the condition if FALSE then we will stop.

• Initialize count = 0 (PROCESS)
• Print Hello World (I/O)
• Increment count by 1 (PROCESS)
• Is count < 10 (DECISION)
• if YES go to step 2 else Stop

Q4. Draw a flowchart to log in to facebook account

This problem can be solved in many ways so, we will encourage you to think and draw a flowchart for this problem using your imagination.

To log in to facebook account we first enter the facbook URL www.facebook.com in our browser like Google, Firefox, Safari, Internet Explorer etc. This request is sent to the facebook server and it responds by sending us the home page of facebook.

Next, we enter our registered Email ID and Password and click the Login button.

Then our login credential is checked. If it is correct, we are show our profile. On the other hand, if the login credential is wrong then an error occurs and we are prompted to re-enter our Email ID and Password.

• Enter www.facebook.com in your browser. (I/O)
• facebook Home page loads (PROCESS)
• Enter your Email ID and Password (I/O)
• Is Email ID and Password Valid (DECISION) if NO then Log in error (PROCESS) go to step 3 else Display facebook Account (I/O) Stop

Note! As there are many ways to solve a given problem so there are many ways to draw a flowchart.

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Solving Equations Flowchart Foldable

By: Author Sarah Carter

Posted on Published: November 19, 2013  - Last updated: August 13, 2022

Categories Algebra Activities & Resources , Equations , Foldables , INBs

I discovered this solving equations flowchart foldable when I still had some students who were getting their steps out of order when trying to solve equations. I downloaded this foldable from In Stillness the Dancing . I had my Algebra 1 students glue it in our interactive notebooks.

I referred to this as our flippy, flappy, foldy thing.  I think this was one of our most-used foldables of the year so far.  Our special education teacher loved it, too.  I guess the reason why I love this so much is that it takes students step by step through the process of solving an equation.  

These are the same questions I would be asking a student if I was sitting by them and helping them.  By giving all of my students this tool and modeling how it works, I am equipping my students to help themselves.  (And, yes, my students remarked that I was WAY TOO happy about this foldable.)

Link to Download Solving Equations Flowchart Foldable

Saturday 13th of May 2017

Thank you for sharing your ideas. They are truly well thought out and very helpful.

Tuesday 7th of February 2017

Thank you for sharing your ideas. You are reenergizing me and inspiring me to try some new-to-me practices. Thank you!

Sarah Carter (@mathequalslove)

Friday 3rd of March 2017

You're welcome! Thanks for reading my blog!

Donna Hoffman

Friday 23rd of December 2016

You are a true inspiration! THANK you for all you do! I teach math 1 6th grade and often need to change things for their level, but the kids really love this book. Thank you again!

Wednesday 19th of April 2017

Thanks for the sweet comment, Donna!

Friday 2nd of September 2016

I have learned the do/undo method...but no examples cover problems like this:

15-8(x-6) / -4 = 2.25

The 15-8 confuses me in the chart

Saturday 16th of July 2016

Thank you so much for sharing! We beginning teachers really appreciate it!!

Tuesday 19th of July 2016

You're very welcome!

How to create a problem-solving flow chart

Problem-solving is one of those topics that we’ve often discussed on this site (check out our Problem Solving guide ). We think it’s one of  THE  vital skills of business. Why? Because you’ll come across problems every day, and you need to arm yourself with the right tools to solve them.

A problem-solving flowchart is one of those tools. It’ll help you take a problem statement, break the problem down into likely causes helping you get to the bottom of what’s gone wrong.

In this post, we’ll cover

• What is a Problem Solving Flow Chart
• How to create a Problem Solving flow chart
• Example 1 of Problem Solving flow chart
• Example 2 of Problem Solving Flow chart
• What flow chart shapes to use
• When should you use a flow chart
• 7 tips on creating your Problem Solving chart

Key Benefits & Likely issues with the tool

Let’s get started!

What is a Problem Solving Flowchart

A Problem Solving flow chart is a diagram that uses shapes, arrows, and text to show a moving sequence of actions and/or activities that help solve a problem.  

How to create a Problem Solving flowchart

• Describe your problem.
• Pose Yes/No Questions that can help identify the cause of the problem
• Question each stage of the process until it is fully examined
• Repeat steps 2 & 3 until you have identified a solution
• Try the solution; if it is successful in addressing the root cause, then you’ve fixed your problem. If not, repeat the process until you have a solution that works.

A problem-solving flowchart attempts to identify a root cause/solution to the trigger that is causing the problem allowing you to change the process and prevent the problem from occurring. 

Let’s now demonstrate the effectiveness of a problem solving flowchart by showing some examples.

Example 1 Problem solving flow chart

In our first example, we’re going to start with something simple to show you the principle of the tool.

We have been given a cup of tea and we don’t like it!  

Let’s use a problem-solving flow chart to find out what’s gone wrong.

We’ve used Excel to capture this flow chart using flowchart shapes (insert –> shapes), you can, of course, use other applications to do this, you don’t’ have to have specialized flow chart software to do this. ( there’s a great flowchart in Excel video here ). Or you can simply use a pen and paper.

Use a rectangle and add your problem statement.

Remember to keep your problem statement unambiguous and straightforward. Here we’ve used “I don’t like my cup of tea.”

Now that we’ve got our problem statement, we’re going to start asking questions.

We’re going to examine the variables that go into a cup of tea in an attempt to find out what’s gone wrong.

** TIP** – Work through your process – rather than start from scratch, if you have a documented process, work through that examining each step to ascertain if there are issues. If not, you might find it useful to research and sketch out the process before starting with your flowchart.

We have a process for the cup of tea, which is:

1/ Boil Water

2/ Place Breakfast Tea teabag in the cup

3/ Add Water

4/ Leave to sit for 2 mins

4/ Remove teabag

5/ Add milk

6/ Add sugar

So our problem solving flow chart needs to examine each of those steps to determine where the failure has occurred. 

We’ll add a question shape (diamond), connect out problem statement to it using an arrow to check if we boiled the kettle. Our Diagram will now look like:

As a question, we want two possible routes – Yes and No.

Our process asks us to boil the kettle if we did, and the answer is Yes, then we can go to the next process step.

If the answer is No, then we have a problem. Our tea will be cold. 

Here we can do one of two things. We can terminate the flow chart, or we can add an activity to rectify the problem (this might be to remake the drink or to perhaps heat the drink up in the microwave).

Our flow chart now looks like this:

Step 2 in our Tea making process was to add a Breakfast-tea tea bag.

So, once again, we’ll ask a question about that step.

“Did we add an English Breakfast teabag.”

As before, we’ll use a question shape, using Yes or No answers. If we performed the process step correctly, we’d move on. If we didn’t, we’ll either end the problem solving (we’ve found the root cause), or we’ll add a corrective action.

Now we’ll repeat this process until we’ve reviewed the whole process.

Our finished flowchart looks like this.

However, we’re not finished.

What happens if we follow the flow chart, and we find we didn’t use boiled water. We remake the tea using boiled water, and we still don’t like it?  

We need to ask some further questions.

We need to update our flow chart to validate that we solved the problem and what to do if we didn’t.

So for each step of the process, our problem solving flowchart now looks like this.

Here’s our completed flow chart.

As you can see, we’ve identified the problem, and we’ve described a corrective action.

But there’s a problem here. With this flowchart, you can still follow it, validating the process, and still end up with a cup of tea that’s unsatisfactory. 

Why is that?

Well, it’s perfectly possible that we started out with a process that’s incorrect. What happens if the process called for using an incorrect tea bag from the start?

So we’ll simplify things by adding a block at the end that if you’re still not happy at the end of reviewing the steps, a full review of the process will be undertaken. This is a simple answer to this problem, and I would expect that you would expand this section in more detail if you were creating a flowchart yourself.

So what does a more complex process look like, how about we look at a business problem?

Example 2 Problem Solving flow chart

OK, so example 1 may have been a bit simple, and you are maybe looking for something in a business context.

So in Example 2, let’s look at a scenario that’s a little more complex.

Let’s assume that your organization has received a non-conforming part. You have been assigned to work with the Vendor to:

• Find out what went wrong
• Prevent recurrence

We’re going to use a problem solving flow chart to help us do that.

As with the first example, we’re going to state the problem.

“The part is non conforming.”

Using the production process from the Vendor, we’ll work through the stages to see if we can spot what’s gone wrong.

The diagram below shows an analysis of the first two steps of the production process using a problem-solving flow chart.

The first thing you’ll notice is that on one process step, there may be many questions to ascertain the potential issue.  

Some of these may be complex and require careful thought.

There may be multiple variables (systems, processes, tools, inputs, etc.) that may require attention.

You will need to analyze each process step, in full, to be sure you have caught all the possible causes of the fault.

Which Flow chart shapes should you use.

A problem solving flow chart usually utilizes only a small number of shapes. We show these in the table below.

When should you use a Problem Solving flow chart

There are many many problem tools available.

A flow chart lends itself to be used when:

• You are looking for a tool that is simple to use
• You are looking to use a tool that does not require complex software
• You want to validate a  process.
• You want something that facilitates collaboration
• You want something that you can use to communicate with others

7 Tips on creating great problem solving flow charts

1/ Use standard shapes!

2/ Make it easy to follow!

3/ Keep things on one page

4/ Don’t overload your boxes with text

5/ Go into enough detail. Don’t try and simplify activities as it might hide problems from being seen.

6/ Collaborate. Where you can utilize a team to help document the problem and the activities do so. The more knowledge of the process, the better chance you’ll have of locating the issue.

7/ Use a consistent direction to flow your process, moving things around the page can confuse people who might look at it.

A flow chart can provide you with a great advantage when looking to solve problems. Some of the key benefits include

• A visual aide that’s easy to understand
• Simple to use, does not require hours and hours of training
• A tool that facilitates collaboration
• Effective for aiding communication
• Provides an effective method of analysing a process

However, as with everything, there are some issues to look out for

• Flowchart fails to capture all process steps and therefore root cause analysis is hit and miss
• Lack of knowledge of the process by the individual compiling the flowchart results in inaccurate problem solving
• Inconsistent flow of process makes maps confusing
• Complex processes may be better suited to other tools (fishbone etc)
• Inconsistent formatting and/or use of shapes result in flowchart that is difficult to utilise.

There are a great many tools out there for problem-solving, and flow charts can be used either as a stand-alone tool or conjunction with one of these other tools.

Flowcharts can make for a great problem-solving tool.  

They’re simple to use, effective, and facilitate collaboration.

We hope you’ve found our article useful, in particular the example walkthroughs.

If you’re looking to use the tool, we’d love some feedback from you and hearing how you’ve got on. Why not fire us a message on twitter or use the comments section below.

This article is part of our Problem Solving Guide.   

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• Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Expanded Form Mean, Median & Mode
• Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
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• Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
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• Physics Mechanics
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• Pre Algebra
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• To solve math problems step-by-step start by reading the problem carefully and understand what you are being asked to find. Next, identify the relevant information, define the variables, and plan a strategy for solving the problem.
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Problem-solving – Flowchart example

The flowchart starts with identifying a problem. After the problem is identified, data is gathered and analyzed. Then, the solution is developed and the best solution is identified. If it isn’t successful, the solution development process starts again. If successful, the plan is implemented and is improved continuously.

Edit this diagram in Gleek

Problem-Solving diagram code in Gleek

Start:queue Identify the problem Data gathering Analyze data Solution development Identify the best solution Successful?:diamond Plan implementation Continue to improve Finish:queue Start–>Identify the problem Identify the problem–>Data gathering Data gathering–>Analyze data Analyze data–>Solution development Solution development–>Identify the best solution Identify the best solution–>Successful? Successful?-no->Solution development Successful?-yes->Plan implementation Plan implementation–>Continue to improve Continue to improve–>Finish

About Flowcharts

A flowchart, or flow chart, is a type of diagram that shows a step-by-step view of a process. Flowcharts document the tasks and decisions needed to achieve a specific goal. A basic flowchart is easy to make and understand. Businesses, engineers and software designers often use flowcharts to diagram their ideas.

Similar flowchart examples

Product development flowchart

A/B testing flowchart

Patient transfer in hospital flowchart

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Math Flowchart

Problem Solving Four Operations Flow Chart for Word Problems

What educators are saying

Description.

This purchase comes with 4 different (editable in Microsoft Word) flow charts for your elementary/intermediate classroom. These flow charts are visual references for your students when solving word problems involving addition, subtraction, multiplication and/or division. They help guide students towards choosing the correct operation when solving word problems in math. Each set of flow charts come in color and black/white. One set includes a CUBES reference (CUBES is a problem solving strategy which includes the following steps: Circle the numbers, Underline the question, Box the key words, Evaluate and Solve)

I also have addition/subtraction and multiplication/division flow charts for purchase and a bundle which includes all of my flow charts with my key word reference.

Thank you for your purchase!

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