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What is Problem Solving?.
Quality Glossary Definition: Problem solving
Problem solving is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution; and implementing a solution.
- The problem-solving process
- Problem solving resources
Problem Solving Chart
The Problem-Solving Process
In order to effectively manage and run a successful organization, leadership must guide their employees and develop problem-solving techniques. Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below.
1. Define the problem
Diagnose the situation so that your focus is on the problem, not just its symptoms. Helpful problem-solving techniques include using flowcharts to identify the expected steps of a process and cause-and-effect diagrams to define and analyze root causes .
The sections below help explain key problem-solving steps. These steps support the involvement of interested parties, the use of factual information, comparison of expectations to reality, and a focus on root causes of a problem. You should begin by:
- Reviewing and documenting how processes currently work (i.e., who does what, with what information, using what tools, communicating with what organizations and individuals, in what time frame, using what format).
- Evaluating the possible impact of new tools and revised policies in the development of your "what should be" model.
2. Generate alternative solutions
Postpone the selection of one solution until several problem-solving alternatives have been proposed. Considering multiple alternatives can significantly enhance the value of your ideal solution. Once you have decided on the "what should be" model, this target standard becomes the basis for developing a road map for investigating alternatives. Brainstorming and team problem-solving techniques are both useful tools in this stage of problem solving.
Many alternative solutions to the problem should be generated before final evaluation. A common mistake in problem solving is that alternatives are evaluated as they are proposed, so the first acceptable solution is chosen, even if it’s not the best fit. If we focus on trying to get the results we want, we miss the potential for learning something new that will allow for real improvement in the problem-solving process.
3. Evaluate and select an alternative
Skilled problem solvers use a series of considerations when selecting the best alternative. They consider the extent to which:
- A particular alternative will solve the problem without causing other unanticipated problems.
- All the individuals involved will accept the alternative.
- Implementation of the alternative is likely.
- The alternative fits within the organizational constraints.
4. Implement and follow up on the solution
Leaders may be called upon to direct others to implement the solution, "sell" the solution, or facilitate the implementation with the help of others. Involving others in the implementation is an effective way to gain buy-in and support and minimize resistance to subsequent changes.
Regardless of how the solution is rolled out, feedback channels should be built into the implementation. This allows for continuous monitoring and testing of actual events against expectations. Problem solving, and the techniques used to gain clarity, are most effective if the solution remains in place and is updated to respond to future changes.
You can also search articles , case studies , and publications for problem solving resources.
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Introduction To 8D Problem Solving: Including Practical Applications and Examples
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Root Cause Analysis: The Core of Problem Solving and Corrective Action
One Good Idea: Some Sage Advice ( Quality Progress ) The person with the problem just wants it to go away quickly, and the problem-solvers also want to resolve it in as little time as possible because they have other responsibilities. Whatever the urgency, effective problem-solvers have the self-discipline to develop a complete description of the problem.
Diagnostic Quality Problem Solving: A Conceptual Framework And Six Strategies ( Quality Management Journal ) This paper contributes a conceptual framework for the generic process of diagnosis in quality problem solving by identifying its activities and how they are related.
Weathering The Storm ( Quality Progress ) Even in the most contentious circumstances, this approach describes how to sustain customer-supplier relationships during high-stakes problem solving situations to actually enhance customer-supplier relationships.
The Right Questions ( Quality Progress ) All problem solving begins with a problem description. Make the most of problem solving by asking effective questions.
Solving the Problem ( Quality Progress ) Brush up on your problem-solving skills and address the primary issues with these seven methods.
Refreshing Louisville Metro’s Problem-Solving System ( Journal for Quality and Participation ) Organization-wide transformation can be tricky, especially when it comes to sustaining any progress made over time. In Louisville Metro, a government organization based in Kentucky, many strategies were used to enact and sustain meaningful transformation.
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Making the Connection In this exclusive QP webcast, Jack ReVelle, ASQ Fellow and author, shares how quality tools can be combined to create a powerful problem-solving force.
Adapted from The Executive Guide to Improvement and Change , ASQ Quality Press.
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The easy 4 step problem-solving process (+ examples)
This is the 4 step problem-solving process that I taught to my students for math problems, but it works for academic and social problems as well.
Every problem may be different, but effective problem solving asks the same four questions and follows the same method.
- What’s the problem? If you don’t know exactly what the problem is, you can’t come up with possible solutions. Something is wrong. What are we going to do about this? This is the foundation and the motivation.
- What do you need to know? This is the most important part of the problem. If you don’t know exactly what the problem is, you can’t come up with possible solutions.
- What do you already know? You already know something related to the problem that will help you solve the problem. It’s not always obvious (especially in the real world), but you know (or can research) something that will help.
- What’s the relationship between the two? Here is where the heavy brainstorming happens. This is where your skills and abilities come into play. The previous steps set you up to find many potential solutions to your problem, regardless of its type.
When I used to tutor kids in math and physics , I would drill this problem-solving process into their heads. This methodology works for any problem, regardless of its complexity or difficulty. In fact, if you look at the various advances in society, you’ll see they all follow some variation of this problem-solving technique.
“The gap between understanding and misunderstanding can best be bridged by thought!” ― Ernest Agyemang Yeboah
Generally speaking, if you can’t solve the problem then your issue is step 3 or step 4; you either don’t know enough or you’re missing the connection.
Good problem solvers always believe step 3 is the issue. In this case, it’s a simple matter of learning more. Less skilled problem solvers believe step 4 is the root cause of their difficulties. In this instance, they simply believe they have limited problem-solving skills.
This is a fixed versus growth mindset and it makes a huge difference in the effort you put forth and the belief you have in yourself to make use of this step-by-step process. These two mindsets make a big difference in your learning because, at its core, learning is problem-solving.
Let’s dig deeper into the 4 steps. In this way, you can better see how to apply them to your learning journey.
Step 1: What’s the problem?
The ability to recognize a specific problem is extremely valuable.
Most people only focus on finding solutions. While a “solutions-oriented” mindset is a good thing, sometimes it pays to focus on the problem. When you focus on the problem, you often make it easier to find a viable solution to it.
When you know the exact nature of the problem, you shorten the time frame needed to find a solution. This reminds me of a story I was once told.
When does the problem-solving process start?
The process starts after you’ve identified the exact nature of the problem.
Homeowners love a well-kept lawn but hate mowing the grass.
Many companies and inventors raced to figure out a more time-efficient way to mow the lawn. Some even tried to design robots that would do the mowing. They all were chasing the solution, but only one inventor took the time to understand the root cause of the problem.
Most people figured that the problem was the labor required to maintain a lawn. The actual problem was just the opposite: maintaining a lawn was labor-intensive. The rearrangement seems trivial, but it reveals the true desire: a well-maintained lawn.
The best solution? Remove maintenance from the equation. A lawn made of artificial grass solved the problem . Hence, an application of Astroturf was discovered.
This way, the law always looked its best. Taking a few moments to apply critical thinking identified the true nature of the problem and yielded a powerful solution.
An example of choosing the right problem to work the problem-solving process on
One thing I’ve learned from tutoring high school students in math : they hate word problems.
This is because they make the student figure out the problem. Finding the solution to a math problem is already stressful. Forcing the student to also figure out what problem needs solving is another level of hell.
Word problems are not always clear about what needs to be solved. They also have the annoying habit of adding extraneous information. An ordinary math problem does not do this. For example, compare the following two problems:
What’s the height of h?
A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?
The first is a simple problem. The second is a complex problem. The end goal in both is the same.
The questions require the same knowledge (trigonometric functions), but the second is more difficult for students. Why? The second problem does not make it clear what the exact problem is. Before mathematics can even begin, you must know the problem, or else you risk solving the wrong one.
If you understand the problem, finding the solution is much easier. Understanding this, ironically, is the biggest problem for people.
Check my other articles about math
Problem-solving is a universal language.
Speaking of people, this method also helps settle disagreements.
When we disagree, we rarely take the time to figure out the exact issue. This happens for many reasons, but it always results in a misunderstanding. When each party is clear with their intentions, they can generate the best response.
Education systems fail when they don’t consider the problem they’re supposed to solve. Foreign language education in America is one of the best examples.
The problem is that students can’t speak the target language. It seems obvious that the solution is to have students spend most of their time speaking. Unfortunately, language classes spend a ridiculous amount of time learning grammar rules and memorizing vocabulary.
The problem is not that the students don’t know the imperfect past tense verb conjugations in Spanish. The problem is that they can’t use the language to accomplish anything. Every year, kids graduate from American high schools without the ability to speak another language, despite studying one for 4 years.
Well begun is half done
Before you begin to learn something, be sure that you understand the exact nature of the problem. This will make clear what you need to know and what you can discard. When you know the exact problem you’re tasked with solving, you save precious time and energy. Doing this increases the likelihood that you’ll succeed.
Step 2: What do you need to know?
All problems are the result of insufficient knowledge. To solve the problem, you must identify what you need to know. You must understand the cause of the problem. If you get this wrong, you won’t arrive at the correct solution.
Either you’ll solve what you thought was the problem, only to find out this wasn’t the real issue and now you’ve still got trouble or you won’t and you still have trouble. Either way, the problem persists.
If you solve a different problem than the correct one, you’ll get a solution that you can’t use. The only thing that wastes more time than an unsolved problem is solving the wrong one.
Imagine that your car won’t start. You replace the alternator, the starter, and the ignition switch. The car still doesn’t start. You’ve explored all the main solutions, so now you consider some different solutions.
Now you replace the engine, but you still can’t get it to start. Your replacements and repairs solved other problems, but not the main one: the car won’t start.
Then it turns out that all you needed was gas.
This example is a little extreme, but I hope it makes the point. For something more relatable, let’s return to the problem with language learning.
You need basic communication to navigate a foreign country you’re visiting; let’s say Mexico. When you enroll in a Spanish course, they teach you a bunch of unimportant words and phrases. You stick with it, believing it will eventually click.
When you land, you can tell everyone your name and ask for the location of the bathroom. This does not help when you need to ask for directions or tell the driver which airport terminal to drop you off at.
Finding the solution to chess problems works the same way
The book “The Amateur Mind” by IM Jeremy Silman improved my chess by teaching me how to analyze the board.
It’s only with a proper analysis of imbalances that you can make the best move. Though you may not always choose the correct line of play, the book teaches you how to recognize what you need to know . It teaches you how to identify the problem—before you create an action plan to solve it.
The problem-solving method always starts with identifying the problem or asking “What do you need to know?”. It’s only after you brainstorm this that you can move on to the next step.
Step 3: What do you already know?
The only way to know if you lack knowledge is by gaining some in the first place. All advances and solutions arise from the accumulation and implementation of prior information. You must first consider what it is that you already know in the context of the problem at hand.
Isaac Newton once said, “If I have seen further, it is by standing on the shoulders of giants.” This is Newton’s way of explaining that his advancements in physics and mathematics would be impossible if it were not for previous discoveries.
Mathematics is a great place to see this idea at work. Consider the following problem:
What is the domain and range of y=(x^2)+6?
This simple algebra problem relies on you knowing a few things already. You must know:
- The definition of “domain” and “range”
- That you can never square any real number and get a negative
Once you know those things, this becomes easy to solve. This is also how we learn languages.
An example of the problem-solving process with a foreign language
Anyone interested in serious foreign language study (as opposed to a “crash course” or “survival course”) should learn the infinitive form of verbs in their target language. You can’t make progress without them because they’re the root of all conjugations. It’s only once you have a grasp of the infinitives that you can completely express yourself. Consider the problem-solving steps applied in the following example.
I know that I want to say “I don’t eat eggs” to my Mexican waiter. That’s the problem.
I don’t know how to say that, but last night I told my date “No bebo alcohol” (“I don’t drink alcohol”). I also know the infinitive for “eat” in Spanish (comer). This is what I already know.
Now I can execute the final step of problem-solving.
Step 4: What’s the relationship between the two?
I see the connection. I can use all of my problem-solving strategies and methods to solve my particular problem.
I know the infinitive for the Spanish word “drink” is “beber” . Last night, I changed it to “bebo” to express a similar idea. I should be able to do the same thing to the word for “eat”.
“No como huevos” is a pretty accurate guess.
In the math example, the same process occurs. You don’t know the answer to “What is the domain and range of y=(x^2)+6?” You only know what “domain” and “range” mean and that negatives aren’t possible when you square a real number.
A domain of all real numbers and a range of all numbers equal to and greater than six is the answer.
This is relating what you don’t know to what you already do know. The solutions appear simple, but walking through them is an excellent demonstration of the process of problem-solving.
In most cases, the solution won’t be this simple, but the process or finding it is the same. This may seem trivial, but this is a model for thinking that has served the greatest minds in history.
A recap of the 4 steps of the simple problem-solving process
- What’s the problem? There’s something wrong. There’s something amiss.
- What do you need to know? This is how to fix what’s wrong.
- What do you already know? You already know something useful that will help you find an effective solution.
- What’s the relationship between the previous two? When you use what you know to help figure out what you don’t know, there is no problem that won’t yield.
Learning is simply problem-solving. You’ll learn faster if you view it this way.
What was once complicated will become simple.
What was once convoluted will become clear.
Ed Latimore
I’m a writer, competitive chess player, Army veteran, physicist, and former professional heavyweight boxer. My work focuses on self-development, realizing your potential, and sobriety—speaking from personal experience, having overcome both poverty and addiction.
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THE FOUR-STEP PROBLEM SOLVING PLAN
Overview of “Four-Step Problem Solving”
The “Four-Step Problem Solving” plan helps elementary math students to employ sound reasoning and to develop mathematical language while they complete a four-step problem-solving process. This problem-solving plan consists of four steps: details, main idea, strategy, and how. As students work through each step, they may use “graphic representations” to organize their ideas, to provide evidence of their mathematical thinking, and to show their strategy for arriving at a solution.
In this step, the student is a reader, a thinker, and an analyzer. First, the student reads over the problem and finds any proper nouns (capitalized words). If unusual names of people or places cause confusion, the student may substitute a familiar name and see if the question now makes sense. It may help the student to re-read the problem, summarize the problem, or visualize what is happening. When the student identifies the main idea, he or she should write it down, using words or phrases; that is, complete sentences are unnecessary. Students need to ask themselves questions such as the ones shown below.
- “What is the main idea in the question of this problem?”
- “What are we looking for?”
- “What do we want to find out?”
The student reads the problem again, sentence by sentence, slowly and carefully. The student identifies and records any details, using numbers, words, and phrases. The student looks for extra information—that is, facts in the reading that do not figure into the answer. In this step, the student should also look for hidden numbers, which may be indicated but not clearly expressed. (Example: The problem may refer to “Frank and his three friends.” In solving the problem, the student needs to understand that there are actually four people, even though “four” or “4” is not mentioned in the reading.) Students ask themselves the following kinds of questions.
- “What are the details needed to answer the question?”
- “What are the important details?”
- “What is going on that can help me answer the question?”
- “What details do I need?”
The student chooses a math strategy (or strategies) to find a solution to the problem and uses that strategy to find the answer/solve the problem. Possible strategies, as outlined in the Texas Essential Knowledge and Skills (TEKS) curriculum, include the following.
- use or draw a picture
- look for a pattern
- write a number sentence
- use actions (operations) such as add, subtract, multiply, divide
- make or use a table
- make or use a list
- work a simpler problem
- work backwards to solve a problem
- act out the situation
The preceding list is just a sampling of the strategies used in elementary mathematics. There are many strategies that students can employ related to questions such as the following.
- “What am I going to do to solve this problem?”
- “What is my strategy?”
- “What can I do with the details to get the answer?”
To make sure that their answer is reasonable and that they understand the process clearly, students use words or phrases to describe how they solved the problem. Students may ask themselves questions such as the following.
- “How did I solve the problem?”
- “What strategy did I use?”
- “What were my steps?”
In this step, students must explain the solution strategy they have selected. They must provide reasons for and offer proof of the soundness of their strategy. This step gives students the opportunity to communicate their understanding of math concepts and math vocabulary represented in the problem they solved and to justify their thinking.
Responses on these four parts need not be lengthy—a list of words and numbers might be used for the details, and phrases might be used for the “Main Idea” and “How.”
Benefits of Using “Four-Step Problem Solving Plan”
One of the method's major benefits to students is that it forces them to operate at high levels of thinking. Teachers, using the tried-and-true Bloom’s Taxonomy to describe levels of thinking, want to take students beyond the lower levels and help them reach the upper levels of thinking. Doing the multiple step method requires students to record their thinking about three steps in the process, in addition to actually "working the problem."
A second benefit of extending the process from three steps to four is that having students think at these levels will deepen their understanding of mathematics and improve their fluency in using math language. In the short term, students' performance on assessments will improve, and confidence in their mathematical ability will grow. In the long term, this rigor in elementary school mathematics will prepare students for increased rigor in secondary mathematics, beginning particularly in grade 7.
Another benefit of using “Four-Step Problem Solving” is that it will increase teachers’ ability to identify specific problems students are having and provide them with information to give specific corrective feedback to students.
Extracting and writing the main idea and details and then showing the strategies to solve problems should also help students establish good test-taking habits for online testing.
Educational Research Supporting “Four-Step Problem Solving”
Although scholarly articles do not mention “Four-Step Problem Solving” by name, most educational experts do advocate the use of multi-step problem-solving methods that foster students’ performing at complex levels of thinking. The number of steps often ranges from four to eight.
Conclusions drawn from studying the work of meta-researcher Dr. Robert Marzano published in the book Classroom Instruction That Works (Marzano, Pickering, Pollock) as well as numerous other research studies, indicate that significant improvement in student achievement occurs when teachers use these strategies.
The National Council of Teachers of Mathematics endorses the use of such strategies as those appearing in “Four-Step Problem Solving”—particularly the step requiring students to explain their answers—as effective for producing students’ math competency, as described in NCTM publications such as Principles and Standards for School Mathematics. Excerpts from NCTM documents validate the district's problem-solving strategy. Some of the key ideas and teaching standards identified include the following.
- Teachers need to investigate how their students arrive at answers. Correct answers don't necessarily equate to correct thinking.
- Students need to explore various ways to think about math problems and their solutions.
- Students need to learn to analyze and solve problems on their own.
- Students' discourse in a mathematics classroom should focus on their thinking process as they solved a problem.
Relationship of “Four-Step Problem Solving” and the TEKS
Although the TEKS for elementary math do not mention a graphic organizer for problem-solving, they do require that students in grades 1-5 learn and do the following things in the area of “Underlying Processes and Mathematical Tools.”
- The student applies mathematics to solve problems connected to everyday experiences and activities in and outside of school.
- Identify the mathematics in everyday situations.
- Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.
- Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
- Use tools such as real objects, manipulatives, and technology to solve problems.
- The student communicates about mathematics using informal language.
- Explain and record observations using objects, words, pictures, numbers, and technology.
- Relate informal language to mathematical language and symbols.
- The student uses logical reasoning to make sense of his or her world.
- Make generalizations from patterns or sets of examples and nonexamples.
- Justify why an answer is reasonable and explain the solution process.
Instructional Methods Behind “Four-Step Problem Solving”
Teachers will use a variety of techniques as they instruct students regarding “Four-Step Problem Solving.” They will
- model use of the “Four-Step Problem Solving Plan” with graphic representations as they guide students through the four-step problem-solving process;
- use a think-aloud method to share their reasoning with students;
- employ questioning strategies that provoke students to higher levels of thinking; and
- foster rich dialogue, both in whole-class discussions and for partner/table activities.
For success with “Four-Step Problem Solving,” talking must occur prior to writing. Students will be shown how to bridge the span between math and language to express their reasoning in a way that uses logical sequences and proper math vocabulary terms. Once students have mastered the ability to communicate out loud with the teacher and with peers, they can transition to developing the skill of conducting an “internal dialogue” for solving problems independently.
Students Using “Four-Step Problem Solving”
Use of a common graphic organizer at all schools would greatly benefit our ever-shifting population of students—not only those whose families move often, but also those affected by boundary changes we continue to experience as we grow. District-wide staff development has focused on acquainting all elementary math teaching staff with “Four-Step Problem Solving,” and outlining expectations for students’ problem-solving knowledge and skills outlined in the TEKS at each grade-level.
Because it is the steps in the problem that are important, not the graphic representation itself, vertical math teams on each campus, working with the building principal, have the option of selecting or designing a graphic organizer, as long as it fulfills the four-step approach. Alternatives to “The Q” include a four-pane “window pane” or a simple list of the four steps. Another scheme adopted by some schools is being called SQ-RQ-CQ-HQ, which uses the old three steps plus a new fourth step—the “HQ” is the "how" step. Schools using SQ-RQ-CQ-HQ should consider how the advent of online testing will impact its use.
Putting “The Four-Step Problem Solving Plan” into Action
In class, students will use “Four-Step Problem Solving” in a variety of circumstances.
- Students will participate in whole-class discussion and completion of “Four-Step Problem Solving” pages as the teacher explains math problems to the group. To guide students through the steps, teachers may place a “Four-Step Problem Solving Organizer” transparency on the overhead, affix a “Four-Step Problem Solving Organizer” visual aid to the white board, use a “Four-Step Problem Solving Organizer” poster, or simply draw a “Four-Step Problem Solving Organizer” on the board to fill in the areas of the graphic organizer so that students observe how to solve the problems.
- Students will work in pairs to complete daily work with a partner using four-step problem solving. Having a partner allows the students to discuss aspects of the problem-solving process, a grouping arrangement which helps them develop the language skills needed for completing the steps of the problem-solving process.
- Students will complete assignments on their own using the four steps, allowing teachers to gauge their ability to master the steps needed to complete the problem-solving process.
Students can expect to see “Four-Step Problem Solving” used in all phases of math instruction, including assessments. Students will be given problems and asked to identify the main idea, details, and process used, as well as solve for a calculation.
The district’s expectation is that students will ultimately use “Four-Step Problem Solving” for all story problems, unless directed otherwise. When students clearly understand the process and concepts they are studying, teachers may choose to limit the writing of the “how.” Improved student achievement comes in classrooms that routinely and consistently use all four steps of the process.
Using this approach should reduce the number of problems students are assigned. Completing the “Four-Step Problem Solving” should take only a few minutes. As students become familiar with the graphic organizer, they will be able to increase the pace of their work. Students can save time by writing only the main idea (instead of copying the entire question) and by using words or phrases in describing the “how” (instead of complete sentences).
For years, researchers of results on the National Assessment of Educational Progress ( NAEP ) and the Trends in International Mathematics and Science Study ( TIMSS ) have cited curricular and instructional differences between U.S. schools and schools in countries that outperform us in mathematics. For example, Japanese students study fewer concepts and work fewer problems than American students do. In Japan , students spend their time in exploring multiple approaches to solving a problem, thereby deepening their understanding of mathematics. Depth of understanding is our goal for students, too, and we believe that the four-step problem-solving plan will help us achieve this goal.
The ultimate goal is that students learn to do the four steps without the use of a pre-printed form. This ability becomes necessary on assessments such as TAKS, since security rules prohibit the teacher from distributing any materials. In 2007, when students may first be expected to take TAKS online, students will need a plan for problem-solving on blank paper to ensure that they don’t just, randomly select an answer—they can’t underline and circle on the computer monitor’s glass.
Assessment and Grading with “The Four-Step Problem Solving Plan”
Assignments using “The Four-Step Problem Solving Plan” may include daily work, homework, quizzes, and tests (including district-developed benchmarks). CFISD’s grade-averaging software includes options for all these categories. As with other assignments, grades may be taken for individuals or for partners/groups. Experienced teachers are already familiar with all these grading scenarios.
Teachers may use a rubric for evaluating student work. The rubric describes expectations for students’ responses and guides teachers in giving feedback. Rubrics may be used in many subjects in school, especially for reviewing students’ written compositions in language arts.
A range of “partial credit” options is possible, depending on the teacher’s judgment regarding the student’s reasoning and thoroughness. Students may be asked to redo incomplete portions to earn back points. Each campus makes a decision about whether the process will be included in one grade or if process will be a separate grade.
Knowledge of students’ thinking will help the teacher to provide the feedback and/or the re-teaching that will get a struggling student back on track, or it will allow the teacher to identify students who have advanced understanding in mathematics so that their curriculum can be adjusted. Looking at students' work and giving feedback may require additional time because the teacher is examining each student's thought processes, not just checking for a correct numeric answer.
Because students’ success in communicating their understanding of a math concept does not require that they use formal language mechanics (complete sentences, perfect spelling, etc.) when completing “The Four-Step Problem Solving Plan,” the rubric does not address these skills, leading math teachers to focus and assign grades that represent the students’ mastery of math concepts.
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Easy Problem Solving Using the 4-step Method
June 7, 2017 by Jennifer Haury Category: Guest Author , Management
At a recent hospital town forum, hospital leaders are outlining the changes coming when a lone, brave nurse raises her hand and says, “We just can’t take any more changes. They are layered on top of each other and each one is rolled out in a different way. We are exhausted and it’s overloading us all.”
“Flavor of the Month” Fatigue
Change fatigue. You hear about it in every industry, from government sectors to software design to manufacturing to healthcare and more. When policy and leadership changes and process improvement overlap it’s no surprise when people complain about “flavor of the month,” and resist it just so they can keep some routine to their days.
In a time where change is required just to keep up with the shifting environment, one way to ease fatigue is to standardize HOW we change. If we use a best practice for solving problems, we can ensure that the right people are involved and problems are solved permanently, not temporarily. Better yet, HOW we change can become the habit and routine we long for.
The 4-step Problem Solving Method
The model we’ve used with clients is based on the A3 problem-solving methodology used by many “lean” production-based companies. In addition to being simpler, our 4-step method is visual, which helps remind the user what goes into each box.
The steps are as follows
- Develop a Problem Statement
- Determine Root Causes
- Rank Root Causes in Order of Importance
- Create an Action Plan
Step 1: Develop a Problem Statement
Developing a good problem statement always seems a lot easier than it generally turns out to be. For example, this statement: “We don’t have enough staff,” frequently shows up as a problem statement. However, it suggests the solution—“GET MORE STAFF” — and fails to address the real problem that more staff might solve, such as answering phones in a timely manner.
The trick is to develop a problem statement that does not suggest a solution. Avoiding the following words/phrases: “lack of,” “no,” “not enough,” or “too much” is key. When I start to fall into the trap of suggesting a solution, I ask: “So what problem does that cause?” This usually helps to get to a more effective problem statement.
Once you’ve developed a problem statement, you’ll need to define your target goal, measure your actual condition, then determine the gap. If we ran a restaurant and our problem was: “Customers complaining about burnt toast during morning shift,” the target goal might be: “Toast golden brown 100% of morning shift.”
Focus on a tangible, achievable target goal then measure how often that target is occurring. If our actual condition is: “Toast golden brown 50% of the time,” then our gap is: “Burnt toast 50% of the time.” That gap is now a refined problem to take to Step 2.
Step 2: Determine Root Causes
In Step 2, we want to understand the root causes. For example, if the gap is burnt toast 50% of the time, what are all the possible reasons why?
This is when you brainstorm. It could be an inattentive cook or a broken pop-up mechanism. Cooks could be using different methods to time the toasting process or some breads toast more quickly. During brainstorming, you’ll want to include everyone in the process since observing these interactions might also shed light on why the problem is occurring.
Once we have an idea of why, we then use the 5-why process to arrive at a root cause. Ask “Why?” five times or until it no longer makes sense to ask. Root causes can be tricky. For example, if the pop up mechanism is broken you could just buy a new toaster, right? But if you asked WHY it broke, you may learn cooks are pressing down too hard on the pop up mechanism, causing it to break. In this case, the problem would just reoccur if you bought a new toaster.
When you find you are fixing reoccurring problems that indicates you haven’t solved for the root cause. Through the 5-why process, you can get to the root cause and fix the problem permanently.
Step 3: Rank Root Causes
Once you know what’s causing the problem (and there may be multiple root causes), it’s time to move to Step 3 to understand which causes, if solved for, would close your gap. Here you rank the root causes in order of importance by looking at which causes would have the greatest impact in closing the gap.
There may be times when you don’t want to go after your largest root cause (perhaps because it requires others to change what they are doing, will take longer, or is dependent on other things getting fixed, etc). Sometimes you’ll find it’s better to start with a solution that has a smaller impact but can be done quickly.
Step 4: Create an Action Plan
In Step 4 you create your action plan — who is going to do what and by when. Documenting all of this and making it visible helps to communicate the plan to others and helps hold them accountable during implementation.
This is where your countermeasures or experiments to fix the problem are detailed. Will we train our chefs on how to use a new “pop-up mechanism” free toaster? Will we dedicate one toaster for white bread and one for wheat?
Make sure to measure your results after you’ve implemented your plan to see if your target is met. If not, that’s okay; just go through the steps again until the problem is resolved.
Final Thoughts
Using the 4-step method has been an easy way for teams to change how they solve problems. One team I was working with started challenging their “solution jumps” and found this method was a better way to avoid assumptions which led to never really solving their problems. It was easy to use in a conference room and helped them make their thinking visual so everyone could be involved and engaged in solving the problems their team faced.
Do you have a problem-solving method that you use at your worksite? Let us know in the comments below.
MRSC is a private nonprofit organization serving local governments in Washington State. Eligible government agencies in Washington State may use our free, one-on-one Ask MRSC service to get answers to legal, policy, or financial questions.
About Jennifer Haury
Jennifer Haury is the CEO of All Angles Consulting, LLC and guest authored this post for MRSC.
Jennifer has over 28 years learning in the healthcare industry (17 in leadership positions or consulting in performance improvement and organizational anthropology) and is a Lean Six Sigma Black Belt.
She is a trusted, experienced leader with a keen interest in performance improvement and organizational anthropology. Jennifer is particularly concerned with the sustainability of continuous improvement programs and the cultural values and beliefs that translate into behaviors that either get in our own way or help us succeed in transforming our work.
The views expressed in guest columns represent the opinions of the author and do not necessarily reflect those of MRSC.
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Lesson Plan
Problem-solving steps, view aligned standards, learning objectives.
Students will be able to identify a problem and engage in problem-solving steps to come up with a solution to strengthen their responsible decision-making competency.
Introduction
- Bring students together in a circle, either seated or standing.
- Bring blocks with you to the circle.
- Show the student the blocks and ask them to watch you build a tall castle.
- After you build it, bring out two figurines that you would like to play with in the castle.
- Say out loud, "Hmm....there seems to be a problem. This castle is too small for my toys. How can I make this bigger?"
- Take a few big breaths into your belly and ask the class to breathe with you.
- Explain that deep breathing can help you stay calm and focused when solving a problem.
- Ask the class, "How can I make this castle bigger?"
- Ask, "Would someone like to come up and think of a new way to solve this problem?"
- Invite one student to come up to solve the problem (i.e., make a larger castle).
- Ask your student volunteer, "What would you do here? How would you test a solution?"
- Give the student time to come up with a solution to make a larger castle.
- Identify the problem.
- Look at what solutions have already been tried.
- Think of new ways to solve the problem.
- Try it out!
- Thank your student volunteer for showing you how to solve the problem and send them back to their seats.
- Say, "All of us sometimes come across problems we have to solve, and sometimes friends can help us, too!"
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Plan Do Check Act: A Simple 4 Step Problem Solving Methodology
Plan Do Check Act is a framework that was created by quality guru, Edward Deming as a way of structuring problem solving and continuous improvement.
The generic steps of PDCA are:
Plan – Identify the problem, where you want to be and gather the facts. Start to define the reasons and get to the root causes.
Do – Implement the improvement and test.
Check – Check it’s worked and review the data
Act – If it’s worked, standardise the improvement. If not, tackle the next problem and repeat PDCA again.
This process forms the backbone of a continuous improvement culture.
In fact, Toyota who helped pioneer this method, has built their whole ethos and success around it.
One of their mantras is that everyone in the organisation should make improvements based on the scientific method, under the guidance of a coach.
That scientific method is the “hypothesis”–”experiment”–”evaluation” process, that’s used over and over again. The Plan Do Check Act cycle is a reflection of this.
And everyone adopts it, using the support of a coach or their leader, to help them implement improvements, daily.
Systematic Plan Do Check Act Process
Plan Do Check Act can be used for many different scenarios. In fact, where there’s a problem, it should be used to eliminate it. And it provides a framework to solve it in a structured way.
The role of the coach is to ensure that the PDCA model is being used correctly and people are learning the method. And that they also understand their own processes and systems.
If they understand them by observing and measuring data, they can be best placed to make informed and accurate improvements.
The coach also ensures that they don’t jump to conclusions too soon.
This is a common problem that most inexperienced practitioners make. And it leads to incomplete solutions.
Problems come back, repeatedly .
Plan Do Check Act and 2 Different Reasoning Patterns
Deep within this framework lies two key problem solving techniques:
- Inductive Problem Solving
- Deductive Problem Solving
Inductive problem solving starts with data and generates theories based on that data.
Deductive problem solving starts with theories and proves the theory applies.
So How Does it all Fit?
Using the plan do check act approach, you bind inductive and deductive problem solving together.
The Japanese approach of problem solving and making decisions is to ‘go see’. This means go to the place the problem happens (or the improvement needs to happen), and observe.
By observing and understanding, you learn more about the problem.
Based on your observations, you then make some theories to test and understand more.
And based on the outcomes, you learn.
You can learn by proving that your deductive reasoning hasn’t worked. And by this, I mean, what you thought should have happened, didn’t.
In this scenario, you go again, study the data by using inductive reasoning, and find the next idea that’ll improve the situation.
This is repeated, until you improve the situation and solve the problem.
When you do, you lock the improvement in and standardise the process to ensure the problem doesn’t return.
By following this journey of observing, and analysing data (inductive reasoning) and then making theories on what’s happening (deductive reasoning), you can fix problems and keep them that way.
Plan Do Check Act Model
The Plan Do Check Act model incorporates both of these reasoning modes.
One of the mistakes that many inexperienced problem solvers make is that they just go with their gut feel and focus all their efforts on making judgements…
Without stopping to verify and use the data to support this.
What often happens is that problems tend to come back.
And fixes are normally temporary.
The plan do check act framework allows you to follow a structured way of improving. Using both inductive and deductive reasoning.
Ttaking time to see what’s actually happening when the improvements made. Adjusting, based on the results.
The 9 Step Process to Effective Problem Solving, Built Around Plan Do Check Act
When you encounter a problem, here’s what you can follow, using plan do check act as a guide:
- Define the problem and its impact – Start with identifying what’s wrong; what’s the current state? What’s the problem and what should it all look like in an ideal world?
This first stage of the plan do check act cycle is about understanding the problem, right now. Once understood, it’s time to take note of what it should like, if the problem wasn’t there.
- Understand the facts – This is the inductive problem solving part. Watch, observe and measure the problem with data, first.
What exactly’s happening? What’s the data saying? Are there any trends? Is it happening at certain times of the day / week /month? How often does it happen? Get as much data as possible to allow you to make informed deductive reasoning.
- Contain the problem – As there’s a problem happening right now, this next step is to ensure the problem doesn’t get any bigger. If it’s a process problem, the main aim is to ensure it never reaches the customer.
Containing the problem means taking action to minimise the impact. Limp through whilst you give yourself time to observe and conduct the long-term fix.
- Measure the data – It’s now time to delve deeper into the inductive problem solving phase.
This is done by observation and analysis. What actually is happening? Where is the process failing? What’s the data saying? What are the trends?
- Find the root cause to the problem – You’re now in a position of knowledge. You’ve observed and analysed what’s happening. You’ve also created a list of the many potential root causes.
It’s time to take things a little further by drilling down to find the root causes. Some simple but effective ways ( but not the only way ) of doing this is the use of the Fishbone Diagram and the 5 Whys analysis.
The point is to identify the root causes and create a plan to eliminate them.
- Implement the corrective action – Here’s where you apply the heavy lifting. You’ve looked at the problem; analysed the data, contained the problem and identified a root cause.
It’s time to commit action to overcome the root cause. What things need to be completed to put it to bed?
During this phase of the cycle, you’ll complete your action plan to do just that.
- Check the data after the correction, to ensure its worked – This is pretty self-explanatory. It’s now time to observe some more, and to see if the solution has worked or not.
In the grand scheme of continuous improvement, you’ve learned either way.
If the problem is still there, then you know that what you thought it was, actually wasn’t the case. So it’s time to go again and re-evaluate, passing through the Plan – Do – Check – Act phases again.
If it did work, you’ve also gained a deeper understanding and should now be in control of things.
- Standardise the process to support what you’ve learned – Now, you must extrapolate the lessons learned and lock in the change. In most instances, this would entail a process change of some sort.
Standardising means changing whatever needs to be changed and making it the new way of working. You do this to control of the process. And so, you ensure the problem doesn’t come back.
- Recognise and provide positive feedback – Celebrate a job well done; congratulate the team and let everyone know of the achievement.
Remember, to lead well. Communicate, empower and provide feedback!
This is a particularly forgotten element of continuous improvement and good leadership.
So don’t forget to give people a pat on the back for demonstrating the right behaviours and achievements during the project.
Here’s how these 9 steps fit within the Plan Do Check Act framework:
plan do check act framework
Where can You Use Plan Do Check Act?
You can use this method in every problem your business has.
It could be in identifying persistent perpetual errors that keep happening in processes, no matter how manual they appear.
In fact, the common reasoning when people make errors is to just settle for it being a human error.
The PDCA method can show you another way of looking at things.
And if you adopted these 9 steps, you’ll be pleasantly surprised that this assumption your human error conclusion can turn out to be something that can be controlled more readily.
You can also use it to coach your teams in making improvements.
In mature, lean environments, leaders should coach the PDCA framework, empowering teams to make their own improvements.
Leaders do this by asking 4 key questions to the teams, and getting them to internalise and provide answers around the plan do check act cycle:
- What is it that should be happening?
- What is actually happening?
- What’s the biggest obstacle you’re going to work on improving?
- When can we go and see if it’s worked?
These four questions help coach the plan do check act framework across the organisation.
Plan Do Check Act Can be Used Across All Parts of the Business
The PDCA model can quite literally be used anywhere in the business.
In fact, if you’re serious about implementing a continuous improvement culture, then it must be used everywhere, and at all times.
Other areas that structured PDCA can support improvements, are:
- Improving productivity
- Reducing customer complaints in the same common failings
- Improving staff engagement
- Improving profitability
- Reducing process downtime
- Improving quality
- Reducing cost
- Improving delivery performance
- Eliminating waiting of work
- Improving morale and staff engagement
And many others that you may have thought of yourself.
Brain Power
5 steps (and 4 techniques) for effective problem solving.
Problem solving is the process of reviewing every element of an issue so you can get to a solution or fix it. Problem solving steps cover multiple aspects of a problem that you can bring together to find a solution. Whether that’s in a group collaboratively or independently, the process remains the same, but the approach and the steps can differ.
To find a problem solving approach that works for you, your team, or your company, you have to take into consideration the environment you’re in and the personalities around you.
Knowing the characters in the room will help you decide on the best approach to try and ultimately get to the best solution.
Table of Contents
5 problem solving steps, 4 techniques to encourage problem solving, the bottom line, more tips on problem solving.
No matter what the problem is, to solve it, you nearly always have to follow these problem solving steps. Missing any of these steps can cause the problem to either resurface or the solution to not be implemented correctly.
Once you know these steps, you can then get creative with the approach you take to find the solutions you need.
1. Define the Problem
You must define and understand the problem before you start, whether you’re solving it independently or as a group. If you don’t have a single view of what the problem is, you could be fixing something that doesn’t need fixing, or you’ll fix the wrong problem.
Spend time elaborating on the problem, write it down, and discuss everything, so you’re clear on why the problem is occurring and who it is impacting.
Once you have clarity on the problem, you then need to start thinking about every possible solution . This is where you go big and broad, as you want to come up with as many alternative solutions as possible. Don’t just take the first idea; build out as many as you can through active listening, as the more you create, the more likely you’ll find a solution that has the best impact on the team.
3. Decide on a Solution
Whichever solution you pick individually or as a team, make sure you think about the impact on others if you implement this solution. Ask questions like:
- How will they react to this change?
- Will they need to change anything?
- Who do we need to inform of this change?
4. Implement the Solution
At this stage of problem solving, be prepared for feedback, and plan for this. When you roll out the solution, request feedback on the success of the change made.
5. Review, Iterate, and Improve
Making a change shouldn’t be a one time action. Spend time reviewing the results of the change to make sure it’s made the required impact and met the desired outcomes.
Make changes where needed so you can further improve the solution implemented.
Each individual or team is going to have different needs and may need a different technique to encourage each of the problem solving steps. Try one of these to stimulate the process.
1-2-4 All Approach + Voting
The 1-2-4-All is a good problem solving approach that can work no matter how large the group is. Everyone is involved, and you can generate a vast amount of ideas quickly.
Ideas and solutions are discussed and organized rapidly, and what is great about this approach is the attendees own their ideas, so when it comes to implementing the solutions, you don’t have more work to gain buy-in.
As a facilitator, you first need to present the group with a question explaining the problem or situation. For example, “What actions or ideas would you recommend to solve the company’s lack of quiet working areas?”
With the question clear for all to see, the group then spends 5 minutes to reflect on the question individually. They can jot down their thoughts and ideas on Post-Its.
Now ask the participants to find one or two other people to discuss their ideas and thoughts with. Ask the group to move around to find a partner so they can mix with new people.
Ask the pairs to spend 5 minutes discussing their shared ideas and thoughts.
Next, put the group into groups of two or three pairs to make groups of 4-6. Each group shouldn’t be larger than six as the chances of everyone being able to speak reduces.
Ask the group to discuss one interesting idea they’ve heard in previous rounds, and each group member shares one each.
The group then needs to pick their preferred solution to the problem. This doesn’t have to be voted on, just one that resonated most with the group.
Then ask for three actions that could be taken to implement this change.
Bring everyone back together as a group and ask open questions like “What is the one thing you discussed that stood out for you?” or “Is there something you now see differently following these discussions?”
By the end of the session, you’ll have multiple approaches to solve the problem, and the whole group will have contributed to the future solutions and improvements.
The Lightning Decision Jam
The Lightning Decision Jam is a great way to solve problems collaboratively and agree on one solution or experiment you want to try straight away. It encourages team decision making, but at the same time, the individual can get their ideas and feedback across. [1]
If, as a team, you have a particular area you want to improve upon, like the office environment, for example, this approach is perfect to incorporate in the problem solving steps.
The approach follows a simple loop.
Make a Note – Stick It on The Wall – Vote – Prioritize
Using sticky notes, the technique identifies major problems, encourages solutions, and opens the group up for discussion. It allows each team member to play an active role in identifying both problems and ways to solve them.
Mind Mapping
Mind mapping is a fantastic visual thinking tool that allows you to bring problems to life by building out the connections and visualizing the relationships that make up the problem.
You can use a mind map to quickly expand upon the problem and give yourself the full picture of the causes of the problem, as well as solutions [2] .
The goal of a mind map is to simplify the problem and link the causes and solutions to the problem.
To create a mind map, you must first create the central topic (level 1). In this case, that’s the problem.
Next, create the linked topics (level 2) that you place around and connect to the main central topic with a simple line.
If the central topic is “The client is always changing their mind at the last minute,” then you could have linked topics like:
- How often does this happen?
- Why are they doing this?
- What are they asking for?
- How do they ask for it?
- What impact does this have?
Adding these linking topics allows you to start building out the main causes of the problem as you can begin to see the full picture of what you need to fix. Once you’re happy that you’ve covered the breadth of the problem and its issues, you can start to ideate on how you’re going to fix it with the problem solving steps.
Now, start adding subtopics (level 3) linking to each of the level 2 topics. This is where you can start to go big on solutions and ideas to help fix the problem.
For each of the linked topics (level 2), start to think about how you can prevent them, mitigate them, or improve them. As this is just ideas on paper, write down anything that comes to mind, even if you think the client will never agree to it!
The more you write down, the more ideas you’ll have until you find one or two that could solve the main problem.
Once you run out of ideas, take a step back and highlight your favorite solutions to take forward and implement.
The 5 Why’s
The five why’s can sound a little controversial, and you shouldn’t try this without prepping the team beforehand.
Asking “why” is a great way to go deep into the root of the problem to make the individual or team really think about the cause. When a problem arises, we often have preconceived ideas about why this problem has occurred, which is usually based on our experiences or beliefs.
Start with describing the problem, and then the facilitator can ask “Why?” fives time or more until you get to the root of the problem. It’s tough at first to keep being asked why, but it’s also satisfying when you get to the root of the problem [3] .
As a facilitator, although the basic approach is to ask why, you need to be careful not to guide the participant down a single route.
To help with this, you can use a mind map with the problem at the center. Then ask a why question that will result in multiple secondary topics around the central problem. Having this visual representation of the problem helps you build out more useful why questions around it.
Once you get to the root of the problem, don’t forget to be clear in the actions to put a fix in place to resolve it.
Learn more about how to use the five why’s here .
To fix a problem, you must first be in a position where you fully understand it. There are many ways to misinterpret a problem, and the best way to understand them is through conversation with the team or individuals who are experiencing it.
Once you’re aligned, you can then begin to work on the solutions that will have the greatest impact through effective problem solving steps.
For the more significant or difficult problems to solve, it’s often advisable to break the solution up into smaller actions or improvements.
Trial these improvements in short iterations, and then continue the conversations to review and improve the solution. Implementing all of these steps will help you root out the problems and find useful solutions each time.
- The Simplest Ways to Improve Your Problem Solving Skills
- How to Use the 5 Whys to Get to the Root Cause of Any Problem
- Creative Problem Solving: Create Meaning from Contradictory Ideas
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Module 1: Problem Solving Strategies
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Unlike exercises, there is never a simple recipe for solving a problem. You can get better and better at solving problems, both by building up your background knowledge and by simply practicing. As you solve more problems (and learn how other people solved them), you learn strategies and techniques that can be useful. But no single strategy works every time.
Pólya’s How to Solve It
George Pólya was a great champion in the field of teaching effective problem solving skills. He was born in Hungary in 1887, received his Ph.D. at the University of Budapest, and was a professor at Stanford University (among other universities). He wrote many mathematical papers along with three books, most famously, “How to Solve it.” Pólya died at the age 98 in 1985.1
1. Image of Pólya by Thane Plambeck from Palo Alto, California (Flickr) [CC BY
In 1945, Pólya published the short book How to Solve It , which gave a four-step method for solving mathematical problems:
First, you have to understand the problem.
After understanding, then make a plan.
Carry out the plan.
Look back on your work. How could it be better?
This is all well and good, but how do you actually do these steps?!?! Steps 1. and 2. are particularly mysterious! How do you “make a plan?” That is where you need some tools in your toolbox, and some experience to draw upon.
Much has been written since 1945 to explain these steps in more detail, but the truth is that they are more art than science. This is where math becomes a creative endeavor (and where it becomes so much fun). We will articulate some useful problem solving strategies, but no such list will ever be complete. This is really just a start to help you on your way. The best way to become a skilled problem solver is to learn the background material well, and then to solve a lot of problems!
Problem Solving Strategy 1 (Guess and Test)
Make a guess and test to see if it satisfies the demands of the problem. If it doesn't, alter the guess appropriately and check again. Keep doing this until you find a solution.
Mr. Jones has a total of 25 chickens and cows on his farm. How many of each does he have if all together there are 76 feet?
Step 1: Understanding the problem
We are given in the problem that there are 25 chickens and cows.
All together there are 76 feet.
Chickens have 2 feet and cows have 4 feet.
We are trying to determine how many cows and how many chickens Mr. Jones has on his farm.
Step 2: Devise a plan
Going to use Guess and test along with making a tab
Many times the strategy below is used with guess and test.
Make a table and look for a pattern:
Procedure: Make a table reflecting the data in the problem. If done in an orderly way, such a table will often reveal patterns and relationships that suggest how the problem can be solved.
Step 3: Carry out the plan:
Notice we are going in the wrong direction! The total number of feet is decreasing!
Better! The total number of feet are increasing!
Step 4: Looking back:
Check: 12 + 13 = 25 heads
24 + 52 = 76 feet.
We have found the solution to this problem. I could use this strategy when there are a limited number of possible answers and when two items are the same but they have one characteristic that is different.
Videos to watch:
1. Click on this link to see an example of “Guess and Test”
http://www.mathstories.com/strategies.htm
2. Click on this link to see another example of Guess and Test.
http://www.mathinaction.org/problem-solving-strategies.html
Check in question 1:
Place the digits 8, 10, 11, 12, and 13 in the circles to make the sums across and vertically equal 31. (5 points)
Check in question 2:
Old McDonald has 250 chickens and goats in the barnyard. Altogether there are 760 feet . How many of each animal does he have? Make sure you use Polya’s 4 problem solving steps. (12 points)
Problem Solving Strategy 2 (Draw a Picture). Some problems are obviously about a geometric situation, and it is clear you want to draw a picture and mark down all of the given information before you try to solve it. But even for a problem that is not geometric thinking visually can help!
Videos to watch demonstrating how to use "Draw a Picture".
1. Click on this link to see an example of “Draw a Picture”
2. Click on this link to see another example of Draw a Picture.
Problem Solving Strategy 3 ( Using a variable to find the sum of a sequence.)
Gauss's strategy for sequences.
last term = fixed number ( n -1) + first term
The fix number is the the amount each term is increasing or decreasing by. "n" is the number of terms you have. You can use this formula to find the last term in the sequence or the number of terms you have in a sequence.
Ex: 2, 5, 8, ... Find the 200th term.
Last term = 3(200-1) +2
Last term is 599.
To find the sum of a sequence: sum = [(first term + last term) (number of terms)]/ 2
Sum = (2 + 599) (200) then divide by 2
Sum = 60,100
Check in question 3: (10 points)
Find the 320 th term of 7, 10, 13, 16 …
Then find the sum of the first 320 terms.
Problem Solving Strategy 4 (Working Backwards)
This is considered a strategy in many schools. If you are given an answer, and the steps that were taken to arrive at that answer, you should be able to determine the starting point.
Videos to watch demonstrating of “Working Backwards”
https://www.youtube.com/watch?v=5FFWTsMEeJw
Karen is thinking of a number. If you double it, and subtract 7, you obtain 11. What is Karen’s number?
1. We start with 11 and work backwards.
2. The opposite of subtraction is addition. We will add 7 to 11. We are now at 18.
3. The opposite of doubling something is dividing by 2. 18/2 = 9
4. This should be our answer. Looking back:
9 x 2 = 18 -7 = 11
5. We have the right answer.
Check in question 4:
Christina is thinking of a number.
If you multiply her number by 93, add 6, and divide by 3, you obtain 436. What is her number? Solve this problem by working backwards. (5 points)
Problem Solving Strategy 5 (Looking for a Pattern)
Definition: A sequence is a pattern involving an ordered arrangement of numbers.
We first need to find a pattern.
Ask yourself as you search for a pattern – are the numbers growing steadily larger? Steadily smaller? How is each number related?
Example 1: 1, 4, 7, 10, 13…
Find the next 2 numbers. The pattern is each number is increasing by 3. The next two numbers would be 16 and 19.
Example 2: 1, 4, 9, 16 … find the next 2 numbers. It looks like each successive number is increase by the next odd number. 1 + 3 = 4.
So the next number would be
25 + 11 = 36
Example 3: 10, 7, 4, 1, -2… find the next 2 numbers.
In this sequence, the numbers are decreasing by 3. So the next 2 numbers would be -2 -3 = -5
-5 – 3 = -8
Example 4: 1, 2, 4, 8 … find the next two numbers.
This example is a little bit harder. The numbers are increasing but not by a constant. Maybe a factor?
So each number is being multiplied by 2.
16 x 2 = 32
1. Click on this link to see an example of “Looking for a Pattern”
2. Click on this link to see another example of Looking for a Pattern.
Problem Solving Strategy 6 (Make a List)
Example 1 : Can perfect squares end in a 2 or a 3?
List all the squares of the numbers 1 to 20.
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400.
Now look at the number in the ones digits. Notice they are 0, 1, 4, 5, 6, or 9. Notice none of the perfect squares end in 2, 3, 7, or 8. This list suggests that perfect squares cannot end in a 2, 3, 7 or 8.
How many different amounts of money can you have in your pocket if you have only three coins including only dimes and quarters?
Quarter’s dimes
0 3 30 cents
1 2 45 cents
2 1 60 cents
3 0 75 cents
Videos demonstrating "Make a List"
Check in question 5:
How many ways can you make change for 23 cents using only pennies, nickels, and dimes? (10 points)
Problem Solving Strategy 7 (Solve a Simpler Problem)
Geometric Sequences:
How would we find the nth term?
Solve a simpler problem:
1, 3, 9, 27.
1. To get from 1 to 3 what did we do?
2. To get from 3 to 9 what did we do?
Let’s set up a table:
Term Number what did we do
Looking back: How would you find the nth term?
Find the 10 th term of the above sequence.
Let L = the tenth term
Problem Solving Strategy 8 (Process of Elimination)
This strategy can be used when there is only one possible solution.
I’m thinking of a number.
The number is odd.
It is more than 1 but less than 100.
It is greater than 20.
It is less than 5 times 7.
The sum of the digits is 7.
It is evenly divisible by 5.
a. We know it is an odd number between 1 and 100.
b. It is greater than 20 but less than 35
21, 23, 25, 27, 29, 31, 33, 35. These are the possibilities.
c. The sum of the digits is 7
21 (2+1=3) No 23 (2+3 = 5) No 25 (2 + 5= 7) Yes Using the same process we see there are no other numbers that meet this criteria. Also we notice 25 is divisible by 5. By using the strategy elimination, we have found our answer.
Check in question 6: (8 points)
Jose is thinking of a number.
The number is not odd.
The sum of the digits is divisible by 2.
The number is a multiple of 11.
It is greater than 5 times 4.
It is a multiple of 6
It is less than 7 times 8 +23
What is the number?
Click on this link for a quick review of the problem solving strategies.
https://garyhall.org.uk/maths-problem-solving-strategies.html
- SentryOne Newsletter
4 Steps to Efficiently Solve Problems
Published On: January 26, 2021
Categories: Career, Problem Solving 0
Problems—we all have to deal with minor or major problems in our personal or professional lives. Having a consistent problem-solving approach can be very helpful, and demonstrating strong problem-solving skills can help you stand out in your career.
In this blog post, I'm going to cover a simple problem-solving framework. Although much of what I discuss can be applied to any type of problem, I'll focus on using the framework from a professional standpoint.
"We cannot solve our problems with the same thinking we used when we created them." - Albert Einstein
Categories of Problems
Work-related problems can generally be categorized by the area they impact most. That's not to say a problem can't impact multiple areas, but usually there is an area of primary impact. I find it useful to categorize problems into the following three categories:
- People —These problems center around people, their expectations, and their interactions with other people.
- Product —These problems are related to what you produce at work. The "product" can be tangible or intangible. If you're a home builder, your product would be houses. If you're a software developer, the product would be the application you work on. If you're a sales professional, you produce sales. Problems in this category are often related to the "product" not meeting the expectations of the customer or stakeholder.
- Process —These problems are related to the processes you use at work, generally in the context of producing the work product. The problem could be the process isn't producing the desired result, the process isn't being followed, or the process doesn't account for enough scenarios.
Although the framework described in the sections below works with each of these categories, the specific approaches you take might vary. For example, if you're dealing with a process-related problem, a group discussion to analyze the problem likely makes sense. If it's a people problem, group discussions can be counterproductive, particularly in the early stages.
The Steps (and the Pre-Step)
The framework consists of four steps and a very important pre-step. The four steps are as follows:
- Analyze —Understand the root cause.
- Plan —Determine how to resolve the problem.
- Implement —Put the resolution in place.
- Evaluate —Determine if the resolution is producing the desired results.
I'll discuss these steps further below, but first I want to discuss an important precursor—triage. In emergency medical situations, the triage process is used to prioritize patients: do they need immediate attention to survive, or do they have injuries that aren't immediately life threatening? Sometimes, we're faced with more problems than we can immediately solve, so it's helpful to prioritize them. I find the following questions to be useful in this process:
- Is there an immediate action I need to take to reduce the impact of the problem?
- Is there a reasonable degree of likelihood I can solve this problem?
- If I can solve the problem, can I solve it in a timely manner?
- If I can solve the problem, will it make a significant difference?
The answers to these questions can help you prioritize the order in which you should focus on particular problems. If a problem is causing significant and immediate pain, then you need to stabilize the situation first—often by addressing the symptoms.
For example, if a customer is upset, you need to address their immediate pain before attempting to resolve the root problem. Once you've done so, you can move on to prioritization. If a problem is solvable, can be solved quickly, and has a significant impact, you should focus on it first. If you aren't sure the problem can be solved, or solving it won't have a positive impact, then it should be lower on the priority list.
Once this prioritization has been completed, you can analyze the problem.
The goal for analyzing the problem is to understand the root cause(s). (Yes, problems can have more than one root cause.) If you can address the root cause, you can prevent the problem from recurring. It's important during this process to get multiple perspectives on why the problem occurs. If the problem is in the Product or Process categories, I like to use a group of approximately five people to discuss the root causes. If it's a person problem, a group setting might be counterproductive and individual conversations are better. However, for Person problems, it's critical to get multiple perspectives.
There are many techniques for getting to the root cause of problems. One popular and effective approach is the " 5 whys ." With this approach, you iteratively ask "Why?" about the problem and then each answer until you get to a root cause. For example:
- Why did the upgrade fail? -> The prerequisite updates weren't installed.
- Why weren't the prerequisites installed? -> The person performing the install didn't know there were prerequisites.
- Why didn't the person performing the install know there were prerequisites? -> They didn't read the release notes.
- Why didn't they read the release notes? -> The release notes aren't included or linked to from the installer.
- Why aren't the release notes included or linked to from the installer? -> Because the release notes aren't always required reading for an upgrade.
When using the "5 whys" approach, it's important to look for process failures as the root cause. In many cases, it's easy to get to a why such as "There wasn't enough time" or "We didn't have enough people." If you want to fix the root cause, you need to get to "Why did the process fail to alert us of the problem?"
Once you have one or more root causes, you can start looking at how to resolve them going forward. This is another great time in the process to involve multiple people. Having multiple perspectives can produce innovative approaches to address the root causes. It's also important to remember you might need multiple solutions if you have multiple root causes.
Brainstorming is a good way to generate ideas, but it's helpful to have a method to manage all the ideas that can be produced. Affinity Grouping is an approach that has been around for a long time, and for good reason—it works well. After generating ideas, you group and potentially combine the similar ones. The various ideas in each group can lead to a better, more rounded solution.
An important aspect of the solution(s) you develop is that you can measure the outcomes. I've seen many great ideas that simply didn't result in the desired outcomes for reasons that couldn't be anticipated. If you're able to measure successful outcomes (and unsuccessful outcomes), it helps you adjust more quickly and pivot to different solutions if needed.
Now it's time to put the solution in place. How you do so can vary significantly depending on what the solution is. However, a key consideration should be how the solution will be monitored. This is why it's important to define what success looks like in the planning stage. Those measurements are what you will monitor.
It's important to allow some time before moving to the next step. How much time? It depends—it can be helpful to look at how many times the new solution has been used when determining this. For the example above about release notes, imagine you decided to add an "IMPORTANT" note in a new version of an installer to link people to the release notes. If a week has passed, but only one person has downloaded the new version, then you probably don't have a large enough sample size to evaluate the solution yet. Conversely, if it's only been 24 hours, but 50 people have downloaded the new version, you have a much better sample to work with.
Evaluating the solution requires looking at the outcomes objectively and determining if they match expectations. Often, you will find the solution did improve things, but perhaps not as much as you would have liked. If that's the case, you can refine and iterate on the solution. It might take a few iterations to get the outcomes you would like.
What if the outcomes really don't match expectations? This scenario often indicates the root cause wasn't fully understood, and you might need to jump back to the Analyze step. Revisiting the problem with the additional insight of what did not work can help you uncover other root causes.
The next time you're faced with a problem at work, think TAPIE :
Problem solving is a process—and it's one we need to be able to carry out in a thoughtful and timely manner throughout our careers. Our ability to consistently and efficiently address problems can be what sets us apart.
John Welch is the Chief Technology Officer at SentryOne, where he leads a team in the development of a suite of data and BI products that make monitoring, building, testing, and documenting data solutions faster and more efficient. John has been working with data, business intelligence, and data warehousing technologies since 2001. He was awarded as a Microsoft Most Valued Professional (MVP) 2009 - 2016 due to his commitment to sharing his knowledge with the IT community, and is an SSAS Maestro. John is an experienced speaker, having given presentations at Professional Association for SQL Server (PASS) conferences, the Microsoft Business Intelligence conference, Software Development West (SD West), Software Management Conference (ASM/SM), SQL Bits, and others. He has also contributed to multiple books on SQL Server and business intelligence.
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Dec 5, 2014
The Four P’s to Problem Solving
Prep, plan, perform & perfect.
Being a great designer means you’re able to solve great problems. In more cases than one a client will present you with a problem and your job is to solve that problem using your tools. If you’re a digital designer the tools might be the elements and principles of art and design as well as a graphics application.
All problems need their own specific solutions. We can’t use a generic solution for everything. However we can use the same process, we can approach every project with the same step by step process.
Before we take a look at the process let’s first understand why we think the way we think.
Cognitive Thinking
What I’m about to go over has a lot to do with Psychology however it plays a very valid role in visual communication and the design process. When I say the word Psychology I’m simply referring to an explanation of why we do what we do .
In Psychology we have a term called Cognition or more specifically Cognitive Thinking. Which basically means our mental process or the order in which we think. Cognition is always active, it never stops, even in our subconscious. Problem solving is a form of cognition . Please take note that there are many different ways to solve problems using different techniques and principles.
The process I’m going to share with you is one I have put together over the years of designing and creating. I have broken the process down into the four “P’s” of problem solving.
The Problem Solving Process
- The first step is prep , this is where we understand and diagnose the problem.
- Then our next step is plan . This is where we organize everything before acting.
- The third step is perform . We simply put the plan into action.
- Then our final step is perfect . This is when we check to see if our end goal has fulfilled the problem. If not we can go back, review and rework the solution.
Every Solution derives from a problem. How one gets to that solution is a process. Lets take a look at a typical problem a designer might face and how it might be solved. We simply want to understand how a designer would go about solving a design problem.
We will walk through the process with the story of Marty the designer and his work for Lou’s Cafe .
Prep , is short for preparation . In the preparation phase we simply want to do two things. First understand, and second Diagnose the project.
A well defined problem is understanding the nature of the problem and what information is needed to solve it.
The exact opposite of a well defined problem is an ill defined problem. This is when you know there is a problem but you just don’t understand it.
This is why it’s so crucial for us to clearly understand the problem before moving forward. If you’re not prepared how can you get the right solution?
In this particular project the problem appears to be predefined. The client in this case Lou has asked Marty for a website. Now just because Lou asked for this doesn’t mean that’s the problem. Lou simply assumed this because his sales were down and everyone else on the block has a website.
For Marty to understand the root of the problem he had to contact Lou and ask him a couple questions before moving forward.
Marty called Lou and set up an appointment to meet with him. They planned to meet the very next day at the cafe. Marty has had meetings with clients many times before as he has been doing this for over ten years.
On the phone Marty always keeps his conversations light and asks key questions without directly asking factual questions, like: “Who are your regular customers?” instead of “What’s your target market?”. Marty really tries to get inside clients mind and thought process with his business to fully understand what the problem might be.
When Marty read that Lou wanted a website he was curious what made him come to this conclusion?
The next day Marty had trouble finding the cafe so he showed up a little later than expected. When Marty opened the door his nostrils filled with the most amazing desert aroma. He was greeted by Lou who had an iconic mustache, slicked hair and spoke as if he known him forever. Lou made Marty feel at home as he offered him a slice of his signature peanut butter pie.
Marty and Lou sat at a table as Marty drove the conversation. Lou explained that his regular customers were gone as most of them have passed or moved. Also the neighborhood isn’t what it used to be. Lou said he feels disconnected from his community now and he really needs help as the business is failing. Marty assured Lou that he would do everything he could and would help out. He said he needed some time to construct a plan and he will get back to him within a weeks time.
After that meeting Marty had a clear understanding of what the problems were. He also understood what he needed to do. Marty then wrote down the problems he identified.
Identifiable problems
- The Cafe is hard to find
- There is absolutely no brand identity
- Need to bring the experience to the people
Initial diagnosis for the problems
- Make the Cafe more visible
- Develop a brand identity for the Cafe
- Convey the Cafe’s personality to the community through print and digital mediums
Marty was now ready to move onto his next step, the planning stage.
The second step of the problem solving process for a designer is planning. We know what the problem is and what the diagnoses is, we now just need to plan for a solution.
In the planning phase you simply want to list what you think you need to do to carry out a great solution to the problem or in this case problems.
The planning process is nothing more than an educated guess or if you want to get all scientific; the hypothesis. Lets take a look at how this pans out in our story
Marty knows what the problems are and he’s diagnosed them. He needs to put together an educated guess on how to solve the problems. In the design world this documenting of the educated guess might be know as a proposal .
A proposal is what, in our case Marty is to present to the Lou the Client, on how he plans to fix the problems. The proposal basically lists the diagnosed problems and a list of solutions Marty feels will solve these problems. These are the proposed solutions Marty listed for Lou:
- Make the Cafe more visible using signage signage and listing the cafe on Google Maps.
- Convey the experience of the cafe through print and digital mediums
Marty then presents the proposal to Lou. Lou is a little hesitant at first but feels confident with Marty and trusts his expertise.
Now the planning stage is read for action we’re ready to move onto the next step, Performing.
We are onto our third step in the problem solving process, Performing. This is where we put our design skills to the test. We use the design elements and principles of design to perform solutions for our problems at hand.
In this particular case Marty will start the design process and start to form his solution for Lou’s Cafe. Lets take a look at his steps to success.
Marty’s process varies from project to project. However he seems to have the same approach when he’s in the performance stage. Marty works quick and focused, with all of his attention dialed in on solving the problem.
Carrying out this step didn’t always come easy to Marty, or any designer for that matter. There are always things that hold us back especially in this step. The perform step is the most difficult and stressful. At the same time it’s the most rewarding when completed.
Here are a couple of tips when performing:
- You must be passionate and talk yourself through the problems
- It’s always a good idea to break project down into steps or sprints for quick wins
- Positivity is key, always be positive
- Avoid all distractions, turn the phone off, avoid social media and email
- Keep it simple and clear, always remind yourself the problem you’re solving
- Always go with your gut feeling
- Be confident about your work, own it.
Let’s get back to the story. This is how Marty executed his performance.
- He did some research and gathered inspiration
- He took a look at Lou’s competitors to see how he could make Lou’s stand out from the rest
- He designed a style guide for Lou’s Cafe
- Then designed he designed all the mediums for the Cafe, from signage to a website to packaging, etc…
- Next got quotes on everything and then organized it for Lou to look over.
Marty then went to show Lou all that he had done. Lou was estatic but surprised at the cost. Marty emphasized the importance of design and how it will speak quality to his business. Lou agreed.
Marty then went back to his studio and finished up all his design work for Lou. He then sent everything to print and finished building everything out for the site. He also listed Lou’s Cafe on a few online applications to help the community find and rate the Cafe.
When he was finished Marty felt great, he felt rewarded. He knew this was going to be a huge impact for Lou and his business.
As you can see the performance part of the problem solving process can be quite stressful and tedious. However it’s the most rewarding of them all.
Now that we understand the performance stage lets take a look at the final stage in the problem solving process.
The last step in the problem solving process is the perfection stage. This is where we reevaluate everything and see if we need to go back and change anything.
I don’t want you to think the third step we just went over is a rough draft of some sort, it’s not at all. You should deliver a finalized product that you feel best solves the problem or problems at hand in that step.
However with that said there is always room for improvement, always. Especially when it comes to dealing with web applications and design.
In the perfection stage the first thing we want to do is define the initial problem and look at it with a fresh set of eyes. Here are the original problems:
- The Cafe was hard to find
- No brand identity
Now let’s evaluate our approach and solutions to those problems
- Did we design a solution to make the Cafe more visible? Yes
- Is the brand consistent? Yes
- Did we bring the experience to the people? Yes
Everything appeared to have worked out well for Lou’s Cafe, until about a year later. Two things happened:
- The local health committee was currently fighting obesity amongst the community and cracked down on Lou’s specialty pies.
- Because of the uproar someone had vandalized the signage pointing to the shop.
Lou didn’t know what to do so he called up Marty who had originally solved these problems and asked him for help.
You might be asking yourself why would Lou call Marty about these issues they have nothing to do with design aesthetics or code development. You’re forgetting one thing, Lou doesn’t look at Marty as a designer or a developer he looks at him as a problem solver .
Once Lou told Marty about his problem, Marty assured Lou he would help out and get back to him as soon as possible.
This is what the Perfection stage is all about. You simple reevaluate the problems and cycle through the process over and over until its currently perfected.
Take note though. This process is never really perfected, as there are so many variables to deal with. The only thing we can do is, prep, plan, perform over and over.
This process is the same with any other industry. Take the automotive industry for example. Every year they put out a new car that is better than the last. How much better?… not much. They just solve problems as they come along. Take for example when the following happened…
- Cars are reaching high speeds and drivers are being tossed around in collisions — Hence the design for the seat belt came along
- Having a hard time seeing when it’s raining? — The birth of windshield wipers
- Need more environmentally safe fueling options — The birth of the electric car
In design there is always room for perfection, even more so there is always room for problem solvers like Marty.
In Marty’s case he processed Lou’s problems like any other:
Preparation
Understand and diagnose the problem. In this case the community and city wasn’t happy with the high calorie food Lou was serving.
Marty’s Plan
- Call Lou and ensure him everything is going to be fine, he has a solution
- Create a recipe for a healthier menu. Also share your recipe with the public to show you care about their health. This will have this published in the paper as well.
- Apply a new sign higher so vandals cannot reach it as easily. Also add a tagline to the sign saying “Lou’s Cafe” — A hometown healthy choice. Stop in for our famous recipe . Then have the recipe nicely printed and ready for them at the door when they walk in.
Lou immediately responded with I can’t give away my secret recipe like that, it will ruin my business.
Marty replied “Lou no one can bake like you” Even if they try as hard as they can, they won’t be able to perfect your skill without years of training” They will come buy it from you as your the best at it. Lou smiled and hugged Marty.
Lou and Marty put the plan into action. Everything went so well Lou was given a key to the city for helping out his community. To this day the signage and tagline hangs high above the street where people are guided into the shop for Lou’s one of a kind healthy recipe.
Until this day the problem has been solved, as its current status is — Perfected. ☺
Follow the Process & Discover the Solution
As you can see the problem solving process is a cycle; prep, plan, perform and perfect. You must use your steps wisely and always focus on clearly fulfilling the problem with a solution.
Being a great problem solver takes time and practice. You must stay humble and positive when crafting a solution. Always be ready for critiques and don’t let your ego get the best of you.
Simply follow these steps and you are well on your way to becoming not only a great designer but a great problem solver.
More from Mat Helme
Designer & Illustrator @google
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Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below. Step. Characteristics. 1. Define the problem. Differentiate fact from opinion. Specify underlying causes. Consult each faction involved for information.
The 4-Step Problem-Solving Process . This document is the third in a series intended to help school and district leaders maximize the effectiveness and fluidity of their multi-tiered system of supports (MTSS) across different learning environments. Specifically, the document is designed to support the use of problem solving to improve
Generally speaking, if you can't solve the problem then your issue is step 3 or step 4; you either don't know enough or you're missing the connection. Good problem solvers always believe step 3 is the issue. In this case, it's a simple matter of learning more. Less skilled problem solvers believe step 4 is the root cause of their ...
The "Four-Step Problem Solving" plan helps elementary math students to employ sound reasoning and to develop mathematical language while they complete a four-step problem-solving process. This problem-solving plan consists of four steps: details, main idea, strategy, and how. As students work through each step, they may use "graphic ...
How to solve Math problems using the 4 step plan
The 4-step Problem Solving Method. The model we've used with clients is based on the A3 problem-solving methodology used by many "lean" production-based companies. In addition to being simpler, our 4-step method is visual, which helps remind the user what goes into each box. The steps are as follows. Develop a Problem Statement; Determine ...
The problem-solving process has four steps that can lead you to a successful solution: 1. Defining the problem, 2. Generating possible solutions. 3. Evaluate and select a solution. 4.
The Four Steps of Problem Solving SUBJECT TEACHER GRADE DATE. MAT150 Kendal Tucker 00 6/13/ OVERVIEW. Students are to solve word problems by using the four steps of problem solving. We will solve word problems as a class with visual representations to the equations expressed in our word problem.
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In this lesson, students will learn the steps in solving a problem, discuss solutions from the story "Mr. Rabbit and the Lovely Present," and use these same problem-solving skills when they build shapes with pattern blocks. Students will be able to identify a problem and engage in problem-solving ...
Polya's 4-Step Process. George Polya was a mathematician in the 1940s. He devised a systematic process for solving problems that is now referred to by his name: the Polya 4-Step Problem-Solving ...
The generic steps of PDCA are: Plan - Identify the problem, where you want to be and gather the facts. Start to define the reasons and get to the root causes. Do - Implement the improvement and test. Check - Check it's worked and review the data. Act - If it's worked, standardise the improvement. If not, tackle the next problem and ...
SOLVE 1. Use your strategy to solve the problem. 2. Pay close attention to the details of the problem. 3. If the plan does not work, revise it or start over with a different plan. CHECK 1. Does your answer make sense? 2. Is your answer close to your estimate? 3. Did you answer the question? Make a Model Draw a Diagram Use a Venn Diagram
4. Implement the Solution. At this stage of problem solving, be prepared for feedback, and plan for this. When you roll out the solution, request feedback on the success of the change made. 5. Review, Iterate, and Improve. Making a change shouldn't be a one time action.
Step 2: Devise a plan. Going to use Guess and test along with making a tab. Many times the strategy below is used with guess and test. Make a table and look for a pattern: Procedure: Make a table reflecting the data in the problem.
The Steps (and the Pre-Step) The framework consists of four steps and a very important pre-step. The four steps are as follows: Analyze —Understand the root cause. Plan —Determine how to resolve the problem. Implement —Put the resolution in place. Evaluate —Determine if the resolution is producing the desired results.
5.0. (97) $5.00. Zip. If you teach elementary-level mathematics, you have likely heard of and at one point utilized Polya's Four Step Plan for problem-solving. Using the Understand, Plan, Solve, and Check (UPSC) model, students are able to solve single and multi-step word problems. This resource pack is based on Polya's model with a significant ...
Solve the following problem using Polya's Four-Step Method. Explain your solution as a step-by-step process, listing each of the four steps in the appropriate place and describing briefly how you applied each step to the problem. Answer using complete sentences. A zookeeper is moving penguins and polar bears into their new exhibit.
The Problem Solving Process. The first step is prep, this is where we understand and diagnose the problem.; Then our next step is plan.This is where we organize everything before acting. The third ...
The final step is to plan actions to enhance the supporting forces and reduce or eliminate the opposing forces. You can use the scores and the diagram to prioritize the most critical and feasible ...