4 step plan in problem solving

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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.

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.

Learn the method I used to earn a physics degree, learn Spanish, and win a national boxing title

• I was a terrible math student in high school who wrote off mathematics. I eventually overcame my difficulties and went on to earn a B.A. Physics with a minor in math
• I pieced together the best works on the internet to teach myself Spanish as an adult
• *I didn’t start boxing until the very old age of 22, yet I went on to win a national championship, get a high-paying amateur sponsorship, and get signed by Roc Nation Sports as a profession.

I’ve used this method to progress in mentally and physically demanding domains.

While the specifics may differ, I believe that the general methods for learning are the same in all domains.

This free e-book breaks down the most important techniques I’ve used for learning.

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.

Follow me on Twitter.

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Polya's Problem Solving Process | Overview & Steps

Anita Dunn graduated from Saint Mary's College with a Bachelor's of Science in Mathematics, and graduated from Purdue University with a Master's of Science in Mathematics. She has been certified as a Developmental Education Specialist through the Kellogg Institute. She has more than 10 years of experience as a college professor.

Maria has taught University level psychology and mathematics courses for over 20 years. They have a Doctorate in Education from Nova Southeastern University, a Master of Arts in Human Factors Psychology from George Mason University and a Bachelor of Arts in Psychology from Flagler College.

Kathryn has taught high school or university mathematics for over 10 years. She has a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S. in Mathematics from Florida State University, and a B.S. in Mathematics from the University of Wisconsin-Madison.

Additional Example of Using Polya's Four-Step Problem-Solving Process

In the following example, use Polya's Four-Step Problem-Solving Process as outlined in the video lesson. Be sure to execute each step of the process and to state what that step involves.

Farmer Brown has many animals on his farm. He has 72 chickens, which make up 60% of his total animals, and the rest of his animals are sheep. How many legs in total do his animals have?

1) Step One of Polya's Process is to understand the problem. We are trying to count how many legs the animals have in total. The animals are chickens (which have 2 legs each) and sheep (which have 4 legs each).

2) Step Two of Polya's Process is to devise a plan. We will work with an equation. An example of an equation to use to solve the problem is (72 chickens * 2 legs) + (number of sheep * 4 legs) = total legs. However, we do not know the number of sheep. We know that 60% of the total number of animals is equal to 72, so if n is the total number of animals, we have 0.60n = 72 so the total number of animals is 72/0.6 = 120. Then the number of sheep is the remaining amount of animals. A revised equation to use to solve the problem is (72 chickens * 2 legs) + ((120-72) sheep * 4 legs) = total legs.

3) Step Three is to carry out the plan. We will solve our equation. 120 - 72 = 48 sheep, and so we have (72 * 2) + (48 * 4) = total legs. 72 * 2 = 144 and 48 * 4 = 192, so the total number of legs is 144+192 = 336 legs.

4) Step Four is to look back. Does this answer make sense? There should be more legs than animals and the number should be an even number (the animals each have an even number of legs) and 336 fits this. We can check that 0.6(120) = 72 chickens and that 0.4(120) = 48 to make sure the number of animals is correct. Our answer checks out.

How can Polya's Four-Step Problem-Solving Process help you solve problems?

Guide to Discussion

This is a pretty open-ended question - something that may help guide students on their discussion is to talk about word problems in math class. For many students, the hardest part of word problems is finding out what is even being asked and translating it into an equation - Polya's process helps with these things.

What is Polya's 4 steps in problem solving?

Polya's four step method for problem solving is

1) Understand the Problem-Make sure you understand what the question is asking and what information will be used to solve the problem.

2) Devise a Plan-Figure out what method you will use to solve the problem.

3) Carry out the Plan-Use that method to solve the problem

4) Look Back-Double check your answer and make sure it is reasonable.

What made George Polya famous?

George Polya's book: "How to Solve it" sold over a million copies and has been translated into at least 21 different languages. He is most famous for his "four step problem solving process" which helps students solve word problems.

What is Polya's first principle for solving problems?

Polya's first principle for solving problems is arguably one of the most important steps: Understand the Problem. You first need to make sure you understand any vocabulary words, understand what the problem is asking for, and understand what information is given in the problem which will help you solve it.

Table of Contents

Polya's problem solving process, how to solve using polya's method, lesson summary.

George Polya (1887-1985) was born in Hungary. He received his Ph.D. in mathematics at the University of Budapest. For many years he served as a professor at the Swiss Federal Institute of Technology in Zurich. Then, in 1940, Dr. Polya moved to the United States where he taught briefly at Brown University, and then he moved to Stanford University.

Dr. Polya maintained a lifelong interest in the thought processes we use when we solve math problems. Dr. Polya wrote many books, including How to Solve It (1945). This book sold over a million copies in at least 21 different languages. His methods are now commonly used amongst students when solving word problems. (Long et al., 2015)

His four step process can be summarized by

• Understand the Problem

Devise a Plan

• Carry out the Play

Understand the problem

Are there any vocabulary words you don't understand within the problem? If so, it'd be a good idea to look them up.

Figure out what you are being asked to find.

Can you restate the problem in your own words?

Would a diagram or a picture help you to solve the problem? If so, draw it.

Do you have enough information to solve the problem? Is there information included which you don't need?

Example: Isaac has 5 apples and he has 10 friends. He wants to give 2 apples to each of his friends. How many apples does he need to buy?

For the "understand the problem" step, we want to decide what we are being asked to find. Thankfully, the last sentence tells us. We want to find out "how many apples does he need to buy?" In other words, how many more apples does he need.

Do we have enough information? We know that he has 5 apples already. He has 10 friends. He wants to give two apples to each of his friends. That should give us the ability to solve this problem.

Decide how you are going to try to solve your problem. You could use any of the following methods:

• use algebra
• use basic arithmetic
• look for a pattern
• guess and check ...guess an answer, see if it works. If it doesn't work, try something else.
• use a model or a diagram...sometimes just by drawing a model we can figure out the answer.
• use a formula

Or, something else! There are many methods we could use here. Be creative!

For our earlier example, we can answer this question a few different ways. We could draw out 10 picture of people. Then we can draw two apples per friend, and count out how many Isaac currently has and count how many he needs.

If we had a classroom of children, we could have ten of them stand up and hand out 5 apples. Then we could figure out how many more apples we need to make sure each child has two apples. Hint: The kids could hold out their empty hands, so the other children could count how many more apples are needed.

We could use a bit of arithmetic, finding out how many apples he needs for all of his friends and subtracting to find out how many more he needs.

To solve my example problem, I'm going to use arithmetic.

Carry out the Plan

This is where we do the math and figure out our answer! Whatever you decided your plan was earlier.

Back to my example problem: we know that Isaac has 10 friends and each friend needs two apples. We can multiply {eq}2*10=20 {/eq}

So Isaac needs 20 apples. He currently has 5 apples. Therefore we can subtract {eq}20 - 5 = 15 {/eq}

Therefore Isaac needs 15 more apples. This is how many he will be buying.

This is the step everyone wants to skip. And yet it is also one of the most important steps. Basically, you will be checking your answer and thinking about whether or not your answer makes sense.

• Is there another way I could solve this problem?
• Does my answer make sense?
• Are there similar problems that I could use this strategy on? This will help you later on as you complete more problems.

Thinking about my example problem: Does the answer make sense? Yes, 15 apples is a reasonable number of apples, considering we started with 5 apples and we needed 2 apples per person for 10 people.

I can take a quick look at my arithmetic and make sure I didn't make a simple mistake. Sometimes it's even a good idea to completely redo the problem, it is sometimes easier to find a mistake this way.

Can I solve this problem some other way? I could also draw out a picture to see if the answer is correct. It doesn't have to be fancy, some stick figures for the friends and circles for the apples works just fine. We could color in 5 of the circles to show that Isaac currently has those apples, and then count the rest.

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• 0:32 Understanding the Problem
• 1:47 Devise a Plan
• 2:32 Carry out the Plan
• 3:33 Look Back
• 5:04 Example
• 6:56 Lesson Summary

Let's try this method with another example problem.

Two trains leave the train station at the same time. They are going in opposite directions. One train is going 60 miles an hour, while the other train is going 50 miles an hour. In two hours, how far apart are the trains?

Understand the problem:

What is the question asking us? It is asking us how far apart the trains are after 2 hours.

What information is important here? The trains leave the station at the same time. They are going in opposite directions. One has a rate of 60 miles an hour, the other has a rate of 50 miles an hour.

We are finding the distance given the rate and the time, so we should remember the distance formula: {eq}d=r*t {/eq}

A diagram may help us:

Make a plan:

How are we going to solve this problem. We could label the diagram and show how far each of the trains have traveled away from the train station after two hours. We could use arithmetic. We could make a formula and solve it for 2 hours.

Carry out the plan:

Let's make a formula!

First we need to define the variables that we will use.

We want to know the distance between the trains, so let d= distance between the trains.

We know that the distance is going to depend on the amount of time, so let's let t=time since the trains departed the station.

We also know that d=r*t, and that the trains are moving away from each other, so the total distance between the two trains will be found by adding the distance the first train has traveled and the distance the second train has traveled.

This gives us the following formula: {eq}d=60t+50t {/eq}

We want to know the distance between the trains after two hours, so let {eq}t=2 {/eq}

And we get {eq}d=60*2+50*2 = 120 + 100 = 220 {/eq}

So, our answer is that after 2 hours, the trains will be 220 miles apart.

Does the answer make sense? Yes, 220 miles is a reasonable distance between two trains moving farther apart after two hours.

Could we do it a different way? Yes. We could find out the distance the first train moves after two hours: 120 miles, and the distance the second train moves after 2 hours: 100 miles, and then add them together to get 220 miles.

Polya's problem-solving process is a systematic method to solve a mathematical problem. By following each step, students are more likely to be able to solve the problem correctly.

Video Transcript

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 Process .

In this lesson, we will discuss each step of the Polya process while working through the solution to a problem. At the end of the lesson, you will have the opportunity to try more examples before taking your quiz.

Understanding the Problem

So, to start, let's think about a party. Sally was having a party. She invited 20 women and 15 men. She made 1 dozen blue cupcakes and 3 dozen red cupcakes. At the end of the party there were only 5 cupcakes left. How many cupcakes were eaten?

The first step of Polya's Process is to Understand the Problem . Some ways to tell if you really understand what is being asked is to:

• State the problem in your own words.
• Pinpoint exactly what is being asked.
• Identify the unknowns.
• Figure out what the problem tells you is important.
• Identify any information that is irrelevant to the problem.

In our example, we can understand the problem by realizing that we don't need the information about the gender of the guests or the color of the cupcakes - that is irrelevant. All we really need to know is that we are being asked, 'How many cupcakes are left of the total that were made?' So, we understand the problem.

Now that we understand the problem, we have to Devise a Plan to solve the problem. We could:

• Look for a pattern.
• Review similar problems.
• Make a table, diagram or chart.
• Write an equation.
• Use guessing and checking.
• Work backwards.
• Identify a sub-goal.

In our example, we need a sub-goal of figuring out the actual total number of cupcakes made before we can determine how many were left over.

We could write an equation to show what is unknown and how to find the solution: (1 dozen + 3 dozen) - 5 = number eaten

Carry Out the Plan

The third step in the process is the next logical step: Carry Out the Plan . When you carry out the plan, you should keep a record of your steps as you implement your strategy from step 2.

Our plan involved the sub-goal of finding out how many cupcakes were made total. After that, we needed to know how many were eaten if only 5 remained after the party. To find out, we wrote an equation that would resolve the sub-goal while working toward the main goal.

So, (1 dozen + 3 dozen) - 5 = number eaten. Obviously, we would need the prior knowledge that 1 dozen equals 12.

1 x 12 = 12, and 3 x 12 = 36, so what we really have is (12 + 36) - 5 = number eaten.

12 + 36 = 48 and 48 - 5 = 43

That means that the number of cupcakes eaten is 43.

The final step in the process is very important, but many students skip it, feeling like they have an answer so they can move on now. The final step is to Look Back , which really means to check your work.

• Does the answer make sense? Sometimes you can add wrong or multiply when you should have divided, then your answer comes out clearly wrong if you just stop and think about it. In our problem, we wanted to know how many cupcakes were eaten out of a total of 48. We got the answer 43. 43 is less than 48, so this answer does make sense. (It would not have made sense if we got an answer greater than 48 - how could they eat more than were made?)
• Check your result. Checking your result could mean solving the problem in another way to make sure you come out with the same answer. Basically, in mathematical terms, we are saying that 48 - 5 = 43. If we were to draw out a diagram of the 1 dozen blue cupcakes and 3 dozen red ones, then separate out the 5 that did not get eaten, we would see that we do, indeed, have 43 represented as the eaten cupcakes. Our answer checks out!

And that is all there is to Polya's 4-Step Process to Problem Solving:

So how about you try? Try using Polya's 4-Step Process to solve this riddle: There are 10 people at a party. Each person must say hello to each other person exactly once. How many times is the word 'Hello' said?

Step 1 - Understand the problem Okay, so we have 10 people saying hello, but they don't have to say hello to themselves, only to the 9 other people. I need to know how many times the word 'hello' is said. Got it.

Step 2 - Devise a plan A diagram might be a great to show me what is happening here. If I draw the diagram as a circle with 10 points (representing each of the 10 people), I can visualize each saying hello.

Step 3 - Carry out the plan Drawing the diagram of one person saying hello, we see that each person will have to say hello 9 times, thus there will be 10 people each saying hello 9 times. 10 x 9 = 90 hellos said.

Finally, Step 4 - Check your work 90 hellos might not make sense if there are 10 people; you might think the answer should have been 100. Well, to check our work with a problem like this, we could set up a different diagram. If we put the people in a straight line and then count them saying hello to each other one at a time, we will again see that the final tally is 90 hellos. 90 must be the correct answer. Remembering that they do not have to say hello to themselves may help you see why the answer can't be 100.

In this lesson, we reviewed Polya's 4-Step Process for Problem Solving , which is simply a systematic process used to reach a solution to a problem.

• Understand the Problem Restating the problem and identifying necessary information is a key to this step.
• Devise a Plan Use equations, diagrams, tables or any other tool needed to create a plan for solving the problem.
• Carry Out Your Plan Just do it!
• Look Back This means to review your work to double check your answer.

If you use these four steps when you approach any problem, be it math or otherwise, you will find your path to the solution much more direct and easy. Good luck!

Learning Outcomes

Following this lesson, you should have the ability to:

• Describe the steps in Polya's 4-Step Process for Problem Solving
• Explain the importance of having a plan to solve problems
• Apply Polya's process to problems

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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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2.1: George Polya's Four Step Problem Solving Process

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Step 1: Understand the Problem

• Do you understand all the words?
• Can you restate the problem in your own words?
• Do you know what is given?
• Do you know what the goal is?
• Is there enough information?
• Is there extraneous information?
• Is this problem similar to another problem you have solved?

Step 2: Devise a Plan: Below are some strategies one might use to solve a problem. Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.)

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Overview of the Problem-Solving Mental Process

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

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

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

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Unit 1: Algebra foundations

Unit 2: solving equations & inequalities, unit 3: working with units, unit 4: linear equations & graphs, unit 5: forms of linear equations, unit 6: systems of equations, unit 7: inequalities (systems & graphs), unit 8: functions, unit 9: sequences, unit 10: absolute value & piecewise functions, unit 11: exponents & radicals, unit 12: exponential growth & decay, unit 13: quadratics: multiplying & factoring, unit 14: quadratic functions & equations, unit 15: irrational numbers, unit 16: creativity in algebra.

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Number Line

• \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
• \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
• \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
• \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
• \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
• How do you solve word problems?
• To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
• How do you identify word problems in math?
• Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
• Is there a calculator that can solve word problems?
• Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
• What is an age problem?
• An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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• High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,...

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