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Algebra Topics  - Introduction to Word Problems

Algebra topics  -, introduction to word problems, algebra topics introduction to word problems.

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Algebra Topics: Introduction to Word Problems

Lesson 9: introduction to word problems.

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What are word problems?

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem. For instance, does this sound familiar?

Johnny has 12 apples. If he gives four to Susie, how many will he have left?

You could solve this problem by looking at the numbers and figuring out what the problem is asking you to do. In this case, you're supposed to find out how many apples Johnny has left at the end of the problem. By reading the problem, you know Johnny starts out with 12 apples. By the end, he has 4 less because he gave them away. You could write this as:

12 - 4 = 8 , so you know Johnny has 8 apples left.

Word problems in algebra

If you were able to solve this problem, you should also be able to solve algebra word problems. Yes, they involve more complicated math, but they use the same basic problem-solving skills as simpler word problems.

You can tackle any word problem by following these five steps:

  • Read through the problem carefully, and figure out what it's about.
  • Represent unknown numbers with variables.
  • Translate the rest of the problem into a mathematical expression.
  • Solve the problem.
  • Check your work.

We'll work through an algebra word problem using these steps. Here's a typical problem:

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took two days, and the van cost $360. How many miles did she drive?

It might seem complicated at first glance, but we already have all of the information we need to solve it. Let's go through it step by step.

Step 1: Read through the problem carefully.

With any problem, start by reading through the problem. As you're reading, consider:

  • What question is the problem asking?
  • What information do you already have?

Let's take a look at our problem again. What question is the problem asking? In other words, what are you trying to find out?

The rate to rent a small moving van is $30 per day, plus $0.50 per mile. Jada rented a van to drive to her new home. It took 2 days, and the van cost $360. How many miles did she drive?

There's only one question here. We're trying to find out how many miles Jada drove . Now we need to locate any information that will help us answer this question.

There are a few important things we know that will help us figure out the total mileage Jada drove:

  • The van cost $30 per day.
  • In addition to paying a daily charge, Jada paid $0.50 per mile.
  • Jada had the van for 2 days.
  • The total cost was $360 .

Step 2: Represent unknown numbers with variables.

In algebra, you represent unknown numbers with letters called variables . (To learn more about variables, see our lesson on reading algebraic expressions .) You can use a variable in the place of any amount you don't know. Looking at our problem, do you see a quantity we should represent with a variable? It's often the number we're trying to find out.

Since we're trying to find the total number of miles Jada drove, we'll represent that amount with a variable—at least until we know it. We'll use the variable m for miles . Of course, we could use any variable, but m should be easy to remember.

Step 3: Translate the rest of the problem.

Let's take another look at the problem, with the facts we'll use to solve it highlighted.

The rate to rent a small moving van is $30 per day , plus $0.50 per mile . Jada rented a van to drive to her new home. It took 2 days , and the van cost $360 . How many miles did she drive?

We know the total cost of the van, and we know that it includes a fee for the number of days, plus another fee for the number of miles. It's $30 per day, and $0.50 per mile. A simpler way to say this would be:

$30 per day plus $0.50 per mile is $360.

If you look at this sentence and the original problem, you can see that they basically say the same thing: It cost Jada $30 per day and $0.50 per mile, and her total cost was $360 . The shorter version will be easier to translate into a mathematical expression.

Let's start by translating $30 per day . To calculate the cost of something that costs a certain amount per day, you'd multiply the per-day cost by the number of days—in other words, 30 per day could be written as 30 ⋅ days, or 30 times the number of days . (Not sure why you'd translate it this way? Check out our lesson on writing algebraic expressions .)

$30 per day and $.50 per mile is $360

$30 ⋅ day + $.50 ⋅ mile = $360

As you can see, there were a few other words we could translate into operators, so and $.50 became + $.50 , $.50 per mile became $.50 ⋅ mile , and is became = .

Next, we'll add in the numbers and variables we already know. We already know the number of days Jada drove, 2 , so we can replace that. We've also already said we'll use m to represent the number of miles, so we can replace that too. We should also take the dollar signs off of the money amounts to make them consistent with the other numbers.

30 ⋅ 2 + .5 ⋅ m = 360

Now we have our expression. All that's left to do is solve it.

Step 4: Solve the problem.

This problem will take a few steps to solve. (If you're not sure how to do the math in this section, you might want to review our lesson on simplifying expressions .) First, let's simplify the expression as much as possible. We can multiply 30 and 2, so let's go ahead and do that. We can also write .5 ⋅ m as 0.5 m .

60 + .5m = 360

Next, we need to do what we can to get the m alone on the left side of the equals sign. Once we do that, we'll know what m is equal to—in other words, it will let us know the number of miles in our word problem.

We can start by getting rid of the 60 on the left side by subtracting it from both sides .

The only thing left to get rid of is .5 . Since it's being multiplied with m , we'll do the reverse and divide both sides of the equation with it.

.5 m / .5 is m and 300 / 0.50 is 600 , so m = 600 . In other words, the answer to our problem is 600 —we now know Jada drove 600 miles.

Step 5: Check the problem.

To make sure we solved the problem correctly, we should check our work. To do this, we can use the answer we just got— 600 —and calculate backward to find another of the quantities in our problem. In other words, if our answer for Jada's distance is correct, we should be able to use it to work backward and find another value, like the total cost. Let's take another look at the problem.

According to the problem, the van costs $30 per day and $0.50 per mile. If Jada really did drive 600 miles in 2 days, she could calculate the cost like this:

$30 per day and $0.50 per mile

30 ⋅ day + .5 ⋅ mile

30 ⋅ 2 + .5 ⋅ 600

According to our math, the van would cost $360, which is exactly what the problem says. This means our solution was correct. We're done!

While some word problems will be more complicated than others, you can use these basic steps to approach any word problem. On the next page, you can try it for yourself.

Let's practice with a couple more problems. You can solve these problems the same way we solved the first one—just follow the problem-solving steps we covered earlier. For your reference, these steps are:

If you get stuck, you might want to review the problem on page 1. You can also take a look at our lesson on writing algebraic expressions for some tips on translating written words into math.

Try completing this problem on your own. When you're done, move on to the next page to check your answer and see an explanation of the steps.

A single ticket to the fair costs $8. A family pass costs $25 more than half of that. How much does a family pass cost?

Here's another problem to do on your own. As with the last problem, you can find the answer and explanation to this one on the next page.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo. Between the two of them, they donated $280. How much money did Mo give?

Problem 1 Answer

Here's Problem 1:

A single ticket to the fair costs $8. A family pass costs $25 more than half that. How much does a family pass cost?

Answer: $29

Let's solve this problem step by step. We'll solve it the same way we solved the problem on page 1.

Step 1: Read through the problem carefully

The first in solving any word problem is to find out what question the problem is asking you to solve and identify the information that will help you solve it . Let's look at the problem again. The question is right there in plain sight:

So is the information we'll need to answer the question:

  • A single ticket costs $8 .
  • The family pass costs $25 more than half the price of the single ticket.

Step 2: Represent the unknown numbers with variables

The unknown number in this problem is the cost of the family pass . We'll represent it with the variable f .

Step 3: Translate the rest of the problem

Let's look at the problem again. This time, the important facts are highlighted.

A single ticket to the fair costs $8 . A family pass costs $25 more than half that . How much does a family pass cost?

In other words, we could say that the cost of a family pass equals half of $8, plus $25 . To turn this into a problem we can solve, we'll have to translate it into math. Here's how:

  • First, replace the cost of a family pass with our variable f .

f equals half of $8 plus $25

  • Next, take out the dollar signs and replace words like plus and equals with operators.

f = half of 8 + 25

  • Finally, translate the rest of the problem. Half of can be written as 1/2 times , or 1/2 ⋅ :

f = 1/2 ⋅ 8 + 25

Step 4: Solve the problem

Now all we have to do is solve our problem. Like with any problem, we can solve this one by following the order of operations.

  • f is already alone on the left side of the equation, so all we have to do is calculate the right side.
  • First, multiply 1/2 by 8 . 1/2 ⋅ 8 is 4 .
  • Next, add 4 and 25. 4 + 25 equals 29 .

That's it! f is equal to 29. In other words, the cost of a family pass is $29 .

Step 5: Check your work

Finally, let's check our work by working backward from our answer. In this case, we should be able to correctly calculate the cost of a single ticket by using the cost we calculated for the family pass. Let's look at the original problem again.

We calculated that a family pass costs $29. Our problem says the pass costs $25 more than half the cost of a single ticket. In other words, half the cost of a single ticket will be $25 less than $29.

  • We could translate this into this equation, with s standing for the cost of a single ticket.

1/2s = 29 - 25

  • Let's work on the right side first. 29 - 25 is 4 .
  • To find the value of s , we have to get it alone on the left side of the equation. This means getting rid of 1/2 . To do this, we'll multiply each side by the inverse of 1/2: 2 .

According to our math, s = 8 . In other words, if the family pass costs $29, the single ticket will cost $8. Looking at our original problem, that's correct!

So now we're sure about the answer to our problem: The cost of a family pass is $29 .

Problem 2 Answer

Here's Problem 2:

Answer: $70

Let's go through this problem one step at a time.

Start by asking what question the problem is asking you to solve and identifying the information that will help you solve it . What's the question here?

To solve the problem, you'll have to find out how much money Mo gave to charity. All the important information you need is in the problem:

  • The amount Flor donated is three times as much the amount Mo donated
  • Flor and Mo's donations add up to $280 total

The unknown number we're trying to identify in this problem is Mo's donation . We'll represent it with the variable m .

Here's the problem again. This time, the important facts are highlighted.

Flor and Mo both donated money to the same charity. Flor gave three times as much as Mo . Between the two of them, they donated $280 . How much money did Mo give?

The important facts of the problem could also be expressed this way:

Mo's donation plus Flor's donation equals $280

Because we know that Flor's donation is three times as much as Mo's donation, we could go even further and say:

Mo's donation plus three times Mo's donation equals $280

We can translate this into a math problem in only a few steps. Here's how:

  • Because we've already said we'll represent the amount of Mo's donation with the variable m , let's start by replacing Mo's donation with m .

m plus three times m equals $280

  • Next, we can put in mathematical operators in place of certain words. We'll also take out the dollar sign.

m + three times m = 280

  • Finally, let's write three times mathematically. Three times m can also be written as 3 ⋅ m , or just 3 m .

m + 3m = 280

It will only take a few steps to solve this problem.

  • To get the correct answer, we'll have to get m alone on one side of the equation.
  • To start, let's add m and 3 m . That's 4 m .
  • We can get rid of the 4 next to the m by dividing both sides by 4. 4 m / 4 is m , and 280 / 4 is 70 .

We've got our answer: m = 70 . In other words, Mo donated $70 .

The answer to our problem is $70 , but we should check just to be sure. Let's look at our problem again.

If our answer is correct, $70 and three times $70 should add up to $280 .

  • We can write our new equation like this:

70 + 3 ⋅ 70 = 280

  • The order of operations calls for us to multiply first. 3 ⋅ 70 is 210.

70 + 210 = 280

  • The last step is to add 70 and 210. 70 plus 210 equals 280 .

280 is the combined cost of the tickets in our original problem. Our answer is correct : Mo gave $70 to charity.

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5 Easy Steps to Solving Word Problems

child learning how to solve a word problem

Word problems strike fear into the hearts of many students, and the trauma can even carry into adulthood. This is why word problems are the topic of many education jokes.

“If two trains start at the same station and travel in opposite directions at the same speed, when will the bacon be ready for breakfast?”

This is obviously a silly scenario, but it shows how word problems are regarded by many: a mangle of confusion that doesn’t make sense and can’t be solved!

Why Are Word Problems Difficult for Children?

Why can word problems be so confusing and scary? There are a few possible reasons.

  • Word problems are often introduced to us at an age before our skills of abstract thinking are fully developed. However, a student’s imagination is a great asset to use in understanding word problems!
  • Word problems are sometimes simply included as the “harder problems” at the end of homework assignments and the student is never really taught how to approach them.
  • It is sometimes ignored that a student’s math and reading ability come into play when word problems are assigned. But if the second grade math student is still only reading on a first-grade level, he will have difficulty solving word problems even if he is otherwise good at math! It can thus be helpful to assess both a student’s math and reading ability to set him up for success. The tutoring service provided by masterygenius.com is a great option since both math and reading skills can be addressed.

A quick tip before we get started…

Explain to students that the word “problem” really means “question.” A word problem is just asking a question to which the students must find an answer. Show them that you need to identify the question before you even worry about which math operations are going to be used. Word problems can be treated like mysteries: the students are the detectives that are going to use the clues in the question to find the answer!

So what are the five easy steps to solving word problems? Let’s take a look!

Five Easy Steps to Solving Word Problems (WASSP)

  • Write (or draw) what you know.
  • Ask the question.
  • Set up a math problem that could answer the question.
  • Solve the math problem to get an answer.
  • Put the answer in a sentence to see if the answer makes sense!

Let’s look at an example word problem to demonstrate these steps.

Matt has twelve cookies he can give to his friends during lunchtime. If Matt has three friends sitting at his table, how many cookies can Matt give to each of his friends?

1. Write (or draw) what you know.

It is important to convince students that they do not have to immediately know what math operation is required to solve the problem. They first need only understand the scenario itself. In this example, the student could simply write down “12 cookies” and “3 friends,” or draw Matt with 12 cookies sitting at a table with three other children.

2. Ask the question.

Again, we don’t need to know what the math operation is yet! We just need to identify what is actually being asked. What do we NOT know?

The student could write, “How many cookies can each of Matt’s friends have?”

Alternatively, the student could draw a question mark over each friend’s head, maybe with a thought bubble of a cookie!

3. Set up a math problem that could answer the question.

  • It can be a good idea to teach students “clue” words or phrases in problems which can identify what math operation may be needed. However, this should not be the student’s only skill for deciding what math operation to use, because these “clue” words can sometimes be confusing. For example, the phrases “how many in all” and “how many more” seem very similar to a student, but the first phrase indicates addition and the second phrase indicates subtraction!
  • It is good for a student to also be able to reason what math operation is needed based on understanding the scenario itself (which is a better builder of true critical thinking skills). This is why the first two steps (write what you know and ask the question) are so important. The student that has a true understanding of the scenario will be better equipped to reason what math operation is needed.

In this example, the “clue” word (if you are using that method of reasoning) would be “each,” which indicates division. Or, the student could understand that Matt has to split, or divide, the cookies among his friends. Thus a division problem is needed!

Dividing 12 cookies among 3 friends means 12 is divided by 3.

4. Solve the problem.

It is important to note that using units can be a good idea . Otherwise, the answer could be misunderstood. Is it 4 cookies, or 4 friends, or something else?

12 cookies ÷ 3 friends = 4 cookies per friend

5. Put the answer in a sentence to see if the answer makes sense.

“Each of Matt’s friends can have four cookies.”

Does this answer make sense? It seems reasonable. How could this step help identify an incorrect answer?

What if the student had decided this was a multiplication problem?

12 cookies × 3 friends = 36 cookies per friend

If the student then writes a sentence using the answer, he may realize the answer can’t be right.

“Each of Matt’s friends can have 36 cookies.”

How would that be possible if Matt only had 12 cookies to start with? This must not be a multiplication problem. Let’s try again!

Practice the Five Easy Steps for Word-Problem Success!

Steps 1 and 2 ( Write what you know and Ask the question) help the student gain an understanding of the scenario.

Steps 3 and 4 ( Set up the math problem and Solve the problem) can be more easily navigated with critical thinking once the scenario is understood.

Step 5 ( Put the answer in a sentence) can help the student decide whether the answer makes sense.

Now your student is ready for word-problem success!

Make sure to start at the student’s level of understanding so he can experience success and build confidence, moving on to more challenging problems as appropriate. Customized curriculum is always best, which again makes masterygenius.com a great option if tutoring is needed. Students are assessed and then matched with a curriculum that strikes balance between building confidence and tackling challenges, leading to topic mastery.

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SOLVING WORD PROBLEMS: A VISUAL APPROACH: HOME

which list correctly identifies the steps to solving a word problem

Step 1: Identify the given information in the problem.

Underline the information in your problem. Then create a checklist. As you use the information in your solution, make sure to check off each box.

Understanding a math word problem is 50% of the work. So give yourself a pat on the back when you’ve finished it! 

Step 2: Find the question in the passage and state it in your own words.

Underline the question with a different color than you used for the first step. After you have underlined the question, write the information out in your own words, so that you understand what is being asked. 

Step 3: Devise a strategy to solve the problem.

Now that you have collected the information you need to solve the problem, you need to come up with a strategy to conquer the problem.

Think about what’s being asked. Is there a formula you need to use? Do you need to calculate a percentage for your final answer? Write out the steps you need to use to solve the problem, so that you can carry out your plan.

THE STEPS TO SOLVING A WORD PROBLEM

  • Identify the given information.
  • Find the question and state it in your own words.
  • Devise a strategy to solve the problem.
  • Carry out your plan.

Use three different colored pencils/pens to separate each of the first three parts of the problem solving process.

Here are a few examples of how to use this process in solving a mathematical problem.

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Ask the asc for help.

Need Academic Help? Contact the Academic Success Center (ASC)!

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Step 4: Once you have created a plan, then you need to solve the problem. Make sure you have used all the given information in the problem, answered the question, and followed each step in your strategy.

Keep Calm.   Be confident.  You’ve got this! 

which list correctly identifies the steps to solving a word problem

  • Last Updated: Nov 22, 2017 12:17 PM
  • URL: https://guides.kendall.edu/wordproblems

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5 Steps to Word Problem Solving

Close-up of student working on math homework.

How to Factorise a Quadratic Expression

Word problems often confuse students simply because the question does not present itself in a ready-to-solve mathematical equation. You can answer even the most complex word problems, provided you understand the mathematical concepts addressed. While the degree of difficulty may change, the way to solve word problems involves a planned approach that requires identifying the problem, gathering the relevant information, creating the equation, solving and checking your work.

Identify the Problem

Begin by determining the scenario the problem wants you to solve. This might come as a question or a statement. Either way, the word problem provides you with all the information you need to solve it. Once you identify the problem, you can determine the unit of measurement for the final answer. In the following example, the question asks you to determine the total number of socks between the two sisters. The unit of measurement for this problem is pairs of socks.

"Suzy has eight pairs of red socks and six pairs of blue socks. Suzy's brother Mark owns eight socks. If her little sister owns nine pairs of purple socks and loses two of Suzy's pairs, how many pairs of socks do the sisters have left?"

Gather Information

Create a table, list, graph or chart that outlines the information you know, and leave blanks for any information you don't yet know. Each word problem may require a different format, but a visual representation of the necessary information makes it easier to work with.

In the example, the question asks how many socks the sisters own together, so you can disregard the information about Mark. Also, the color of the socks doesn't matter. This eliminates much of the information and leaves you with only the total number of socks that the sisters started with and how many the little sister lost.

Create an Equation

Translate any of the math terms into math symbols. For example, the words and phrases "sum," "more than," "increased" and "in addition to" all mean to add, so write in the "+" symbol over these words. Use a letter for the unknown variable, and create an algebraic equation that represents the problem.

In the example, take the total number of pairs of socks Suzy owns -- eight plus six. Take the total number of pairs that her sister owns -- nine. The total pairs of socks owned by both sisters is 8 + 6 + 9. Subtract the two missing pairs for a final equation of (8 + 6 + 9) - 2 = n, where n is the number of pairs of socks the sisters have left.

Solve the Problem

Using the equation, solve the problem by plugging in the values and solving for the unknown variable. Double-check your calculations along the way to prevent any mistakes. Multiply, divide and subtract in the correct order using the order of operations. Exponents and roots come first, then multiplication and division, and finally addition and subtraction.

In the example, after adding the numbers together and subtracting, you get an answer of n = 21 pairs of socks.

Verify the Answer

Check if your answer makes sense with what you know. Using common sense, estimate an answer and see if you come close to what you expected. If the answer seems absurdly large or too small, search through the problem to find where you went wrong.

In the example, you know by adding up all the numbers for the sisters that you have a maximum of 23 socks. Since the problem mentions that the little sister lost two pairs, the final answer must be less than 23. If you get a higher number, you did something wrong. Apply this logic to any word problem, regardless of the difficulty.

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  • Mt. San Antonio College: Five-Step Strategy to Solving Word Problems

About the Author

Avery Martin holds a Bachelor of Music in opera performance and a Bachelor of Arts in East Asian studies. As a professional writer, she has written for Education.com, Samsung and IBM. Martin contributed English translations for a collection of Japanese poems by Misuzu Kaneko. She has worked as an educator in Japan, and she runs a private voice studio out of her home. She writes about education, music and travel.

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which list correctly identifies the steps to solving a word problem

Last updated on March 16, 2020 by Jamie Sears

4 Simple Steps to Solve a Word Problem

which list correctly identifies the steps to solving a word problem

It might seem obvious that we need to start the problem solving process by reading the problem, but the reality is that students want to start doing something with the numbers before they finish reading. I require my students to set down their pencil or dry erase marker and read the entire problem. I ask them to visualize what the problem is stating rather than trying to form a plan to solve. I have found that they are much more successful when they really think about what they know BEFORE they start drawing and solving.

which list correctly identifies the steps to solving a word problem

After my students have read through the entire problem once, they will begin rereading the problem. This time, I ask that they just read one sentence or phrase at a time. They should draw a math model as they read. The models tend to be much more accurate if students are only reading one piece of the problem at a time. However, sometimes they will get to the end of the problem and discover that their model is not going to help them solve. That’s okay! Use the power of the eraser! I call them models rather than drawings because I want my students to understand that math models are not the same as a picture you might draw in art class. No one needs to be an artist in math class!

Models that my students might draw (because I have modeled them): Equal Group Pictures Tape Diagrams (also known as Bar Modeling) Number Bonds Arrays Number Lines

which list correctly identifies the steps to solving a word problem

Most students want to jump to writing an equation or number sentence, but in my class, it can’t be done until the model is drawn. Once the model is drawn students can better understand what the unknown is and write a number sentence that will help them to accurately solve the word problem. I always remind my students that they need to examine the model before writing the equation. After they solve the equation they need to ask if it is reasonable and then put it back into their model to check for accuracy.

which list correctly identifies the steps to solving a word problem

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September 9, 2015 at 10:13 pm

Love this! Do you have the signs of the steps to hang up?

September 10, 2015 at 12:39 am

I like these steps and that you display them. Something so easy, yet brilliant!

Tina Crofts' Classroom

September 10, 2015 at 12:44 pm

I happened to chance upon your blog and found it very interesting!

We have recently launched a science app that uses augmented reality to enhance classroom teaching. The app has 3D models for kindergarten to grade 12. I thought you might want to check it out and may be review it on your blog, if possible.

It is a paid app(with a few models free) but in case you are interested in trying it out I will be happy to provide you with a free copy.

The link to the app is: 

iPhone/iPad https://itunes.apple.com/us/app/augmenter-augmented-reality/id997354409?ls=1&mt=8

android: https://play.google.com/store/apps/details?id=com.augmented.android

You can also search for the app on the app store as 'Augmenter'.

Do let me know if you would be interested. I am really Looking forward to your response.

happy teaching!

Antara [email protected] http://augmenterapp.com/

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which list correctly identifies the steps to solving a word problem

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which list correctly identifies the steps to solving a word problem

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which list correctly identifies the steps to solving a word problem

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which list correctly identifies the steps to solving a word problem

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which list correctly identifies the steps to solving a word problem

Strategies for Solving Word Problems – Math

which list correctly identifies the steps to solving a word problem

It’s one thing to solve a math equation when all of the numbers are given to you but with word problems, when you start adding reading to the mix, that’s when it gets especially tricky.

The simple addition of those words ramps up the difficulty (and sometimes the math anxiety) by about 100!

How can you help your students become confident word problem solvers? By teaching your students to solve word problems in a step by step, organized way, you will give them the tools they need to solve word problems in a much more effective way.

Here are the seven strategies I use to help students solve word problems.

1. read the entire word problem.

Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too.

2. Think About the Word Problem

Students need to ask themselves three questions every time they are faced with a word problem. These questions will help them to set up a plan for solving the problem.

Here are the questions:

A. what exactly is the question.

What is the problem asking? Often times, curriculum writers include extra information in the problem for seemingly no good reason, except maybe to train kids to ignore that extraneous information (grrrr!). Students need to be able to stay focused, ignore those extra details, and find out what the real question is in a particular problem.

B. What do I need in order to find the answer?

Students need to narrow it down, even more, to figure out what is needed to solve the problem, whether it’s adding, subtracting, multiplying, dividing, or some combination of those. They’ll need a general idea of which information will be used (or not used) and what they’ll be doing.

This is where key words become very helpful. When students learn to recognize that certain words mean to add (like in all, altogether, combined ), while others mean to subtract, multiply, or to divide, it helps them decide how to proceed a little better

Here’s a Key Words Chart I like to use for teaching word problems. The handout could be copied at a smaller size and glued into interactive math notebooks. It could be placed in math folders or in binders under the math section if your students use binders.

One year I made huge math signs (addition, subtraction, multiplication, and divide symbols) and wrote the keywords around the symbols. These served as a permanent reminder of keywords for word problems in the classroom.

If you’d like to download this FREE Key Words handout, click here:

which list correctly identifies the steps to solving a word problem

C. What information do I already have?

This is where students will focus in on the numbers which will be used to solve the problem.

3. Write on the Word Problem

This step reinforces the thinking which took place in step number two. Students use a pencil or colored pencils to notate information on worksheets (not books of course, unless they’re consumable). There are lots of ways to do this, but here’s what I like to do:

  • Circle any numbers you’ll use.
  • Lightly cross out any information you don’t need.
  • Underline the phrase or sentence which tells exactly what you’ll need to find.

4. Draw a Simple Picture and Label It

Drawing pictures using simple shapes like squares, circles, and rectangles help students visualize problems. Adding numbers or names as labels help too.

For example, if the word problem says that there were five boxes and each box had 4 apples in it, kids can draw five squares with the number four in each square. Instantly, kids can see the answer so much more easily!

5. Estimate the Answer Before Solving

Having a general idea of a ballpark answer for the problem lets students know if their actual answer is reasonable or not. This quick, rough estimate is a good math habit to get into. It helps students really think about their answer’s accuracy when the problem is finally solved.

6. Check Your Work When Done

This strategy goes along with the fifth strategy. One of the phrases I constantly use during math time is, Is your answer reasonable ? I want students to do more than to be number crunchers but to really think about what those numbers mean.

Also, when students get into the habit of checking work, they are more apt to catch careless mistakes, which are often the root of incorrect answers.

7. Practice Word Problems Often

Just like it takes practice to learn to play the clarinet, to dribble a ball in soccer, and to draw realistically, it takes practice to become a master word problem solver.

When students practice word problems, often several things happen. Word problems become less scary (no, really).

They start to notice similarities in types of problems and are able to more quickly understand how to solve them. They will gain confidence even when dealing with new types of word problems, knowing that they have successfully solved many word problems in the past.

If you’re looking for some word problem task cards, I have quite a few of them for 3rd – 5th graders.

This 3rd grade math task cards bundle has word problems in almost every one of its 30 task card sets..

There are also specific sets that are dedicated to word problems and two-step word problems too. I love these because there’s a task card set for every standard.

CLICK HERE to take a look at 3rd grade:

3rd Grade Math Task Cards Mega Bundle | 3rd Grade Math Centers Bundle

This 4th Grade Math Task Cards Bundle also has lots of word problems in almost every single of its 30 task card sets. These cards are perfect for centers, whole class, and for one on one.

CLICK HERE to see 4th grade:

th Grade 960 Math Task Cards Mega Bundle | 4th Grade Math Centers

This 5th Grade Math Task Cards Bundle is also loaded with word problems to give your students focused practice.

CLICK HERE to take a look at 5th grade:

5th Grade Math Task Cards Mega Bundle - 5th Grade Math Centers

Want to try a FREE set of math task cards to see what you think?

3rd Grade: Rounding Whole Numbers Task Cards

4th Grade: Convert Fractions and Decimals Task Cards

5th Grade: Read, Write, and Compare Decimals Task Cards

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  • \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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Module 9: Multi-Step Linear Equations

Apply a problem-solving strategy to basic word problems, learning outcomes.

  • Practice mindfulness with your attitude about word problems
  • Apply a general problem-solving strategy to solve word problems

 Approach Word Problems with a Positive Attitude

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

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

A cartoon image of a girl with a sad expression writing on a piece of paper is shown. There are 5 thought bubbles. They read,

Negative thoughts about word problems can be barriers to success.

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

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

A cartoon image of a girl with a confident expression holding some books is shown. There are 4 thought bubbles. They read,

When it comes to word problems, a positive attitude is a big step toward success.

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

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

Use a Problem-Solving Strategy for Word Problems

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

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

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

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

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

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

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

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

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

  • Let [latex]p=[/latex] the original price of the shirt

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

The top line reads:

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

  • We found that [latex]p=36[/latex], which means the original price was [latex]\text{\$36}[/latex]. Does [latex]\text{\$36}[/latex] make sense in the problem? Yes, because [latex]18[/latex] is one-half of [latex]36[/latex], and the shirt was on sale at half the original price.

Step 7. Answer the question with a complete sentence.

  • The problem asked “What was the original price of the shirt?” The answer to the question is: “The original price of the shirt was [latex]\text{\$36}[/latex].”

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

The top reads,

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

Problem-Solving Strategy

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

For a review of how to translate algebraic statements into words, watch the following video.

Let’s use this approach with another example.

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

In the next example, we will apply our Problem-Solving Strategy to applications of percent.

Nga’s car insurance premium increased by [latex]\text{\$60}[/latex], which was [latex]\text{8%}[/latex] of the original cost. What was the original cost of the premium?

  • Write Algebraic Expressions from Statements: Form ax+b and a(x+b). Authored by : James Sousa (Mathispower4u.com) for Lumen Learning. Located at : https://youtu.be/Hub7ku7UHT4 . License : CC BY: Attribution
  • Question ID 142694, 142722, 142735, 142761. Authored by : Lumen Learning. License : CC BY: Attribution . License Terms : IMathAS Community License, CC-BY + GPL
  • Prealgebra. Provided by : OpenStax. License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]

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Identifying Operations in Word Problems Worksheets

How to Identify What Operations Need to Take Place to Solve Word Problems - We often start students off with solving word problems with cues or prompts to help them understand the math involved in solving them. What happens when you remove those cues or prompts? Yes, a bit of that deer in headlights look covers your classroom. The best way to determine what operations you will need to introduce to the values that are presented in the problem is to read the problem carefully and look for words that indicate what is being asked of you. There are many different types of words and phrases that will indicate a certain operation. Addition is often signified through the use of the words: increase, total, both, altogether, and in all. Subtraction lean more towards phrases such as: gave away, how many/much more, change, and decrease. Division is all about splitting things up and sharing them; any word that implies that and you know what you must do. Multiplication is often confused with addition, but the words: product, by, factors, and lots are a good of reference for you.

Aligned Standard: 4.OA.3

  • Ice Cream Parlor Step-by-Step Lesson - How many ice cream cups do you need for tomorrow?
  • Guided Lesson - We calculate the amount of baking supplies we need, how many students are in a set of classes and how many rooms a maid cleaned.
  • Guided Lesson Explanation - These are all one-step problems that just take some time to visualize.
  • Practice Worksheet - Lots of problems packed into a little space.
  • Basic Word Problems Puzzle 5-Pack - This is a real neat number puzzle format for you.
  • Identify Operations Word Problems 5-Pack - These are spaced out in an awkwardly cool way.
  • Introductory Word Problems 5-Pack - These are very simple compared to others. Great for kids that are behind or have organization issues.
  • Matching Worksheet - The answers for these are much larger than all the other sheets.
  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

The problems you will see here summed up my entire summer between grand kids, kids, and husband.

  • Homework 1 - John has $40 in his pocket. He found $8 in the couch. How much money does John have?
  • Homework 2 - Ali wants to send books from New York to Washington. He has 1,500 books. He packed these books in 30 boxes. How many books were packed in each box?
  • Homework 3 - 125 boys and 110 girls attend the school dance. What is the total number of students participating?

Practice Worksheets

You will find a lot of different time conversions here. Students should be fluent in transitions between hours, minutes, and seconds.

  • Practice 1 - A company has 458 clients in America, 514 clients in Hong Kong and 142 clients in Japan. Write the total number of clients.
  • Practice 2 - How many days are there in 5 months and 3 weeks?
  • Practice 3 - Molly sells 30 kg of apples in a day. How many apples will she sell in a 2 weeks?

Math Skill Quizzes

Outside of the random conversions of the units of time, these are problems that kids will run into during a typical day in their lives.

  • Quiz 1 - Eva wants to make coffee for 6 people. For this she needs 800 ml of milk, but she has only 450 ml of milk. How much more milk does she need?
  • Quiz 2 - Andrew has 50 candies. He distributes these candies to 5 children equally. Find the share of candies for each child.
  • Quiz 3 - Kayla went shopping to buy shoes. He bought 5 pairs of shoes, but he already had 7 pairs. How many pairs of shoes does he have now?

Tips for Solving Word Problems

As you start learning advanced mathematical skills, you are bound to encounter mathematical word problems. These problems state the information needed to solve the mathematical problem by using logic, equation, and a few mathematical operations. These word problems are the test of your mathematical understanding and reading comprehension. Most children struggle with these problems. Below, we have given a few tips that will help you in understanding these problems quickly and solving them easily. Be organized - Word problems can be confusing, so the first thing you need to do is, attempt it with a clear and organized mind space Read the problem carefully and slowly - Most word problems are crammed with a lot of information. Read the problem more than once and try to figure out relevant information Highlight the necessary information - Once you have read the problem cross out the unnecessary or extra information. Make sure that this information is not required. Highlight the necessary information. This way, referencing back to the problem becomes easier. Visualize - Visualization of the problem makes it helpful in understanding what is happening in the problem. Draw a picture or a graph for a better representation of the problem. Look for the keywords - Highlighting the keywords helps you in translating the words into mathematical operations. These keywords are the clues about which operation to use in the problem. These worksheets and lessons will help students learn to spot keyword terms in word problems that indicate specific math operations.

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Identify the Correct Steps to Solve Word Problems Worksheet

Put your skills to the test by practicing to identify the correct steps to solve word problems..

Identify the Correct Steps to Solve Word Problems Worksheet

Know more about Identify the Correct Steps to Solve Word Problems Worksheet

Kids often develop misconceptions about concepts in mathematics, including word problems. It is important to help them get over those misconceptions. Students will strengthen their problem-solving ability by working with multi-step word problems in this worksheet. They will on a set of a variety of scenarios and identify the correct steps to solve it. Your student will develop the required confidence by solving a variety of problems on word problems.

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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."

which list correctly identifies the steps to solving a word problem

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

which list correctly identifies the steps to solving a word problem

  • 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.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

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."

which list correctly identifies the steps to solving a word problem

Which list correctly identifies the steps to solving a word problem? Select one: a. Read the problem, convert English terms to mathematical terms, solve the problem, list the answer with correct units b. Read the problem, solve the problem, convert English ferms to mathematical terms, list the answer with correct units c. Read the problem, convert English terms to mathematical terms, list the answer with correct units, solve the problem d. Convert English terms to mathematical terms, read the problem, solve the problem, list the answer with correct units

Education Corner

Strategies for Solving Math Word Problems

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Math word problems can be tricky and often challenging to solve. Employing the SQRQCQ method can make solving math word problems easier and less intimidating.

The SQRQCQ method is particularly useful for children with learning disabilities and can be used effectively in special education programs. SQRQCQ is an abbreviation for Survey, Question, Read, Question, Compute, and Question.

Step 1 – SURVEY the Math Problem

The first step to solving a math word problem is to read the problem in its entirety to understand what you are being asked to solve. After you read it, you can decide the most relevant aspects of the problem that need to be solved and what aspects are not relevant to solving the problem. The idea here is to get a general understanding.

Step 2 – QUESTION

Once you have an idea of what you’re attempting to solve, you need to determine what formulas, steps, or equations should be utilized in order to find the correct answer. It is impossible to find an answer if you can’t determine what needs to be solved. Basically, what are the questions being asked by the problem?

Step 3 – REREAD

Now that you’ve determined what needs to be solved, reread the problem and pay close attention to specific details. Determine which aspects of the problem are interrelated. Identify all relevant facts and information needed to solve the problem. As you do, write them down.

Step 4 – QUESTION

Now that you’re familiar with specific details and how different facts and information within the problem are interrelated, determine what formulas or equations must be used to set up and solve the problem. Be sure to write down what steps or operations you will use for easy reference.

Step 5 – COMPUTE

Use the formulas and/or equations identified in the previous step to complete the calculations. Be sure to follow the steps you outlined while setting up an equation or using a formula. As you complete each step, check it off your list.

Step 6 – QUESTION

Once you’ve completed the calculations, review the final answer and make sure it is correct and accurate. If it does not appear logical, review the steps you took to find the answer and look for calculation or set-up errors. Recalculate the numbers or make other changes until you get an answer that makes sense.

How does SQRQCQ help students with learning disabilities?

Math word problems tend to be especially challenging for Learning Disabled (LD) students. LD students often lack “Concept Imagery”, or the ability to visualize the whole problem by creating a complete mental image. They often jump right into calculations and computations without understanding what the problem is asking or what they’re looking for.

LD students may also struggle to understand the words or wording within math word problems correctly. The inability to correctly interpret and understand wording greatly impacts their math reasoning skills and often leads them to making the wrong calculations and arriving incorrect conclusions.

Remembering and manipulating information and details in their working memory is another challenge some LD students face as they try to see the whole picture. Slow processing of information, followed by frustration and anxiety, will often lead LD students to try and get through math word problems as quickly as possible – which is why they often jump straight into computations in their attempt to make it to the finish line as quickly as possible.

SQRQCQ is a metacognitive guide that provides LD students with a logical order for solving math word problems. It provides just enough direction to guide them through the reasoning process without overwhelming them. SQRQCQ is also a mnemonic that is easy for students to remember and which they can fall back on when completing homework or taking tests.

Read also: – A Guide for St u dying Math

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Humor That Works

The 5 Steps of Problem Solving

5-steps-of-problem-solving-humor-that-works-3

Problem solving is a critical skill for success in business – in fact it’s often what you are hired and paid to do. This article explains the five problem solving steps and provides strategies on how to execute each one.

Defining Problem Solving

Before we talk about the stages of problem solving, it’s important to have a definition of what it is. Let’s look at the two roots of problem solving — problems and solutions.

Problem – a state of desire for reaching a definite goal from a present condition [1] Solution – the management of a problem in a way that successfully meets the goals set for treating it

[1] Problem solving on Wikipedia

One important call-out is the importance of having a goal. As defined above, the solution may not completely solve problem, but it does meet the goals you establish for treating it–you may not be able to completely resolve the problem (end world hunger), but you can have a goal to help it (reduce the number of starving children by 10%).

The Five Steps of Problem Solving

With that understanding of problem solving, let’s talk about the steps that can get you there. The five problem solving steps are shown in the chart below:

problem solving steps

However this chart as is a little misleading. Not all problems follow these steps linearly, especially for very challenging problems. Instead, you’ll likely move back and forth between the steps as you continue to work on the problem, as shown below:

problem solving steps iterative

Let’s explore of these steps in more detail, understanding what it is and the inputs and outputs of each phase.

1. Define the Problem

aka What are you trying to solve? In addition to getting clear on what the problem is, defining the problem also establishes a goal for what you want to achieve.

Input:  something is wrong or something could be improved. Output: a clear definition of the opportunity and a goal for fixing it.

2. Brainstorm Ideas

aka What are some ways to solve the problem? The goal is to create a list of possible solutions to choose from. The harder the problem, the more solutions you may need.

Input: a goal; research of the problem and possible solutions; imagination. Output: pick-list of possible solutions that would achieve the stated goal.

3. Decide on a Solution

aka What are you going to do? The ideal solution is effective (it will meet the goal), efficient (is affordable), and has the fewest side effects (limited consequences from implementation).

Input:  pick-list of possible solutions; decision-making criteria. Output: decision of what solution you will implement.

4. Implement the Solution

aka What are you doing? The implementation of a solution requires planning and execution. It’s often iterative, where the focus should be on short implementation cycles with testing and feedback, not trying to get it “perfect” the first time.

Input:  decision; planning; hard work. Output:  resolution to the problem.

5. Review the Results

aka What did you do? To know you successfully solved the problem, it’s important to review what worked, what didn’t and what impact the solution had. It also helps you improve long-term problem solving skills and keeps you from re-inventing the wheel.

Input:  resolutions; results of the implementation. Output: insights; case-studies; bullets on your resume.

Improving Problem Solving Skills

Once you understand the five steps of problem solving, you can build your skill level in each one. Often we’re naturally good at a couple of the phases and not as naturally good at others. Some people are great at generating ideas but struggle implementing them. Other people have great execution skills but can’t make decisions on which solutions to use. Knowing the different problem solving steps allows you to work on your weak areas, or team-up with someone who’s strengths complement yours.

Want to improve your problem solving skills? Want to perfect the art of problem solving?  Check out our training programs or try these 20 problem solving activities to improve creativity .

THIS FREE 129 SECOND QUIZ WILL SHOW YOU

what is your humor persona?

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22 thoughts on “The 5 Steps of Problem Solving”

which list correctly identifies the steps to solving a word problem

very helpful and informative training

which list correctly identifies the steps to solving a word problem

Thank you for the information

which list correctly identifies the steps to solving a word problem

YOU ARE AFOOL

which list correctly identifies the steps to solving a word problem

I’m writing my 7th edition of Effective Security Management. I would like to use your circular graphic illustration in a new chapter on problem solving. You’re welcome to phone me at — with attribution.

which list correctly identifies the steps to solving a word problem

Sure thing, shoot us an email at [email protected] .

which list correctly identifies the steps to solving a word problem

i love your presentation. It’s very clear. I think I would use it in teaching my class problem solving procedures. Thank you

which list correctly identifies the steps to solving a word problem

It is well defined steps, thank you.

which list correctly identifies the steps to solving a word problem

these step can you email them to me so I can print them out these steps are very helpful

which list correctly identifies the steps to solving a word problem

I like the content of this article, it is really helpful. I would like to know much on how PAID process (i.e. Problem statement, Analyze the problem, Identify likely causes, and Define the actual causes) works in Problem Solving.

which list correctly identifies the steps to solving a word problem

very useful information on problem solving process.Thank you for the update.

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which list correctly identifies the steps to solving a word problem

It makes sense that a business would want to have an effective problem solving strategy. Things could get bad if they can’t find solutions! I think one of the most important things about problem solving is communication.

which list correctly identifies the steps to solving a word problem

Well in our school teacher teach us –

1) problem ldentification 2) structuring the problem 3) looking for possible solutions 4) lmplementation 5) monitoring or seeking feedback 6) decision making

Pleace write about it …

which list correctly identifies the steps to solving a word problem

I teach Professional communication (Speech) and I find the 5 steps to problem solving as described here the best method. Your teacher actually uses 4 steps. The Feedback and decision making are follow up to the actual implementation and solving of the problem.

which list correctly identifies the steps to solving a word problem

i know the steps of doing some guideline for problem solving

which list correctly identifies the steps to solving a word problem

steps are very useful to solve my problem

which list correctly identifies the steps to solving a word problem

The steps given are very effective. Thank you for the wonderful presentation of the cycle/steps/procedure and their connections.

which list correctly identifies the steps to solving a word problem

I like the steps for problem solving

which list correctly identifies the steps to solving a word problem

It is very useful for solving difficult problem i would reccomend it to a friend

which list correctly identifies the steps to solving a word problem

this is very interesting because once u have learned you will always differentiate the right from the wrong.

which list correctly identifies the steps to solving a word problem

I like the contents of the problem solving steps. informative.

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I make an effort to appreciate the humor of everyday life....

This question helps us further the advancement of humor research to make it more equitable.

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IMAGES

  1. Steps to Solve Word Problems by Samantha McConnell

    which list correctly identifies the steps to solving a word problem

  2. Problem Solving: Two Step Word Problems

    which list correctly identifies the steps to solving a word problem

  3. Solving a Word Problem by Tutor Juls

    which list correctly identifies the steps to solving a word problem

  4. Solving a Word Problem by Tutor Juls

    which list correctly identifies the steps to solving a word problem

  5. Steps for solving Word Problems by goofygoober

    which list correctly identifies the steps to solving a word problem

  6. Solving Word Problem Anchor Chart

    which list correctly identifies the steps to solving a word problem

VIDEO

  1. Solving Word Problems (Simplifying Math)

  2. easy system to solve word problems.wmv

  3. 4 Steps in Solving Problems

  4. How to solve a word problem with systems of equations

  5. 12

  6. Grade 2 Math 6.13, Word problem solving, choose the operation

COMMENTS

  1. Algebra Topics: Introduction to Word Problems

    Step 4: Solve the problem. It will only take a few steps to solve this problem. To get the correct answer, we'll have to get m alone on one side of the equation. m + 3m = 280. To start, let's add m and 3m. That's 4m. 4m = 280. We can get rid of the 4 next to the m by dividing both sides by 4. 4m / 4 is m, and 280 / 4 is 70. m = 70. We've got ...

  2. The 4 Steps to Solving Word Problems

    Generally, solving a word problem involves four easy steps: Read through the problem and set up a word equation — that is, an equation that contains words as well as numbers. Plug in numbers in place of words wherever possible to set up a regular math equation. Use math to solve the equation. Answer the question the problem asks.

  3. 5 Easy Steps to Solving Word Problems

    1. Write (or draw) what you know. It is important to convince students that they do not have to immediately know what math operation is required to solve the problem. They first need only understand the scenario itself.

  4. SOLVING WORD PROBLEMS: A VISUAL APPROACH: HOME

    Step 1: Identify the given information in the problem. Underline the information in your problem. Then create a checklist. As you use the information in your solution, make sure to check off each box. Understanding a math word problem is 50% of the work. So give yourself a pat on the back when you've finished it! STEP TWO

  5. 5 Steps to Word Problem Solving

    5 Steps to Word Problem Solving ••• Updated April 24, 2017 By Avery Martin Word problems often confuse students simply because the question does not present itself in a ready-to-solve mathematical equation. You can answer even the most complex word problems, provided you understand the mathematical concepts addressed.

  6. Algebra 1:solving word problems Flashcards

    The first step of solving a word problem. identify the unknown (and known, if necessary information) The second step of solving a word problem. Represent one of the unknowns with a variable. The third step of solving a word problem. express the other unknowns in terms of the variable. The fourth step of solving a word problem. write an equation.

  7. Solving Word Problems: Steps & Examples

    Learn the steps used in solving word problems which include visualizing the problem, writing the equation, and solving the equation with examples of how it's done. Our Word Problem Yes,...

  8. 4 Simple Steps to Solve a Word Problem

    Arrays. Number Lines. Most students want to jump to writing an equation or number sentence, but in my class, it can't be done until the model is drawn. Once the model is drawn students can better understand what the unknown is and write a number sentence that will help them to accurately solve the word problem.

  9. Apply a Problem-Solving Strategy to Word Problems

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

  10. Strategies for Solving Word Problems

    1. Read the Entire Word Problem Before students look for keywords and try to figure out what to do, they need to slow down a bit and read the whole word problem once (and even better, twice). This helps kids get the bigger picture to be able to understand it a little better too. 2. Think About the Word Problem

  11. Word Problems Calculator

    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. Show more Why users love our Word Problems Calculator Related Symbolab blog posts Middle School Math Solutions - Simultaneous Equations Calculator

  12. Apply a Problem-Solving Strategy to Basic Word Problems

    Even if you know the answer right away, using algebra will better prepare you to solve problems that do not have obvious answers. Write the equation. 18= 1 2p 18 = 1 2 p. Multiply both sides by 2. 2⋅18=2⋅ 1 2p 2 ⋅ 18 = 2 ⋅ 1 2 p. Simplify. 36=p 36 = p. Step 6. Check the answer in the problem and make sure it makes sense.

  13. Identifying Operations in Word Problems Worksheets

    Practice Worksheet - Lots of problems packed into a little space. Basic Word Problems Puzzle 5-Pack - This is a real neat number puzzle format for you. Identify Operations Word Problems 5-Pack - These are spaced out in an awkwardly cool way. Introductory Word Problems 5-Pack - These are very simple compared to others.

  14. Identify the Correct Steps to Solve Word Problems Worksheet

    Kids often develop misconceptions about concepts in mathematics, including word problems. It is important to help them get over those misconceptions. Students will strengthen their problem-solving ability by working with multi-step word problems in this worksheet. They will on a set of a variety of scenarios and identify the correct steps to solve it. Your student will develop the required ...

  15. The Problem-Solving Process

    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.

  16. Which list correctly identifies the steps to solving a word problem

    Which list correctly identifies the steps to solving a word problem? Select one: a. Read the problem, convert English terms to mathematical terms, solve the problem, list the answer with correct units b.

  17. Which list correctwhich list correctly identifies the steps to solving

    There is no one definitive list of steps to solving a word problem, as different types of problems may require different approaches. However, a general set of steps that can be useful in solving many word problems is: 1. Read the problem carefully to understand what it is asking. 2.

  18. What is Problem Solving? Steps, Process & Techniques

    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.

  19. Strategies for Solving Math Word Problems

    Step 1 - SURVEY the Math Problem The first step to solving a math word problem is to read the problem in its entirety to understand what you are being asked to solve. After you read it, you can decide the most relevant aspects of the problem that need to be solved and what aspects are not relevant to solving the problem.

  20. Chapter 11: Problem Solving Flashcards

    Terms in this set (20) b. Discuss and document individual views until everyone agrees the nature of the problem. The first step in problem solving is to: a. Descriptive, functional, and prescriptive. The main approaches to examining how groups solve problems are: d. Forming, storming, norming, and performing.

  21. The 5 Steps of Problem Solving

    The implementation of a solution requires planning and execution. It's often iterative, where the focus should be on short implementation cycles with testing and feedback, not trying to get it "perfect" the first time. Input: decision; planning; hard work. Output: resolution to the problem. 5.

  22. The Four-Step Problem-Solving Process Flashcards

    a sequence of organized steps to follow when making decisions. Understanding the Problem. construct a mental representation of the problem, based on the information provided in the problem and one's own previous experience. to attain clarity, to determine the question asked, and to identify the information given. Devising a Plan.

  23. THE PROBLEM-SOLVING PROCESS Flashcards

    Step 1: Define the Problem. Differentiate fact from opinion. Specify underlying causes. Consult each faction involved for information. State the problem specifically. Identify what standard or expectation is violated. Determine in which process the problem lies. Avoid trying to solve the problem without data.