what is the five step strategy for solving word problems

5 Easy Steps to Solve Any Word Problem in Math

  • February 27, 2021

Picture this my teacher besties.  You are solving word problems in your math class and every student, yes every student knows how to solve word problems without immediately entering a state of confusion!  They know how to attack the problem head-on and have a method to solve every single problem that is presented to them.  

tips-to-solve-word-problems-in-math

How Do You Solve Word Problems in Math?

Ask yourself this, what do you think is the #1 phrase a student says as soon as they see a word problem? 

You guessed it, my teacher friend,  I don’t know how to do this!  I think the most common question I get when I’m teaching my math classes, is how do I solve this?  

Students see word problems and immediately enter freak-out mode!  Let’s take solving word problems in the classroom and make it easier for students to SOLVE the problem!

problem-solving-strategies-in-math

How to Solve Word Problems Step by Step 

There are so many methods   that students can choose from when learning how to solve word problems.  The 4 step method is the foundation for all of the methods that you will see, but what about a variation of the 4 step method that every student can do just because they get it. 

Students are most likely confused about how to solve word problems because they have never used a consistent method over the years.   I’m all about consistency in my classroom.  Fortunately, in my school district, I get to teach most of the students year after year because of how small our class sizes are.   So I’m going to give you a method based on the 4 step method, that allows all students to be successful at solving word problems.  

Even the most unmotivated math student will learn how to solve word problems and not skip them!

steps-to-solving-word-problems-in-mathematics

Tips, Tricks, and  Teaching Strategies to Solving Word Problems in Math

Going back to the 4 step method just in case you need a refresher.  If you know me at all a little reminder of “oh yeah I remember that now” always helps me!  

4 steps in solving word problems in math:

  • Understand the Problem
  • Plan the solution
  • Solve the Problem 
  • Check the solution

This 4 step method is the basis of the method I’m going to tell you all about.  The problem isn’t with the method itself, it is the fact that most students see word problems and just start panicking!

Why can they do an entire assignment and then see a word problem and then suddenly stop?  Is there a reason why books are designed with word problems at the end? 

These are questions that I constantly have asked myself over the last several years.  I finally got to the point where my students needed a consistent approach to solving word problems that worked every single time.  

The first thing I knew I needed to start doing was introducing students to word problems at the beginning of each lesson.

Once students first see the word problems at the beginning of the lesson, they are less likely to be scared of them when it comes time to do it by themselves! 

This also will increase their confidence in the classroom.  In case you missed it, I shared all about how I increase my students’ confidence in the classroom.  

Wonder how increasing their confidence will help keep them motivated in the classroom?

So confident motivated students will see word problems that could be on their homework, any standardized test, and say I GOT THIS! 

steps-to-solving-word-problems-in-mathematics

Steps to Solving Word Problems in Mathematics

We are ready to SOLVE any word problem our students are going to encounter in math class.  

Here are my 5 easy steps to SOLVE any word problem in math:

  • S – State the objective
  • O – Outline your plan
  • L – Look for Key Details – Information 
  • V –  Verify and Solve
  • E – Explain and check your solution

Do you want to learn how to implement this 5 steps problem-solving strategy into your classroom?  I’m hosting a FREE workshop all about how to implement this strategy in your classroom!  

problem-solving-strategies-for-math

I am so excited to be offering a workshop to increase students’ confidence in solving word problems.  The workshop is held in my Facebook Group The Round Robin Math Community. It also will be sent straight to your inbox and you can watch it right now!

If you’re interested, join today and all the details will be sent to you ASAP!

I will see you there!

PS.  Need the SOLVE method for your bulletin board for your students’ math journals/notebooks?  Check out this bulletin board resource here:

problem solving bulletin board

Love, Robin

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what is the five step strategy for solving word problems

Hi, I'm Robin!

 I am a secondary math teacher with over 19 years of experience! If you’re a teacher looking for help with all the tips, tricks, and strategies for passing the praxis math core test, you’re in the right place!

I also create engaging secondary math resources for grades 7-12! 

Learn more about me and how I can help you here .

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10 Best Strategies for Solving Math Word Problems

Solving word problem chart

1. Understand the Problem by Paraphrasing

2. identify key information and variables, 3. translate words into mathematical symbols, 4. break down the problem into manageable parts, 5. draw diagrams or visual representations, 6. use estimation to predict answers, 7. apply logical reasoning for unknown variables, 8. leverage similar problems as templates, 9. check answers in the context of the problem, 10. reflect and learn from mistakes.

Have you ever observed the look of confusion on a student’s face when they encounter a math word problem ? It’s a common sight in classrooms worldwide, underscoring the need for effective strategies for solving math word problems . The main hurdle in solving math word problems is not just the math itself but understanding how to translate the words into mathematical equations that can be solved.

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Generic advice like “read the problem carefully” or “practice more” often falls short in addressing students’ specific difficulties with word problems. Students need targeted math word problem strategies that address the root of their struggles head-on. 

A Guide on Steps to Solving Word Problems: 10 Strategies 

One of the first steps in tackling a math word problem is to make sure your students understand what the problem is asking. Encourage them to paraphrase the problem in their own words. This means they rewrite the problem using simpler language or break it down into more digestible parts. Paraphrasing helps students grasp the concept and focus on the problem’s core elements without getting lost in the complex wording.

Original Problem: “If a farmer has 15 apples and gives away 8, how many does he have left?”

Paraphrased: “A farmer had some apples. He gave some away. Now, how many apples does he have?”

This paraphrasing helps students identify the main action (giving away apples) and what they need to find out (how many apples are left).

Play these subtraction word problem games in the classroom for free:

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Students often get overwhelmed by the details in word problems. Teach them to identify key information and variables essential for solving the problem. This includes numbers , operations ( addition , subtraction , multiplication , division ), and what the question is asking them to find. Highlighting or underlining can be very effective here. This visual differentiation can help students focus on what’s important, ignoring irrelevant details.

  • Encourage students to underline numbers and circle keywords that indicate operations (like ‘total’ for addition and ‘left’ for subtraction).
  • Teach them to write down what they’re solving for, such as “Find: Total apples left.”

Problem: “A classroom has 24 students. If 6 more students joined the class, how many students are there in total?”

Key Information:

  • Original number of students (24)
  • Students joined (6)
  • Looking for the total number of students

Here are some fun addition word problems that your students can play for free:

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The transition from the language of word problems to the language of mathematics is a critical skill. Teach your students to convert words into mathematical symbols and equations. This step is about recognizing keywords and phrases corresponding to mathematical operations and expressions .

Common Translations:

  • “Total,” “sum,” “combined” → Addition (+)
  • “Difference,” “less than,” “remain” → Subtraction (−)
  • “Times,” “product of” → Multiplication (×)
  • “Divided by,” “quotient of” → Division (÷)
  • “Equals” → Equals sign (=)

Problem: “If one book costs $5, how much would 4 books cost?”

Translation: The word “costs” indicates a multiplication operation because we find the total cost of multiple items. Therefore, the equation is 4 × 5 = $20

Complex math word problems can often overwhelm students. Incorporating math strategies for problem solving, such as teaching them to break down the problem into smaller, more manageable parts, is a powerful approach to overcome this challenge. This means looking at the problem step by step rather than simultaneously trying to solve it. Breaking it down helps students focus on one aspect of the problem at a time, making finding the solution more straightforward.

Problem: “John has twice as many apples as Sarah. If Sarah has 5 apples, how many apples do they have together?”

Steps to Break Down the Problem:

Find out how many apples John has: Since John has twice as many apples as Sarah, and Sarah has 5, John has 5 × 2 = 10

Calculate the total number of apples: Add Sarah’s apples to John’s to find the total,  5 + 10 = 15

By splitting the problem into two parts, students can solve it without getting confused by all the details at once.

Explore these fun multiplication word problem games:

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Diagrams and visual representations can be incredibly helpful for students, especially when dealing with spatial or quantity relationships in word problems. Encourage students to draw simple sketches or diagrams to represent the problem visually. This can include drawing bars for comparison, shapes for geometry problems, or even a simple distribution to better understand division or multiplication problems .

Problem: “A garden is 3 times as long as it is wide. If the width is 4 meters, how long is the garden?”

Visual Representation: Draw a rectangle and label the width as 4 meters. Then, sketch the length to represent it as three times the width visually, helping students see that the length is 4 × 3 = 12

Estimation is a valuable skill in solving math word problems, as it allows students to predict the answer’s ballpark figure before solving it precisely. Teaching students to use estimation can help them check their answers for reasonableness and avoid common mistakes.

Problem: “If a book costs $4.95 and you buy 3 books, approximately how much will you spend?”

Estimation Strategy: Round $4.95 to the nearest dollar ($5) and multiply by the number of books (3), so 5 × 3 = 15. Hence, the estimated total cost is about $15.

Estimation helps students understand whether their final answer is plausible, providing a quick way to check their work against a rough calculation.

Check out these fun estimation and prediction word problem worksheets that can be of great help:

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When students encounter problems with unknown variables, it’s crucial to introduce them to logical reasoning. This strategy involves using the information in the problem to deduce the value of unknown variables logically. One of the most effective strategies for solving math word problems is working backward from the desired outcome. This means starting with the result and thinking about the steps leading to that result, which can be particularly useful in algebraic problems.

Problem: “A number added to three times itself equals 32. What is the number?”

Working Backward:

Let the unknown number be x.

The equation based on the problem is  x + 3x = 32

Solve for x by simplifying the equation to 4x=32, then dividing by 4 to find x=8.

By working backward, students can more easily connect the dots between the unknown variable and the information provided.

Practicing problems of similar structure can help students recognize patterns and apply known strategies to new situations. Encourage them to leverage similar problems as templates, analyzing how a solved problem’s strategy can apply to a new one. Creating a personal “problem bank”—a collection of solved problems—can be a valuable reference tool, helping students see the commonalities between different problems and reinforcing the strategies that work.

Suppose students have solved a problem about dividing a set of items among a group of people. In that case, they can use that strategy when encountering a similar problem, even if it’s about dividing money or sharing work equally.

It’s essential for students to learn the habit of checking their answers within the context of the problem to ensure their solutions make sense. This step involves going back to the original problem statement after solving it to verify that the answer fits logically with the given information. Providing a checklist for this process can help students systematically review their answers.

Checklist for Reviewing Answers:

  • Re-read the problem: Ensure the question was understood correctly.
  • Compare with the original problem: Does the answer make sense given the scenario?
  • Use estimation: Does the precise answer align with an earlier estimation?
  • Substitute back: If applicable, plug the answer into the problem to see if it works.

Problem: “If you divide 24 apples among 4 children, how many apples does each child get?”

After solving, students should check that they understood the problem (dividing apples equally).

Their answer (6 apples per child) fits logically with the number of apples and children.

Their estimation aligns with the actual calculation.

Substituting back 4×6=24 confirms the answer is correct.

Teaching students to apply logical reasoning, leverage solved problems as templates, and check their answers in context equips them with a robust toolkit for tackling math word problems efficiently and effectively.

One of the most effective ways for students to improve their problem-solving skills is by reflecting on their errors, especially with math word problems. Using word problem worksheets is one of the most effective strategies for solving word problems, and practicing word problems as it fosters a more thoughtful and reflective approach to problem-solving

These worksheets can provide a variety of problems that challenge students in different ways, allowing them to encounter and work through common pitfalls in a controlled setting. After completing a worksheet, students can review their answers, identify any mistakes, and then reflect on them in their mistake journal. This practice reinforces mathematical concepts and improves their math problem solving strategies over time.

3 Additional Tips for Enhancing Word Problem-Solving Skills

Before we dive into the importance of reflecting on mistakes, here are a few impactful tips to enhance students’ word problem-solving skills further:

1. Utilize Online Word Problem Games

A word problem game

Incorporate online games that focus on math word problems into your teaching. These interactive platforms make learning fun and engaging, allowing students to practice in a dynamic environment. Games can offer instant feedback and adaptive challenges, catering to individual learning speeds and styles.

Here are some word problem games that you can use for free:

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2. Practice Regularly with Diverse Problems

Word problem worksheet

Consistent practice with a wide range of word problems helps students become familiar with different questions and mathematical concepts. This exposure is crucial for building confidence and proficiency.

Start Practicing Word Problems with these Printable Word Problem Worksheets:

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3. Encourage Group Work

Solving word problems in groups allows students to share strategies and learn from each other. A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students’ problem-solving toolkit.

Conclusion 

Mastering math word problems is a journey of small steps. Encourage your students to practice regularly, stay curious, and learn from their mistakes. These strategies for solving math word problems are stepping stones to turning challenges into achievements. Keep it simple, and watch your students grow their confidence and skills, one problem at a time.

Frequently Asked Questions (FAQs)

How can i help my students stay motivated when solving math word problems.

Encourage small victories and use engaging tools like online games to make practice fun and rewarding.

What's the best way to teach beginners word problems?

Begin with simple problems that integrate everyday scenarios to make the connection between math and real-life clear and relatable.

How often should students practice math word problems?

Regular, daily practice with various problems helps build confidence and problem-solving skills over time.

what is the five step strategy for solving word problems

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what is the five step strategy for solving word problems

Strategies for Solving Word Problems – Math

what is the five step strategy for solving word problems

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:

what is the five step strategy for solving word problems

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

Thanks so much for stopping by!

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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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A Math Word Problem Framework That Fosters Conceptual Thinking

This strategy for selecting and teaching word problems guides students to develop their understanding of math concepts.

Photo of middle school teacher with students

Word problems in mathematics are a powerful tool for helping students make sense of and reason with mathematical concepts. Many students, however, struggle with word problems because of the various cognitive demands. As districtwide STEAM professional development specialists, we’ve spent a lot of time focusing on supporting our colleagues and students to ensure their success with word problems. We found that selecting the right word problems, as well as focusing on conceptual understanding rather than procedural knowledge, provides our students with real growth.

As our thinking evolved, we began to instill a routine that supports teaching students to solve with grit by putting them in the driver’s seat of the thinking. Below you’ll find the routine that we’ve found successful in helping students overcome the challenges of solving word problems.

Not all word problems are created equal

Prior to any instruction, we always consider the quality of the task for teaching and learning. In our process, we use word problems as the path to mathematics instruction. When selecting the mathematical tasks for students, we always consider the following questions:

  • Does the task align with the learning goals and standards?
  • Will the task engage and challenge students at an appropriate level, providing both a sense of accomplishment and further opportunities for growth?
  • Is the task open or closed? Open tasks provide multiple pathways to foster a deeper understanding of mathematical concepts and skills. Closed tasks can still provide a deep understanding of mathematical concepts and skills if the task requires a high level of cognitive demand. 
  • Does the task encourage critical thinking and problem-solving skills?
  • Will the task allow students to see the relevance of mathematics to real-world situations?
  • Does the task promote creativity and encourage students to make connections between mathematical concepts and other areas of their lives?

If we can answer yes to as many of these questions as possible, we can be assured that our tasks are rich. There are further insights for rich math tasks on NRICH and sample tasks on Illustrative Mathematics and K-5 Math Teaching Resources .

Developing conceptual understanding

Once we’ve selected the rich math tasks, developing conceptual understanding becomes our instructional focus. We present students with Numberless Word Problems and simultaneously use a word problem framework to focus on analysis of the text and to build conceptual understanding, rather than just memorization of formulas and procedures. 

  • First we remove all of the numbers and have students read the problem focusing on who or what the problem is about; they visualize and connect the scenario to their lives and experiences. 
  • Next we have our students rewrite the question as a statement to ensure that they understand the questions.
  • Then we have our students read the problem again and have them think analytically. They ask themselves these questions: Are there parts? Is there a whole? Are things joining or separating? Is there a comparison? 
  • Once that’s completed, we reveal the numbers in the problem. We have the students read the problem again to determine if they have enough information to develop a model and translate it into an equation that can be solved.
  • After they’ve solved their equation, we have students compare it against their model to check their answer.  

Collaboration and workspace are key to building the thinking

To build the thinking necessary in the math classroom , we have students work in visibly random collaborative groups (random groups of three for grades 3 through 12, random groups of two for grades 1 and 2). With random groupings, we’ve found that students don’t enter their groups with predetermined roles, and all students contribute to the thinking.

For reluctant learners, we make sure these students serve as the scribe within the group documenting each member’s contribution. We also make sure to use nonpermanent vertical workspaces (whiteboards, windows [using dry-erase markers], large adhesive-backed chart paper, etc.). The vertical workspace provides accessibility for our diverse learners and promotes problem-solving because our students break down complex problems into smaller, manageable steps. The vertical workspaces also provide a visually appealing and organized way for our students to show their work.  We’ve witnessed how these workspaces help hold their attention and improve their focus on the task at hand.

Facilitate and provide feedback to move the thinking along

As students grapple with the task, the teacher floats among the collaborative groups, facilitates conversations, and gives the students feedback. Students are encouraged to look at the work of other groups or to provide a second strategy or model to support their thinking. Students take ownership and make sense of the problem, attempt solutions, and try to support their thinking with models, equations, charts, graphs, words, etc. They work through the problem collaboratively, justifying their work in their small group. In essence, they’re constructing their knowledge and preparing to share their work with the rest of the class. 

Word problems are a powerful tool for teaching math concepts to students. They offer a practical and relatable approach to problem-solving, enabling students to understand the relevance of math in real-life situations. Through word problems, students learn to apply mathematical principles and logical reasoning to solve complex problems. 

Moreover, word problems also enhance critical thinking, analytical skills, and decision-making abilities. Incorporating word problems into math lessons is an effective way to make math engaging, meaningful, and applicable to everyday life.

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CAP Curriculum

  • by CAPCURRICULUM
  • January 28, 2024

Solving math word problems can pose a significant challenge for students. While various processes and strategies exist for solving these problems, not all are equally effective.

There is, however, a strategy called R.I.E.D.S. that’s a game-changer when it comes to solving math word problems. I tried it out with my fourth-grade students, and in just six weeks, their problem-solving skills shot up by 22 percentage points, according to the school district’s benchmark assessment.

In my 20+ years as an educator, I’ve tried many word problem-solving strategies. I have also seen many implemented; some were effective, while others, not so much.

In all honesty, though, strategies are only as effective as the teacher’s implementation. I say this because I’ve seen teachers implement tried-and-true strategies ineffectively, and then blame the students or the strategy for the lack of success, instead of their implementation and execution.

Now, I know you don’t know anything about R.I.D.E.S, so I’m curious about the word problem solving strategy you’re teaching to your students.

If I had to guess, I’d say CUBES. Am I correct?

CUBES: A Popular Strategy for Solving Math Word Problems

Within the last decade (maybe a little longer), I’ve noticed that CUBES has become the go-to strategy for many teachers when it comes to teaching students how to tackle word problems.

CUBES isn’t a bad strategy it’s just that before you go teaching it to your students, you’ve got to tweak a few things.

So, what’s the problem? I had this ongoing debate with some fellow teachers about CUBES not being as effective when you stick too strictly to the steps.

Although there was much evidence suggesting that CUBES wasn’t working for their students, they were adamant that it was an effective strategy. But more than that, they were reluctant to try a new strategy.

I wanted to settle this collegial debate with a bit of outside-school evidence, so I threw a math word problem at my son to see his approach to problem solving.

I couldn’t believe what I was observing.

My Son Too!

Before even reading the word problem, my son began going through a routine. He started by circling all of the numbers.

The whole time he’s circling, I’m sitting there thinking…WTF!

After circling the numbers, he underlined the question. I knew where he was going next, so I stopped him. I couldn’t sit back and watch him reinforce a bad habit.

To confirm my assumption about the strategy he was using, I asked him why he circled the numbers first.

His response? “That’s what you’re supposed to do first. Circle the numbers.” 

I had to break it to him — circling numbers shouldn’t be the first thing you do.

Now, my son being the argumentative person he is, disagreed. He explained that he was following his teacher’s directions and that his work would be marked wrong if he didn’t stick to the steps.

So, I asked him flat out, “Are you using the CUBES strategy?”

“Yep!” he proudly responded.

Instantly, I thought about the teacher at my school who was emotionally attached to CUBES, despite it not working for her students.

Guess what? It wasn’t working for my son either.

As educators, we need to keep in ming — it’s not about what we like and our preferences; it’s about what works for our students.

A Directive to Stop Using Cubes

what is the five step strategy for solving word problems

So, picture this: The math coordinator from the district swings by our school for a visit, doing the whole walkthrough and support thing. Afterward, during our debrief, she sings music to my ears and tells me that the CUBES posters plastered on the walls gotta go.

Turns out, she wasn’t a fan of CUBES either, echoing my sentiments. The minute she walked out the door, I made a beeline for every classroom with those posters and broke the news about the district directive.

Now, I get it, if you’re a teacher, you might be side-eyeing me for bossing other teachers around and reducing teacher autonomy. But hey, sometimes you gotta do what you gotta do.

I believe in teacher autonomy and buy-in, but not when it adversely impacts students’ learning. 

See, if a strategy isn’t cutting it for the students, no matter how much we like it, there are only two moves: either give it a makeover or kick it to the curb. Why? ‘Cause that’s what 1 thing highly effective teachers do .

Here’s the real reason why we had to ditch CUBES:

  • It wasn’t working for our students – they problem skills were below grade-level.
  • Teachers were clinging to it without giving it a facelift, stuck in their ways.
  • There were more effective methods in the toolbox.

So, What is CUBES?

CUBES is a math word problem-solving strategy, with each letter representing an actionable step. 

CUBES math word problem solving strategy poster.

If you search the web, you’ll discover several variations of CUBES. Some variations strengthen the strategy, but holes still remain. For example, the Caffeine Queen Teacher discusses CUBES in her blog titled How to Teach Math Word Problems – CUBES Math Strategy . She refined the strategy by adding a critical and necessary component: read to understand the problem. Everything else, though, stayed the same. After they read, they began circling numbers.

3 Holes in the CUBES Strategy

Issue #1 : The initial step instructs students to circle key numbers.

This poses a challenge because it’s impossible to determine which numbers are crucial without first reading the problem and pinpointing the question and/or task.

Problem #2 : CUBES advises students to circle, underline, and box various types of information.

This implies that students have to recall what to circle, underline, and box.

While it might not seem like a big deal, it results in inconsistencies in how students approach coding word problems. For instance, when I asked students in one class about the specific actions for each letter, they provided different responses.

Let me throw a scenario at you: Do students need to circle all numbers in the following word problem?

“Danielle had 5 red apples, 3 shirts, and 3 green apples. How many apples did Danielle have?”

No, they don’t—which is precisely why circling all numbers from the get-go is futile and a waste of time.

The Hole That Leads to Frustration

Issue #3 : When it comes to the “B” in CUBES, many teachers advise students to box key words and phrases (e.g., altogether, in all, and how many more) that suggest the operation to perform.

This becomes problematic because key words and phrases are not always present in word problems.

Consider this problem:

“Maria saw three yellow butterflies. She also saw eight orange butterflies. How many butterflies did Maria see?”

When students exclusively tackle problems containing key words, they face difficulties when approaching problems lacking them. This leads to frustration and a tendency for students to give up when they encounter unfamiliar scenarios.

Another snag with this strategy is that students often end up boxing irrelevant words.

Take this problem, for example:

“Justin baked two pies for his first baking contest. Unfortunately, the testers said the pies weren’t sweet enough, and he lost. The second time he entered the contest, he added 1 cup of lemon juice and twice the amount of sugar. How much sugar did he put in the first recipe if he put 4 cups of sugar in the second recipe?”

In such problems, I’ve observed students boxing words like “added” and “twice.” While “twice” is relevant and necessary to solve the problem, “added” is not. However, students box it because they perceive it as a math clue word, leading to unnecessary misconceptions.

A Better Strategy For Solving Word Problems: R.I.E.D.S.

As I mentioned earlier, R.I.E.D.S. is tried-and-true After giving it a shot for just six weeks, my students’ word problem skills shot up by 22 percentage points, soaring from 54% to a solid 76%.

Now, you’re probably curious about what sets R.I.E.D.S. apart from CUBES, right? Let me break it down.

First off, while reading might be implied in CUBES, R.I.E.D.S. explicitly tells students to read the problem for understanding. This is crucial because, from my experience, some students don’t dive into the reading until after they’ve already done the first three steps in the CUBES strategy, which is a gap in the strategy.

Only after students have read and fully grasped the problem should they start digging in.

Secondly, it’s not about boxing key words with R.I.E.D.S. It’s all about identifying the relevant info needed to crack the problem.

Thirdly, with R.I.E.D.S., students use the question or task in the problem to guide their decision-making, from spotting relevant details to figuring out which operation(s) to use.

Fourthly, R.I.E.D.S. calls out developing a plan, a crucial step to solving word problems. A step that engages students in metacognitive thinking

Solving Word Problems Using R.I.E.D.S.

R.I.E.D.S. is a simple five-step strategy for cracking word problems. Let me break it down for you:

Step 1: Read and Understand the Problem

The goal here is to get students reading and truly getting what the problem is about. We want them to explain the situation in the problem without diving into the numbers. For example, look at this problem:

“There are 15 cupcakes. The first-grade students ate 7 of the cupcakes. How many cupcakes are left?”

If your students tackle this problem, you want them to say something like, “There are some cupcakes, and the students ate some.”

Teachers often tell me that their students struggle with determining what operation is needed to solve the problem. When students focus on the situation instead of the numbers, the operation needed to solve the problem sometimes becomes obvious.

Just think about it. If there were some cupcakes and the students ate some, it’s obvious that the subtracting is the operation needed to solve the problem.

Step 2: Identify the Question/Task

This step is the engine of the whole process. It’s crucial that students pinpoint (box, underline, highlight, etc.) the question/task and understand what’s being asked.

Step 3: Extract Relevant Information

After identifying the question or task, students need to read and reread each sentence, grabbing the info they need to solve the problem. They should keep going back to the question/task, asking themselves: “Are there any details from this sentence that can help me solve the problem?”

what is the five step strategy for solving word problems

Step 4: Develop a Plan

During this step, students think about how to tackle the problem, considering different problem-solving strategies, such as make a table, work backwards, use logical reasons, find a pattern, solve a simpler problem , etc.

It’s crucial that students are exposed to a variety of problem solving strategies and given opportunities to solve problems that require the use of various strategies.

Step 5: Solve

This step is straightforward; students simply record their answer.

Recommendations for Success

To help your students master this strategy and become skillful at solving math word problems, I have a few recommendations for you:

  • Devote Dedicated Time: Set aside a chunk of your math block specifically for problem-solving, around 10-15 minutes. For real proficiency, students need daily chances to dive into problem-solving, tackling at least two problems each day.
  • Diversify Word Problems: Mix it up! Ensure that the word problems your students tackle cover various types, such as take-away, add-to, end unknown, change unknown, etc. When all problems involve the same operation, things get too predictable, and the critical thinking needed takes a hit. Check out this link for a variety of word problem types to keep things fresh.
  • Reasoning Matters: Ask your students to explain why they chose certain details to help them solve the problem. Spend time discussing why those details matter in the context of the problem.
  • Start Simple, Go Gradual: Kick off with single-step problems before diving into the complexity of multiple-step word problems.
  • Gradual Release and Think Aloud: Use the gradual release model until students begin showing mastery with the strategy and various types of word problems. When modeling problem-solving, think aloud. Let your students in on your thought process. It’s like giving them a backstage pass to your brain.
  • Teach Strategies and Foster Thinking: Equip your students with problem-solving strategies. Encourage them to ponder the methods they could use to crack a problem, supporting both flexible and metacognitive thinking. These are key skills for becoming adept problem-solvers.

Remember, to ace many word problems, students need a plan before they dive into computation. So, expose them to a variety of problem-solving strategies – it’s the roadmap to success!

How Did R.I.E.D.S. Come About?

Here’s how R.I.E.D.S. came into the picture.

Back in the 2008-2009 school year, we got our fall benchmark scores and were handed the mission to pick a standard to boost student achievement by the next benchmark assessment. I went with a math standard: solving word problems using the four operations.

Now, once I committed to leveling up my students’ word problem-solving game, I needed something that actually worked. I had tried two problem-solving strategies (I don’t recall their names), but they just weren’t cutting it.

So, I started thinking about the way I personally tackled word problems and wondered, “How can I turn this into a step-by-step, kid-friendly process?” And that’s when the magic of R.I.E.D.S. started brewing.

Word Problems and End-of-Grade Assessments

Let me tell you about our End-of-Grade state math assessment here in Georgia – it’s like a word problem marathon.

They don’t just throw isolated computations at our students. Nope. It’s all about diving into word problems.

Now, picture this – even if your students can crunch numbers like math wizards, without a solid strategy for tackling word problems, they might just miss the mark on that math assessment.

And that’s where R.I.E.D.S. comes in.

It’s the key to unlocking math success in the world of word problems.

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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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How to Solve Multi-Step Word Problems

Multi-step word problems may initially seem daunting, but with a structured approach, they become manageable and less intimidating. Here, we provide a step-by-step guide to help you navigate these complex problems with ease.

How to Solve Multi-Step Word Problems

A Step-by-step Guide to Solving Multi-Step Word Problems

Step 1: understand the problem.

The first step in solving multi-step word problems is to read the problem carefully. Look for keywords and phrases that suggest what arithmetic operation(s) you will need to apply. Words like ‘in total’, ‘altogether’ or ‘sum’ suggest an addition, ‘less than’ or ‘remain’ hint towards subtraction, ‘product’ or ‘times’ indicate multiplication, and ‘quotient’ or ‘divided by’ point to division.

Step 2: Identify the Steps Needed

After understanding the problem, list out the necessary steps to reach the solution. Each word problem is a unique puzzle with its sequence of operations. Some problems may require you to perform multiplication before addition, while others may need subtraction followed by division.

Step 3: Assign Variables

For problems with unknown quantities, assign a variable (for example, \(X\) or \(Y\)) to each unknown. This strategy makes it easier to organize information and apply arithmetic operations.

Step 4: Write Equations

Formulate equations based on the identified steps and assigned variables. Keep in mind the order of operations (BIDMAS/BODMAS) – Brackets, Indices/Orders, Division and Multiplication (from left to right), Addition, and Subtraction (from left to right).

Step 5: Solve the Equations

Solving the equations might require simple substitution or more advanced techniques like elimination or matrix method in the case of multiple variables. Don’t forget to check your solutions to make sure they satisfy the original equations.

Step 6: Answer the Question

Finally, ensure that your answer responds to the question asked in the problem. For example, if the problem is asking for the total number of apples, your answer should be a number and mention ‘apples’.

Practical Example

Let’s apply these steps to a sample problem: “Sarah bought \(2\) books. Each book cost twice as much as a pen. She bought \(4\) pens. If each pen cost \($5\), how much did she spend in total?”

Step 1: The problem involves multiplication (each book cost twice as much as a pen) and addition (total amount spent).

Step 2: First, find the cost of a book and then calculate the total cost.

Step 3: Let’s say \(X\) is the cost of a book.

Step 4: The equations will be \(X = 2 \times the\:cost\:of\:a\:pen\) and Total cost = cost of books + cost of pens.

Step 5: Substituting the given cost of a pen (\($5\)), we find \(X = $10\). The total cost is then calculated as \((2 \times $10) + (4 \times $5) = $40\).

Step 6: The total amount Sarah spent is \($40\).

In conclusion, with a systematic approach, you can effectively solve any multi-step word problem. Remember, practice is the key. The more problems you solve, the better you will become at identifying the necessary steps and solving them accurately.

by: Effortless Math Team about 10 months ago (category: Articles )

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what is the five step strategy for solving word problems

  • January 3, 2021
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CUBES Math Strategy for Word Problems

The CUBES math strategy is a tool teachers use to aid students with problem solving. Do you have students that when faced with a word problem they seem to freeze and have no idea where to start?

The math CUBE strategy provides those students with a starting point, a set of steps to perform in order to solve a particular math word problem.

What is the CUBES strategy?

This strategy helps students break down word problems by creating five steps they must follow in order to solve. CUBES is an acronym that is easily remembered by students.

C – Circle the numbers

U – Underline the question

B – Box the key words

E – Evaluate and Eliminate unnecessary information

S – Solve and check

Why use the CUBES math strategy?

  • It gives students a starting point when they are faced with word problems. We know many kids fear word problems and many times they have no idea where to start.
  • It makes kids aware of what the problem is asking – this might seem simple but forcing kids to underline the question is a good way to make them read what is the problem asking me to do.
  • It brings out all the numbers in the problem – sometimes word problems present numbers in numerical form, word form, or any other tricky form. Circling the numbers forces kids to look through the problem to find numbers in any form.

If you are looking for a digital way to use CUBES, I have created a set of Google slides where students can annotate the word problems, write an equation, and solve.

CUBES Math Strategy Word Problems

https://youtu.be/0iL3v7V6jVA

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what is the five step strategy for solving word problems

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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what is the five step strategy for solving word problems

4 Math Word Problem Solving Strategies

Solving Math Word Problems

5 Strategies to Learn to Solve Math Word Problems

A critical step in math fluency is the ability to solve math word problems. The funny thing about solving math word problems is that it isn’t just about math. Students need to have strong reading skills as well as the growth mindset needed for problem-solving. Strong problem solving skills need to be taught as well. In this article, let’s go over some strategies to help students improve their math problem solving skills when it comes to math word problems. These skills are great for students of all levels but especially important for students that struggle with math anxiety or students with animosity toward math.

Signs of Students Struggling with Math Word Problems

It is important to look at the root cause of what is causing the student to struggle with math problems. If you are in a tutoring situation, you can check your students reading level to see if that is contributing to the issue. You can also support the student in understanding math keywords and key phrases that they might need unpacked. Next, students might need to slow their thinking down and be taught to tackle the word problem bit by bit.

How to Help Students Solve Math Word Problems

Focus on math keywords and mathematical key phrases.

The first step in helping students with math word problems is focusing on keywords and phrases. For example, the words combined or increased by can mean addition. If you teach keywords and phrases they should watch out for students will gain the cues needed to go about solving a word problem. It might be a good idea to have them underline or highlight these words.

Cross out Extra Information

Along with highlighting important keywords students should also try to decipher the important from unimportant information. To help emphasize what is important in the problem, ask your students to cross out the unimportant distracting information.  This way, it will allow them to focus on what they can use to solve the problem.

Encourage Asking Questions

As you give them time to read, allow them to have time to ask questions on what they just read. Asking questions will help them understand what to focus on and what to ignore. Once they get through that, they can figure out the right math questions and add another item under their problem-solving strategies.

Draw the Problem

A fun way to help your students understand the problem is through letting them draw it on graph paper. For example, if a math problem asks a student to count the number of fruits that Farmer John has, ask them to draw each fruit while counting them. This is a great strategy for visual learners.

Check Back Once They Answer

Once they figured out the answer to the math problem, ask them to recheck their answer. Checking their answer is a good habit for learning and one that should be encouraged but students need to be taught how to check their answer. So the first step would be to review the word problem to make sure that they are solving the correct problem. Then to make sure that they set it up right. This is important because sometimes students will check their equation but will not reread the word problem and make sure that the equation is set up right. So always have them do this first! Once students believe that they have read and set up the correct equation, they should be taught to check their work and redo the problem, I also like to teach them to use the opposite to double check, for example if their equation is 2+3=5, I will show them how to take 5 which is the whole and check their work backwards 5-3 and that should equal 2. This is an important step and solidifies mathematical thinking in children.

Mnemonic Devices

Mnemonic devices are a great way to remember all of the types of math strategy in this post. The following are ones that I have heard of and wanted to share:

Solving Math Word Problems

CUBES Word Problem Strategy

Cubes is a mnemonic to remember the following steps in solving math word problems:

C: Circle the numbers

U: Underline the question

B: Box in the key words

E: Eliminate the information

S: Solve the problem & show your work

RISE Word Problem Strategy

Rise is another way to explain the steps needed to solve problems:

R: Read and reread

I: Illustrate what is being asked

S: Solve by writing your equation or number sentences

E: Explain your thinking

RISE Math Word Problem Strategy

COINS Word Problem Strategy

C: Comprehend the questions

O: Observe the data

I: Illustrate the problem

N: Write the number sentence (equation)

Understand -Plan – Solve – Check Word Problem Strategy

This is a simple step solution to show students the big picture. I think this along with one of the mnemonic devices helps students with better understanding of the approach.

Understand: What is the question asking? Do you understand all the words?

Plan: What would be a reasonable answer? In this stage students are formulating their approach to the word problem. 

Solve: What strategies will I use to solve this problem? Am I showing my thinking? Here students use the strategies outlined in this post to attack the problem.

Check: Students will ask themselves if they answered the question and if their answer makes sense. 

Understand -Plan - Solve - Check Word Problem Strategy

If you need word problems to use with your classroom, you can check out my word problems resource below.

Math Word Problems

Teaching students how to approach and solve math word problems is an important skill. Solving word problems is the closest math skill that resembles math in the real world. Encouraging students to slow their thinking, examine and analyze the word problem and encourage the habit of answer checking will give your students the learning skills that can be applied not only to math but to all learning. I also wrote a blog post on a specific type of math word problem called cognitively guided instruction you can read information on that too. It is just a different way that math problems are written and worth understanding to teach problem solving, click here to read .

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20 Effective Math Strategies To Approach Problem-Solving 

Katie Keeton

Math strategies for problem-solving help students use a range of approaches to solve many different types of problems. It involves identifying the problem and carrying out a plan of action to find the answer to mathematical problems.  

Problem-solving skills are essential to math in the general classroom and real-life. They require logical reasoning and critical thinking skills. Students must be equipped with strategies to help them find solutions to problems.

This article explores mathematical problem solving strategies, logical reasoning and critical thinking skills to help learners with solving math word problems independently in real-life situations. 

What are problem-solving strategies?

Problem-solving strategies in math are methods students can use to figure out solutions to math problems. Some problem-solving strategies: 

  • Draw a model
  • Use different approaches
  • Check the inverse to make sure the answer is correct

Students need to have a toolkit of math problem-solving strategies at their disposal to provide different ways to approach math problems. This makes it easier to find solutions and understand math better. 

Strategies can help guide students to the solution when it is difficult ot know when to start.

The ultimate guide to problem solving techniques

The ultimate guide to problem solving techniques

Download these ready-to-go problem solving techniques that every student should know. Includes printable tasks for students including challenges, short explanations for teachers with questioning prompts.

20 Math Strategies For Problem-Solving

Different problem-solving math strategies are required for different parts of the problem. It is unlikely that students will use the same strategy to understand and solve the problem. 

Here are 20 strategies to help students develop their problem-solving skills. 

Strategies to understand the problem

Strategies that help students understand the problem before solving it helps ensure they understand: 

  • The context
  • What the key information is
  • How to form a plan to solve it

Following these steps leads students to the correct solution and makes the math word problem easier .

Here are five strategies to help students understand the content of the problem and identify key information. 

1. Read the problem aloud

Read a word problem aloud to help understand it. Hearing the words engages auditory processing. This can make it easier to process and comprehend the context of the situation.

2. Highlight keywords 

When keywords are highlighted in a word problem, it helps the student focus on the essential information needed to solve it. Some important keywords help determine which operation is needed.  For example, if the word problem asks how many are left, the problem likely requires subtraction.  Ensure students highlight the keywords carefully and do not highlight every number or keyword. There is likely irrelevant information in the word problem.

3. Summarize the information

Read the problem aloud, highlight the key information and then summarize the information. Students can do this in their heads or write down a quick summary.  Summaries should include only the important information and be in simple terms that help contextualize the problem.

4. Determine the unknown

A common problem that students have when solving a word problem is misunderstanding what they are solving. Determine what the unknown information is before finding the answer.  Often, a word problem contains a question where you can find the unknown information you need to solve. For example, in the question ‘How many apples are left?’ students need to find the number of apples left over.

5. Make a plan

Once students understand the context of the word problem, have dentified the important information and determined the unknown, they can make a plan to solve it.  The plan will depend on the type of problem. Some problems involve more than one step to solve them as some require more than one answer.  Encourage students to make a list of each step they need to take to solve the problem before getting started.

Strategies for solving the problem 

1. draw a model or diagram.

Students may find it useful to draw a model, picture, diagram, or other visual aid to help with the problem solving process.  It can help to visualize the problem to understand the relationships between the numbers in the problem. In turn, this helps students see the solution.

math problem that needs a problem solving strategy

Similarly, you could draw a model to represent the objects in the problem:

math problem requiring problem solving

2. Act it out

This particular strategy is applicable at any grade level but is especially helpful in math investigation in elementary school . It involves a physical demonstration or students acting out the problem using movements, concrete resources and math manipulatives .  When students act out a problem, they can visualize and contectualize the word problem in another way and secure an understanding of the math concepts.  The examples below show how 1st-grade students could “act out” an addition and subtraction problem:

3. Work backwards

Working backwards is a popular problem-solving strategy. It involves starting with a possible solution and deciding what steps to take to arrive at that solution.  This strategy can be particularly helpful when students solve math word problems involving multiple steps. They can start at the end and think carefully about each step taken as opposed to jumping to the end of the problem and missing steps in between.

For example,

problem solving math question 1

To solve this problem working backwards, start with the final condition, which is Sam’s grandmother’s age (71) and work backwards to find Sam’s age. Subtract 20 from the grandmother’s age, which is 71.  Then, divide the result by 3 to get Sam’s age. 71 – 20 = 51 51 ÷ 3 = 17 Sam is 17 years old.

4. Write a number sentence

When faced with a word problem, encourage students to write a number sentence based on the information. This helps translate the information in the word problem into a math equation or expression, which is more easily solved.  It is important to fully understand the context of the word problem and what students need to solve before writing an equation to represent it.

5. Use a formula

Specific formulas help solve many math problems. For example, if a problem asks students to find the area of a rug, they would use the area formula (area = length × width) to solve.   Make sure students know the important mathematical formulas they will need in tests and real-life. It can help to display these around the classroom or, for those who need more support, on students’ desks.

Strategies for checking the solution 

Once the problem is solved using an appropriate strategy, it is equally important to check the solution to ensure it is correct and makes sense. 

There are many strategies to check the solution. The strategy for a specific problem is dependent on the problem type and math content involved.

Here are five strategies to help students check their solutions. 

1. Use the Inverse Operation

For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7. As good practice, encourage students to use the inverse operation routinely to check their work. 

2. Estimate to check for reasonableness

Once students reach an answer, they can use estimation or rounding to see if the answer is reasonable.  Round each number in the equation to a number that’s close and easy to work with, usually a multiple of ten.  For example, if the question was 216 ÷ 18 and the quotient was 12, students might round 216 to 200 and round 18 to 20. Then use mental math to solve 200 ÷ 20, which is 10.  When the estimate is clear the two numbers are close. This means your answer is reasonable. 

3. Plug-In Method

This method is particularly useful for algebraic equations. Specifically when working with variables.  To use the plug-in method, students solve the problem as asked and arrive at an answer. They can then plug the answer into the original equation to see if it works. If it does, the answer is correct.

Problem solving math problem 2

If students use the equation 20m+80=300 to solve this problem and find that m = 11, they can plug that value back into the equation to see if it is correct. 20m + 80 = 300 20 (11) + 80 = 300 220 + 80 = 300 300 = 300 ✓

4. Peer Review

Peer review is a great tool to use at any grade level as it promotes critical thinking and collaboration between students. The reviewers can look at the problem from a different view as they check to see if the problem was solved correctly.   Problem solvers receive immediate feedback and the opportunity to discuss their thinking with their peers. This strategy is effective with mixed-ability partners or similar-ability partners. In mixed-ability groups, the partner with stronger skills provides guidance and support to the partner with weaker skills, while reinforcing their own understanding of the content and communication skills.  If partners have comparable ability levels and problem-solving skills, they may find that they approach problems differently or have unique insights to offer each other about the problem-solving process.

5. Use a Calculator

A calculator can be introduced at any grade level but may be best for older students who already have a foundational understanding of basic math operations. Provide students with a calculator to allow them to check their solutions independently, accurately, and quickly. Since calculators are so readily available on smartphones and tablets, they allow students to develop practical skills that apply to real-world situations.  

Step-by-step problem-solving processes for your classroom

In his book, How to Solve It , published in 1945, mathematician George Polya introduced a 4-step process to solve problems. 

Polya’s 4 steps include:

  • Understand the problem
  • Devise a plan
  • Carry out the plan

Today, in the style of George Polya, many problem-solving strategies use various acronyms and steps to help students recall. 

Many teachers create posters and anchor charts of their chosen process to display in their classrooms. They can be implemented in any elementary, middle school or high school classroom. 

Here are 5 problem-solving strategies to introduce to students and use in the classroom.

CUBES math strategy for problem solving

How Third Space Learning improves problem-solving 

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Explore the range of problem solving resources for 2nd to 8th grade students. 

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Third Space Learning offers one-on-one math tutoring to help students improve their math skills. Highly qualified tutors deliver high-quality lessons aligned to state standards. 

Former teachers and math experts write all of Third Space Learning’s tutoring lessons. Expertly designed lessons follow a “my turn, follow me, your turn” pedagogy to help students move from guided instruction and problem-solving to independent practice. 

Throughout each lesson, tutors ask higher-level thinking questions to promote critical thinking and ensure students are developing a deep understanding of the content and problem-solving skills.

what is the five step strategy for solving word problems

Problem-solving

Educators can use many different strategies to teach problem-solving and help students develop and carry out a plan when solving math problems. Incorporate these math strategies into any math program and use them with a variety of math concepts, from whole numbers and fractions to algebra. 

Teaching students how to choose and implement problem-solving strategies helps them develop mathematical reasoning skills and critical thinking they can apply to real-life problem-solving.

READ MORE : 8 Common Core math examples

There are many different strategies for problem-solving; Here are 5 problem-solving strategies: • draw a model  • act it out  • work backwards  • write a number sentence • use a formula

Here are 10 strategies of problem-solving: • Read the problem aloud • Highlight keywords • Summarize the information • Determine the unknown • Make a plan • Draw a model  • Act it out  • Work backwards  • Write a number sentence • Use a formula

1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

Some strategies you can use to solve challenging math problems are: breaking the problem into smaller parts, using diagrams or models, applying logical reasoning, and trying different approaches.

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what is the five step strategy for solving word problems

3 Word Problem Solving Strategies To Improve Word Problem Performance

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The ability to solve word problems doesn’t necessarily come easily to all students. We can improve our students’ ability to solve story problems with a few simple word problem-solving strategies. When it comes to comprehending, understanding, and solving word problems, sometimes it is helpful to move beyond traditional word problems and try a new word problem type that is designed to support students in tackling these tricky skills!

In order to solve word problems, students need to be able to:

  • Comprehend the action or context of a word problem
  • Understand the question or missing piece of information
  • Develop a mathematically sound plan for solving for the missing information.
  • Accurately calculate to find their solution.

It’s a balance between comprehension, an understanding of math concepts, and an ability to carry out math concepts. Identifying which of these steps are strengths or needs for your students can help you to choose a strategy that will best improve their word problem performance.

Word Problem Solving Strategy #1: Numberless Word Problems

Who is this strategy for? If your students are struggling to understand the action, context or question in a story problem, discussion and numberless word problems will be a word problem-solving strategy that can help your students tremendously! This strategy also helps your “number pluckers” who see numbers, pluck and add together regardless of context! Numberless word problems slow your students down!

Using a tool such as numberless word problems can help your students in their understanding precisely because the numberless word problem strategy emphasizes discussion every step of the way!

How do I use this strategy? As you solve numberless word problems you begin with a problem with no numbers at all and ask a variety of questions as you discuss and slowly add information back into the problem.

Reagan picked flowers for a bouquet! She picked both roses and carnations.

When you initially present the problem, ask your students questions such as

  • Who is the story problem about?
  • What is happening in this story?
  • What are you wondering about?

Reagan picked flowers for a bouquet! She picked 7 roses and also some carnations.

  • What new information do we have?
  • What do you think we might learn next?
  • What *could* be the number of carnations in the bouquet? What might make sense?

Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations.

  • What new information do we know?
  • What do you know about the story?
  • What happened in the story?
  • Could we draw a picture or diagram to match the story?
  • What might we be wondering about the bouquet?
  • What questions could we answer about the bouquet?

Reagan picked flowers for a bouquet! She picked 7 roses and 8 carnations. How many flowers are in the bouquet in all?

  • What is the question wondering?
  • Do we have enough information to answer that question?
  • Where do we see the 7 roses in our diagram?
  • Where do we see the 8 carnations in our diagram?
  • How can we use the diagram to answer the question of how many flowers are in the bouquet in all?

DONE FOR YOU NUMBERLESS WORD PROBLEMS

Kindergarten | 1st Grade | 2nd Grade | 3rd Grade | 4th Grade

Word Problem Solving Strategy #2: Guided Visual Models

Who is this strategy for? Visual models help your students to organize the information they know as well as to visualize the missing piece of information. Drawing visual models helps lead your students to an equation. This strategy is ideal for students who understand what a word problem is asking but have difficulty connecting the action of a word problem to an equation.

A visual model might include:

  • A math drawing (simple circles or an organic representation)
  • A number bond (number bonds can be used beyond addition and subtraction! Adding more “parts” can help to visualize multiplication and division as well!)
  • Tape diagrams

How can I use this strategy? As you are supporting your students in using these visual models, continually ask questions and draw connections between the word problem and their diagram.

Frank built a tower using 16 blocks. He took 7 blocks off of his tower and gave them to Declan so he could build a tower as well. How many blocks does Frank have left?

  • Could you draw a picture that shows what happened?
  • Frank had 16 blocks. Was that all of the blocks in the story or part of them? Where would we put the total in our number bond?
  • Frank gave away 7 blocks. Was that all of the blocks or a part of the blocks? Where would we put the part in our number bond?
  • And we’re wondering how many blocks Frank has left. Where is the missing part in our number bond? Could we write a question mark in that part?

If your students are familiar with number bonds or tape diagrams, knowing that they are missing a part will lead them to writing a subtraction equation or a missing addend addition equation to solve.

**If your students are not familiar with how to find a missing part or missing whole in an equation this is a topic that needs to be addressed as well! Your students are missing foundational math understandings that are critical to their word problem-solving strategy. Additional practice with both fact families and missing numbers in an equation will be helpful to your students!

Word Problem Strategy #3: Problem Sorts

Who is this strategy for? This strategy is for ALL students! When your students examine problems to help understand the underlying structures and problem types , solving word problems becomes easier.

If you were to be asked to cook dinner for a group of people at the drop of a hat, you would likely have a much easier time putting together a pizza than you would a complicated curry dish. You understand the underlying structure of a pizza- crust, sauce, cheese, toppings- and because you know this structure, given any different type of pizza (BBQ, Traditional, Garlic, Buffalo Chicken) you would be able to use the structure to come up with a recipe quickly and easily.

Understanding and recognizing problem types can do the same thing for our students! Understanding that in a “put together” problem there are going to be parts and that those parts can be put together using addition makes these problems much easier to solve!

How can I use this strategy? One way to help your students to recognize and understand problem types is to sort word problems. In a problem sort, you aren’t attending to the matter of solving the problem at all . Instead, you are reading the problems and sorting them based on whether the problem is missing a part or missing the total. If you are working on multiplication and division word problems you might sort based on whether the problem is missing the total , missing the number of groups or missing the group size. Other problem types will lend themselves to different sorting activities.

Additional Word Problem Resources

Using different types of word problem resources can help you to support your students in different ways.

Word Problem Sort Cards   can be a useful tool when you want your students to attend to the structure of math problems. Sort the cards based on problem type or based on the operation your students would use to solve. After sorting, solve the problems together. Reuse the sort as a math center!

Word Problem Notebooks  are a useful tool when you want your students to draw models and visual representations of word problems and to connect these models to an equation.

Numberless Word Problems   help get to the heart of the action or context of a word problem. Because you start with no numbers and employ a great deal of conversation these problems are simple to differentiate and give all students a point of access into the activity.

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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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what is the five step strategy for solving word problems

3 Strategies to Conquer Math Word Problems

what is the five step strategy for solving word problems

Here’s a word problem for you:

Miss Friday’s class does a daily word problem. Ten of her students are great at word problems involving addition, and only 7 seem to understand subtraction word problems. Five of her students are bored with the easy problems. Thirteen students are still struggling with basic math facts and 3 have trouble reading the word problems at all. How many of her students are engaged and learning?

Here’s a better question: “How do you grow confident and effective problem solvers?”

Why Students Struggle with Math Word Problems

Students struggle with math word problems for many reasons, but three of the biggest I’ve encountered include:

Issue #1: Student Confidence For many students, just looking at a word problem leads to anxiety. No one can think clearly with a sense of dread or fear of failure looming!
Issue #2: Flexible Thinking Many kids are taught to solve word problems methodically, with a prescriptive step-by-step plan using key words that don’t always work. Plans are great, but not when students use them as a crutch rather than a tool. Today’s standardized tests and real-world applications require creative thinking and flexibility with strategies.
Issue #3: Differentiation Teachers want students to excel quickly and often push too fast, too soon. In the case of word problems, you have to go slow to go fast. Just like in Guided Reading, you’ll want to give lots of practice with “just-right” problems and provide guided practice with problems just-above the students’ level.

3 Problem Solving Strategies

The solution is to conquer math word problems with engaging classroom strategies that counteract the above issues!

1. Teach a Problem-Solving Routine 

Kids (and adults) are notoriously impulsive problem solvers. Many students see a word problem and want to immediately snatch out those numbers and “do something” with them. When I was in elementary school, this was actually a pretty reliable strategy! But today, kids are asked to solve much more complex problems, often with tricky wording or intentional distractors.

Grow flexible thinkers and build confidence by teaching a routine. A problem solving routine simply encourages students to slow down and think before and after solving. I’ve seen lots of effective routines but my favorites always include a “before, during, and after” mindset.

what is the five step strategy for solving word problems

To make the problem solving routine meaningful and effective:

  • Use it often (daily if possible)
  • Incorporate “Turn & Teach” (Students orally explain their thinking and process to a partner.)
  • Allow for “Strategy Share” after solving (Selected students explain their method and thinking.)

what is the five step strategy for solving word problems

2. Differentiate Word Problems 

No, this doesn’t mean to write a different word problem for every student! This can be as simple as adjusting the numbers in a problem or removing distractors for struggling students. Scaffolding word problems will grow confidence and improve problem solving skills by gradually increasing the level difficulty as the child is ready. This is especially effective when you are trying to teach students different structures of word problems to go with a certain operation.

For example, comparison subtraction problems are very challenging for some students. By starting with a simple version, you allow students to focus on the problem itself, rather than becoming intimidated or frustrated.

what is the five step strategy for solving word problems

I’ve had great success in using scaffolded problems with my guided math groups. After solving the easier problem, students realize that it’s not that tricky and are ready to take on the tougher ones!

3. Compare Problems Side-by-Side 

To develop flexible thinking, nothing is more powerful than analyzing and comparing word problems. Start by using problems that have similar stories and numbers, but different problem structures. Encourage conversation, use visual representations, and have students explain the difference in structure and operation. Here’s an example showing student work on two similar problems about monkeys. Click here to download a blank copy of these problems. My freebie includes several variations to help you differentiate.

what is the five step strategy for solving word problems

Use these three strategies to get kids thinking and talking about their problem solving strategies while building that “oh-so-important” confidence, and you CAN conquer math word problems!

what is the five step strategy for solving word problems

Kady Dupre has worked as a classroom teacher, instructional coach, and intervention teacher in elementary grades. She loves creating learning resources for students and teachers. She authors Teacher Trap , a blog aimed at sharing her challenges, successes, and insights as a teacher.

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  • ELEMENTARY TEACHING , MATH

How to Teach Word Problems: Strategies for Elementary Teachers

If you are looking for tips and ideas for how to teach word problems to your elementary students, then you’ve found the right place! We know that teaching elementary students how to solve word problems is important for math concept and skill application, but it sure can feel like a daunting charge without knowing about the different types, the best practices for teaching them, and common misconceptions to plan in advance for, as well as having the resources you need. All this information will make you feel confident about how to teach addition, subtraction, multiplication, and division word problems! Teaching students how to solve word problems will be so much easier!

This blog post will address the following questions:

  • What is a word problem?
  • What is a multi-step word problem?
  • Why are elementary math word problems important?
  • Why are math word problems so hard for elementary students?
  • What are the types of word problems?
  • How do I teach math word problems in a systematic way?
  • What are the best elementary math word problem strategies I can teach my students and what are some tips for how to teach math word problems strategies?
  • Do you have any helpful tips for how to teach word problems?
  • What are the common mistakes I should look for that my students may make?
  • How do I address my students’ common misconceptions surrounding elementary math word problems?

girl in class raising her hand to solve a word problem

What is a Word Problem?

A word problem is a math situation that calls for an equation to be solved.  Students must apply their critical thinking skills to determine how to solve the problem.  Word problems give students the opportunity to practice turning situations into numbers.  This is critical as students progress in their education, as well as in their day-to-day life.  By teaching students how to solve word problems in a strategic way, you are setting them up for future success!

What is a Multi-Step Word Problem?

A multi-step word problem , also known as a two-step word problem or two-step equation word problem, is a math situation that involves more than one equation having to be answered in order to solve the ultimate question.  This requires students to apply their problem solving skills to determine which operation or operations to use to tackle the problem and find the necessary information.  In some cases, the situation may call for mixed operations, and in others the operations will be the same.  Multi-step word problems offer students the opportunity to practice the skill of applying different math concepts with a given problem.

elementary students practicing math word problems

Why are Word Problems Important in Math?

Word problems are essential in math because they give students the opportunity to apply what they have learned to a real life situation.  In addition, it facilitates students in developing their higher order thinking and critical thinking skills, creativity, positive mindset toward persevering while problem solving, and confidence in their math abilities.  Word problems are an effective tool for teachers to determine whether or not students understand and can apply the concepts and skills they learned to a real life situation.

Why do Students Struggle with Math Word Problems?

Knowing why students have trouble with word problems will help you better understand how to teach them. The reason why math word problems are difficult for your students is because of a few different reasons. First, students need to be able to fluently read and comprehend the text. Second, they need to be able to identify which operations and steps are needed to find the answer. Finally, they need to be able to accurately calculate the answer. If you have students who struggle with reading or English is their second language (ESL), they may not be able to accurately show what they know and can do because of language and literacy barriers. In these cases, it is appropriate to read the text aloud to them or have it translated into their native language for assignments and assessments.

what is the five step strategy for solving word problems

Types of Word Problems

Knowing the different types of word problems will help you better understand how to teach math word problems. Read below to learn about the four types of basic one-step addition and subtraction word problems, the subcategories within each of them, and specific examples for all of them. Two-step equation word problems can encompass two of the same type or two separate types (also known as mixed operation word problems).

This type of word problem involves an action that increases the original amount. There are three kinds: Result unknown, change unknown, and initial quantity unknown.

Result Unknown

Example : There were 7 kids swimming in the pool. 3 more kids jumped in. How many kids are in the pool now? (7 + 3 = ?)

Change Unknown

Example : There were 8 kids swimming in the pool. More kids jumped in. Now there are 15 kids in the pool. How many kids jumped in? (8 + ? = 15)

Initial Quantity Unknown

Example : There were kids swimming in the pool. 2 kids jumped in. Now there are 6 kids in the pool. How many kids were swimming in the pool at first? (? + 2 = 6)

2. Separate

This type of word problem involves an action that decreases the original amount. There are three kinds: Result unknown, change unknown, and initial quantity unknown.

Example: There were 12 kids swimming in the pool. 6 of the kids got out of the pool. How many kids are in the pool now? (12 – 6 = ?)

Example: There were 9 kids swimming in the pool. Some of the kids got out of the pool. Now there are 4 kids in the pool. How many kids got out of the pool? (9 – ? = 4)

Example: There were kids swimming in the pool. 3 of the kids got out of the pool. Now there are 2 kids in the pool. How many kids were in the pool at first? (? – 3 = 2)

3. Part-Part-Whole

This type of word problem does not involve an action like the join and separate types. Instead, it is about defining relationships among a whole and two parts. There are two kinds: result unknown and part unknown.

Example: There are 5 boys and 9 girls swimming in the pool. How many kids are in the pool? (5 + 9 = ?)

Part Unknown

Example: There are 12 kids swimming in the pool. 8 of them are girls and the rest of them are boys. How many boys are swimming in the pool? (8 + ? = 12)

This type of word problem does not involve an action or relationship like the three other types. Instead, it is about comparing two different unrelated items. There are two kinds: Difference unknown and quantity unknown.

Difference Unknown

Example: There are 2 kids in the pool. There are 7 kids in the yard. How many more kids are in the yard than in the pool? (2 + ? = 7 or 7 – 2 = ?)

Quantity Unknown

Example 1: There are 5 kids in the pool. There are 3 fewer kids playing in the yard. How many kids are playing in the yard? (5 – 3 = ?)

Example 2: There are 2 kids in the pool. There are 10 more kids playing in the yard than in the pool. How many kids are playing in the yard? (2 + 10 = ?)

elementary students solving word problems digitally

How to Solve Word Problems in 5 Easy Steps

Here are 5 steps that will help you teach word problems to your 1st, 2nd, 3rd, 4th or 5th grade students:

  • Read the problem.
  • Read the problem a second time and make meaning of it by visualizing, drawing pictures, and highlighting important information (numbers, phrases, and questions).
  • Plan how you will solve the problem by organizing information in a graphic organizer and writing down equations and formulas that you will need to solve.
  • Implement the plan and determine answer.
  • Reflect on your answer and determine if it is reasonable.  If not, check your work and start back at step one if needed.  If the answer is reasonable, check your answer and be prepared to explain how you solved it and why you chose the strategies you did.

5 Math Word Problem Strategies

Here are 5 strategies for how to teach elementary word problems:

Understand the math situation and what the question is asking by picturing what you read in your head while you are reading.

Draw Pictures

Make meaning of what the word problem is asking by drawing a picture of the math situation.

Make Models

Use math tools like base-ten blocks to model what is happening in the math situation.

Highlight Important Information

Underline or highlight important numbers, phrases, and questions.

Engage in Word Study

Look for key words and phrases like “less” or “in all.” Check out this blog post if you are interested in learning more about math word problem keywords and their limitations.

10 Tips for Teaching Students How to Solve Math Word Problems

Here are 10 tips for how to teach math word problems:

  • Model a positive attitude toward word problems and math.
  • Embody a growth mindset.
  • Model! Provide plenty of direct instruction.
  • Give lots of opportunities to practice.
  • Explicitly teach strategies and post anchor charts so students can access them and remember prior learning.
  • Celebrate the strategies and process rather than the correct answer.
  • Encourage students to continue persevering when they get stuck.
  • Invite students to act as peer tutors.
  • Provide opportunities for students to write their own word problems.
  • Engage in whole-group discussions when solving word problems as a class.

elementary students solving word problems

Common Misconceptions and Errors When Students Learn How to Solve Math Word Problems

Here are 5 common misconceptions or errors elementary students have or make surrounding math word problems:

1. Use the Incorrect Operation

Elementary students often apply the incorrect operations because they pull the numbers from a word problem and add them without considering what the question is asking them or they misunderstand what the problem is asking.  Early in their experience with word problems, this strategy may work most of the time; however, its effectiveness will cease as the math gets more complex.  It is important to instruct students to develop and apply problem-solving strategies.

Although helpful in determining the meaning, elementary students rely solely on key words and phrases in a word problem to determine what operation is being called for. Again, this may be an effective strategy early on in their math career, but it should not be the only strategy students use to determine what their plan of attack is.

2. Get Stuck in a Fixed Mindset

Some elementary students give up before starting a word problem because they think all word problems are too hard.  It is essential to instill a positive mindset towards math in students. The best way to do that is through modeling. If you portray an excitement for math, many of your students will share that same feeling.

3. Struggle with Reading Skills Component

For first and second graders (as well as struggling readers and ESL students), it is common for students to decode the text incorrectly. Along the same lines, some elementary students think they can’t solve word problems because they do not know how to read yet.  The purpose of word problems is not to assess whether a child can read or not.  Instead, the purpose is to assess their critical thinking and problem-solving skills.  As a result, it is appropriate to read word problems to elementary students.

4. Calculate Incorrectly

You’ll find instances where students will understand what the question is asking, but they will calculate the addends or the subtrahend from the minuend incorrectly. This type of error is important to note when analyzing student responses because it gives you valuable information for when you plan your instruction.

5. Encode Response Incorrectly

Another error that is important to note when analyzing student responses is when you find that they encode their solution in writing incorrectly. This means they understand what the problem is asking, they solve the operations correctly, document their work meticulously, but then write the incorrect answer on the line.

How to Address Common Misconceptions Surrounding Math Word Problems

You might be wondering, “What can I do in response to some of these misconceptions and errors?” After collecting and analyzing the data, forming groups based on the results, and planning differentiated instruction, you may want to consider trying out these prompts:

  • Can you reread the question aloud to me?
  • What is the question asking us to do?
  • How can we represent the information and question?
  • Can we represent the information and question with an equation?
  • What is our first step?
  • What is our next step?
  • Can you think of any strategies we use to help us solve?
  • How did you find your answer?
  • Can you walk me through how you found your answer step by step?
  • What do we need to remember when recording our answer?

what is the five step strategy for solving word problems

Now that you have all these tips and ideas for how to teach word problems, we would love for you to try these word problem resources with your students. They offer students opportunities to practice solving word problems after having learned how to solve word problems. You can download word problem worksheets specific to your grade level (along with lots of other math freebies) in our free printable math resources bundle using this link: free printable math activities for elementary teachers .

Check out my monthly word problem resources !

  • 1st Grade Word Problems
  • 2nd Grade Word Problems
  • 3rd Grade Word Problems
  • 4th Grade Word Problems
  • 5th Grade Word Problems

Check out this blog post offering ideas and strategies for teaching math word problems! This is helpful for 1st, 2nd, 2rd, 4th, and 5th grade classroom teachers. Make teaching and solving word problems fun and easy for elementary students! #wordproblems #mathwordproblems #teachingideas #teachingstrategies #elementarymath #realworldmath

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5 Strategies to Teach Multi-Step Word Problems: Teacher’s Guide

strategies for teaching multistep word problems

Hey there, Teacher! Are you ready to empower your students with the skills they need to conquer multi-step word problems? Look no further! This comprehensive blog post is your go-to resource for effective strategies that will transform your classroom into a problem-solving powerhouse. Let’s dive in and unleash your students’ problem-solving potential!

Table of Contents

Word Problems

Word problems are an essential part of math education, as they help develop critical thinking and problem-solving skills.

Multi-step word problems, in particular, provide an excellent opportunity for students to apply their math skills in real-life scenarios.

Teaching students how to solve one-step word problems or multi-step word problems can be a complex task as it can be a challenging concept for most students to grasp.

However, with the right strategies and guidance, teachers can help their students become proficient problem solvers.

Strategies to Teach Multi-Step Word Problems

5 strategies for teaching multistep word problems

Now, let’s delve into the 5 strategies that teachers can employ to effectively teach multi-step word problem-solving to their students.

Model the Problem-Solving Process

Provide clear problem-solving strategies.

  • Provide Scaffolded Practice

Differentiate Instruction

  • Practice Regularly for Proficiency

One of the most effective ways to help students understand and solve multi-step word problems is by modeling the problem-solving process.

When teachers model the steps involved in solving a problem, students can observe and learn from their thinking and approach.

This approach helps students develop a deeper understanding of the problem and the strategies required to solve it.

modeling multistep word problem solving process

You can use the following approaches when modeling the problem-solving process.

Step-by-Step Approach

Storytelling approach, real-life examples.

When modeling the problem-solving process, it is crucial to take a step-by-step approach.

Break down the problem into smaller, manageable parts, and demonstrate how to tackle each part systematically.

By breaking down the problem, students can focus on one step at a time, reducing confusion and overwhelm.

Another effective strategy is to take a storytelling approach when presenting multi-step word problems.

Create narratives or scenarios around the problems, making them more interesting and captivating for students.

By presenting problems in a story format, students can visualize the context and relate to the characters or situations involved.

This approach enhances their problem-solving abilities and engages their imagination.

To make the modeling process more engaging and relatable, incorporate real-life examples into the multi-step word problems.

Relating the problems to situations that students encounter in their daily lives helps them connect with the content and see the practical applications of mathematical concepts.

For instance, you can present a word problem involving shopping or calculating distances during a trip.

As a teacher, your role is to equip your students with effective problem-solving strategies that will empower them to confidently tackle multi-step word problems.

strategies for solving multistep word problems

Here are some key multi-step problem-solving strategies to share with your students:

Read the Problem Carefully

Identify the question, plan and break down the problem, choose the correct operations, solve step-by-step, check and reflect.

The first step in solving a multi-step word problem is to read the problem carefully.

Emphasize the importance of taking the time to understand the given information.

Encourage your students to identify the essential details, underline or highlight important numbers or quantities.

By comprehending the problem thoroughly, students will lay a strong foundation for their problem-solving journey.

After understanding the given information, students should identify the question they need to answer.

Guide your students to identify the question or the unknown they need to solve.

Assist them in recognizing what information is missing and what they are being asked to find.

Encourage them to clearly define the question to maintain focus and direction throughout the problem-solving process.

Teach your students to develop a plan and break down the problem into smaller, more manageable steps.

By doing so, they can avoid feeling overwhelmed by the complexity of multi-step word problems.

Discuss possible approaches, such as drawing diagrams, making tables, or using equations.

By having a plan in place or by creating a roadmap for the problem-solving journey, students can proceed with confidence and avoid making unnecessary mistakes.

Guide your students in choosing the correct operations or mathematical strategies for each step of the problem.

Help them consider the problem’s context and the relationships between different quantities.

By selecting the appropriate operations, such as addition, subtraction, multiplication, or division, students can accurately solve each component of the multi-step word problem.

Encourage your students to solve the problem step-by-step, following the plan they devised earlier.

By solving each step individually and linking them together, students can see the overall problem as a series of interconnected components, making it easier to navigate and solve.

Remind students to show their work neatly and clearly. This approach not only helps students organize their thoughts but also allows you, as their teacher, to identify any errors or misconceptions they may have.

Provide guidance and support as needed throughout their problem-solving process.

After obtaining a solution, it’s essential that students check their answer.

Teach your students the importance of checking their work and reflecting on their solution.

Encourage them to evaluate whether their answer makes sense within the context of the problem. They can do this by revisiting the original problem, reapplying the given information, and verifying if the solution satisfies the question asked.

This step promotes critical thinking and helps students identify and correct any mistakes they may have made.

Scaffolded Practice

As a teacher, it is crucial to provide scaffolded practice to support your students in mastering multi-step word problems.

Scaffolded practice involves breaking down the problem-solving process into smaller, manageable steps and gradually increasing the complexity of the problems.

This approach allows students to build their skills incrementally and gain confidence as they progress.

strategies to implement scaffolded multistep word problem practice

Here are some strategies to implement scaffolded practice:

Start with Simple Problems

Provide guided practice, increase complexity gradually, use visual aids and models, break down complex problems, provide independent practice opportunities.

Begin by introducing your students to simple, one-step word problems .

These problems will help them understand the basics of problem-solving and build their confidence.

Provide clear explanations and model the problem-solving process step-by-step.

Reinforce the importance of reading the problem carefully and identifying the key information.

Guide your students through practice problems by solving them together as a class.

Discuss the steps involved and explain the reasoning behind each step.

Encourage students to ask questions and engage in discussions about problem-solving strategies.

Offer support and guidance as needed, ensuring that students understand each concept before moving on.

Gradually increase the complexity of the problems as your students become more comfortable with one-step word problems.

Introduce multistep word problems by adding another step or operation at a time.

Provide clear explanations of each step and emphasize the relationships between different quantities in the problem.

Encourage students to apply the problem-solving strategies they have learned.

Utilize visual aids and models to help students visualize the problem and understand the relationships between different quantities.

Use diagrams, charts, or manipulatives to represent the information given in the problem. This visual representation can enhance students’ understanding and support their problem-solving process.

For complex multi-step word problems, break them down into smaller components.

Guide students through each step, explaining the rationale behind each operation and encouraging them to show their work.

This step-by-step approach helps students tackle complex problems more effectively and reduces feelings of overwhelm.

Offer opportunities for students to practice independently.

Provide worksheets or online resources that offer a range of multi-step word problems at various difficulty levels.

Encourage students to work through the problems on their own, applying the strategies they have learned. Offer feedback and support as they progress.

As a teacher, it is essential to differentiate your instruction to meet the diverse needs of your students.

Differentiation allows you to tailor your teaching methods, materials, and assessments to accommodate the individual learning styles, abilities, and interests of your students.

strategies for differentiating multistep word problems instructions

Here are some strategies for differentiating instruction in multi-step word problem-solving:

Assess Readiness and Grouping

Offer multiple problem-solving approaches, vary the level of difficulty, flexible grouping strategies, accommodations and supports, formative assessments and feedback.

Assess the readiness of your students by evaluating their prior knowledge and skills related to multi-step word problems.

Group students based on their readiness levels, whether they require additional support or enrichment.

Provide targeted instruction and resources to address the specific needs of each group.

Recognize that students have different learning styles and preferences.

Offer a variety of problem-solving approaches to cater to their individual needs.

Provide visual representations, manipulatives, or verbal explanations to support visual, kinesthetic, or auditory learners.

Allow students to choose the method that best suits their learning style.

Recognize that students have different levels of proficiency in problem-solving.

Differentiate the level of difficulty in the problems you assign.

Provide additional challenge problems for high-achieving students and offer extra support or modified problems for those who may struggle.

Adjust the complexity of the problems to ensure that each student is appropriately challenged.

Implement flexible grouping strategies to allow students to learn from and support each other.

Arrange students in pairs or small groups based on their strengths and weaknesses.

Encourage collaborative problem-solving activities where students can share their strategies, explain their thinking, and learn from their peers.

Offer opportunities for peer tutoring or mentoring.

Recognize the diverse needs of students with learning disabilities or English language learners.

Provide accommodations and support to ensure their understanding and success.

Adapt the materials, provide visual cues or graphic organizers, offer additional time, or provide translated resources when necessary.

Collaborate with special education or language support specialists to address individual needs effectively.

Use formative assessments to gather ongoing feedback on students’ progress in multi-step word problem-solving.

Monitor their understanding, identify misconceptions, and provide timely feedback. Offer specific guidance and support based on individual needs.

Encourage students to reflect on their problem-solving strategies and provide self-assessment opportunities.

Practice Multi-Step Word Problems Regularly for Proficiency

It is important to emphasize the value of regular practice to help your students achieve proficiency in solving multi-step word problems.

Consistent practice not only reinforces problem-solving strategies and concepts but also builds confidence and fluency in applying them.

regular multistep word problem practice

Here are some strategies to promote regular practice:

Assign Regular Problem-Solving Exercises

  • Integrate Multistep Word Problems in Daily Lessons
  • Encourage Independent Practice

Offer Problem-Solving Discussions and Presentations

Assign regular problem-solving exercises as part of your students’ homework or in-class activities.

Provide a variety of multi-step word problems that cover different mathematical concepts and real-life scenarios.

Gradually increase the difficulty level of the problems to challenge your students and foster their growth.

Integrate Multi-Step Word Problems in Daily Lessons

Incorporate multi-step word problems into your daily math lessons. Introduce them as real-world applications of the mathematical concepts you are teaching.

Show your students how these problems relate to their everyday lives and the importance of problem-solving skills in various contexts.

Inspire active participation and engagement during problem-solving activities.

Encourage Independent Practice of Multi-Step Word Problems

independent multistep word problems practice

Encourage your students to practice independently outside of class.

Recommend math resources, such as textbooks, workbooks, or online platforms, that provide additional multi-step word problems for practice.

Encourage them to set aside dedicated time each week to work on problem-solving skills.

Remind them of the benefits of consistent practice in building proficiency.

solving multistep word problems discussions

Create opportunities for students to present and discuss their problem-solving strategies with the class.

Encourage them to explain their thinking, justify their solutions, and engage in constructive discussions.

This not only enhances their communication skills but also exposes them to different problem-solving approaches and fosters a collaborative learning environment.

Recommended Materials for Multi-Step Word Problems Practice

multistep word problems worksheets and task cards

To enhance your students’ practice in solving multi-step word problems, consider incorporating the following recommended materials:

Math Workbooks

Online problem-solving platforms, math games and activities, task cards and worksheets.

Math workbooks provide a structured approach to practicing multi-step word problems.

Look for workbooks that specifically focus on problem-solving skills and offer a variety of problem types and difficulty levels.

These workbooks typically include step-by-step explanations and examples, providing students with opportunities to apply their problem-solving strategies independently.

Encourage your students to work through the problems in the workbooks, highlighting the importance of showing their work and explaining their reasoning.

You can assign specific pages or problem sets from the workbook as part of their regular practice routine.

Leverage the power of technology by using online problem-solving platforms.

These platforms offer interactive multi-step word problems that engage students and provide immediate feedback.

Look for platforms that align with your curriculum and allow you to track students’ progress.

Online problem-solving platforms often provide a range of difficulty levels and adaptive features that adjust the complexity of the problems based on individual performance.

Encourage your students to explore these platforms during their independent practice time or assign specific problems for them to solve online.

Engage your students in learning through math games and activities.

These interactive and hands-on experiences make practice enjoyable and foster a positive attitude towards problem-solving.

Look for math games and activities that specifically focus on multi-step word problems.

You can create your own games using task cards or find existing games that align with your curriculum.

Set up problem-solving stations where students rotate and solve different multi-step word problems in a game format.

These activities promote collaboration, critical thinking, and a deeper understanding of problem-solving strategies.

Task cards and worksheets provide targeted practice opportunities for multi-step word problems.

While worksheets offer a collection of problems on a single sheet, task cards typically consist of individual problems on small cards.

These resources allow for flexibility in assigning practice and can be tailored to the specific needs of your students.

Select task cards or worksheets that align with the topics and skills you want your students to practice.

Consider using a variety of formats, such as multiple-choice, open-ended, or guided questions, to cater to different learning preferences.

Provide clear instructions and encourage students to work through the problems independently or in small groups.

If you’re looking for engaging worksheets and task cards for multi-step word problems to use with your students, then my differentiated worksheets and task cards will be a perfect fit for you. You can find them at my resources stores below:

  • Website shop
  • Made by Teachers store

Congratulations, teachers! You have now equipped yourself with a toolkit of effective strategies and resources to teach multi-step word problems with confidence.

By providing clear problem-solving strategies, implementing scaffolded practice, differentiating your instruction, and promoting regular practice, you are setting your students up for success.

Embrace the journey of teaching and learning multi-step word problems, celebrate the progress of your students, and watch as they develop into proficient problem solvers.

Remember, with your guidance and support, their potential knows no bounds!

how to teach multistep word problems

Multistep Word Problems – FAQs

What are two-step and multi-step problems.

Two-step and multi-step problems are types of word problems that require multiple mathematical operations to be performed to find the solution. In two-step problems, students need to apply two operations, such as addition and subtraction or multiplication and division, to solve the problem. Multi-step problems may involve more than two operations and often require students to perform a series of steps to arrive at the final answer.

Why Are Multi-Step Word Problems So Important?

Multi-step word problems are important because they reflect real-world situations that students may encounter in their daily lives. By solving these problems, students develop critical thinking, analytical reasoning, and problem-solving skills. Multi-step word problems also help students apply mathematical concepts in context, promoting a deeper understanding of the subject matter.

Why do students struggle with multi-step word problems?

Students often struggle with multi-step word problems due to several reasons. First, these problems require higher-level thinking skills, such as analyzing and synthesizing information. Second, students may find it challenging to identify the relevant information and determine which operations to use. Additionally, students may struggle with organizing their thoughts and applying problem-solving strategies effectively.

What are the common errors in solving multi-step word problems?

Common errors in solving multi-step word problems include:

  • Misinterpreting the problem: Failing to understand the problem correctly and misidentifying the key information.
  • I ncorrect selection of operations: Choosing the wrong operations or using them in the wrong order.
  • Calculation errors: Making mistakes in performing arithmetic calculations.
  • Forgetting to check the answer: Neglecting to verify if the solution aligns with the question asked and the context of the problem.

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4.9: Strategies for Solving Applications and Equations

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Learning Objectives

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

  • Use a problem solving strategy for word problems
  • Solve number word problems
  • Solve percent applications
  • Solve simple interest applications

Before you get started, take this readiness quiz.

  • Translate “six less than twice x ” into an algebraic expression. If you missed this problem, review [link] .
  • Convert 4.5% to a decimal. If you missed this problem, review [link] .
  • Convert 0.6 to a percent. If you missed this problem, review [link] .

Have you ever had any negative experiences in the past with word problems? When we feel we have no control, and continue repeating negative thoughts, we set up barriers to success. Realize that your negative experiences with word problems are in your past. To move forward you need to calm your fears and change your negative feelings.

Start with a fresh slate and begin to think positive thoughts. Repeating some of the following statements may be helpful to turn your thoughts positive. Thinking positive thoughts is a first step towards success.

  • I think I can! I think I can!
  • While word problems were hard in the past, I think I can try them now.
  • I am better prepared now—I think I will begin to understand word problems.
  • I am able to solve equations because I practiced many problems and I got help when I needed it—I can try that with word problems.
  • It may take time, but I can begin to solve word problems.
  • You are now well prepared and you are ready to succeed. If you take control and believe you can be successful, you will be able to master word problems.

Use a Problem Solving Strategy for Word Problems

Now that we can solve equations, we are ready to apply our new skills to word problems. We will develop a strategy we can use to solve any word problem successfully.

EXAMPLE \(\PageIndex{1}\)

Normal yearly snowfall at the local ski resort is 12 inches more than twice the amount it received last season. The normal yearly snowfall is 62 inches. What was the snowfall last season at the ski resort?

EXAMPLE \(\PageIndex{2}\)

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

He bought two notebooks

EXAMPLE \(\PageIndex{3}\)

Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is eight more than twice the number of crossword puzzles. He completed 22 Sudoku puzzles. How many crossword puzzles did he do?

He did seven crosswords puzzles

We summarize an effective strategy for problem solving.

PROBLEM SOLVING STRATEGY FOR WORD PROBLEMS

  • Read the problem. Make sure all the words and ideas are understood.
  • 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 restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.
  • Solve the equation using proper algebra techniques.
  • Check the answer in the problem to make sure it makes sense.
  • Answer the question with a complete sentence.

Solve Number Word Problems

We will now apply the problem solving strategy to “number word problems.” Number word problems give some clues about one or more numbers and we use these clues to write an equation. Number word problems provide good practice for using the Problem Solving Strategy.

EXAMPLE \(\PageIndex{4}\)

The sum of seven times a number and eight is thirty-six. Find the number.

Did you notice that we left out some of the steps as we solved this equation? If you’re not yet ready to leave out these steps, write down as many as you need.

EXAMPLE \(\PageIndex{5}\)

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

EXAMPLE \(\PageIndex{6}\)

The sum of three times a number and seven is twenty-five. Find the number.

Some number word problems ask us to find two or more numbers. It may be tempting to name them all with different variables, but so far, we have only solved equations with one variable. In order to avoid using more than one variable, we will define the numbers in terms of the same variable. Be sure to read the problem carefully to discover how all the numbers relate to each other.

EXAMPLE \(\PageIndex{7}\)

The sum of two numbers is negative fifteen. One number is nine less than the other. Find the numbers.

EXAMPLE \(\PageIndex{8}\)

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

\(−15,−8\)

EXAMPLE \(\PageIndex{9}\)

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

\(−29,11\)

Consecutive Integers (optional)

Some number problems involve consecutive integers . Consecutive integers are integers that immediately follow each other. Examples of consecutive integers are:

\[\begin{array}{rrrr} 1, & 2, & 3, & 4 \\ −10, & −9, & −8, & −7\\ 150, & 151, & 152, & 153 \end{array}\]

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

\[\begin{array}{ll} n & 1^{\text{st}} \text{integer} \\ n+1 \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; & 2^{\text{nd}}\text{consecutive integer} \\ n+2 & 3^{\text{rd}}\text{consecutive integer} \;\;\;\;\;\;\;\; \text{etc.} \end{array}\]

We will use this notation to represent consecutive integers in the next example.

EXAMPLE \(\PageIndex{10}\)

Find three consecutive integers whose sum is \(−54\).

EXAMPLE \(\PageIndex{11}\)

Find three consecutive integers whose sum is \(−96\).

\(−33,−32,−31\)

EXAMPLE \(\PageIndex{12}\)

Find three consecutive integers whose sum is \(−36\).

\(−13,−12,−11\)

Now that we have worked with consecutive integers, we will expand our work to include consecutive even integers and consecutive odd integers . Consecutive even integers are even integers that immediately follow one another. Examples of consecutive even integers are:

\[24, 26, 28\]

\[−12,−10,−8\]

Notice each integer is two more than the number preceding it. If we call the first one n , then the next one is \(n+2\). The one after that would be \(n+2+2\) or \(n+4\).

Consecutive odd integers are odd integers that immediately follow one another. Consider the consecutive odd integers 63, 65, and 67.

\[63, 65, 67\]

\[n,n+2,n+4\]

Does it seem strange to have to add two (an even number) to get the next odd number? Do we get an odd number or an even number when we add 2 to 3? to 11? to 47?

Whether the problem asks for consecutive even numbers or odd numbers, you do not have to do anything different. The pattern is still the same—to get to the next odd or the next even integer, add two.

EXAMPLE \(\PageIndex{13}\)

Find three consecutive even integers whose sum is \(120\).

EXAMPLE \(\PageIndex{14}\)

Find three consecutive even integers whose sum is 102.

\(32, 34, 36\)

EXAMPLE \(\PageIndex{15}\)

Find three consecutive even integers whose sum is \(−24\).

\(−10,−8,−6\)

When a number problem is in a real life context, we still use the same strategies that we used for the previous examples.

EXAMPLE \(\PageIndex{16}\)

A married couple together earns $110,000 a year. The wife earns $16,000 less than twice what her husband earns. What does the husband earn?

According to the National Automobile Dealers Association, the average cost of a car in 2014 was $28,400. This was $1,600 less than six times the cost in 1975. What was the average cost of a car in 1975?

The average cost was $5,000.

EXAMPLE \(\PageIndex{18}\)

US Census data shows that the median price of new home in the U.S. in November 2014 was $280,900. This was $10,700 more than 14 times the price in November 1964. What was the median price of a new home in November 1964?

The median price was $19,300.

Solve Percent Applications

There are several methods to solve percent equations. In algebra, it is easiest if we just translate English sentences into algebraic equations and then solve the equations. Be sure to change the given percent to a decimal before you use it in the equation.

EXAMPLE \(\PageIndex{19}\)

Translate and solve:

  • What number is 45% of 84?
  • 8.5% of what amount is $4.76?
  • 168 is what percent of 112?
  • What number is 45% of 80?
  • 7.5% of what amount is $1.95?
  • 110 is what percent of 88?

ⓐ 36 ⓑ $26 ⓒ \(125 \% \)

EXAMPLE \(\PageIndex{21}\)

  • What number is 55% of 60?
  • 8.5% of what amount is $3.06?
  • 126 is what percent of 72?

ⓐ 33 ⓑ $36 ⓐ \(175 \% \)

Now that we have a problem solving strategy to refer to, and have practiced solving basic percent equations, we are ready to solve percent applications. Be sure to ask yourself if your final answer makes sense—since many of the applications we will solve involve everyday situations, you can rely on your own experience.

EXAMPLE \(\PageIndex{22}\)

The label on Audrey’s yogurt said that one serving provided 12 grams of protein, which is 24% of the recommended daily amount. What is the total recommended daily amount of protein?

EXAMPLE \(\PageIndex{23}\)

One serving of wheat square cereal has 7 grams of fiber, which is 28% of the recommended daily amount. What is the total recommended daily amount of fiber?

EXAMPLE \(\PageIndex{24}\)

One serving of rice cereal has 190 mg of sodium, which is 8% of the recommended daily amount. What is the total recommended daily amount of sodium?

Remember to put the answer in the form requested. In the next example we are looking for the percent.

EXAMPLE \(\PageIndex{25}\)

Veronica is planning to make muffins from a mix. The package says each muffin will be 240 calories and 60 calories will be from fat. What percent of the total calories is from fat?

EXAMPLE \(\PageIndex{26}\)

Mitzi received some gourmet brownies as a gift. The wrapper said each 28% brownie was 480 calories, and had 240 calories of fat. What percent of the total calories in each brownie comes from fat? Round the answer to the nearest whole percent.

EXAMPLE \(\PageIndex{27}\)

The mix Ricardo plans to use to make brownies says that each brownie will be 190 calories, and 76 calories are from fat. What percent of the total calories are from fat? Round the answer to the nearest whole percent.

It is often important in many fields—business, sciences, pop culture—to talk about how much an amount has increased or decreased over a certain period of time. This increase or decrease is generally expressed as a percent and called the percent change .

To find the percent change, first we find the amount of change, by finding the difference of the new amount and the original amount. Then we find what percent the amount of change is of the original amount.

FIND PERCENT CHANGE

\[\text{change}= \text{new amount}−\text{original amount}\]

change is what percent of the original amount?

EXAMPLE \(\PageIndex{28}\)

Recently, the California governor proposed raising community college fees from $36 a unit to $46 a unit. Find the percent change. (Round to the nearest tenth of a percent.)

EXAMPLE \(\PageIndex{29}\)

Find the percent change. (Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to 55.5 cents from 51 cents.

\(8.8 \% \)

EXAMPLE \(\PageIndex{30}\)

Find the percent change. (Round to the nearest tenth of a percent.) In 1995, the standard bus fare in Chicago was $1.50. In 2008, the standard bus fare was 2.25.

Applications of discount and mark-up are very common in retail settings.

When you buy an item on sale, the original price has been discounted by some dollar amount. The discount rate , usually given as a percent, is used to determine the amount of the discount . To determine the amount of discount, we multiply the discount rate by the original price.

The price a retailer pays for an item is called the original cost . The retailer then adds a mark-up to the original cost to get the list price , the price he sells the item for. The mark-up is usually calculated as a percent of the original cost. To determine the amount of mark-up, multiply the mark-up rate by the original cost.

\[ \begin{align} \text{amount of discount} &= \text{discount rate}· \text{original price} \\ \text{sale price} &= \text{original amount}– \text{discount price} \end{align}\]

The sale price should always be less than the original price.

\[\begin{align} \text{amount of mark-up} &= \text{mark-up rate}·\text{original price} \\ \text{list price} &= \text{original cost}–\text{mark-up} \end{align}\]

The list price should always be more than the original cost.

EXAMPLE \(\PageIndex{31}\)

Liam’s art gallery bought a painting at an original cost of $750. Liam marked the price up 40%. Find

  • the amount of mark-up and
  • the list price of the painting.

EXAMPLE \(\PageIndex{32}\)

Find ⓐ the amount of mark-up and ⓑ the list price: Jim’s music store bought a guitar at original cost $1,200. Jim marked the price up 50%.

ⓐ $600 ⓑ $1,800

EXAMPLE \(\PageIndex{33}\)

Find ⓐ the amount of mark-up and ⓑ the list price: The Auto Resale Store bought Pablo’s Toyota for $8,500. They marked the price up 35%.

ⓐ $2,975 ⓑ $11,475

Solve Simple Interest Applications

Interest is a part of our daily lives. From the interest earned on our savings to the interest we pay on a car loan or credit card debt, we all have some experience with interest in our lives.

The amount of money you initially deposit into a bank is called the principal , P , and the bank pays you interest, I. When you take out a loan, you pay interest on the amount you borrow, also called the principal.

In either case, the interest is computed as a certain percent of the principal, called the rate of interest , r . The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable t , (for time) represents the number of years the money is saved or borrowed.

Interest is calculated as simple interest or compound interest. Here we will use simple interest.

SIMPLE INTEREST

If an amount of money, P , called the principal, is invested or borrowed for a period of t years at an annual interest rate r , the amount of interest, I , earned or paid is

\[ \begin{array}{ll} I=Prt \; \; \; \; \; \; \; \; \; \; \; \; \text{where} & { \begin{align} I &= \text{interest} \\ P &= \text{principal} \\ r &= \text{rate} \\ t &= \text{time} \end{align}} \end{array}\]

Interest earned or paid according to this formula is called simple interest .

The formula we use to calculate interest is \(I=Prt\). To use the formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information in a chart.

EXAMPLE \(\PageIndex{34}\)

Areli invested a principal of $950 in her bank account that earned simple interest at an interest rate of 3%. How much interest did she earn in five years?

\( \begin{aligned} I & = \; ? \\ P & = \; \$ 950 \\ r & = \; 3 \% \\ t & = \; 5 \text{ years} \end{aligned}\)

\(\begin{array}{ll} \text{Identify what you are asked to find, and choose a} & \text{What is the simple interest?} \\ \text{variable to represent it.} & \text{Let } I= \text{interest.} \\ \text{Write the formula.} & I=Prt \\ \text{Substitute in the given information.} & I=(950)(0.03)(5) \\ \text{Simplify.} & I=142.5 \\ \text{Check.} \\ \text{Is } \$142.50 \text{ a reasonable amount of interest on } \$ \text{ 950?} \; \;\;\;\;\; \;\;\;\;\;\; \\ \text{Yes.} \\ \text{Write a complete sentence.} & \text{The interest is } \$ \text{142.50.} \end{array}\)

EXAMPLE \(\PageIndex{35}\)

Nathaly deposited $12,500 in her bank account where it will earn 4% simple interest. How much interest will Nathaly earn in five years?

He will earn $2,500.

EXAMPLE \(\PageIndex{36}\)

Susana invested a principal of $36,000 in her bank account that earned simple interest at an interest rate of 6.5%.6.5%. How much interest did she earn in three years?

She earned $7,020.

There may be times when we know the amount of interest earned on a given principal over a certain length of time, but we do not know the rate.

EXAMPLE \(\PageIndex{37}\)

Hang borrowed $7,500 from her parents to pay her tuition. In five years, she paid them $1,500 interest in addition to the $7,500 she borrowed. What was the rate of simple interest?

\( \begin{aligned} I & = \; \$ 1500 \\ P & = \; \$ 7500 \\ r & = \; ? \\ t & = \; 5 \text{ years} \end{aligned}\)

Identify what you are asked to find, and choose What is the rate of simple interest? a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Change to percent form. Let r = rate of interest. I = P r t 1,500 = ( 7,500 ) r ( 5 ) 1,500 = 37,500 r 0.04 = r 4 % = r Check. I = P r t 1,500 = ? ( 7,500 ) ( 0.04 ) ( 5 ) 1,500 = 1,500 ✓ Write a complete sentence. The rate of interest was 4%. Identify what you are asked to find, and choose What is the rate of simple interest? a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Change to percent form. Let r = rate of interest. I = P r t 1 ,500 = ( 7,500 ) r ( 5 ) 1,500 = 37,500 r 0.04 = r 4 % = r Check. I = P r t 1 ,500 = ? ( 7,500 ) ( 0.04 ) ( 5 ) 1,500 = 1, 500 ✓ Write a complete sentence. The rate of interest was 4%.

EXAMPLE \(\PageIndex{38}\)

Jim lent his sister $5,000 to help her buy a house. In three years, she paid him the $5,000, plus $900 interest. What was the rate of simple interest?

The rate of simple interest was 6%.

EXAMPLE \(\PageIndex{39}\)

Loren lent his brother $3,000 to help him buy a car. In four years, his brother paid him back the $3,000 plus $660 in interest. What was the rate of simple interest?

The rate of simple interest was 5.5%.

In the next example, we are asked to find the principal—the amount borrowed.

EXAMPLE \(\PageIndex{40}\)

Sean’s new car loan statement said he would pay $4,866,25 in interest from a simple interest rate of 8.5% over five years. How much did he borrow to buy his new car?

\( \begin{aligned} I & = \; 4,866.25 \\ P & = \; ? \\ r & = \; 8.5 \% \\ t & = \; 5 \text{ years} \end{aligned}\)

Identify what you are asked to find, What is the amount borrowed (the principal)? and choose a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Let P = principal borrowed. I = P r t 4,866.25 = P ( 0.085 ) ( 5 ) 4,866.25 = 0.425 P 11,450 = P Check. I = P r t 4,866.25 = ? ( 11,450 ) ( 0.085 ) ( 5 ) 4,866.25 = 4,866.25 ✓ Write a complete sentence. The principal was $11,450. Identify what you are asked to find, What is the amount borrowed (the principal)? and choose a variable to represent it. Write the formula. Substitute in the given information. Multiply. Divide. Let P = principal borrowed. I = P r t 4 ,866.25 = P ( 0.085 ) ( 5 ) 4,866.25 = 0.425 P 11,450 = P Check. I = P r t 4 ,866.25 = ? ( 11,450 ) ( 0.085 ) ( 5 ) 4,866.25 = 4,866.25 ✓ Write a complete sentence. The principal was $11,450.

EXAMPLE \(\PageIndex{41}\)

Eduardo noticed that his new car loan papers stated that with a 7.5% simple interest rate, he would pay $6,596.25 in interest over five years. How much did he borrow to pay for his car?

He paid $17,590.

EXAMPLE \(\PageIndex{42}\)

In five years, Gloria’s bank account earned $2,400 interest at 5% simple interest. How much had she deposited in the account?

She deposited $9,600.

Access this online resource for additional instruction and practice with using a problem solving strategy.

  • Begining Arithmetic Problems

Key Concepts

\(\text{change}=\text{new amount}−\text{original amount}\)

\(\text{change is what percent of the original amount?}\)

  • \( \begin{align} \text{amount of discount} &= \text{discount rate}· \text{original price} \\ \text{sale price} &= \text{original amount}– \text{discount price} \end{align}\)
  • \(\begin{align} \text{amount of mark-up} &= \text{mark-up rate}·\text{original price} \\ \text{list price} &= \text{original cost}–\text{mark-up} \end{align}\)
  • If an amount of money, P , called the principal, is invested or borrowed for a period of t years at an annual interest rate r , the amount of interest, I , earned or paid is: \[\begin{aligned} &{} &{} &{I=interest} \nonumber\\ &{I=Prt} &{\text{where} \space} &{P=principal} \nonumber\\ &{} &{\space} &{r=rate} \nonumber\\ &{} &{\space} &{t=time} \nonumber \end{aligned}\]

Practice Makes Perfect

1. List five positive thoughts you can say to yourself that will help you approach word problems with a positive attitude. You may want to copy them on a sheet of paper and put it in the front of your notebook, where you can read them often.

Answers will vary.

2. List five negative thoughts that you have said to yourself in the past that will hinder your progress on word problems. You may want to write each one on a small piece of paper and rip it up to symbolically destroy the negative thoughts.

In the following exercises, solve using the problem solving strategy for word problems. Remember to write a complete sentence to answer each question.

3. There are \(16\) girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys.

4. There are \(18\) Cub Scouts in Troop 645. The number of scouts is three more than five times the number of adult leaders. Find the number of adult leaders.

5. Huong is organizing paperback and hardback books for her club’s used book sale. The number of paperbacks is \(12\) less than three times the number of hardbacks. Huong had \(162\) paperbacks. How many hardback books were there?

58 hardback books

6. Jeff is lining up children’s and adult bicycles at the bike shop where he works. The number of children’s bicycles is nine less than three times the number of adult bicycles. There are \(42\) adult bicycles. How many children’s bicycles are there?

In the following exercises, solve each number word problem.

7. The difference of a number and \(12\) is three. Find the number.

8. The difference of a number and eight is four. Find the number.

9. The sum of three times a number and eight is \(23\). Find the number.

10. The sum of twice a number and six is \(14\). Find the number.

11 . The difference of twice a number and seven is \(17\). Find the number.

12. The difference of four times a number and seven is \(21\). Find the number.

13. Three times the sum of a number and nine is \(12\). Find the number.

14. Six times the sum of a number and eight is \(30\). Find the number.

15. One number is six more than the other. Their sum is \(42\). Find the numbers.

\(18, \;24\)

16. One number is five more than the other. Their sum is \(33\). Find the numbers.

17. The sum of two numbers is \(20\). One number is four less than the other. Find the numbers.

\(8, \;12\)

18 . The sum of two numbers is \(27\). One number is seven less than the other. Find the numbers.

19. One number is \(14\) less than another. If their sum is increased by seven, the result is \(85\). Find the numbers.

\(32,\; 46\)

20 . One number is \(11\) less than another. If their sum is increased by eight, the result is \(71\). Find the numbers.

21. The sum of two numbers is \(14\). One number is two less than three times the other. Find the numbers.

\(4,\; 10\)

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

23. The sum of two consecutive integers is \(77\). Find the integers.

\(38,\; 39\)

24. The sum of two consecutive integers is \(89\). Find the integers.

25. The sum of three consecutive integers is \(78\). Find the integers.

\(25,\; 26,\; 27\)

26. The sum of three consecutive integers is \(60\). Find the integers.

27. Find three consecutive integers whose sum is \(−36\).

\(−11,\;−12,\;−13\)

28. Find three consecutive integers whose sum is \(−3\).

29. Find three consecutive even integers whose sum is \(258\).

\(84,\; 86,\; 88\)

30. Find three consecutive even integers whose sum is \(222\).

31. Find three consecutive odd integers whose sum is \(−213\).

\(−69,\;−71,\;−73\)

32. Find three consecutive odd integers whose sum is \(−267\).

33. Philip pays \($1,620\) in rent every month. This amount is \($120\) more than twice what his brother Paul pays for rent. How much does Paul pay for rent?

34. Marc just bought an SUV for \($54,000\). This is \($7,400\) less than twice what his wife paid for her car last year. How much did his wife pay for her car?

35. Laurie has \($46,000\) invested in stocks and bonds. The amount invested in stocks is \($8,000\) less than three times the amount invested in bonds. How much does Laurie have invested in bonds?

\($13,500\)

36. Erica earned a total of \($50,450\) last year from her two jobs. The amount she earned from her job at the store was \($1,250\) more than three times the amount she earned from her job at the college. How much did she earn from her job at the college?

In the following exercises, translate and solve.

37. a. What number is 45% of 120? b. 81 is 75% of what number? c. What percent of 260 is 78?

a. 54 b. 108 c. 30%

38. a. What number is 65% of 100? b. 93 is 75% of what number? c. What percent of 215 is 86?

39. a. 250% of 65 is what number? b. 8.2% of what amount is $2.87? c. 30 is what percent of 20?

a. 162.5 b. $35 c. 150%

40. a. 150% of 90 is what number? b. 6.4% of what amount is $2.88? c. 50 is what percent of 40?

In the following exercises, solve.

41. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. Geneva wants to leave 16% of the total bill as a tip. How much should the tip be?

42. When Hiro and his co-workers had lunch at a restaurant near their work, the bill was $90.50. They want to leave 18% of the total bill as a tip. How much should the tip be?

43. One serving of oatmeal has 8 grams of fiber, which is 33% of the recommended daily amount. What is the total recommended daily amount of fiber?

44. One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

45. A bacon cheeseburger at a popular fast food restaurant contains 2070 milligrams (mg) of sodium, which is 86% of the recommended daily amount. What is the total recommended daily amount of sodium?

46. A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?

47. The nutrition fact sheet at a fast food restaurant says the fish sandwich has 380 calories, and 171 calories are from fat. What percent of the total calories is from fat?

48. The nutrition fact sheet at a fast food restaurant says a small portion of chicken nuggets has 190 calories, and 114 calories are from fat. What percent of the total calories is from fat?

49. Emma gets paid $3,000 per month. She pays $750 a month for rent. What percent of her monthly pay goes to rent?

50. Dimple gets paid $3,200 per month. She pays $960 a month for rent. What percent of her monthly pay goes to rent?

51. Tamanika received a raise in her hourly pay, from $15.50 to $17.36. Find the percent change.

52. Ayodele received a raise in her hourly pay, from $24.50 to $25.48. Find the percent change.

53. Annual student fees at the University of California rose from about $4,000 in 2000 to about $12,000 in 2010. Find the percent change.

54. The price of a share of one stock rose from $12.50 to $50. Find the percent change.

55. A grocery store reduced the price of a loaf of bread from $2.80 to $2.73. Find the percent change.

−2.5%

56. The price of a share of one stock fell from $8.75 to $8.54. Find the percent change.

57. Hernando’s salary was $49,500 last year. This year his salary was cut to $44,055. Find the percent change.

58. In ten years, the population of Detroit fell from 950,000 to about 712,500. Find the percent change.

In the following exercises, find a. the amount of discount and b. the sale price.

59. Janelle bought a beach chair on sale at 60% off. The original price was $44.95.

a. $26.97 b. $17.98

60. Errol bought a skateboard helmet on sale at 40% off. The original price was $49.95.

In the following exercises, find a. the amount of discount and b. the discount rate (Round to the nearest tenth of a percent if needed.)

61. Larry and Donna bought a sofa at the sale price of $1,344. The original price of the sofa was $1,920.

a. $576 b. 30%

62. Hiroshi bought a lawnmower at the sale price of $240. The original price of the lawnmower is $300.

In the following exercises, find a. the amount of the mark-up and b. the list price.

63. Daria bought a bracelet at original cost $16 to sell in her handicraft store. She marked the price up 45%. What was the list price of the bracelet?

a. $7.20 b. $23.20

64. Regina bought a handmade quilt at original cost $120 to sell in her quilt store. She marked the price up 55%. What was the list price of the quilt?

65. Tom paid $0.60 a pound for tomatoes to sell at his produce store. He added a 33% mark-up. What price did he charge his customers for the tomatoes?

a. $0.20 b. $0.80

66. Flora paid her supplier $0.74 a stem for roses to sell at her flower shop. She added an 85% mark-up. What price did she charge her customers for the roses?

67. Casey deposited $1,450 in a bank account that earned simple interest at an interest rate of 4%. How much interest was earned in two years?

68 . Terrence deposited $5,720 in a bank account that earned simple interest at an interest rate of 6%. How much interest was earned in four years?

69. Robin deposited $31,000 in a bank account that earned simple interest at an interest rate of 5.2%. How much interest was earned in three years?

70. Carleen deposited $16,400 in a bank account that earned simple interest at an interest rate of 3.9% How much interest was earned in eight years?

71. Hilaria borrowed $8,000 from her grandfather to pay for college. Five years later, she paid him back the $8,000, plus $1,200 interest. What was the rate of simple interest?

72. Kenneth lent his niece $1,200 to buy a computer. Two years later, she paid him back the $1,200, plus $96 interest. What was the rate of simple interest?

73. Lebron lent his daughter $20,000 to help her buy a condominium. When she sold the condominium four years later, she paid him the $20,000, plus $3,000 interest. What was the rate of simple interest?

74. Pablo borrowed $50,000 to start a business. Three years later, he repaid the $50,000, plus $9,375 interest. What was the rate of simple interest?

75. In 10 years, a bank account that paid 5.25% simple interest earned $18,375 interest. What was the principal of the account?

76. In 25 years, a bond that paid 4.75% simple interest earned $2,375 interest. What was the principal of the bond?

77. Joshua’s computer loan statement said he would pay $1,244.34 in simple interest for a three-year loan at 12.4%. How much did Joshua borrow to buy the computer?

78. Margaret’s car loan statement said she would pay $7,683.20 in simple interest for a five-year loan at 9.8%. How much did Margaret borrow to buy the car?

Everyday Math

79 . Tipping At the campus coffee cart, a medium coffee costs $1.65. MaryAnne brings $2.00 with her when she buys a cup of coffee and leaves the change as a tip. What percent tip does she leave?

80 . Tipping Four friends went out to lunch and the bill came to $53.75 They decided to add enough tip to make a total of $64, so that they could easily split the bill evenly among themselves. What percent tip did they leave?

Writing Exercises

81. What has been your past experience solving word problems? Where do you see yourself moving forward?

82. Without solving the problem “44 is 80% of what number” think about what the solution might be. Should it be a number that is greater than 44 or less than 44? Explain your reasoning.

83. After returning from vacation, Alex said he should have packed 50% fewer shorts and 200% more shirts. Explain what Alex meant.

84. Because of road construction in one city, commuters were advised to plan that their Monday morning commute would take 150% of their usual commuting time. Explain what this means.

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

This table has four columns and five rows. The first row is a header and it labels each column, “I can…”, “Confidently,” “With some help,” and “No-I don’t get it!” In row 2, the I can was use a problem-solving strategy for word problems. In row 3, the I can was solve number problems. In row 4, the I can was solve percent applications. In row 5, the I can was solve simple interest applications.

b. After reviewing this checklist, what will you do to become confident for all objectives?

The Sassy Maestra

The Only Word Problem Strategy You Need

the only word problem strategy you need

If you’re looking for an easy word problem strategy to transform your 3rd, 4th, or 5th grade class, you are in the right place! Word problems can be such a struggle for students, especially English Learners, but they don’t have to be. 

Does this sound familiar?

You’re teaching word problems. You’ve barely finished reading the problem and you look out into your class. Half of them are completely checked out and waiting for you to to tell them what to do. The other half are jumping in, but they’re just randomly adding and multiplying the numbers without thinking about what they’re actually doing. 

You’re frustrated because you know that word problems are so important. You know that in every day life, almost all of the math we do is word problems. Nobody hands us a ready made division problem to do alone in a cubicle. 

You know that your students need a word problem strategy to help them to slow down and understand the problem. Some students, especially your language learners, need to slow down and make meaning of the words. Other students need to slow down and understand the meaning of the quantities in the word problem and how they relate. 

A lot of students need all of the above. 

So how can you help your students break down and understand word problems?

Transform your class with this word problem strategy

The one word problem strategy you need to try

My favorite strategy for teaching word problems is called Read 3 Ways . It’s fantastic because:

  • You can use it with any word problem 
  • You can use it with any grade level or skill level
  • It’s a fantastic support for language learners 
  • It provides extra challenge for your advanced students 
  • It slows students down so they can’t rush ahead and solve the problem incorrectly

How it works 

As the title implies, in the word problem strategy Read 3 Ways we read the problem, you guessed it, 3 times. 

In the first read you present the problem with the number omitted. If you’re using slides you can easily cover them with a rectangle. If you are projecting from a book on the document camera you can use a tiny scrap of paper or a little base-10 unit block to cover the numbers. 

The one word problem strategy that will transform your class

During the first read you pose this question: What is happening in the story?

Pretty simple right? 

But this simple question leads to some rich discussion. Let’s look at this example. 

Miguel read _____ pages. Clara read ____ more pages than Miguel. Maya read ___ pages less than Clara. 

What is this story about? Well, we have Miguel, Clara, and Maya. They’ve all read a certain number of pages. 

Did they read an equal amount? No. 

How do you know? Well, the words more and less let us know that they read different amounts.

Even though we don’t have the number of pages yet, can we tell who read the most pages? How? Who read the least? How do you know?

Do you see that even without numbers, we can really break this problem apart? 

Second Read

In the second read we read the problem again, except this time with the numbers included. We ask students, “what quantities are there and how do they relate?”

I tell students that 2 isn’t a quantity, but 2 dogs is. 30 isn’t a quantity, but 30 dollars is. Even 1st graders grasp this quickly. 

Let’s continue with our example. 

Miguel read 398 pages. Clara read 102 more pages than Miguel. Maya read 54 pages less than Clara. 

What quantities do we have? Some students might say 398, 102, and 54. Don’t accept that. Who has 398? 398 what? Remember, we’re building deep understanding here. 

Did you notice what’s missing from our word problem still? That’s right- there’s no question! Your speed racers aren’t able to steamroll ahead and instead are forced to slow down and reason through the words. 

But of course you need a question eventually which leads us to…

Transform your 3rd, 4th, and 5th grade math lessons using this word problem strategy

In the third read, you read to generate a question. Ask your students, “what questions can be asked and answered by this question?” 

After giving your students some think time and possibly a pair share, make a list on chart paper or on the board of their questions. 

In our example of pages read, some questions might include:

  • How many pages did Clara read?
  • How many pages did Maya read?
  • How many pages did all 3 students read all together?

Time to solve

At last, it’s time to solve. Reveal the question and let your students get to work! 

Miguel read 398 pages. Clara read 102 more pages than Miguel. Maya read 54 pages less than Clara. How many pages did Miguel, Clara, and Maya read all together?

I’ve found that I’ve done so much foundational work getting to this point that every student gets to work right away. You read that right. Every. Single. Student.

What about your advanced students? Once they finish your question, ask them to tackle questions from the list generated in the 3rd read. They love to answer their classmates’ questions! 

The only word problem strategy you need

Your no prep solution

I love this word problem strategy because once you’re in the swing of the routine it’s very easy for you to facilitate and it really sets up your students for success. 

Although it can be done with any word problem, there is a little legwork in selecting a problem and presenting it to your students. 

That’s why I wrote out Read 3 Ways ready-to-present slides for you. My slides are absolutely zero prep. Just project and go!  

Word problem strategy slides. The text says "making sense of word problems. Add, subtract, multiply. Bundle"

I have 4 sets available, with 10 problems (44 slides) each. Your options are:

  • Addition and subtraction in English
  • Addition and subtraction in Spanish
  • Multiplication in English
  • Multiplication in Spanish 

Whether or not you purchase my slides, let me know how this strategy worked for you by tagging me or DMing me on Instagram .

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what is the five step strategy for solving word problems

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  1. Word problems anchor chart for first grade

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  4. Word Problems Solving Worksheet by Teach Simple

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  5. Problem-Solving Strategies: Definition and 5 Techniques to Try

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  6. 5 Easy Steps to Solve Any Word Problem in Math

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VIDEO

  1. 3 Reads Strategy Solving Word Problems x & /

  2. The "5 Whys" Technique For Problem Solving

  3. 3 Reads Strategy Solving Word Problems + &

  4. Forever Living

  5. One-Step Equation Word Problems

  6. 3 Ways to Use Numberless Word Problems in Upper Elementary

COMMENTS

  1. PDF Five-Step Strategy to Solving Word Problems

    5) Statethe answer clearly in written form. Make sure you answer the question. Ifyou are asked the speed of the slowest train, for example, you should answer, "Theslowest train was traveling at 65 mph." Wewill now solve a word problem using the Five-Step Strategy. A freight train leaves Chicago at 4:30 pm traveling at a speed of 60 mph. Two ...

  2. 5 Easy Steps to Solve Any Word Problem in Math

    We are ready to SOLVE any word problem our students are going to encounter in math class. Here are my 5 easy steps to SOLVE any word problem in math: S - State the objective. O - Outline your plan. L - Look for Key Details - Information. V - Verify and Solve. E - Explain and check your solution.

  3. 10 Best Strategies for Solving Math Word Problems

    A collaborative approach is one of the best strategies for solving math word problems that can unveil multiple methods for tackling the same problem, enriching students' problem-solving toolkit. Related Reading: Best Math Brain Teasers for Kids [with answers] Conclusion . Mastering math word problems is a journey of small steps.

  4. Strategies for Solving Word Problems

    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 ...

  5. 5 Easy Steps to Solving Word Problems

    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.

  6. A Strategy for Teaching Math Word Problems

    This strategy for selecting and teaching word problems guides students to develop their understanding of math concepts. Word problems in mathematics are a powerful tool for helping students make sense of and reason with mathematical concepts. Many students, however, struggle with word problems because of the various cognitive demands.

  7. Apply a Problem-Solving Strategy to Word Problems

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

  8. A Better Strategy For Solving Math Word Problems

    Fourthly, R.I.E.D.S. calls out developing a plan, a crucial step to solving word problems. A step that engages students in metacognitive thinking . Solving Word Problems Using R.I.E.D.S. R.I.E.D.S. is a simple five-step strategy for cracking word problems. Let me break it down for you: Step 1: Read and Understand the Problem

  9. 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.

  10. How to Solve Multi-Step Word Problems

    Step 1: The problem involves multiplication (each book cost twice as much as a pen) and addition (total amount spent). Step 2: First, find the cost of a book and then calculate the total cost. Step 3: Let's say \ (X\) is the cost of a book. Step 4: The equations will be \ (X = 2 \times the\:cost\:of\:a\:pen\) and Total cost = cost of books ...

  11. CUBES Math Strategy for Word Problems

    The math CUBE strategy provides those students with a starting point, a set of steps to perform in order to solve a particular math word problem. What is the CUBES strategy? This strategy helps students break down word problems by creating five steps they must follow in order to solve. CUBES is an acronym that is easily remembered by students.

  12. 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.

  13. 4 Math Word Problem Solving Strategies

    5 Strategies to Learn to Solve Math Word Problems. A critical step in math fluency is the ability to solve math word problems. The funny thing about solving math word problems is that it isn't just about math. Students need to have strong reading skills as well as the growth mindset needed for problem-solving.

  14. PDF Five-Step Strategy to Solving Word Problems

    5) State the answer clearly in written form. Make sure you answer the question. If you are asked the speed of the slowest train, for example, you should answer, "The slowest train was traveling at 65 mph." We will now solve a word problem using the Five-Step Strategy. A freight train leaves Chicago at 4:30 p.m. traveling at a speed of 60 mph.

  15. How to Help Students Who Struggle with Word Problems

    The test makers are hip to the whole key word thing. So while key words may have worked 20 years ago, today's tests are specifically written to outsmart that approach. 2. Pre-Formulating Word Problems. For students to be effective in solving word problems, they need to master the art of formulation.

  16. 20 Effective Math Strategies For Problem Solving

    Here are five strategies to help students check their solutions. 1. Use the Inverse Operation. For simpler problems, a quick and easy problem solving strategy is to use the inverse operation. For example, if the operation to solve a word problem is 56 ÷ 8 = 7 students can check the answer is correct by multiplying 8 × 7.

  17. 3 Word Problem Solving Strategies To Improve Word ...

    Drawing visual models helps lead your students to an equation. This strategy is ideal for students who understand what a word problem is asking but have difficulty connecting the action of a word problem to an equation. A visual model might include: A math drawing (simple circles or an organic representation) A number bond (number bonds can be ...

  18. 5 Steps to Word Problem Solving

    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 ...

  19. 3 Strategies to Conquer Math Word Problems

    3 Problem Solving Strategies. The solution is to conquer math word problems with engaging classroom strategies that counteract the above issues! 1. Teach a Problem-Solving Routine. Kids (and adults) are notoriously impulsive problem solvers. Many students see a word problem and want to immediately snatch out those numbers and "do something ...

  20. How to Teach Word Problems: Strategies for Elementary Teachers

    A multi-step word problem, also known as a two-step word problem or two-step equation word problem, is a math situation that involves more than one equation having to be answered in order to solve the ultimate question. This requires students to apply their problem solving skills to determine which operation or operations to use to tackle the ...

  21. 5 Strategies to Teach Multi-Step Word Problems: Teacher's Guide

    Strategies to Teach Multi-Step Word Problems. Now, let's delve into the 5 strategies that teachers can employ to effectively teach multi-step word problem-solving to their students. Model the Problem-Solving Process. Provide Clear Problem-Solving Strategies. Provide Scaffolded Practice.

  22. 4.9: Strategies for Solving Applications and Equations

    How To Use a Problem Solving Strategy for Word Problems. Read the problem. Make sure all the words and ideas are understood. 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 restate the problem in one sentence with all the important ...

  23. The Only Word Problem Strategy You Need

    The one word problem strategy you need to try. My favorite strategy for teaching word problems is called Read 3 Ways. It's fantastic because: You can use it with any word problem. You can use it with any grade level or skill level. It's a fantastic support for language learners. It provides extra challenge for your advanced students.