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10 Best Strategies for Solving Math Word Problems

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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.

strategies in solving math word problems

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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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strategies in solving math word problems

Strategies for Solving Word Problems – Math

strategies in solving math 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:

strategies in solving math 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

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14 Effective Ways to Help Your Students Conquer Math Word Problems

If a train leaving Minneapolis is traveling at 87 miles an hour…

Word Problems WeAreTeachers

Word problems can be tricky for a lot of students, but they’re incredibly important to master. After all, in the real world, most math is in the form of word problems. “If one gallon of paint covers 400 square feet, and my wall measures 34 feet by 8 feet, how many gallons do I need?” “This sweater costs $135, but it’s on sale for 35% off. So how much is that?” Here are the best teacher-tested ideas for helping kids get a handle on these problems.

1. Solve word problems regularly

strategies in solving math word problems

This might be the most important tip of all. Word problems should be part of everyday math practice, especially for older kids. Whenever possible, use word problems every time you teach a new math skill. Even better: give students a daily word problem to solve so they’ll get comfortable with the process.

Learn more: Teaching With Jennifer Findlay

2. Teach problem-solving routines

Word Problems Teacher Trap

There are a LOT of strategies out there for teaching kids how to solve word problems (keep reading to see some terrific examples). The important thing to remember is that what works for one student may not work for another. So introduce a basic routine like Plan-Solve-Check that every kid can use every time. You can expand on the Plan and Solve steps in a variety of ways, but this basic 3-step process ensures kids slow down and take their time.

Learn more: Word Problems Made Easy

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3. Visualize or model the problem

strategies in solving math word problems

Encourage students to think of word problems as an actual story or scenario. Try acting the problem out if possible, and draw pictures, diagrams, or models. Learn more about this method and get free printable templates at the link.

Learn more: Math Geek Mama

4. Make sure they identify the actual question

strategies in solving math word problems

Educator Robert Kaplinsky asked 32 eighth grade students to answer this nonsensical word problem. Only 25% of them realized they didn’t have the right information to answer the actual question; the other 75% gave a variety of numerical answers that involved adding, subtracting, or dividing the two numbers. That tells us kids really need to be trained to identify the actual question being asked before they proceed. 

Learn more: Robert Kaplinsky

5. Remove the numbers

strategies in solving math word problems

It seems counterintuitive … math without numbers? But this word problem strategy really forces kids to slow down and examine the problem itself, without focusing on numbers at first. If the numbers were removed from the sheep/shepherd problem above, students would have no choice but to slow down and read more carefully, rather than plowing ahead without thinking. 

Learn more: Where the Magic Happens Teaching

6. Try the CUBES method

strategies in solving math word problems

This is a tried-and-true method for teaching word problems, and it’s really effective for kids who are prone to working too fast and missing details. By taking the time to circle, box, and underline important information, students are more likely to find the correct answer to the question actually being asked.

Learn more: Teaching With a Mountain View

7. Show word problems the LOVE

Word Problems Jennifer Findlay

Here’s another fun acronym for tackling word problems: LOVE. Using this method, kids Label numbers and other key info, then explain Our thinking by writing the equation as a sentence. They use Visuals or models to help plan and list any and all Equations they’ll use. 

8. Consider teaching word problem key words

strategies in solving math word problems

This is one of those methods that some teachers love and others hate. Those who like it feel it offers kids a simple tool for making sense of words and how they relate to math. Others feel it’s outdated, and prefer to teach word problems using context and situations instead (see below). You might just consider this one more trick to keep in your toolbox for students who need it.

Learn more: Book Units Teacher

9. Determine the operation for the situation

strategies in solving math word problems

Instead of (or in addition to) key words, have kids really analyze the situation presented to determine the right operation(s) to use. Some key words, like “total,” can be pretty vague. It’s worth taking the time to dig deeper into what the problem is really asking. Get a free printable chart and learn how to use this method at the link.

Learn more: Solving Word Problems With Jennifer Findlay

10. Differentiate word problems to build skills

strategies in solving math word problems

Sometimes students get so distracted by numbers that look big or scary that they give up right off the bat. For those cases, try working your way up to the skill at hand. For instance, instead of jumping right to subtracting 4 digit numbers, make the numbers smaller to start. Each successive problem can be a little more difficult, but kids will see they can use the same method regardless of the numbers themselves.

Learn more: Differentiating Math 

11. Ensure they can justify their answers

strategies in solving math word problems

One of the quickest ways to find mistakes is to look closely at your answer and ensure it makes sense. If students can explain how they came to their conclusion, they’re much more likely to get the answer right. That’s why teachers have been asking students to “show their work” for decades now.

Learn more: Madly Learning

12. Write the answer in a sentence

strategies in solving math word problems

When you think about it, this one makes so much sense. Word problems are presented in complete sentences, so the answers should be too. This helps students make certain they’re actually answering the question being asked… part of justifying their answer.

Learn more: Multi-Step Word Problems

13. Add rigor to your word problems

strategies in solving math word problems

A smart way to help kids conquer word problems is to, well… give them better problems to conquer. A rich math word problem is accessible and feels real to students, like something that matters. It should allow for different ways to solve it and be open for discussion. A series of problems should be varied, using different operations and situations when possible, and even include multiple steps. Visit both of the links below for excellent tips on adding rigor to your math word problems.

Learn more: The Routty Math Teacher and Alyssa Teaches

14. Use a problem-solving rounds activity.

Word Problems Teacher Trap 3

Put all those word problem strategies and skills together with this whole-class activity. Start by reading the problem as a group and sharing important information. Then, have students work with a partner to plan how they’ll solve it. In round three, kids use those plans to solve the problem individually. Finally, they share their answer and methods with their partner and the class. Be sure to recognize and respect all problem-solving strategies that lead to the correct answer.

Learn more: Teacher Trap

Like these word problem tips and tricks? Learn more about Why It’s Important to Honor All Math Strategies .

Plus, 60+ Awesome Websites For Teaching and Learning Math .

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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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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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strategies in solving math word problems

The Best Word Problem Strategies that Build Strong Mathematicians

The best word problem strategies.

Ah, word problems. They are SO important for our students to understand, yet one of the most challenging parts of math instruction. Word problems are unique in that they are not JUST about math – they require reading comprehension, as well. Therefore, even students who excel at math can often struggle with word problems. As teachers, it can be difficult to know which word problem strategies to teach.

In this post, I am going to share some of the common strategies for teaching word problems and why they are or aren’t effective. I would also highly encourage you to check out this post , where I share ideas for reaching all your students in your word problem instruction.

Math Word Problem Solving Strategies

There are many word problem strategies out there, but some are more effective than others. Let’s take a look at some of the different strategies and whether or not they are beneficial.

Word problem keyword strategies

Teaching Keywords in Word Problem Instruction

Growing up, many of us were probably told that certain words in story problems indicated a specific operation. For example, “more” means addition, “fewer” means subtraction, “each” means multiplication. And while often this is the case, sometimes it is not. For example, take the following problem:

Katie picked 4 apples fewer than Marvin. If Katie picked 12 apples, how many did Marvin pick?

In this problem, the word “fewer” is used. Normally this would indicate subtraction, but if you really look at what the question is asking, you will find that we actually need to add to solve. Because of this, the keyword strategy is not effective.

That being said, I personally believe the words and language used in a problem are still worth noting. The word “fewer” is still significant; the problem lies in assuming it automatically means subtraction. As a teacher, I always taught my students to pay attention to important words, but never taught them that certain words always mean a certain operation.

Instead of using the term “keywords,” I refer to them as “important words” or “context clues”. Because reading comprehension is a major part of solving word problems, we cannot entirely ignore the language used. I do think it’s worth taking the time to encourage students to look for certain words in problems, such as the words listed above. The important thing is that we do not tell them what to do with those words – only that they are important. More on this later, but I thought it was worth noting here.

Using Attack Strategies

Another common strategy for teaching word problems is what’s known as an attack strategy. Attack strategies involve a series of steps (or “plan of attack”) to follow when solving word problems. Common attack strategies include:

  • RDW ( R ead the problem, D raw a model, W rite the equation)
  • CUBES ( C ircle the numbers, U nderline the question, B ox the keywords/context clues, E valuate the problem, S olve & check)
  • RUN ( R ead the problem, U nderline the question, N ame the problem type)
  • FOPS ( F ind the problem, O rganize information with a diagram, P lan to solve the problem, S olve the problem)

Word problem attack strategies

There are many more – these are just a few examples. Attack strategies can certainly be helpful when used correctly. T hey are easy to remember and give students a clear plan for solving. Many attack strategies use fun acronyms like the ones listed above; however even strategies that do not spell out words can still be effective.

These strategies are effective largely because they focus on reading and understanding the problem first, and then solving. As we all know, many students like to simply pull out the numbers and start doing math instead of actually taking the time to read the problem. Attack strategies help solve that issue.

Numberless Word Problems

In 2014, Brian Bushart popularized the idea of removing the numbers from word problems. This is to help students understand what is actually happening in the problem. He details the process in this blog post , which is a GREAT read and I highly recommend checking it out (once you’re done reading this one!).

Numberless word problem strategies

In short, numberless word problems are effective because they cause students to take a step back and really look at what the problem is asking. Eventually, of course, you’ll want to add the numbers back in. But starting out with the numbers removed and engaging in a discussion of what is actually happening in the problem is an effective first step in gaining comprehension.

Schema-Based Instruction

Of all the word problem strategies out there, schema-based instruction is the one with the most research backing it. Schema-based instruction (or SBI) involves categorizing word problems into particular types, or schemas, which will help you determine how to solve the problem.

Schemas can be additive or multiplicative. There are 3 main additive schemas: combine, compare, and change. Combine problems involve putting together two or more numbers to find a total. Compare involves finding the greater set, lesser set, or the difference. In change problems, an amount either increases or decreases over time.

strategies in solving math word problems

Likewise, there are also 3 main multiplicative schemas: equal groups, comparison, and proportions. Equal groups involves a unit or group being multiplied by a specific number to find a product. In comparison problems, a set is multiplied a number of times for a product. The proportions schema focuses on the relationships among quantities.

strategies in solving math word problems

The idea behind schema-based instruction is that all word problems fit into one of these schemas. Each schema has a unique graphic organizer and process for solving a problem that fits that schema. SBI is often accompanied with an attack strategy – such as RUN , for example. Students will first R ead the problem, then U nderline the questions, and finally N ame the problem type (schema) before solving. This last step of identifying the schema will help students understand how to solve the problem.

Part-Part-Whole Instruction

This isn’t really a strategy, per se. But, it is an important concept for students to understand in order to be successful with word problems. Understanding part-part-whole relationships is a critical aspect of number sense. My approach to teaching word problems involves a major emphasis on part-part-whole. Granted – I taught second grade, where word problems were mostly solved by addition and subtraction. Part-part-whole works with multiplication and division, too, but looks a little bit different.

My process for walking students through word problems always included having students identify whether each number represented a part or the whole, and which (a part or the whole) was missing. This was helpful because my students knew that a missing part means subtraction , and a missing whole means addition.

strategies in solving math word problems

Identifying what each number represented is where the “keywords” I mentioned above come in. Words like “more,” “fewer,” and “each” – while they do NOT tell us how to solve – are important context clues to help us decide whether each number given is a part or the whole.

I used the CUBES attack strategy to go with this. However, instead of boxing “keywords,” we boxed “context clues”. Again, those words are still important – they just don’t tell us how to solve. The words are important because they tell us which numbers are greater or less than other numbers, or if a certain number represents a group. All are important things to know in determining the parts and the whole.

Once students identify what each number represents, they are able to solve. I’ve found that students who were correctly able to determine the parts and the whole in a word problem were VERY successful in finding the answer.

strategies in solving math word problems

Free Training for Word Problem Strategies

Want to learn more about how to effectively teach word problems? I’m hosting a FREE video training series that you won’t want to miss! It’s launching THIS MONDAY, 9/21, so make sure you join the waitlist so you don’t miss out. Upon signing up, you will receive my free 30-page e-book for how to differentiate word problem instruction in your classroom. CLICK HERE TO JOIN THE WAITLIST , or sign up using the form below.

How do you teach word problems?

strategies in solving math word problems

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strategies in solving math word problems

This article was incredibly helpful as a whole.

I do have a minor suggestion. Your font for the last graphic titled, “Tools for Teaching Part-Whole Relationships,” has a very confusing layout. I spent far too long trying to figure out what that first one with the abacus said and ended up relying on Google auto-fill. I don’t mind cursive in general, but a cleaner one might cause less confusion for those who homeschool or are looking to help our children in their school math and might not be familiar with that term. Even after Google’s help with auto-fill, I had to really look at that word as written to see how it was laid out in that font.

strategies in solving math word problems

Andrea DeVico

I love your numberless problems and schema strategies. Could you share your e-book with me?

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Math Word Problems: Examples and Solution Strategies

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Do you shudder every time you see a word problem on a test? If so, you may need extra practice - and a little coaching - to better understand how to tackle this type of problem. Read on to find practice word problems for fifth, sixth and seventh grade, as well as solutions, explanations and problem-solving strategies.

Why Do I Have to Solve Word Problems?

If you dislike math word problems, you're not alone. Many students find these problems challenging because they require application of math concepts to real-world situations. Word problems often force you to think about math operations in new ways and to use creative thinking, which may not be your strong suits.

Even though word problems can be hard, they are important for a number of reasons. First, these problems will appear on almost every standardized math test you take, including college entrance exams. Also, as you get older, you'll likely have to solve word problems as a part of your everyday life. For example, any time you have to figure out which sale item offers the best value, you'll be solving a word problem.

If you don't fully understand word problems, don't hesitate to ask your teacher for help. You can also practice at home on your own or with assistance from your parents.

Problems and Solutions by Grade

Matt and Jan order two pizzas. When they're finished eating, 1/4 of the first pizza remains, as well as 3/6 of the second pizza. How much pizza do they have left?

On a map, the scale is 250 feet = 1 inch. How many inches would be needed to represent 1,700 feet?

After not selling well for five months, an item is marked down by 15%. It initially sold for $22. How much does it cost now?

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Math word problems can be confusing, but there are ways you can help your sixth grader understand them. Read on to learn more about how to best solve math word problems.

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Maneuvering the Middle

Student-Centered Math Lessons

Math Problem Solving Strategies

strategies in solving math word problems

How many times have you been teaching a concept that students are feeling confident in, only for them to completely shut down when faced with a word problem?  For me, the answer is too many to count.  Word problems require problem solving strategies. And more than anything, word problems require decoding, eliminating extra information, and opportunities for students to solve for something that the question is not asking for .  There are so many places for students to make errors! Let’s talk about some problem solving strategies that can help guide and encourage students!

Problem solving strategies are a must teach skill. Today I analyze strategies that I have tried and introduce the strategy I plan to use this school year. | maneuveringthemiddle.com

1. C.U.B.E.S.

C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work.  

  • Why I like it: Gives students a very specific ‘what to do.’
  • Why I don’t like it: With all of the annotating of the problem, I’m not sure that students are actually reading the problem.  None of the steps emphasize reading the problem but maybe that is a given.

strategies in solving math word problems

2. R.U.N.S.

R.U.N.S. stands for read the problem, underline the question, name the problem type, and write a strategy sentence. 

  • Why I like it: Students are forced to think about what type of problem it is (factoring, division, etc) and then come up with a plan to solve it using a strategy sentence.  This is a great strategy to teach when you are tackling various types of problems.
  • Why I don’t like it: Though I love the opportunity for students to write in math, writing a strategy statement for every problem can eat up a lot of time.

strategies in solving math word problems

3. U.P.S. CHECK

U.P.S. Check stands for understand, plan, solve, and check.

  • Why I like it: I love that there is a check step in this problem solving strategy.  Students having to defend the reasonableness of their answer is essential for students’ number sense.
  • Why I don’t like it: It can be a little vague and doesn’t give concrete ‘what to dos.’ Checking that students completed the ‘understand’ step can be hard to see.

Problem solving strategies are a must teach skill. Today I analyze strategies that I have tried and introduce the strategy I plan to use this school year.  | maneuveringthemiddle.com

4. Maneuvering the Middle Strategy AKA K.N.O.W.S.

Here is the strategy that I adopted a few years ago.  It doesn’t have a name yet nor an acronym, (so can it even be considered a strategy…?)

UPDATE: IT DOES HAVE A NAME! Thanks to our lovely readers, Wendi and Natalie!

  • Know: This will help students find the important information.
  • Need to Know: This will force students to reread the question and write down what they are trying to solve for.
  • Organize:   I think this would be a great place for teachers to emphasize drawing a model or picture.
  • Work: Students show their calculations here.
  • Solution: This is where students will ask themselves if the answer is reasonable and whether it answered the question.

Problem solving strategies are a must teach skill. Today I analyze strategies that I have tried and introduce the strategy I plan to use this school year. | maneuveringthemiddle.com

Ideas for Promoting Showing Your Work

  • White boards are a helpful resource that make (extra) writing engaging!
  • Celebrating when students show their work. Create a bulletin board that says ***I showed my work*** with student exemplars.
  • Take a picture that shows your expectation for how work should look and post it on the board like Marissa did here.

Show Work Digitally

Many teachers are facing how to have students show their work or their problem solving strategy when tasked with submitting work online. Platforms like Kami make this possible. Go Formative has a feature where students can use their mouse to “draw” their work. 

If you want to spend your energy teaching student problem solving instead of writing and finding math problems, look no further than our All Access membership . Click the button to learn more. 

strategies in solving math word problems

Students who plan succeed at a higher rate than students who do not plan.   Do you have a go to problem solving strategy that you teach your students? 

Problem solving strategies are a must teach skill. Today I analyze strategies that I have tried and introduce the strategy I plan to use this school year. | maneuveringthemiddle.com

Editor’s Note: Maneuvering the Middle has been publishing blog posts for nearly 8 years! This post was originally published in September of 2017. It has been revamped for relevancy and accuracy.

strategies in solving math word problems

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18 comments.

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October 4, 2017 at 7:55 pm

As a reading specialist, I love your strategy. It’s flexible, “portable” for any problem, and DOES get kids to read and understand the problem by 1) summarizing what they know and 2) asking a question for what they don’t yet know — two key comprehension strategies! How about: “Make a Plan for the Problem”? That’s the core of your rationale for using it, and I bet you’re already saying this all the time in class. Kids will get it even more because it’s a statement, not an acronym to remember. This is coming to my reading class tomorrow with word problems — thank you!

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October 4, 2017 at 8:59 pm

Hi Nora! I have never thought about this as a reading strategy, genius! Please let me know how it goes. I would love to hear more!

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December 15, 2017 at 7:57 am

Hi! I am a middle school teacher in New York state and my district is “gung ho” on CUBES. I completely agree with you that kids are not really reading the problem when using CUBES and only circling and boxing stuff then “doing something” with it without regard for whether or not they are doing the right thing (just a shot in the dark!). I have adopted what I call a “no fear word problems” procedure because several of my students told me they are scared of word problems and I thought, “let’s take the scary out of it then by figuring out how to dissect it and attack it! Our class strategy is nearly identical to your strategy:

1. Pre-Read the problem (do so at your normal reading speed just so you basically know what it says) 2. Active Read: Make a short list of: DK (what I Definitely Know), TK (what I Think I Know and should do), and WK (what I Want to Know– what is the question?) 3. Draw and Solve 4. State the answer in a complete sentence.

This procedure keep kids for “surfacely” reading and just trying something that doesn’t make sense with the context and implications of the word problem. I adapted some of it from Harvey Silver strategies (from Strategic Teacher) and incorporated the “Read-Draw-Write” component of the Eureka Math program. One thing that Harvey Silver says is, “Unlike other problems in math, word problems combine quantitative problem solving with inferential reading, and this combination can bring out the impulsive side in students.” (The Strategic Teacher, page 90, Silver, et al.; 2007). I found that CUBES perpetuates the impulsive side of middle school students, especially when the math seems particularly difficult. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics. So far this method is going really well with my students and they are experiencing higher levels of confidence and greater success in solving.

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October 5, 2017 at 6:27 am

Hi! Another teacher and I came up with a strategy we call RUBY a few years ago. We modeled this very closely after close reading strategies that are language arts department was using, but tailored it to math. R-Read the problem (I tell kids to do this without a pencil in hand otherwise they are tempted to start underlining and circling before they read) U-Underline key words and circle important numbers B-Box the questions (I always have student’s box their answer so we figured this was a way for them to relate the question and answer) Y-You ask yourself: Did you answer the question? Does your answer make sense (mathematically)

I have anchor charts that we have made for classrooms and interactive notebooks if you would like them let me me know….

October 5, 2017 at 9:46 am

Great idea! Thanks so much for sharing with our readers!

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October 8, 2017 at 6:51 pm

LOVE this idea! Will definitely use it this year! Thank you!

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December 18, 2019 at 7:48 am

I would love an anchor chart for RUBY

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October 15, 2017 at 11:05 am

I will definitely use this concept in my Pre-Algebra classes this year; I especially like the graphic organizer to help students organize their thought process in solving the problems too.

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April 20, 2018 at 7:36 am

I love the process you’ve come up with, and think it definitely balances the benefits of simplicity and thoroughness. At the risk of sounding nitpicky, I want to point out that the examples you provide are all ‘processes’ rather than strategies. For the most part, they are all based on the Polya’s, the Hungarian mathematician, 4-step approach to problem solving (Understand/Plan/Solve/Reflect). It’s a process because it defines the steps we take to approach any word problem without getting into the specific mathematical ‘strategy’ we will use to solve it. Step 2 of the process is where they choose the best strategy (guess and check, draw a picture, make a table, etc) for the given problem. We should start by teaching the strategies one at a time by choosing problems that fit that strategy. Eventually, once they have added multiple strategies to their toolkit, we can present them with problems and let them choose the right strategy.

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June 22, 2018 at 12:19 pm

That’s brilliant! Thank you for sharing!

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May 31, 2018 at 12:15 pm

Mrs. Brack is setting up her second Christmas tree. Her tree consists of 30% red and 70% gold ornaments. If there are 40 red ornaments, then how many ornaments are on the tree? What is the answer to this question?

June 22, 2018 at 10:46 am

Whoops! I guess the answer would not result in a whole number (133.333…) Thanks for catching that error.

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July 28, 2018 at 6:53 pm

I used to teach elementary math and now I run my own learning center, and we teach a lot of middle school math. The strategy you outlined sounds a little like the strategy I use, called KFCS (like the fast-food restaurant). K stands for “What do I know,” F stands for “What do I need to Find,” C stands for “Come up with a plan” [which includes 2 parts: the operation (+, -, x, and /) and the problem-solving strategy], and lastly, the S stands for “solve the problem” (which includes all the work that is involved in solving the problem and the answer statement). I find the same struggles with being consistent with modeling clearly all of the parts of the strategy as well, but I’ve found that the more the student practices the strategy, the more intrinsic it becomes for them; of course, it takes a lot more for those students who struggle with understanding word problems. I did create a worksheet to make it easier for the students to follow the steps as well. If you’d like a copy, please let me know, and I will be glad to send it.

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February 3, 2019 at 3:56 pm

This is a supportive and encouraging site. Several of the comments and post are spot on! Especially, the “What I like/don’t like” comparisons.

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March 7, 2019 at 6:59 am

Have you named your unnamed strategy yet? I’ve been using this strategy for years. I think you should call it K.N.O.W.S. K – Know N – Need OW – (Organise) Plan and Work S – Solution

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September 2, 2019 at 11:18 am

Going off of your idea, Natalie, how about the following?

K now N eed to find out O rganize (a plan – may involve a picture, a graphic organizer…) W ork S ee if you’re right (does it make sense, is the math done correctly…)

I love the K & N steps…so much more tangible than just “Read” or even “Understand,” as I’ve been seeing is most common in the processes I’ve been researching. I like separating the “Work” and “See” steps. I feel like just “Solve” May lead to forgetting the checking step.

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March 16, 2020 at 4:44 pm

I’m doing this one. Love it. Thank you!!

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September 17, 2019 at 7:14 am

Hi, I wanted to tell you how amazing and kind you are to share with all of us. I especially like your word problem graphic organizer that you created yourself! I am adopting it this week. We have a meeting with all administrators to discuss algebra. I am going to share with all the people at the meeting.

I had filled out the paperwork for the number line. Is it supposed to go to my email address? Thank you again. I am going to read everything you ahve given to us. Have a wonderful Tuesday!

strategies in solving math word problems

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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.

strategies in solving math 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?

strategies in solving math 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

  • Read more about: ELEMENTARY TEACHING , MATH

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Pivot Learning

Word Problems? No Problem! — Effective Strategies for Solving Math Word Problems

Black girl thinking

Outside of the classroom, much of the math we encounter is in the form of word problems. “I’m having 12 people for Thanksgiving dinner. Each person will eat 1.5 pounds of turkey. How big of a turkey do I need to buy?” Yet, inside the classroom, how to solve word problems can leave students and teachers scratching their heads.

During this on-demand webinar, Dr. Sarah R. Powell will share:

  • Two ineffective word-problem practices and why not to use them
  • The importance of an attack strategy when working through word problems
  • Common word-problem structures that help students see consistency with word-problem solving
  • How to incorporate an attack strategy and a focus on structure in your math instruction

Empower your students with effective strategies that will help them take on word problems with confidence.

Dr. Sarah R. Powell

CORE is a subsidiary of Pivot Learning.

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strategies in solving math word problems

3 Strategies to Conquer Math Word Problems

strategies in solving math 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.

strategies in solving math 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.)

strategies in solving math 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.

strategies in solving math 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.

strategies in solving math 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!

strategies in solving math 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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  • 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

strategies in solving math 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 first-grade students ate some.”

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

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: “Can I pull out any details from this sentence that will help me solve the problem?”

Step 4: Develop a Plan

Here, students think about how to tackle the problem, considering different problem-solving strategies.

Step 5: Solve

For this step, it’s straightforward – students just record their answer.

Recommendations for Success

To help your students master this strategy and become skillful at solving math word problems, I’ve got 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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3 Word Problem Solving Strategies To Improve Word Problem Performance

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!

Word Problem Solving Strategies for elementary students

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?

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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Effective Strategies to Help Students Solve Math Word Problems

word problems

Ah, math word problems – these tricky equations can be the bane of a math teacher’s existence. While difficult for many children to master, math word problems are incredibly important as most of the real world’s math is in the form of a question. For example, “How many gallons of paint do I need to buy if one gallon covers 300 square feet, and my wall is 35 feet long by 8 feet tall?”

The challenging part about teaching word problems is the fact that reading comprehension is a big part of understanding the problem. Even the most mathematically gifted student may have issues solving story problems if their reading skills aren’t up to par. As such, it can be a struggle to find a one-size-fits-all strategy for teaching how to solve math word problems.

Let’s take a look at some of the most effective math problem-solving strategies to help students tackle math word problems.

Make Solving Word Problems a Daily Activity

Problem of the day

One of the best ways to get students accustomed to solving word problems is to have them solve them regularly.

Practice makes perfect, after all, so every time you teach a new skill, present a word problem that encourage your students to use that skill to solve the problem.

You can also give your students a daily word problem to solve at home with time at the beginning of each class to discuss the problem and how they reached their answers.

Teach a Plan of Attack

Cubes

One of the most common strategies for solving word problems is teaching a plan of attack that gives students a step-by-step method for reaching the right answer. There are a lot of attack strategies you can teach, with the most popular being:

  • CUBES – Circle the numbers, Underline the question, Box the keywords, Evaluate the problem, Solve
  • RDW – Read the problem, Draw a model, Write the Equation
  • FOPS – Find the problem, Organize the information, Plan how to solve the problem, Solve the problem
  • RUN – Read the Problem, Underline the question, Name the problem type

Teaching attack strategies for solving math story problems is helpful because it gives students a clear plan to follow to find the answer. It makes them focus on reading and understanding the problem rather than just picking out numbers and trying to solve them.

Of course, there is no one-size-fits-all attack strategy. What works for one student may not work for another. It’s a good idea to give kids a basic plan to follow such as Plan, Solve, Check, which will help them slow down and take their time to solve the problem using whatever attack strategy works best for them.

Visualize the Problem

Visualize the Problem

To help students understand the problem better, encourage them to visualize the words. Have them act out the scenario or draw pictures or diagrams to show what’s happening in the problem. Often, seeing the problem spelled out in this manner helps kids see the problem-solving path better.

Take the Numbers Out of the Equation

Numbers Out of the Equation

Another math problem-solving strategy that works well to help students understand what a word problem is really asking is to take all the numbers out of the equation.

It sounds counter-intuitive, but without numbers to worry about, kids are forced to focus on the words and what they’re saying rather than trying to solve the problem without fully comprehending the task.

This strategy is effective because it encourages reading comprehension, which is vital to solving word problems correctly.

At some point, you’ll need to add the numbers back in to solve the problem, but not until you’re sure your students understand exactly what the problem is asking.

Teach Students to Identify Keywords or Context Clues

math vocab

This strategy is one that teachers either love or hate. Some feel it is an outdated approach to math word problem solving, while others feel it gives students a simple way to make sense of what the problem is saying.

For example, the word “more” usually means to add, while the word “fewer” means to subtract. Another example is the word “each,” which typically means to multiply. The problem with teaching keywords in this manner is that these actions aren’t always the right path for solving the problem.

If you teach your students to look for keywords in word problems, it’s a good idea not to mention that certain words mean certain operations, but rather, that certain words are important clues to how the problem should be solved. Refer to these words as context clues and have your students identify these clues to figure out the right operation for the correct solution.

Psst…shameless plug time! I have a cool chart that works as an English to math translator. This translation wall chart is great for setting up the math sentences and equations required for solving word problems. You can find it at my Teachers Pay Teachers store ! It has bright colors that are hard for your students to miss, especially if you use your chart for wall art.

I also have a bingo game that can students matches word descriptions with math expressions. You can check that out in my i nfinity math creations.com store !

Word Phrase

Ask Students to Justify Their Answers

Justify Your Answer

Teachers have demanded that students show their work for years. As frustrating as it is for students to show their work, it’s a vital part of understanding and solving word problems. The better a student can justify their answer, the more likely they are to get the answer right.

Implement a 4-step process for justifying their work when solving a math word problem.

  • Outline the steps you took to solve the problem
  • Tell what math problem-solving strategies and operations you used
  • Label your work
  • Write a sentence that answers the problem’s question and includes your answer

Your students may question why they need to write their answer in sentence form, but if you think about it, it makes perfect sense. Math word problems are written in sentences, so the answer should be written as such, too. It’s a great way to help students know they are definitely answering the question the word problem is asking.

Solving math word problems can be challenging for students and just as frustrating for teachers, but because much of the real world’s math comes in the form of a question, learning to solve word problems is important.

With these math problem-solving strategies, however, hopefully, both you and your students will solve math word problems much easier and with less intimidation than before.

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Sat / act prep online guides and tips, the complete guide to sat math word problems.

feature_words-1

About 25% of your total SAT Math section will be word problems, meaning you will have to create your own visuals and equations to solve for your answers. Though the actual math topics can vary, SAT word problems share a few commonalities, and we’re here to walk you through how to best solve them.

This post will be your complete guide to SAT Math word problems. We'll cover how to translate word problems into equations and diagrams, the different types of math word problems you’ll see on the test, and how to go about solving your word problems on test day.

Feature Image: Antonio Litterio /Wikimedia

What Are SAT Math Word Problems?

A word problem is any math problem based mostly or entirely on a written description. You will not be provided with an equation, diagram, or graph on a word problem and must instead use your reading skills to translate the words of the question into a workable math problem. Once you do this, you can then solve it.

You will be given word problems on the SAT Math section for a variety of reasons. For one, word problems test your reading comprehension and your ability to visualize information.

Secondly, these types of questions allow test makers to ask questions that'd be impossible to ask with just a diagram or an equation. For instance, if a math question asks you to fit as many small objects into a larger one as is possible, it'd be difficult to demonstrate and ask this with only a diagram.

Translating Math Word Problems Into Equations or Drawings

In order to translate your SAT word problems into actionable math equations you can solve, you’ll need to understand and know how to utilize some key math terms. Whenever you see these words, you can translate them into the proper mathematical action.

For instance, the word "sum" means the value when two or more items are added together. So if you need to find the sum of a and b , you’ll need to set up your equation like this: a+b.

Also, note that many mathematical actions have more than one term attached, which can be used interchangeably.

Here is a chart with all the key terms and symbols you should know for SAT Math word problems:

Now, let's look at these math terms in action using a few official examples:

body_sat_math_sample_question_1

We can solve this problem by translating the information we're given into algebra. We know the individual price of each salad and drink, and the total revenue made from selling 209 salads and drinks combined. So let's write this out in algebraic form.

We'll say that the number of salads sold = S , and the number of drinks sold = D . The problem tells us that 209 salads and drinks have been sold, which we can think of as this:

S + D = 209

Finally, we've been told that a certain number of S and D have been sold and have brought in a total revenue of 836 dollars and 50 cents. We don't know the exact numbers of S and D , but we do know how much each unit costs. Therefore, we can write this equation:

6.50 S + 2 D = 836.5

We now have two equations with the same variables ( S and D ). Since we want to know how many salads were sold, we'll need to solve for D so that we can use this information to solve for S . The first equation tells us what S and D equal when added together, but we can rearrange this to tell us what just D equals in terms of S :

Now, just subtract S from both sides to get what D equals:

D = 209 − S

Finally, plug this expression in for D into our other equation, and then solve for S :

6.50 S + 2(209 − S ) = 836.5

6.50 S + 418 − 2 S = 836.5

6.50 S − 2 S = 418.5

4.5 S = 418.5

The correct answer choice is (B) 93.

body_sat_math_sample_question_2

This word problem asks us to solve for one possible solution (it asks for "a possible amount"), so we know right away that there will be multiple correct answers.

Wyatt can husk at least 12 dozen ears of corn and at most 18 dozen ears of corn per hour. If he husks 72 dozen at a rate of 12 dozen an hour, this is equal to 72 / 12 = 6 hours. You could therefore write 6 as your final answer.

If Wyatt husks 72 dozen at a rate of 18 dozen an hour (the highest rate possible he can do), this comes out to 72 / 18 = 4 hours. You could write 4 as your final answer.

Since the minimum time it takes Wyatt is 4 hours and the maximum time is 6 hours, any number from 4 to 6 would be correct.

body_Latin

Though the hardest SAT word problems might look like Latin to you right now, practice and study will soon have you translating them into workable questions.

Typical SAT Word Problems

Word problems on the SAT can be grouped into three major categories:

  • Word problems for which you must simply set up an equation
  • Word problems for which you must solve for a specific value
  • Word problems for which you must define the meaning of a value or variable

Below, we look at each world problem type and give you examples.

Word Problem Type 1: Setting Up an Equation

This is a fairly uncommon type of SAT word problem, but you’ll generally see it at least once on the Math section. You'll also most likely see it first on the section.

For these problems, you must use the information you’re given and then set up the equation. No need to solve for the missing variable—this is as far as you need to go.

Almost always, you’ll see this type of question in the first four questions on the SAT Math section, meaning that the College Board consider these questions easy. This is due to the fact that you only have to provide the setup and not the execution.

body_sat_math_sample_question_3

To solve this problem, we'll need to know both Armand's and Tyrone's situations, so let's look at them separately:

Armand: Armand sent m text messages each hour for 5 hours, so we can write this as 5m —the number of texts he sent per hour multiplied by the total number of hours he texted.

Tyrone: Tyrone sent p text messages each hour for 4 hours, so we can write this as 4 p —the number of texts he sent per hour multiplied by the total number of hours he texted.

We now know that Armand's situation can be written algebraically as 5m , and Tyrone's can be written as 4 p . Since we're being asked for the expression that represents the total number of texts sent by Armand and Tyrone, we must add together the two expressions:

The correct answer is choice (C) 5m + 4 p

Word Problem Type 2: Solving for a Missing Value

The vast majority of SAT Math word problem questions will fall into this category. For these questions, you must both set up your equation and solve for a specific piece of information.

Most (though not all) word problem questions of this type will be scenarios or stories covering all sorts of SAT Math topics , such as averages , single-variable equations , and ratios . You almost always must have a solid understanding of the math topic in question in order to solve the word problem on the topic.

body_sat_math_sample_question_4

Let's try to think about this problem in terms of x . If Type A trees produced 20% more pears than Type B did, we can write this as an expression:

x + 0.2 x = 1.2 x = # of pears produced by Type A

In this equation, x is the number of pears produced by Type B trees. If we add 20% of x (0.2 x ) to x , we get the number of pears produced by Type A trees.

The problem tells us that Type A trees produced a total of 144 pears. Since we know that 1.2 x is equal to the number of pears produced by Type A, we can write the following equation:

1.2 x = 144

Now, all we have to do is divide both sides by 1.2 to find the number of pears produced by Type B trees:

x = 144 / 1.2

The correct answer choice is (B) 120.

You might also get a geometry problem as a word problem, which might or might not be set up with a scenario, too. Geometry questions will be presented as word problems typically because the test makers felt the problem would be too easy to solve had you been given a diagram, or because the problem would be impossible to show with a diagram. (Note that geometry makes up a very small percentage of SAT Math . )

body_SAT_word_problem_5

This is a case of a problem that is difficult to show visually, since x is not a set degree value but rather a value greater than 55; thus, it must be presented as a word problem.

Since we know that x must be an integer degree value greater than 55, let us assign it a value. In this case, let us call x 56°. (Why 56? There are other values x could be, but 56 is guaranteed to work since it's the smallest integer larger than 55. Basically, it's a safe bet!)

Now, because x = 56, the next angle in the triangle—2 x —must measure the following:

Let's make a rough (not to scale) sketch of what we know so far:

body_triangle_ex_1

Now, we know that there are 180° in a triangle , so we can find the value of y by saying this:

y = 180 − 112 − 56

One possible value for y is 12. (Other possible values are 3, 6, and 9. )

Word Problem Type 3: Explaining the Meaning of a Variable or Value

This type of problem will show up at least once. It asks you to define part of an equation provided by the word problem—generally the meaning of a specific variable or number.

body_sat_math_sample_question_6

This question might sound tricky at first, but it's actually quite simple.

We know tha t P is the number of phones Kathy has left to fix, and d is the number of days she has worked in a week. If she's worked 0 days (i.e., if we plug 0 into the equation), here's what we get:

P = 108 − 23(0)

This means that, without working any days of the week, Kathy has 108 phones to repair. The correct answer choice, therefore, is (B) Kathy starts each week with 108 phones to fix.

body_juggle

To help juggle all the various SAT word problems, let's look at the math strategies and tips at our disposal.

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SAT Math Strategies for Word Problems

Though you’ll see word problems on the SAT Math section on a variety of math topics, there are still a few techniques you can apply to solve word problems as a whole.

#1: Draw It Out

Whether your problem is a geometry problem or an algebra problem, sometimes making a quick sketch of the scene can help you understand what exactly you're working with. For instance, let's look at how a picture can help you solve a word problem about a circle (specifically, a pizza):

body_sat_math_sample_question_7_2

If you often have trouble visualizing problems such as these, draw it out. We know that we're dealing with a circle since our focus is a pizza. We also know that the pizza weighs 3 pounds.

Because we'll need to solve the weight of each slice in ounces, let's first convert the total weight of our pizza from pounds into ounces. We're given the conversion (1 pound = 16 ounces), so all we have to do is multiply our 3-pound pizza by 16 to get our answer:

3 * 16 = 48 ounces (for whole pizza)

Now, let's draw a picture. First, the pizza is divided in half (not drawn to scale):

body_sat_math_sample_question_7_diagram_1

We now have two equal-sized pieces. Let's continue drawing. The problem then says that we divide each half into three equal pieces (again, not drawn to scale):

body_sat_math_sample_question_7_diagram_2

This gives us a total of six equal-sized pieces. Since we know the total weight of the pizza is 48 ounces, all we have to do is divide by 6 (the number of pieces) to get the weight (in ounces) per piece of pizza:

48 / 6 = 8 ounces per piece

The correct answer choice is (C) 8.

As for geometry problems, remember that you might get a geometry word problem written as a word problem. In this case, make your own drawing of the scene. Even a rough sketch can help you visualize the math problem and keep all your information in order.

#2: Memorize Key Terms

If you’re not used to translating English words and descriptions into mathematical equations, then SAT word problems might be difficult to wrap your head around at first. Look at the chart we gave you above so you can learn how to translate keywords into their math equivalents. This way, you can understand exactly what a problem is asking you to find and how you’re supposed to find it.

There are free SAT Math questions available online , so memorize your terms and then practice on realistic SAT word problems to make sure you’ve got your definitions down and can apply them to the actual test.

#3: Underline and/or Write Out Important Information

The key to solving a word problem is to bring together all the key pieces of given information and put them in the right places. Make sure you write out all these givens on the diagram you’ve drawn (if the problem calls for a diagram) so that all your moving pieces are in order.

One of the best ways to keep all your pieces straight is to underline your key information in the problem, and then write them out yourself before you set up your equation. So take a moment to perform this step before you zero in on solving the question.

#4: Pay Close Attention to What's Being Asked

It can be infuriating to find yourself solving for the wrong variable or writing in your given values in the wrong places. And yet this is entirely too easy to do when working with math word problems.

Make sure you pay strict attention to exactly what you’re meant to be solving for and exactly what pieces of information go where. Are you looking for the area or the perimeter? The value of x, 2x, or y?

It’s always better to double-check what you’re supposed to find before you start than to realize two minutes down the line that you have to begin solving the problem all over again.

#5: Brush Up on Any Specific Math Topic You Feel Weak In

You're likely to see both a diagram/equation problem and a word problem for almost every SAT Math topic on the test. This is why there are so many different types of word problems and why you’ll need to know the ins and outs of every SAT Math topic in order to be able to solve a word problem about it.

For example, if you don’t know how to find an average given a set of numbers, you certainly won’t know how to solve a word problem that deals with averages!

Understand that solving an SAT Math word problem is a two-step process: it requires you to both understand how word problems work and to understand the math topic in question. If you have any areas of mathematical weakness, now's a good time to brush up on them—or else SAT word problems might be trickier than you were expecting!

body_ready-1

All set? Let's go!

Test Your SAT Math Word Problem Knowledge

Finally, it's time to test your word problem know-how against real SAT Math problems:

Word Problems

1. No Calculator

body_sat_math_test_question_1

2. Calculator OK

body_sat_math_test_question_2

3. Calculator OK

body_sat_math_test_question_3

4. Calculator OK

body_sat_math_test_question_4

Answers: C, B, A, 1160

Answer Explanations

1. For this problem, we have to use the information we're given to set up an equation.

We know that Ken spent x dollars, and Paul spent 1 dollar more than Ken did. Therefore, we can write the following equation for Paul:

Ken and Paul split the bill evenly. This means that we'll have to solve for the total amount of both their sandwiches and then divide it by 2. Since Ken's sandwich cost x dollars and Paul's cost x + 1, here's what our equation looks like when we combine the two expressions:

Now, we can divide this expression by 2 to get the price each person paid:

(2 x + 1) / 2

But we're not finished yet. We know that both Ken and Paul also paid a 20% tip on their bills. As a result, we have to multiply the total cost of one bill by 0.2, and then add this tip to the bill. Algebraically, this looks like this:

( x + 0.5) + 0.2( x + 0.5)

x + 0.5 + 0.2 x + 0.1

1.2 x + 0.6

The correct answer choice is (C) 1.2 x + 0.6

2. You'll have to be familiar with statistics in order to understand what this question is asking.

Since Nick surveyed a random sample of his freshman class, we can say that this sample will accurately reflect the opinion (and thus the same percentages) as the entire freshman class.

Of the 90 freshmen sampled, 25.6% said that they wanted the Fall Festival held in October. All we have to do now is find this percentage of the entire freshmen class (which consists of 225 students) to determine how many total freshmen would prefer an October festival:

225 * 0.256 = 57.6

Since the question is asking "about how many students"—and since we obviously can't have a fraction of a person!—we'll have to round this number to the nearest answer choice available, which is 60, or answer choice (B).

3. This is one of those problems that is asking you to define a value in the equation given. It might look confusing, but don't be scared—it's actually not as difficult as it appears!

First off, we know that t represents the number of seconds passed after an object is launched upward. But what if no time has passed yet? This would mean that t = 0. Here's what happens to the equation when we plug in 0 for t :

h (0) = -16(0)2 + 110(0) + 72

h (0) = 0 + 0 + 72

As we can see, before the object is even launched, it has a height of 72 feet. This means that 72 must represent the initial height, in feet, of the object, or answer choice (A).

4. You might be tempted to draw a diagram for this problem since it's talking about a pool (rectangle), but it's actually quicker to just look at the numbers given and work from there.

We know that the pool currently holds 600 gallons of water and that water has been hosed into it at a rate of 8 gallons a minute for a total of 70 minutes.

To find the amount of water in the pool now, we'll have to first solve for the amount of water added to the pool by hose. We know that 8 gallons were added each minute for 70 minutes, so all we have to do is multiply 8 by 70:

8 * 70 = 560 gallons

This tells us that 560 gallons of water were added to our already-filled, 600-gallon pool. To find the total amount of water, then, we simply add these two numbers together:

560 + 600 = 1160

The correct answer is 1160.

body_sleepy-1

Aaaaaaaaaaand time for a nap.

Key Takeaways: Making Sense of SAT Math Word Problems

Word problems make up a significant portion of the SAT Math section, so it’s a good idea to understand how they work and how to translate the words on the page into a proper expression or equation. But this is still only half the battle.

Though you won’t know how to solve a word problem if you don’t know what a product is or how to draw a right triangle, you also won’t know how to solve a word problem about ratios if you don’t know how ratios work.

Therefore, be sure to learn not only how to approach math word problems as a whole, but also how to narrow your focus on any SAT Math topics you need help with. You can find links to all of our SAT Math topic guides here to help you in your studies.

What’s Next?

Want to brush up on SAT Math topics? Check out our individual math guides to get an overview of each and every topic on SAT Math . From polygons and slopes to probabilities and sequences , we've got you covered!

Running out of time on the SAT Math section? We have the know-how to help you beat the clock and maximize your score .

Been procrastinating on your SAT studying? Learn how you can overcome your desire to procrastinate and make a well-balanced prep plan.

Trying to get a perfect SAT score? Take a look at our guide to getting a perfect 800 on SAT Math , written by a perfect scorer.

Want to improve your SAT score by 160 points?

Check out our best-in-class online SAT prep program . We guarantee your money back if you don't improve your SAT score by 160 points or more.

Our program is entirely online, and it customizes what you study to your strengths and weaknesses . If you liked this Math strategy guide, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next.

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Courtney scored in the 99th percentile on the SAT in high school and went on to graduate from Stanford University with a degree in Cultural and Social Anthropology. She is passionate about bringing education and the tools to succeed to students from all backgrounds and walks of life, as she believes open education is one of the great societal equalizers. She has years of tutoring experience and writes creative works in her free time.

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Home / Blog / Math / 5 Effective Strategies to Solve Math Word Problems for Kids

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5 Effective Strategies to Solve Math Word Problems for Kids

Math word problems can often seem intimidating and confusing for kids. The complexity of the language used, and the presence of unnecessary information can easily throw them off track. However, with the right strategies in place, solving one step word problems can become much easier and more manageable for young kids. 

strategies in solving math word problems

Let’s explore five effective strategies that can help kids approach and solve challenging or easy one step word problems with confidence. These strategies can help them become more comfortable with word problems and develop the skills needed to excel at math.

Table of Contents

5 Effective Ways to Solve Math Word Problems for Kids

To illustrate the below strategies, let’s consider the following word problem:

“Sarah is planning to bake cookies for her friends. She wants to make three different types of cookies: chocolate chip, peanut butter, and oatmeal raisin. Each batch of chocolate chip cookies requires 2 cups of flour, 1 cup of sugar, and 1/2 cup of butter. The recipe for peanut butter cookies calls for 1 1/2 cups of flour, 3/4 cup of sugar, and 1/4 cup of butter. Finally, the oatmeal raisin cookies require 2 1/4 cups of flour, 1 1/4 cups of sugar, and 1/3 cup of butter. If Sarah wants to make a total of 30 cookies, how much of each ingredient does she need?”

strategies in solving math word problems

Practice Restating the Problem

When kids do not understand the question properly, they are unsure which operation (+, −, ×, or ÷ ) to use to answer that question. 

Research suggests that word problems can be better understood by young kids when keywords are identified, the relevant information is gathered, and visual representations are created.

Examples of such keywords are:

  • Addition keywords: “add(ed) to,” “all together,” “combine” 
  • Subtraction keywords: “fewer than,” “remaining,” “take away” 
  • Multiplication keywords: “times,” “every,” “triple” 
  • Division keywords: “per,” “each”

Word problems can be complexly worded or include unnecessary information, confusing kids. It is crucial to pay attention to keywords (hints as to what the problem is requesting you to do) and key information when attempting to identify the right action. 

Teach your little one to restate the problem in their own words, focusing on the essential information and discarding irrelevant details. The practice can help them identify the problem’s core and determine what needs to be fixed.

So, for the above word problem, the restated problem will be:

“Sarah is planning to bake three types of cookies: chocolate chip, peanut butter, and oatmeal raisin. She needs to know how much flour, sugar, and butter she should use to make a total of 30 cookies.”

Visualize or Model the Problem

Help your little ones to visualize word problems by encouraging them to view them as real-life scenarios or stories. This can be achieved through various techniques, such as acting out the problem or creating diagrams, pictures, or models. By visualizing the problem, kids can gain a clear understanding of the situation and can better comprehend the question being asked.

For example:

  • Encourage your little one to imagine themselves in Sarah’s situation. 
  • Ask them to picture themselves in a kitchen surrounded by ingredients and baking tools. 
  • Use physical objects or drawings to represent the ingredients and quantities. 
  • Create a simple diagram or picture to represent the overall baking process. For instance, draw three separate sections, each representing one type of cookie.

Remove the Numbers

In a counterintuitive approach, consider removing the numbers from the word problem initially. This strategy encourages young kids to focus on understanding the problem without being distracted by numerical values. By removing the numbers, they can read the problem more attentively and think critically before proceeding with calculations.

Using this technique, kids can examine the problem more carefully and consider the quantity of the ingredients needed for each kind of cookie. 

This strategy encourages kids:

  • To focus first on recognizing the issue 
  • The connections between various components
  • Then start the calculations.

Try the CUBES Method

The CUBES method is a technique for approaching word problems effectively.

This method helps kids identify key elements so that critical details are not missed by instructing them to: 

C ircle 

U nderline 

E valuate important information

Using the CUBES method, kids can become more attentive and precise in problem-solving.

So the above word problem would be C : Circle the key elements and numbers in the problem.

U : Underline the question being asked, i.e., “How much of each ingredient does Sarah need to make a total of 30 cookies?” B : Box any keywords or action words.

E : Evaluate the information given and plan to solve the problem.

S : Solve the problem using the plan.

Share feedback and reflection

Provide constructive feedback for their attempts at problem-solving and point out their accomplishments and areas for development. Ask them questions like, “How did you come to this conclusion?,” or “What could you do differently next time”. This way, you can encourage self-reflection in them, and kids are able to assess their own thinking skills and come up with better ideas to advance their problem-solving skills.

Math word problems don’t have to be an intimidating challenge; rather, they can be seen as exciting opportunities to apply math concepts and solve real-life challenges. 

By implementing these strategies, you can create a supportive learning environment, empowering kids to approach math word problems with confidence and success. With practice and persistence, they will develop strong problem-solving skills that will serve them well throughout their academic journey and beyond. So let’s equip our young learners with these effective strategies and watch them excel in math.

Boost your child’s ability to solve math word problems with BYJU’S Math Companion . This powerful tool offers personalized support and guidance, ensuring your child becomes a confident math problem solver.They have qualified tutors, personalized learning, 1-on-1 sessions, and a wealth of interactive resources for transformative learning.

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5 Effective Ways to Solve Math Word Problems for Kids

Practice restating the problem.

  • Addition keywords: “add(ed) to,” “all together,” “combine” 
  • Subtraction keywords: “fewer than,” “remaining,” “take away” 
  • Multiplication keywords: “times,” “every,” “triple” 
  • Division keywords: “per,” “each”

Visualize or Model the Problem

  • Encourage your little one to imagine themselves in Sarah’s situation. 
  • Ask them to picture themselves in a kitchen surrounded by ingredients and baking tools. 
  • Use physical objects or drawings to represent the ingredients and quantities. 
  • Create a simple diagram or picture to represent the overall baking process. For instance, draw three separate sections, each representing one type of cookie.

Remove the Numbers

  • To focus first on recognizing the issue 
  • The connections between various components
  • Then start the calculations.

Try the CUBES Method

Share feedback and reflection.

w

  • H. Boonen, A. J., & Jolles, J. (n.d.). COMPREHENSION and VISUALIZATION -Teaching Students to Solve Word Problems | Open Access Journals . COMPREHENSION and VISUALIZATION -Teaching Students to Solve Word Problems | Open Access Journals. https://www.rroij.com/open-access/comprehension–visualization-teaching-students-to-solve-word-problems.php?aid=62476  
  • Lian Wan, C. T., & Abdullah, N. A. (2023, January 2). Using CUBES strategy in a remote setting for primary mathematics word problems | Teo Lian Wan | Jurnal Elemen . Using CUBES Strategy in a Remote Setting for Primary Mathematics Word Problems | Teo Lian Wan | Jurnal Elemen. https://doi.org/10.29408/jel.v9i1.6864  

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SyMETRI: Science & Mathematics Education Teaching Inquiry

Faculty of education math and science research group.

SyMETRI: Science & Mathematics Education Teaching Inquiry

What’s Worth Solving? An Expert Study to Identify Problem-Finding Strategies Within Socio-Scientific Issues

Summary of SyMETRI Meeting: February 12th, 2024 by Qiaochu Xu

Presenter/Guest Speaker: Balraj Rathod from Department of Curriculum and Pedagogy, Faculty of Education, UBC Date: February 12th, 2024 Host: Dr. Cynthia Nicol

In the SyMETRI meeting on February 12th, 2024, PhD student Balraj Rathod presented insights from his work conducted in India at the International Society of the Learning Sciences Annual Meeting 2022.

Balraj’s paper is titled: ‘ What’s Worth Solving? An Expert Study to Identify Problem-Finding Strategies Within Socio-Scientific Issues. ‘ The complexity of socio-scientific issues permeates through society’s social, political, cultural, environmental, and economic fabric. However, the question arises: how do we navigate these intricacies to identify the problems that require action? Balraj explores problem-finding processes through a modeling study wherein three STEM domain experts negotiated the controversial issue of a plastic ban in Mumbai, India. His findings indicate that the strategic use of collaborative argumentation and socio-scientific reasoning competencies can aid in identifying problems worth solving.

Here are some slides from his presentation:

strategies in solving math word problems

Balraj also generously shared his strategies for proceeding from a paper to a conference and ultimately to publication. SyMETRI members actively engaged in the discussion, asking questions regarding his methodology, reasons for choosing the experts in his study, and suggestions for improving the research method. As his doctoral dissertation builds on this work, conversing with the SyMETRI members provided a valuable venue for garnering new ideas.

Balraj Rathod is Ph.D. student in Curriculum Studies focusing on science and environmental education. His research interest is understanding how critical literacies can be extended to foster emancipatory agency for youth climate action in Mumbai, India (i.e., how to go from concern for the environment to action). He uses narrative inquiry and phenomenological approaches to draw the essence of what it means ‘to protect the natural world.’

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  1. 10 Best strategies for solving math word problems in 2024

    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.

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    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

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    Attack strategies involve a series of steps (or "plan of attack") to follow when solving word problems. Common attack strategies include: RDW ( R ead the problem, D raw a model, W rite the equation) CUBES ( C ircle the numbers, U nderline the question, B ox the keywords/context clues, E valuate the problem, S olve & check)

  9. Math Word Problems

    You should begin by making the two fractions equivalent. The denominator for both fractions should be 24 because 6 x 4 = 24. Multiply 1/4 x 6/6, which equals 6/24, and 3/6 x 4/4, which equals 12/24. Then, add the equivalent fractions: 6/24 + 12/24 = 18/24. Don't forget to simplify your answer; in this case, you should divide both the numerator ...

  10. Math Problem Solving Strategies

    1. C.U.B.E.S. C.U.B.E.S stands for circle the important numbers, underline the question, box the words that are keywords, eliminate extra information, and solve by showing work. Why I like it: Gives students a very specific 'what to do.'

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

    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?

  12. Word Problems? No Problem!

    — Effective Strategies for Solving Math Word Problems November 10, 2021 Outside of the classroom, much of the math we encounter is in the form of word problems. "I'm having 12 people for Thanksgiving dinner. Each person will eat 1.5 pounds of turkey. How big of a turkey do I need to buy?"

  13. 3 Strategies to Conquer Math Word Problems

    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!

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    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.

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    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.

  16. Effective Strategies to Help Students Solve Math Word Problems

    There are a lot of attack strategies you can teach, with the most popular being: CUBES - Circle the numbers, Underline the question, Box the keywords, Evaluate the problem, Solve. RDW - Read the problem, Draw a model, Write the Equation. FOPS - Find the problem, Organize the information, Plan how to solve the problem, Solve the problem.

  17. PDF Strategies for Problem Solving

    Step 4: Check the Solution. After working through the plan and coming up with a solution, it is important to see first of all if the solution makes sense. Then, if it seems to be reasonable, check to be sure that it is accurate. In other words, do a quick estimate first, and then check to be sure the answer is exact.

  18. The Complete Guide to SAT Math Word Problems

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  22. 5 Effective Strategies to Solve Math Word Problems for Kids

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  23. 5 Effective Strategies to Solve Math Word Problems for Kids

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  24. What's Worth Solving? An Expert Study to Identify Problem-Finding

    Balraj explores problem-finding processes through a modeling study wherein three STEM domain experts negotiated the controversial issue of a plastic ban in Mumbai, India. His findings indicate that the strategic use of collaborative argumentation and socio-scientific reasoning competencies can aid in identifying problems worth solving.