problem solving read and analyze the following word problems

Module 9: Multi-Step Linear Equations

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

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

 Approach Word Problems with a Positive Attitude

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

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

Negative thoughts about word problems can be barriers to success.

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

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

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

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

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

Use a Problem-Solving Strategy for Word Problems

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

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

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

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

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

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

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

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

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

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

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

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

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

Step 7. Answer the question with a complete sentence.

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

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

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

Problem-Solving Strategy

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

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

Let’s use this approach with another example.

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

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

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

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

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Strategies for Solving Word Problems – Math

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:

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:

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:

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:

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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Reading Comprehension and Math Word Problems: Enhancing Problem-Solving Skills

Reading comprehension and math word problems are two key components of a solid educational foundation. Many students often face challenges when understanding complex texts and solving word problems. This article explores the relationship between reading comprehension and math word problems and how students can develop efficient strategies to excel in both areas.

Understanding the basics of reading comprehension is crucial for learners, as it equips them with the necessary skills to decipher meaning from age-appropriate texts. Similarly, when solving mathematical word problems, students must utilize their comprehension abilities to interpret and extract relevant information from the problem. By applying reading comprehension strategies to word problems, learners can boost their problem-solving skills and excel in subjects that require textual analysis.

Bridging the gap between reading comprehension and word problem-solving is achievable by equipping students with the right tools and techniques. Students can benefit from learning strategies that can be applied across different subjects, ensuring a well-rounded education. The following sections of the article offer valuable insights into using these strategies and commonly asked questions.

Key Takeaways

Strengthening reading comprehension skills supports success in math word problems.

Application of comprehension strategies improves problem-solving across various subjects.

Learners should focus on versatile techniques for a well-rounded education.

Understanding the Basics of Reading Comprehension

Reading comprehension is a critical skill for all students, as it enables them to grasp the meaning and significance of text. Students can develop their reading comprehension by focusing on accuracy, understanding the context, and applying the acquired information.

In the context of reading comprehension, accuracy refers to the ability of students to read words and sentences correctly. It is essential for students to have a solid foundation in phonics and vocabulary in order to improve their reading accuracy. To achieve this, they can frequently practice reading texts that are appropriate to their level and gradually increase the difficulty as they gain confidence.

The next aspect of reading comprehension is understanding the context in which a text is written. This requires the students to comprehend the meaning of individual words and phrases and their relationships within the text. To enhance their contextual understanding, students should learn to identify the main ideas, supporting details, and implicit information present in a text.

Additionally, students should consciously try to apply the information they have comprehended. This can be achieved by summarizing, discussing, or even responding to questions related to the text. By actively engaging with the material, students are more likely to retain the information and improve their overall reading comprehension.

Providing students with various types of texts, such as fiction, non-fiction, and poetry, can help them enhance their comprehension skills. Exposure to different genres allows them to encounter diverse language styles, themes, and structures, which in turn contributes to the development of their cognitive abilities.

Reading comprehension is an essential skill that not only improves a student’s academic performance but also contributes to their overall development. With continued practice, patience, and effort, students are capable of enhancing their comprehension skills, enabling them to better understand and appreciate the world around them.

Understanding Word Problems

Mathematics in word problems.

Word problems are essential in mathematics, as they present real-life situations where math is required to find a solution. They involve various mathematical operations, such as addition, subtraction, multiplication, and division. Geometry word problems may also include concepts like area, volume, or angle measures. Solving these problems is crucial for developing a deeper understanding of mathematical concepts and enhancing problem-solving skills.

Relevance of Word Problems

Math word problems are highly relevant in daily life as well as in various professions. They help students develop critical thinking and decision-making abilities. In subjects like science, engineering, and finance, mathematical word problems often serve as the foundation for complex problem-solving tasks. Thus, mastering word problems is critical for success in both academic and professional settings.

Challenges in Word Problems

Solving word problems can be challenging for multiple reasons:.

• Language Processing: Students must first understand the problem’s context, which sometimes requires them to process challenging vocabulary or complex sentence structures.
• Identifying Operations: Once the problem is understood, students need to identify the appropriate mathematical operation(s) (add, subtract, multiply, divide) and apply them to the given numbers.
• Working with Fractions: Dividing fractions and solving problems that involve fractions can be particularly tricky for some learners.
• Decoding: Translation of a problem from words to mathematical notation may be an obstacle for certain students.

Despite the challenges, learning to solve mathematical word problems is essential in developing mathematical literacy and problem-solving abilities. By practicing and mastering various types of word problems, students can build confidence in their mathematical skills and apply them in real-life situations.

Strategies to Solve Word Problems Identifying Key Words

To effectively solve mathematical word problems, it is important to identify key words within the text. These words often indicate the operation to perform or provide crucial information for solving the problem. Common key words for addition include sum , total , more , and added to , while subtraction problems often include words like difference , less , fewer , and minus . Multiplication and division problems may contain key words like times , product , divided by , and quotient . Recognizing these words can help guide the problem-solving process.

Problem-Solving Framework

A structured problem-solving framework can aid in approaching these types of problems systematically. Following a simple four-step process can improve students’ ability to find solutions:

• Understand the problem: Read the problem carefully, identifying the key information and unknowns.
• Devise a plan: Determine the appropriate operation(s), using the key words and other contextual clues.
• Implement the plan: Perform the necessary calculations, ensuring accuracy and understanding of each step.
• Review the solution: Check the solution against the original problem statement to ensure it is reasonable and complete.

Applying this framework to each word problem will build confidence and increase success in problem-solving.

Using Visual and Manipulative Resources

Visual representations and manipulatives can be extremely beneficial in helping students understand and solve word problems. For example, using diagrams, tables, or number lines can help visualize the problem, making it easier to identify the necessary steps for solving.

• Diagrams : Sketching simple diagrams can clarify relationships between values and simplify complex problems. Examples include bar models, area models, and Venn diagrams.
• Tables : Organizing data into a table can illustrate patterns, highlight relationships, and streamline calculations.
• Number Lines : Using a number line can help visualize addition, subtraction, multiplication, and division operations, making it easier to grasp the concept of a given problem.

Similarly, manipulatives such as counters, fraction strips, or base-ten blocks can provide a hands-on approach to understanding abstract concepts and visualizing mathematical relationships. Students can physically manipulate these tools to explore, discover, and demonstrate their understanding of the problem-solving process.

In conclusion, using strategic approaches like identifying key words, employing a problem-solving framework, and incorporating visual representations and manipulatives can greatly enhance the ability to tackle complex math word problems, ultimately leading to a more successful and enjoyable learning experience.

Reading Comprehension and Word Problem Solving in Different Subjects

Math and science.

Reading comprehension is crucial in math and science subjects, as it involves understanding complex concepts and word problems. Students must be able to interpret the information given and apply mathematical and scientific principles to solve problems accurately. This involves breaking down the problem into smaller parts, identifying key terms and variables, and selecting the appropriate formulas or methods to use.

• Math: In math, word problems can involve a wide range of topics, such as algebra, geometry, and calculus. Students need to decipher the context, translate it into mathematical expressions, and solve for the desired variables.
• Science: Science subjects like physics, chemistry, and biology also require reading comprehension skills. Students need to understand scientific texts, grasp experiment procedures, and analyze data presented in various formats (tables, graphs, etc.).

Narrative and Social Studies

Reading comprehension and word problem-solving skills are also essential in understanding the context and drawing accurate conclusions in narrative and social studies subjects.

• Narrative: In literature, reading comprehension involves analyzing the plot, characters, and themes, as well as understanding the author’s purpose and perspective. Additionally, it requires deciphering figurative language, symbolism, and other literary devices.
• Social Studies: In subjects like history and geography, students need to read and comprehend texts about different cultures, political systems, and historical events. They may need to analyze primary and secondary sources, compare different perspectives, and evaluate the reliability of the information provided.

Both math/science and narrative/social studies subjects require strong reading comprehension skills to navigate and solve word problems or understand complex concepts successfully. By honing these skills, students can improve their overall academic performance and develop a more comprehensive understanding of various topics across different disciplines.

Application of Reading Comprehension Strategies

Reading comprehension strategies are essential for understanding and solving math word problems. By applying these strategies, students can significantly improve their ability to analyze and solve complex problems.

Firstly, identifying the main idea of a problem helps students focus on the most important information. This involves recognizing the key elements of the given problem and disregarding any unnecessary details. For example, in a problem about calculating the total price of items, the main idea is to find the product of the quantity and the unit price.

Visualizing the problem is another effective strategy. By creating a mental or physical image of the problem, students can better understand the relationships between the different elements involved. This may include drawing a diagram or sketch, or even using physical objects to represent the components of the problem.

Utilizing context clues can help students infer meaning and fill in any gaps in their understanding. Context clues can come in the form of definitions, examples, or descriptions that help to clarify unfamiliar terms or concepts. This is particularly helpful for problems with complex or technical language.

Making connections to prior knowledge or experiences allows students to apply previously learned concepts to new problems. This encourages critical thinking and fosters a deeper understanding of the subject matter. When confronted with a math word problem that uses similar concepts or ideas, students can draw on their past experiences to approach the problem confidently.

Another strategy is asking questions while reading through the problem. This practices active engagement with the text and promotes comprehension. Students should pose questions to themselves, such as “What is the problem asking?” or “What information is necessary for solving this problem?”. By doing so, they are better equipped to identify important information and organize their approach in a logical manner.

 In summary, incorporating reading comprehension strategies into math word problems enables students to better decipher complex problems, recognize important information, and develop critical thinking skills. By mastering these strategies, students are well on their way to becoming confident and proficient problem solvers.

Frequently Asked Questions

What are effective strategies for solving math word problems.

To solve math word problems effectively, try the following strategies:

• Read the problem carefully and identify critical information.
• Visualize the problem by drawing a model or diagram.
• Translate words into mathematical expressions or equations.
• Determine the proper operations to apply.
• Solve the equation step by step, continuously checking for accuracy.
• Verify the solution by plugging it back into the original problem.

How can I improve my child's reading comprehension skills for math?

To help your child enhance their reading comprehension skills in math, consider these approaches:

• Encourage regular reading to develop vocabulary and language skills.
• Discuss word problems, exploring how language and math concepts are connected.
• Practice breaking problems down into smaller, more manageable parts.
• Teach strategies for identifying key words and phrases that signal mathematical operations.
• Provide opportunities to practice problem-solving in a variety of contexts.

What is the impact of reading comprehension on problem-solving in mathematics?

Reading comprehension greatly impacts problem-solving in mathematics, as it enables students to understand and interpret word problems accurately. Strong reading comprehension skills allow students to identify relevant information, choose appropriate strategies, and apply mathematical concepts to arrive at the correct solution.

How can teachers support special education students with word problems?

Teachers can support special education students in tackling math word problems by:

• Providing clear instructions and explanations.
• Using visual aids and manipulatives to represent mathematical concepts.
• Breaking problems down into smaller steps.
• Encouraging students to use personal strategies, such as highlighting keywords or drawing diagrams.
• Offering additional practice opportunities and targeted interventions as needed.

What is the correlation between reading comprehension competence and mathematical problem-solving skills?

There is a strong correlation between reading comprehension competence and mathematical problem-solving skills. Improved reading comprehension fosters better understanding of word problems and the ability to select appropriate strategies to solve them. Consequently, increased proficiency in reading comprehension contributes to enhanced math performance.

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

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• Middle School Math Solutions – Inequalities Calculator Next up in our Getting Started maths solutions series is help with another middle school algebra topic - solving...

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Why do students struggle with math word problems? (And What to Try)

Word problems can be a real challenge for students of all ages. While some learners quickly grasp the concepts and transfer these skills to multi-step word problems, others struggle with even the most straightforward, basic word problems. As teachers, we must understand why this is so to help students succeed.

In this blog post, we'll explore common issues that cause difficulty when solving word problems and potential solutions that can assist learners in becoming more proficient problem-solvers. So, let's dive into what makes word problems so tricky and how you can help your students master them!

How to Help Learners Conquer Word Problems: Common Challenges & Solutions

Problem #1: students have difficulty reading & understanding the problems..

Word problems can be a daunting task for students of all ages. Solving math problems demands students to comprehend mathematical terms and have solid decoding abilities. If either of these skills is lacking, students may need help understanding the meaning behind certain words and phrases.

Considering that only a few sentences can determine the solution to a problem, it is essential to comprehend the language used in word problems. Yet, only  32% of 4th graders are proficient readers, according to the National Assessment of Educational Progress .

The challenge of comprehending the language in word problems is not only difficult for students who struggle with reading but can also be an obstacle for high-achieving math students. Often, these students know how to solve a problem but need help understanding what the problem is asking.

Word problems further complicate matters due to their use of language that's different from how we communicate.

For example, students may read a problem that says, “Sarah is baking a pie for her grandmother's birthday. She needs 7 apples for the recipe. At the store, apples are $2 a piece. If she has $11, will she have enough money to make the pie?”

Students must decode the words and phrases used to understand what the problem is asking them.

Solution: Provide word problems in audio formats & consider how you can incorporate explicit teaching into your math problem-solving routine.

One common strategy for addressing this is to read the problems aloud. Technology can help with this. Recording and storing problems where students can listen to them repeatedly can be helpful. However, you will need to teach your students to use this technology purposefully to help them better understand the word problems they are tackling. Without proper instruction, these recorded problems are no more helpful than reading the problems themselves.

However, this only addresses issues with decoding. It is essential to explain to students the meaning of words and math terms used in questions. A  Problem of the Day format  offers an excellent opportunity to deeply discuss a single problem with students without taking over your entire math lesson.

Explaining these concepts helps students build a stronger foundation for understanding word problems and increases their math comprehension.

Problem #2 :  Students have gaps in vocabulary that would help with math word problems.

Sometimes, story problems require students to have an understanding of math vocabulary. When students don't wholly understand math vocabulary, they struggle to understand what the problems are asking.

This is more than just decoding!

Even if they can read these words, they may need help understanding how to solve the problems. A strong foundation in math vocabulary is integral to any math classroom.

Solution: Explicitly teach and review math vocabulary regularly.

Ensure that students have a strong foundation in math vocabulary by explicitly teaching terms and concepts. This can be done through direct instruction, visual representations, and activities reinforcing the concepts.

Review these terms regularly throughout the year to ensure they stay fresh in students' minds.

Problem #3:  Students lack efficient & effective strategies.

Often, students are taught to use keywords early on. However, as problems become more complex, this quickly becomes an ineffective and inefficient strategy For addressing multi-step word problems.

Research has shown keywords often misdirect students' efforts and derail problem-solving with math word problems.

As a result, many state tests now purposefully include tricky problems designed to fool students who have been taught keywords as a problem-solving strategy.

Solution :  Teach a problem-solving strategy, like CUBES, that helps students break the problem down efficiently.

While keywords are ineffective, giving students a framework for breaking down word problems and identifying the information that CAN help them is a great way to support their problem-solving efforts.

The CUBES strategy (Circle, Underline, Box, Evaluate, Solve) can help older students with math word problems . This strategy helps them break down problems into manageable steps that make sense to them.

Problem #4:  Difficulty mapping out and visualizing the story behind each problem can lead to confusion in solving for an answer.

Another familiar struggle students face when solving word problems is difficulty mapping out and visualizing the story behind each problem. This can lead to confusion in solving for an answer because students may be unable to see how all the pieces fit together. In other words, they don't have a complete understanding of the context of the problem.

Solution:  Give students an active way to create a picture of what the problem is asking them.

Diagrams with labels, breaking the problem into simpler parts, and making a step-by-step plan with math word problems can help students understand the situation. Having them explain the story in their own words helps them clarify what they're trying to solve.

Encourage students who automatically add all the numbers to slow down and process the question with numberless word problems.

A numberless word problem is a story problem that does not include numbers . Instead, students are asked to analyze the problem without numbers before they are given the numbers to solve. This can help students notice patterns in the problem and determine what operations will be necessary for solving it. Adding these types of word problems to your instructional routine can be a great way to help students slow down and focus on understanding the scenario being presented in the problem. 

By providing students with different ways to visualize word problems, we can increase their chances of success and provide meaningful math instruction. Equipping them with the right tools and strategies gives them a better chance of tackling any difficult word problem they may encounter.

Problem #5:  Those with poor numeracy skills are disadvantaged when attempting to solve math word problems.

Computational fluency  is a common buzzword in math circles these days. We often discuss whether students know their math facts. However, math fact fluency becomes even more critical when students dive into more challenging word problems.

According to cognitive load theory, students focusing on rote processes such as basic facts have fewer mental resources left for higher-level thinking and processing.

In other words, the more mental energy it takes to work through the first step of a two-step problem, the less likely the student will have the resources to persist in accurately making it through the rest of the problem.

Solution: Build fact fluency practice into your routine in fun, engaging ways. 

Fact fluency practice doesn't have to be boring, but it is integral to being an effective mathematician. Therefore, finding ways to build it into your math class is essential.

Here are some of my favorite online games that students love:  30+ Awesome Online Games for Math Fact Practice .

Problem #6:  Students lack experience or are only provided with structured word problem practice.

Some curricula only include problems that follow a specific pattern or directly connect to the skill learned in a given lesson. However, formulaic word problems, where students follow a specific set of steps repeatedly, promote complacency.

Students begin to approach every word problem with the same steps. Soon they are grabbing numbers instead of taking the time to comprehend the problem and how best to address it.

Additionally, many word problems require students to apply knowledge from multiple different units to solve the problem. This can be challenging for students still working on mastering previously taught skills. It overwhelms those who have missed chunks of their instruction due to illness or being pulled from instruction.

As a result, these word problems often begin to feel impossible. 

Solution:  Incorporate variety into your problem-solving and allow for productive struggle.

Students need to be provided with an opportunity to approach a variety of different problems across time. They need to see problems that come in various formats. They need uniquely worded problems. This novelty prevents them from sticking with a rote set of strategies. The goal is to get them critically thinking about the problem at hand .

Offering variety builds confidence, competence, and the ability to address any problem they are given. Many students lack confidence in word problems. Varied experience reduces fears and helps students develop a bank of strategies to overcome barriers when complex problems arise.

To help foster independence, you can also support students through the gradual release process. Provide learners with a step-by-step guide to ensure they have completed the problem-solving process's critical steps when you aren't doing problems with them. This can help boost their confidence and reduce the risk of careless mistakes.

I've created a free mini-book for students with guiding questions and steps to help them independently complete word problems.

Get it here.

Building the math problem solver's toolbox

Word problems can be difficult for learners, but with the right strategies and resources, teachers can help their students learn to approach word problems confidently. By providing a variety of word problems that come in various formats and require different steps to solve, teachers can allow their students to develop problem-solving skills and build confidence when addressing any problem they are given.

Don't forget to grab the free problem solver's guide!

I hope you found this post helpful. Problem-solving is an essential skill for learners. Learn more about word problems or check out my Daily Problem Solving for engaging and meaningful word problem practice. 

Powerful online learning at your pace

The 3 Reads Protocol for Solving Word Problems

Raise your hand if you wish your students were more confident and successful in solving word problems. Right, that’s what I thought. And the answer probably doesn’t change much based on your grade level. Face it, word problems are just plain hard!

What DOESN’T WORK

Over the years, very well-intentioned teachers have developed strategies designed to help students solve word problems . Two such strategies that are still quite prevalent are “problem-solving” models and the use of keywords. The idea is that if you follow these steps and look for these keywords, you will be able to solve any word problem. Unfortunately, it’s just not that simple, and despite their widespread use, these strategies are not very effective.

If you look at the CUBES problem-solving model, reading the problem is not even one of the steps! And if you’re thinking,  Well, of course students know to read the problem! you might want to watch this model in action. I have more often than not seen students just literally start circling numbers (and not even the labels that go with the numbers…) without ever having read the problem. And keywords are not reliable either. Some word problems have no keywords, and keywords in multi-step problems end up confusing students because of the mixed messages they send.

So can we just agree that something else is needed and put these “strategies” to rest? Students fail at solving word problems for one reason—they don’t understand what the problem is asking them to do. It’s a comprehension problem, so students need reading comprehension skills.

The 3 Reads Protocol

Let me first say that if you search the Internet for 3 Reads Protocol , you’ll find that there are slightly differing versions. What I’m about to describe is the version that I find to be particularly effective. Regardless of the version, we are reading the problem three different times and each reading has a different focus.

The 3 Reads Protocol is a guided learning experience. Students are presented with the problem in stages, and with each read the teacher asks probing questions. Looking at an example is probably the easiest way to understand the protocol, so let’s dive in.

To begin the 3 Reads Protocol, the teacher presents the students with a problem, and the class reads the problem together. Probably the easiest way to do this is with a PowerPoint or Google Slides file. Notice that with the first read, there are no numbers and no question. We just want the students to understand what the story is about and make a mental picture. Without numbers, students have to focus on the meaning of the words! After reading the problem together, the teacher asks what the story is about and calls on students for responses. Don’t be surprised if the responses are very general at first ( girls, flowers,  etc.). Ask for additional details, if necessary. Ideally, for this problem, you’d like the students to offer the names of the girls and the types of flowers.

For the second read, the problem is again presented to the students, but this time it includes the numbers. Read the problem again whole class. The questions you will ask now are all related to the numbers in the story. Our goal is for the students to understand that it’s not just 10, it’s 10 daisies . Students might also offer relationships—e.g., Natassja picked more daisies than Ayriale.

Finally, with the third read, students are asked to generate questions that could be answered using the information in the problem. Even though the problem looks just like it did for the second read, don’t skip the reading part! Some problems won’t lend themselves to very many different questions. I like to use this problem as an example because many different questions can be generated. Why? Because there are lots of different numbers in the problem. Here’s a sampling of questions that could be asked. I’m sure you can think of many others.

• How many flowers did Ayriale pick?
• How many flowers did Ayriale and Natassja pick?
• Which girl picked more flowers? How many more?
• How many daisies did the girls pick?

That’s the protocol in a nutshell! Once a question or questions have been generated, you can have students go on to solve the problem.

Frequently asked questions

1. When students are solving word problems independently, do I ask them to ignore the numbers and the question?

No! That would be pretty much impossible for them to do. By routinely solving problems using the 3 Reads Protocol with either the whole class or in small groups, you are helping students develop good reading habits that will transfer to their independent work. When they are working independently, the idea is that they will automatically think about the context, identify what the numbers mean within that context, and better understand what the question is asking them to find.

2. Where do I find problems for the 3 Reads Protocol?

I’m sure you can find some that have already been prepared, but it’s super easy to make your own! Just set up a PowerPoint or Google Slides file and format it however you like. Maybe you want a colorful border or a particular font. Use problems that you already have from your resources—textbooks, supplemental books, etc. You’ll need two slides for each problem. On the first slide, type the problem from your resource, leaving out the numbers and the question. On the second slide, add in the numbers. Use a nice big font so students can easily read the problem when projected on your interactive whiteboard. That’s all there is to it!

If you have other questions, add them in the comments below, and I’ll add them to the FAQ. I’d also love to hear how the 3 Reads Protocol is working out in your classroom!

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16 Comments

fantastic thoughts! I LOVE this approach. I’ve used a resource from Lucky Little Learners that is called Numberless Word Problems. This 3 reads protocol will work perfectly with that resource!

Yes! It does include elements of numberless word problems, which I was first introduced to by Brian Bushart .

I appreciate your thoughts on problem solving however the use of CUBES has been totally effective for the past three years with my students who never attempt word problems. You stated that not circling the “labels”, I suppose you mean units connected to the problem. I use this strategy daily and we circle both numbers and units. I’ve made it my own. Let me also reiterate that this strategy works exceptionally well with students who have low reading abilities too. I spend 5 weeks on CUBES and we slowly work our way into the Three Read Protocol which also helps the “non-reader”

Thank you for sharing your experiences! Since you transition to Three Reads, I’m curious why you wouldn’t start with it. I’d also be interested to know what grade level you teach.

I teach both 7th and 8th grade, and many times they have not had any experience with either. CUBEs is embedded with 3-read. I read the question. Students read the questions, we use cubes to understand quantities and the operations ( C and B) used to bring these quantities together. Then we underline the question to provide clarity and to determine what type of answer we are seeking. In our data, we found that our students do not attempt word problems on any formative assessments so we had to start with decreasing student fear of problem-solving and reading. When I used CUBES, I found that many students could answer the question however they had no idea what to do (operations) with the numbers due to a lack of experience,(key operational words) not knowledge ( they always wanted to add). Immediately, students would attempt word problems because CUBES allowed them to pull out what they needed, producing increased math confidence. As we continued with problem-solving, the 3 read protocol was introduced when solving multi-step word problems, student growth was tremendous!

Excellent post!

Thank you! This strategy has so much potential for teaching students to approach word problems in a much more meaningful way!

Hello! This strategy looks great and reaffirms how I’ve been teaching my son to read the problems through as many times as he needs to understand. Now I have the right questions to ask with each reading! Thank you! My question, are there still some strategies to go along with this protocol that you have found to be helpful to use in conjunction i.e. drawing a picture, making a chart, etc. Thanks so much!

I’m so glad this provides you with the missing link! Drawing a picture or diagram is another powerful strategy that goes really well with 3 Reads because it helps students visualize what’s going on in the problem.

Thank you for your post. The Three Read strategy is a gentle reminder of the power of cross-curricular reading strategies; coupling this annotation and graphic organizers will help students develop ways to process and solve simple to more complex multi-step word problems.

I am a math interventionist at an elementary school. We see students K-5 and realize how important it is for us to have a common process/language when it comes to word problems. Looking forward to learning more about this and helping guide our school, thank you!

I absolutely agree about using common language and strategies campus-wide! It’s so much more effective than students having to adjust to their teacher’s language/strategies every new year.

Thank you! I am going to try Three Reads Protocol for the first time next week with my 4th grade students. I am excited. I have had students read word problems all the way through before trying to solve the problem, however, I love the 3 Reads approach and the questions that go with each read. Thank you for breaking it down.

It’s a very powerful strategy! Good luck.

Many of the problems already include the question or questions. When first teaching the strategy, I can take the questions away and then we can compare to see if one of our questions matched the questions posed, but how to do facilitate the strategy when the question is there and you can’t take it away (thinking of assessments).

The idea is that when done regularly, students will develop comprehension skills that will transfer to solving “normal” word problems. They’ll know, for example, that reading it through the first time and ignoring the numbers helps them focus on what’s happening in the problem. You certainly want to help them make that connection, though. You might even show them a normal problem and explicitly model how to use 3 read strategies when the numbers and question are present.

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Guiding Curiosity, Igniting Imagination!

4 Math Word Problem Solving Strategies

5 Strategies to Learn to Solve Math Word Problems

A critical step in math fluency is the ability to solve math word problems. The funny thing about solving math word problems is that it isn’t just about math. Students need to have strong reading skills as well as the growth mindset needed for problem-solving. 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:

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

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. 

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

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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SOLVING WORD PROBLEMS: A VISUAL APPROACH: HOME

Step 1: Identify the given information in the problem.

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

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

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

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

Step 3: Devise a strategy to solve the problem.

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

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

THE STEPS TO SOLVING A WORD PROBLEM

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

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

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

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Ask the asc for help.

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

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

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

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Praxis Core Math

Course: praxis core math   >   unit 1.

• Algebraic properties | Lesson
• Algebraic properties | Worked example
• Solution procedures | Lesson
• Solution procedures | Worked example
• Equivalent expressions | Lesson
• Equivalent expressions | Worked example
• Creating expressions and equations | Lesson
• Creating expressions and equations | Worked example

Algebraic word problems | Lesson

• Algebraic word problems | Worked example
• Linear equations | Lesson
• Linear equations | Worked example
• Quadratic equations | Lesson
• Quadratic equations | Worked example

What are algebraic word problems?

What skills are needed.

• Translating sentences to equations
• Solving linear equations with one variable
• Evaluating algebraic expressions
• Solving problems using Venn diagrams

How do we solve algebraic word problems?

• Define a variable.
• Write an equation using the variable.
• Solve the equation.
• If the variable is not the answer to the word problem, use the variable to calculate the answer.

What's a Venn diagram?

• 7 + 10 − 13 = 4 ‍   brought both food and drinks.
• 7 − 4 = 3 ‍   brought only food.
• 10 − 4 = 6 ‍   brought only drinks.
• Your answer should be
• an integer, like 6 ‍  
• a simplified proper fraction, like 3 / 5 ‍  
• a simplified improper fraction, like 7 / 4 ‍  
• a mixed number, like 1   3 / 4 ‍  
• an exact decimal, like 0.75 ‍  
• a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
• (Choice A)   $ 4 ‍   A $ 4 ‍  
• (Choice B)   $ 5 ‍   B $ 5 ‍  
• (Choice C)   $ 9 ‍   C $ 9 ‍  
• (Choice D)   $ 14 ‍   D $ 14 ‍  
• (Choice E)   $ 20 ‍   E $ 20 ‍  
• (Choice A)   10 ‍   A 10 ‍  
• (Choice B)   12 ‍   B 12 ‍  
• (Choice C)   24 ‍   C 24 ‍  
• (Choice D)   30 ‍   D 30 ‍  
• (Choice E)   32 ‍   E 32 ‍  
• (Choice A)   4 ‍   A 4 ‍  
• (Choice B)   10 ‍   B 10 ‍  
• (Choice C)   14 ‍   C 14 ‍  
• (Choice D)   18 ‍   D 18 ‍  
• (Choice E)   22 ‍   E 22 ‍  

Things to remember

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Word problem situations and the best way to build student confidence

by Jennifer Van Blair | Oct 12, 2022 | Math

A few years ago, my students tanked a word problem situations assessment. When talking with my principal at the time, he said, “If we improve students’ reading abilities, then their word problem understanding will improve also.”

Intrigued by this thought, I looked at the scores on this assessment focusing on at level readers. The assumption is that if students struggle to read, then they will struggle with word problems as well. Before I tell you what the data showed, let’s take a little quiz:

Guess what the data actually showed? Of the students that were at level readers, only 3 of them passed the assessment. 70% of my at level readers had failed the test. So the claim that if we focus on improving reading in order to increase math scores was false from my own personal experience.

What was the problem then? If students could solve the same types of problems when presented to them from a procedural standpoint, but failed when the same type of operation was required in a word problem situation,  the issue was related to the way I was teaching word problems in the first place, not reading comprehension.

How do we teach word problem situations?

My first year teaching, I remember sitting in another teacher’s classroom during a professional development. 

Hanging on the wall was a set of steps for solving word problems. At the time, I thought this was a novel idea, so I snapped a picture so that I could make my own version of it in my classroom. I made it and used it for a few years. Let me tell you right now, word problem situation success DID NOT improve.

Being in the classroom for over 10 years, and being an avid user of Pinterest and Instagram, I found that this model, known as CUBES, was not novel. 

The idea is that we want to make word problems as simple as possible for your students. So, we use a set of repeatable steps and simplify the process. We think our students will be more successful because we have simplified word problem situations. However, circling numbers, boxing keywords, and underlining the question does little for our students. 

Boxing keywords and placing a bulletin board doesn’t improve student success. Neither does a keyword bulletin board. It does lead to a lack of understanding when it comes to solving word problem situations.  It was shown that students who rely on keyword identification strategies, rather than comprehending word problems as the stories that they are, are MORE often incorrect.

Word problems are stories. When we teach reading, we teach our students to identify story elements like characters, setting, and plot. This allows them to check their understanding. We encourage them to visualize the story. The same strategies work with story problems also. Word problem situation instruction needs to be more than just a reduced formula of circle, box, and underline. 

Genres of Word Problem Situations:

Just as stories come in a variety of genres, word problems come in a variety of types. At the elementary level, there are eight different types of word problem situations commonly encountered:

Brain science, specifically cognitive load theory , states that by building familiarity with lower level concepts, more brain power can be devoted to higher level thinking skills. 

Deciding what operations should be used to solve a problem is a higher level thinking skill. A similar study focused on how experts approach new types of physics problems.

The shorthand version of this research showed that experts relied on previous problems they encountered, the associated equations and operations they used to solve those problems, and decided if those same solutions were useful with this new type of problem.

They were MORE accurate than novices at approaching these same problems.. The freshman physics students who lacked the experience with these problem types and the associated equations to solve were MORE often wrong as they relied on keywords to help decide what to do.

As math teachers this means that we need to give our students opportunities to work with word problem situations. They need experiences in solving them. This will broaden their depth of knowledge for future problem solving situations.

Word Problem Situation Sorts:

How do we do this? Word Problem Sorts are a fantastic way to help students develop their understanding of word problem situations. The best part is, you probably have a number of examples of word problems that you can use already at your fingertips. 

You have access to your:

• School adopted curriculum
• Task cards for different word problem situations

My favorite type of word problem sorts are those that involve numberless word problems.

When we remove the numbers from word problems, we are focusing student attention NOT on actually solving the problem, but the context of the situation. Instead of having students solve the problems, asking students to think about what kind of problems these are and classify them accordingly is more meaningful in developing their understanding of word problem situations. 

How do you do a word problem situations sort:

Keep it simple:.

• Decide if you are going to focus on ALL eight types of word problems, or one or two types.
• Deciding to use ALL eight types is a great beginning and end of the year activity. Why? This is a wonderful time to get to know your students, their thoughts, feelings and experiences with word problems. Furthermore, it gives you a baseline of understanding to track student progress over the year.
• Even if you choose one word problem type, within it there are three different types of situations that arise. Take for example ADD TO PROBLEMS . You have the starting amount, the difference, and the RESULT. This means, depending on what information you do or do not have, you can have problems that have the TOTAL (result), the STARTING amount, or that have the DIFFERENCE. In this one problem type, your students will have to discuss if they would need to ADD to find the solution, or subtract.
• Choosing two or three different problem types may be beneficial on a unit about MULTIPLICATION. Situations that call for multiplication include AREA PROBLEMS, ARRAY PROBLEMS, and EQUAL GROUP PROBLEMS. Having students sort problems based on the type of word problem situation is a great way to focus students on context clues when deciding the types of word problems they are working on.

Split students into groups

• In order to increase participation and support learning in a large group setting, having students work in pairs, or triads at the most, gives students more opportunities to engage in the learning process. Quiet students feel more comfortable talking in a small group setting. It is important to consider the equity of experiences and opportunities for students to engage with word problems. Small groups increase access to content, and help reluctant students to participate more.

Give student groups either the SAME set of cards with the same problems, or split situations up among the WHOLE class.

Either of these methods will give students opportunities to discuss, listen to other groups, and discuss whether or not they agree with their classmates.

If you are using a small set of cards with each small group getting one card, display the types of word problems or situations that the class has. For example, you could tell the class that some word problems require one of the four operations, and that there are ONLY 2 of each operation in the entire class. 

Student groups can then make their case for which operation they believe their situation calls for in order to solve and why. With either approach, your students are going to be talking, discussing, and thinking at a higher level during your math block time.

Keep it a mystery

Instead of justifying student responses as correct or incorrect, leave it till the end. Hold out the reveal, allowing for lively debate and drama in your math class. Imagine if there were only two situation cards that called for MULTIPLICATION, but 3 groups claimed that their word problem called for this operation? You have created drama and left students in a state of dilemma, a time of TRUE mathematical growth according to Joan Boaler in her book Mathematical Mindsets .  

To conclude, and to help you get started with a word problem sort, I have a set of 8 word problems for you to try in your classroom.

These problems are NUMBERLESS, so they can be used in any upper elementary classroom. I invite you to try them with your students and focus not on solving these problems, but in sparking lively debate and discussion in your math classroom.

Don’t forget to come back and share in the comments how it went.

Want to learn more? I have created a course on PopPD ALL about word problems. I walk you through my three step approach to building confident word problem solvers. Check it out!

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Upper Elementary Teaching Blog

Solving Word Problems Without Relying on Key Words

One of the toughest things about teaching fifth grade is definitely the word problems. By fifth grade, a lot of students have become so dependent on using key words that they no longer even read for meaning when they’re solving word problems. However, as fifth grade teachers know, key words only take the students so far.

I have read many articles and blog posts that are adamant against teaching key words, but many of them do not offer an alternative. About three years ago, I created a strategy for teaching my students to solve word problems that does not rely on key words, and I want to share it with you today.

What to Teach Instead of Key Words – Teach Situations

I really want my students to understand what the problem is asking them to do. Keeping this in mind, I teach word problems in terms of what the situation of the word problem is versus what key word is in the word problem.

Before I taught this strategy, many of my students read word problems in order to find the key words. They did not read to understand what the problem was really telling them or asking them.

To combat this, I teach them to think of word problems more as situations. When a student looks at a word problem from a situation standpoint, they are reading for meaning and really understanding what operation is required to solve the problem.

Introductory Lesson to Stop Relying on Key Words

To get students to stop relying on key words and think of situations instead, I do an introductory lesson involving four word problems (shown above).

Each of the word problems use the word total . However, the word problems each require a different operation.

When discussing the word problems, we always have a big discussion about how each of the word problems uses total but they are not all adding or even multiplying. This really gets the students to understand that key words alone cannot always be relied upon.

During this lesson, I stress the importance of really understanding the situation that the word problem is describing to figure out which operation to use. A link to download the printable of the four word problems I use will be available at the end of this post.

Solving Word Problems by Focusing on Situations

After teaching the lesson involving the four word problems, I move right into discussing different situations and how those situations can be translated through a word problem.

As a class, we discuss different situations and determine which operation would be used to solve the word problems that involve that situation.

Together, we create an anchor chart of different situations under the operation that would be used to solve the situation. We add to this anchor chart as the year progresses and the students are exposed to more word problems with varying situations (For example: taking part of a part when multiplying fractions).

I use the printable chart above to help me generate a list of situations to discuss with students. Many of the fraction situations I don’t introduce until later on in the year once we start fractions.

Speaking of fractions, when we really start digging into multiplication and division of fractions, I always have to revisit the idea of using situations to help solve word problems versus key words. The fifth grade level fraction word problems are really tricky and many of my students revert back to key words because they are overwhelmed. At this point, I typically give students the printable version of the chart for them to refer to on a daily basis as they solve word problems.

Moving away from key words and having students think about operations in terms of situations instead has made a huge difference in the way my students think about and solve word problems.

When they are solving a tricky word problem, I always remind them to revisit the situation chart and see which situation matches the word problem. This gets them away from relying solely on key words and builds their confidence with word problems. It also helps them be more successful when solving multi-part word problems.  To read more about how I teach multi-part word problems, click here.

Download the FREE Word Problems without Key Words Printables Here!

P.S. If you are in need of word problems, click here to see the sets I have in my TeachersPayTeachers store.

Share the Knowledge!

Reader interactions, 17 comments.

February 10, 2016 at 12:35 pm

This is a great resource! My students are constantly struggling with figuring out which operation to use in a math problem. I will be having my students glue this resource into their notebook for a constant reference. Thank you!

February 10, 2016 at 5:34 pm

Mine struggled until I started doing this, too. It did take some work upfront to remind them to refer to the situation. However, it really does help with their conceptual understanding of word problems once they get used to it. I would love to know how it goes with your students.

February 11, 2016 at 10:21 am

This is just perfectly written and so true. Kids need to know the process and operations not just key words! Thanks for sharing!

February 17, 2016 at 6:48 pm

Do you have more of these type of similarly written different operation problems for sale to use a review on these? I really love this way of teaching!

April 9, 2016 at 1:15 pm

This is fantastic! I’m a high school special education teacher and word problems are nearly impossible for a few of my kids. I think this will help tremendously. Thanks for sharing.

September 22, 2016 at 8:18 am

This is a great approach! We are constatntly trying to find ways to make numeracy an problem solving “real”, considering the situation fits perfectly into our goal. Thank you!

October 1, 2016 at 7:46 pm

Another great one, Jennifer! I am going to try this strategy in my class. I took a course over the summer that stated we should find other methods of teaching students to solve word problems and not solely rely on key words. I aggreed because every year, I have students add numbers that should be multiplied because the problem asked for a total. I have learned overtime that using manipulatives and drawing pictures aid in less errors being made, and the course I took made this apparent. This post and freebie are certainly beneficial. Thank you!

November 27, 2016 at 6:34 am

thank you. In the past, and currently, I try to get them to draw diagrams. This will help them without having to draw, which many resist.

December 12, 2016 at 9:29 pm

Thank you! I find myself “teaching” my son …seems like more than the teacher does. This is very helpful!

March 8, 2017 at 9:48 am

Jennifer, It is so refreshing t see a teacher actually thinking about the learning from their student’s point of view. There is so much that we do in our heads and take for granted. We forget to be explicit in out teaching- opening up our thought processes to students. Great job with this!

July 10, 2018 at 12:12 pm

I agree with other posters – this is such a great strategy. I teach third grade, and I’ve found that some of my students don’t even read the problem, they just look for the numbers and a keyword because they don’t truly understand what to do! I have tried focusing on visualizing the problem and really getting students to picture/imagine what is happening in the problem in order to figure out what operation to use. With this strategy, though, I find that some of my struggling learners still have a really hard time identifying the operation, even when using manipulatives to visualize. Do you have any tips for those students who are really struggling to grasp these problem solving strategies?

December 7, 2018 at 12:34 pm

Hey, is it okay if I adapt your situations for my 6th graders? I want to add determining the amount left to subtraction when taking one amount from another to subtraction and add in the word percent to the situation of finding a part of a whole number and finding a part of a part.

April 24, 2020 at 3:38 pm

This is amazing. Thank you so much for all the help to all of us!

October 27, 2020 at 6:23 pm

I found your resource and will be using it to teach word problem solving to my fourth graders this week. Your resource looks so lovely and the content so valuable. Will be heading to TPT to pick up some of your word problems! Thanks so much.

October 26, 2023 at 12:42 pm

HI! I am trying to download the Free Word Problems without Key Words and I can’t seem to get it to work. I hope to be able to get it. I love the fact that key words are the main idea here. Can you help me to get this resource? Thank you so much!

October 26, 2023 at 1:00 pm

Hi Kimberly, try this direct link: https://jenniferfindley.com/wp-content/uploads/2016/02/Teaching-Word-Problems-with-Situations-Poster.pdf

November 5, 2023 at 9:17 pm

I 100% agree with teaching situations instead of key words. I teach 6th grade math and I teach them to stop and think about what is happening in this situation. The key words may work better in the lower grade but I have found them not to be so helpful in sixth along with the fact that many of the students just grab a key word and go with it.

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I’m Jennifer Findley: a teacher, mother, and avid reader. I believe that with the right resources, mindset, and strategies, all students can achieve at high levels and learn to love learning. My goal is to provide resources and strategies to inspire you and help make this belief a reality for your students.

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Overview of the Problem-Solving Mental Process

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

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

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

Frequently Asked Questions

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

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

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

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

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

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

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

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

2. Defining the Problem

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

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

3. Forming a Strategy

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

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

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

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

4. Organizing Information

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

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

5. Allocating Resources

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

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

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

6. Monitoring Progress

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

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

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

7. Evaluating the Results

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

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

A Word From Verywell​

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

Get Advice From The Verywell Mind Podcast

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

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You can become a better problem solving by:

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

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

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

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

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

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

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

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• Section 3. Defining and Analyzing the Problem

Chapter 17 Sections

• Section 1. An Introduction to the Problem-Solving Process
• Section 2. Thinking Critically
• Section 4. Analyzing Root Causes of Problems: The "But Why?" Technique
• Section 5. Addressing Social Determinants of Health and Development
• Section 6. Generating and Choosing Solutions
• Section 7. Putting Your Solution into Practice
• Main Section

The nature of problems

Clarifying the problem, deciding to solve the problem, analyzing the problem.

We've all had our share of problems - more than enough, if you come right down to it. So it's easy to think that this section, on defining and analyzing the problem, is unnecessary. "I know what the problem is," you think. "I just don't know what to do about it."

Not so fast! A poorly defined problem - or a problem whose nuances you don't completely understand - is much more difficult to solve than a problem you have clearly defined and analyzed. The way a problem is worded and understood has a huge impact on the number, quality, and type of proposed solutions.

In this section, we'll begin with the basics, focusing primarily on four things. First, we'll consider the nature of problems in general, and then, more specifically, on clarifying and defining the problem you are working on. Then, we'll talk about whether or not you really want to solve the problem, or whether you are better off leaving it alone. Finally, we'll talk about how to do an in-depth analysis of the problem.

So, what is a problem? It can be a lot of things. We know in our gut when there is a problem, whether or not we can easily put it into words. Maybe you feel uncomfortable in a given place, but you're not sure why. A problem might be just the feeling that something is wrong and should be corrected. You might feel some sense of distress, or of injustice.

Stated most simply, a problem is the difference between what is , and what might or should be . "No child should go to bed hungry, but one-quarter of all children do in this country," is a clear, potent problem statement. Another example might be, "Communication in our office is not very clear." In this instance, the explanation of "what might or should be" is simply alluded to.

As these problems illustrate, some problems are more serious than others; the problem of child hunger is a much more severe problem than the fact that the new youth center has no exercise equipment, although both are problems that can and should be addressed. Generally, problems that affect groups of people - children, teenage mothers, the mentally ill, the poor - can at least be addressed and in many cases lessened using the process outlined in this Chapter.

Although your organization may have chosen to tackle a seemingly insurmountable problem, the process you will use to solve it is not complex. It does, however, take time, both to formulate and to fully analyze the problem. Most people underestimate the work they need to do here and the time they'll need to spend. But this is the legwork, the foundation on which you'll lay effective solutions. This isn't the time to take shortcuts.

Three basic concepts make up the core of this chapter: clarifying, deciding, and analyzing. Let's look at each in turn.

If you are having a problem-solving meeting, then you already understand that something isn't quite right - or maybe it's bigger than that; you understand that something is very, very wrong. This is your beginning, and of course, it makes most sense to...

• Start with what you know . When group members walk through the door at the beginning of the meeting, what do they think about the situation? There are a variety of different ways to garner this information. People can be asked in advance to write down what they know about the problem. Or the facilitator can lead a brainstorming session to try to bring out the greatest number of ideas. Remember that a good facilitator will draw out everyone's opinions, not only those of the more vocal participants.
• Decide what information is missing . Information is the key to effective decision making. If you are fighting child hunger, do you know which children are hungry? When are they hungry - all the time, or especially at the end of the month, when the money has run out? If that's the case, your problem statement might be, "Children in our community are often hungry at the end of the month because their parents' paychecks are used up too early."

Compare this problem statement on child hunger to the one given in "The nature of problems" above. How might solutions for the two problems be different?

• Facts (15% of the children in our community don't get enough to eat.)
• Inference (A significant percentage of children in our community are probably malnourished/significantly underweight.)
• Speculation (Many of the hungry children probably live in the poorer neighborhoods in town.)
• Opinion (I think the reason children go hungry is because their parents spend all of their money on cigarettes.)

When you are gathering information, you will probably hear all four types of information, and all can be important. Speculation and opinion can be especially important in gauging public opinion. If public opinion on your issue is based on faulty assumptions, part of your solution strategy will probably include some sort of informational campaign.

For example, perhaps your coalition is campaigning against the death penalty, and you find that most people incorrectly believe that the death penalty deters violent crime. As part of your campaign, therefore, you will probably want to make it clear to the public that it simply isn't true.

Where and how do you find this information? It depends on what you want to know. You can review surveys, interviews, the library and the internet.

• Define the problem in terms of needs, and not solutions. If you define the problem in terms of possible solutions, you're closing the door to other, possibly more effective solutions. "Violent crime in our neighborhood is unacceptably high," offers space for many more possible solutions than, "We need more police patrols," or, "More citizens should have guns to protect themselves."
• Define the problem as one everyone shares; avoid assigning blame for the problem. This is particularly important if different people (or groups) with a history of bad relations need to be working together to solve the problem. Teachers may be frustrated with high truancy rates, but blaming students uniquely for problems at school is sure to alienate students from helping to solve the problem.

You can define the problem in several ways; The facilitator can write a problem statement on the board, and everyone can give feedback on it, until the statement has developed into something everyone is pleased with, or you can accept someone else's definition of the problem, or use it as a starting point, modifying it to fit your needs.

After you have defined the problem, ask if everyone understands the terminology being used. Define the key terms of your problem statement, even if you think everyone understands them.

The Hispanic Health Coalition, has come up with the problem statement "Teen pregnancy is a problem in our community." That seems pretty clear, doesn't it? But let's examine the word "community" for a moment. You may have one person who defines community as "the city you live in," a second who defines it as, "this neighborhood" and a third who considers "our community" to mean Hispanics.

At this point, you have already spent a fair amount of time on the problem at hand, and naturally, you want to see it taken care of. Before you go any further, however, it's important to look critically at the problem and decide if you really want to focus your efforts on it. You might decide that right now isn't the best time to try to fix it. Maybe your coalition has been weakened by bad press, and chance of success right now is slim. Or perhaps solving the problem right now would force you to neglect another important agency goal. Or perhaps this problem would be more appropriately handled by another existing agency or organization.

You and your group need to make a conscious choice that you really do want to attack the problem. Many different factors should be a part of your decision. These include:

Importance . In judging the importance of the issue, keep in mind the f easibility . Even if you have decided that the problem really is important, and worth solving, will you be able to solve it, or at least significantly improve the situation? The bottom line: Decide if the good you can do will be worth the effort it takes. Are you the best people to solve the problem? Is someone else better suited to the task?

For example, perhaps your organization is interested in youth issues, and you have recently come to understand that teens aren't participating in community events mostly because they don't know about them. A monthly newsletter, given out at the high schools, could take care of this fairly easily. Unfortunately, you don't have much publishing equipment. You do have an old computer and a desktop printer, and you could type something up, but it's really not your forte. A better solution might be to work to find writing, design and/or printing professionals who would donate their time and/or equipment to create a newsletter that is more exciting, and that students would be more likely to want to read.

Negative impacts . If you do succeed in bringing about the solution you are working on, what are the possible consequences? If you succeed in having safety measures implemented at a local factory, how much will it cost? Where will the factory get that money? Will they cut salaries, or lay off some of their workers?

Even if there are some unwanted results, you may well decide that the benefits outweigh the negatives. As when you're taking medication, you'll put up with the side effects to cure the disease. But be sure you go into the process with your eyes open to the real costs of solving the problem at hand.

Choosing among problems

You might have many obstacles you'd like to see removed. In fact, it's probably a pretty rare community group that doesn't have a laundry list of problems they would like to resolve, given enough time and resources. So how do you decide which to start with?

A simple suggestion might be to list all of the problems you are facing, and whether or not they meet the criteria listed above (importance, feasibility, et cetera). It's hard to assign numerical values for something like this, because for each situation, one of the criteria may strongly outweigh the others. However, just having all of the information in front of the group can help the actual decision making a much easier task.

Now that the group has defined the problem and agreed that they want to work towards a solution, it's time to thoroughly analyze the problem. You started to do this when you gathered information to define the problem, but now, it's time to pay more attention to details and make sure everyone fully understands the problem.

Answer all of the question words.

The facilitator can take group members through a process of understanding every aspect of the problem by answering the "question words" - what, why, who, when, and how much. This process might include the following types of questions:

What is the problem? You already have your problem statement, so this part is more or less done. But it's important to review your work at this point.

Why does the problem exist? There should be agreement among meeting participants as to why the problem exists to begin with. If there isn't, consider trying one of the following techniques.

• The "but why" technique. This simple exercise can be done easily with a large group, or even on your own. Write the problem statement, and ask participants, "Why does this problem exist?" Write down the answer given, and ask, "But why does (the answer) occur?"

"Children often fall asleep in class," But why? "Because they have no energy." But why? "Because they don't eat breakfast." But why?

Continue down the line until participants can comfortably agree on the root cause of the problem . Agreement is essential here; if people don't even agree about the source of the problem, an effective solution may well be out of reach.

• Start with the definition you penned above.
• Draw a line down the center of the paper. Or, if you are working with a large group of people who cannot easily see what you are writing, use two pieces.
• On the top of one sheet/side, write "Restraining Forces."
• On the other sheet/side, write, "Driving Forces."
• Under "Restraining Forces," list all of the reasons you can think of that keep the situation the same; why the status quo is the way it is. As with all brainstorming sessions, this should be a "free for all;" no idea is too "far out" to be suggested and written down.
• In the same manner, under "Driving Forces," list all of the forces that are pushing the situation to change.
• When all of the ideas have been written down, group members can edit them as they see fit and compile a list of the important factors that are causing the situation.

Clearly, these two exercises are meant for different times. The "but why" technique is most effective when the facilitator (or the group as a whole) decides that the problem hasn't been looked at deeply enough and that the group's understanding is somewhat superficial. The force field analysis, on the other hand, can be used when people are worried that important elements of the problem haven't been noticed -- that you're not looking at the whole picture.

Who is causing the problem, and who is affected by it? A simple brainstorming session is an excellent way to determine this.

When did the problem first occur, or when did it become significant? Is this a new problem or an old one? Knowing this can give you added understanding of why the problem is occurring now. Also, the longer a problem has existed, the more entrenched it has become, and the more difficult it will be to solve. People often get used to things the way they are and resist change, even when it's a change for the better.

How much , or to what extent, is this problem occurring? How many people are affected by the problem? How significant is it? Here, you should revisit the questions on importance you looked at when you were defining the problem. This serves as a brief refresher and gives you a complete analysis from which you can work.

If time permits, you might want to summarize your analysis on a single sheet of paper for participants before moving on to generating solutions, the next step in the process. That way, members will have something to refer back to during later stages in the work.

Also, after you have finished this analysis, the facilitator should ask for agreement from the group. Have people's perceptions of the problem changed significantly? At this point, check back and make sure that everyone still wants to work together to solve the problem.

The first step in any effective problem-solving process may be the most important. Take your time to develop a critical definition, and let this definition, and the analysis that follows, guide you through the process. You're now ready to go on to generating and choosing solutions, which are the next steps in the problem-solving process, and the focus of the following section.

Print Resources

Avery, M., Auvine, B., Streibel, B., & Weiss, L. (1981). A handbook for consensus decision making: Building united judgement . Cambridge, MA: Center for Conflict Resolution.

Dale, D., & Mitiguy, N. Planning, for a change: A citizen's guide to creative planning and program development .

Dashiell, K. (1990). Managing meetings for collaboration and consensus . Honolulu, HI: Neighborhood Justice Center of Honolulu, Inc.

Interaction Associates (1987). Facilitator institute . San Francisco, CA: Author.

Lawson, L., Donant, F., & Lawson, J. (1982). Lead on! The complete handbook for group leaders . San Luis Obispo, CA: Impact Publishers.

Meacham, W. (1980). Human development training manual . Austin, TX: Human Development Training.

Morrison, E. (1994). Leadership skills: Developing volunteers for organizational success . Tucson, AZ: Fisher Books.