Math Word Problems: Your Essential Handbook for Success

Ask any teacher or student what their least favorite thing about math is and more than likely you will hear the response of word problems come up again and again. They are no picnic for parents either! For students staring down a word problem, it can feel like they are being tested on an entirely different skill than the computational skill they just spent days or weeks learning and practicing. Teachers experience their own frustrations around word problems, as they often lack enough classroom time to teach them and even if they magically had more time they don’t have great resources for doing so. 

The Importance of Word Problems in Math

Despite how frustrating word problems can be, make no mistake: they ARE important. The goal of math education is ultimately that a student can understand and apply math in real-world situations. After all, it doesn’t matter if they can add, subtract, multiply and divide when given a computational problem if they can’t also determine when to use each operation when solving problems.

To measure that understanding, assessments turn to word problems. This is true for most unit/chapter tests as well as for standardized tests like the state tests most students take each spring. Makes sense, right? Word problems can present students with all sorts of scenarios that mimic what they might encounter in the real world. I don’t remember the last time someone walked up to me and asked me to solve a math problem on demand (outside of the classroom of course!) but I have solved lots of math problems this week. For example, I used multiplication & division when figuring out how many packages of snacks to purchase for my son’s sports team, factoring in the number of kids, how many snacks/drinks to provide for each one, the number of items in each package and how much money I planned to spend. Now that would make a great word problem!

What might be surprising though is just how heavily word problems are weighted on those standardized tests. Just visit your state’s assessment website and look at the math practice tests or even test questions released from previous years. In fact, in a study conducted at the University of Texas in Austin, 747 high stakes test questions from grades 3, 4, 5, 6, 7 and 8 were analyzed by a team of expert educators and out of those 747 problems, 92% (690 problems) of them were found to be text-based. This is the opposite of how word problem instruction is weighted in most classrooms, as teachers generally spend a majority of instructional time on computational math skills and much less time on word problems. 

Whether we're talking about overall math success or specifically doing well on assessments, word problems are undeniably crucial. Serving as e as a bridge between theoretical knowledge and practical application. they offer students opportunities to demonstrate their problem-solving abilities in diverse real-world scenarios.

Why Are Word Problems Such a Challenge for Students?

So why do so many students struggle with word problems? Even those who otherwise do well in math or say that they love it can become frustrated and give up when confronted with a word problem. The type of thinking word problems require is very different from strictly computational math problems and can quickly become overwhelming for several reasons. 

1. So. Many. Steps. In order to arrive at a correct answer students have to 1) first and foremost read the problem and understand what is being asked, which will sometimes also require them to decode and interpret unfamiliar words, 2) decide what information in the problem is relevant and many times also decide what information is irrelevant, 3) determine how to solve the problem…add, subtract, multiply, divide? Or more than one of those???, and then 4) finally do the math. A mistake on any one of these steps will result in an incorrect answer. 
2. They don’t know where to start. Students are sometimes simply not explicitly taught a strategy for how to work through the steps to successfully solve word problems. Lacking a framework for how to approach them, many students simply freeze. 
3. Ineffective Strategies. When a strategy for solving word problems is implemented in the classroom, more times than not it involves looking for keywords in the problem to determine what operation to use to solve it. This can be somewhat effective in the early elementary years of mathematics, but becomes extremely unreliable in the upper elementary grades and into middle school leaving students feeling even more frustrated and defeated.
4. Not Enough Practice. Like other math skills, students need LOTS of practice solving word problems to become proficient - but are just not getting that practice time as most practice and homework focuses more heavily on computational skills. 
5. Learning Differences. While word problems can be hard for all students, those with learning differences or challenges can face an extra layer of difficulty. Students who struggle with reading, for example, may otherwise do great in math but have trouble with word problems. It is also not uncommon for students with ADHD or who are autistic to experience executive dysfunction, which can negatively impact their planning, organizing and reasoning skills along with their ability to initiate action, identify a problem, or break a problem into smaller steps - ALL of which are required to solve word problems. 

Common Mistakes Students Make when Solving Word Problems

The first step in helping students become better problem solvers is understanding where they go wrong. In order for a student to be successful when solving math word problems, they need to slow down and read the problem while actively comprehending it. The most common mistakes we see students make come down to two main areas: speed and reading comprehension. 

Mistake #1 - They do not read the problem. In a rush to get the work done, sometimes a student will skip over reading the problem entirely! So many times, if the math lesson of the day was an operation such as division, they will just take the numbers out of the problem and divide them.  

Mistake #2 - They perform the wrong operation.  It’s almost impossible for a student to figure out how to solve a problem if they don’t understand the story or scenario that the problem presents. However, many students have been taught to bypass the understanding part of reading the problem by just looking for keywords in word problems, which can lead them to perform the wrong operation. 

Mistake #3 - They make simple computational errors. Speed strikes again! Once a student figures out how to solve the problem, they sometimes get in a hurry and make careless mistakes when actually doing the math. 

Mistake #4 - They stop too soon. It’s not unusual for word problems to require multiple steps in order to arrive at the correct answer. A student might get the first step correct and think they are done - either because they are going too fast or perhaps didn’t understand the problem enough to realize more steps would be needed.

Effective Strategies for Teaching Word Problems

Students need to be taught an efficient strategy to use when solving word problems that they can rely on.  When solving a long division problem or when evaluating an expression using the order of operations, students learn clear, straightforward rules and steps to take to arrive at an answer.  In order to feel confident and be successful in solving word problems, they need to be taught a similar systematic approach. 

Teach an attack strategy.

A word problem attack strategy is a series of steps that students follow to help them stay on track and confidently solve a word problem.  Most attack strategies are a 3-5 letter word that is easy to remember and spell in which each letter of the word stands for a step that students complete in sequential order.  For example, the RUN attack strategy provides simple, actionable steps through an acronym that is both easy to remember and spell: RUN

R - Read and understand the problem

U - Underline and cross out

N - Name the problem type and solve.

Ditch the keywords.

Vocabulary is an essential part of mathematics, especially when it comes to word problems.  It’s important to discuss the meaning of words and phrases like “how many more” and “in all” in the context of the problem they are presented in.  However, teaching that these words and phrases are always linked to a specific operation is a big mistake.  In a study conducted at the University of Texas in Austin, 690 text-based problems released from high stakes tests from grades 3, 4, 5, 6, 7 and 8 were analyzed by a team of expert educators to determine whether or not using a keyword strategy to solve the problem was effective. The study concluded that using a keyword strategy on these test items was effective less than 50% of the time on single step problems and less than 10% of the time on multi-step problems.

Use a schema-based approach.

A word problem’s schema, or type, refers to a classification of the word problem based on the underlying structure of the word problem story. Most word problems students encounter in math can be categorized into 6 different schemas, or types.  Schema based word problem instruction teaches students how to identify a word problem’s type and how to solve each type using a specific corresponding visual organizer or equation. In our FREE Ultimate Guide to Solving Math Word Problems, we break down the 6 most common types of word problems and provide guidance and strategies on how they can be identified and solved.

Model solving word problems with explicit instruction methods. 

Explicit instruction refers to a teaching method in which content is presented in a clear, highly structured and sequential manner. It consists of direct instruction that includes modeling with step-by-step instruction and think-alouds followed by scaffolded guided practice and finally independent practice.  A great way to think of and remember explicit instruction as a teacher is the phrase, “I Do, We Do, You Do.”  When teaching students how to solve word problems it is extremely important to use explicit instruction and be consistent with it. The Iris Center Peabody College Vanderbilt University states that, “Research has indicated that teaching mathematics in this manner is highly effective and can significantly improve a student’s ability to perform mathematical operations as well as to solve word problems.” 

While word problems may often be met with frustration by both students and teachers alike, their significance in math education cannot be overstated.  By acknowledging the challenges posed by word problems and actively addressing them through targeted instruction and practice, educators can empower students to approach these problems with confidence and competence.