The Best Word Problem Strategies
Ah, word problems. They are SO important for our students to understand, yet one of the most challenging parts of math instruction. Word problems are unique in that they are not JUST about math – they require reading comprehension, as well. Therefore, even students who excel at math can often struggle with word problems. As teachers, it can be difficult to know which word problem strategies to teach.
In this post, I am going to share some of the common strategies for teaching word problems and why they are or aren’t effective. I would also highly encourage you to check out this post, where I share ideas for reaching all your students in your word problem instruction.
Math Word Problem Solving Strategies
There are many word problem strategies out there, but some are more effective than others. Let’s take a look at some of the different strategies and whether or not they are beneficial.
Teaching Keywords in Word Problem Instruction
Growing up, many of us were probably told that certain words in story problems indicated a specific operation. For example, “more” means addition, “fewer” means subtraction, “each” means multiplication. And while often this is the case, sometimes it is not. For example, take the following problem:
Katie picked 4 apples fewer than Marvin. If Katie picked 12 apples, how many did Marvin pick?
In this problem, the word “fewer” is used. Normally this would indicate subtraction, but if you really look at what the question is asking, you will find that we actually need to add to solve. Because of this, the keyword strategy is not effective.
That being said, I personally believe the words and language used in a problem are still worth noting. The word “fewer” is still significant; the problem lies in assuming it automatically means subtraction. As a teacher, I always taught my students to pay attention to important words, but never taught them that certain words always mean a certain operation.
Instead of using the term “keywords,” I refer to them as “important words” or “context clues”. Because reading comprehension is a major part of solving word problems, we cannot entirely ignore the language used. I do think it’s worth taking the time to encourage students to look for certain words in problems, such as the words listed above. The important thing is that we do not tell them what to do with those words – only that they are important. More on this later, but I thought it was worth noting here.
Using Attack Strategies
Another common strategy for teaching word problems is what’s known as an attack strategy. Attack strategies involve a series of steps (or “plan of attack”) to follow when solving word problems. Common attack strategies include:
- RDW (Read the problem, Draw a model, Write the equation)
- CUBES (Circle the numbers, Underline the question, Box the keywords/context clues, Evaluate the problem, Solve & check)
- RUN (Read the problem, Underline the question, Name the problem type)
- FOPS (Find the problem, Organize information with a diagram, Plan to solve the problem, Solve the problem)
There are many more – these are just a few examples. Attack strategies can certainly be helpful when used correctly. They are easy to remember and give students a clear plan for solving. Many attack strategies use fun acronyms like the ones listed above; however even strategies that do not spell out words can still be effective.
These strategies are effective largely because they focus on reading and understanding the problem first, and then solving. As we all know, many students like to simply pull out the numbers and start doing math instead of actually taking the time to read the problem. Attack strategies help solve that issue.
Numberless Word Problems
In 2014, Brian Bushart popularized the idea of removing the numbers from word problems. This is to help students understand what is actually happening in the problem. He details the process in this blog post, which is a GREAT read and I highly recommend checking it out (once you’re done reading this one!).
In short, numberless word problems are effective because they cause students to take a step back and really look at what the problem is asking. Eventually, of course, you’ll want to add the numbers back in. But starting out with the numbers removed and engaging in a discussion of what is actually happening in the problem is an effective first step in gaining comprehension.
Of all the word problem strategies out there, schema-based instruction is the one with the most research backing it. Schema-based instruction (or SBI) involves categorizing word problems into particular types, or schemas, which will help you determine how to solve the problem.
Schemas can be additive or multiplicative. There are 3 main additive schemas: combine, compare, and change. Combine problems involve putting together two or more numbers to find a total. Compare involves finding the greater set, lesser set, or the difference. In change problems, an amount either increases or decreases over time.
Likewise, there are also 3 main multiplicative schemas: equal groups, comparison, and proportions. Equal groups involves a unit or group being multiplied by a specific number to find a product. In comparison problems, a set is multiplied a number of times for a product. The proportions schema focuses on the relationships among quantities.
The idea behind schema-based instruction is that all word problems fit into one of these schemas. Each schema has a unique graphic organizer and process for solving a problem that fits that schema. SBI is often accompanied with an attack strategy – such as RUN, for example. Students will first Read the problem, then Underline the questions, and finally Name the problem type (schema) before solving. This last step of identifying the schema will help students understand how to solve the problem.
This isn’t really a strategy, per se. But, it is an important concept for students to understand in order to be successful with word problems. Understanding part-part-whole relationships is a critical aspect of number sense. My approach to teaching word problems involves a major emphasis on part-part-whole. Granted – I taught second grade, where word problems were mostly solved by addition and subtraction. Part-part-whole works with multiplication and division, too, but looks a little bit different.
My process for walking students through word problems always included having students identify whether each number represented a part or the whole, and which (a part or the whole) was missing. This was helpful because my students knew that a missing part means subtraction, and a missing whole means addition.
Identifying what each number represented is where the “keywords” I mentioned above come in. Words like “more,” “fewer,” and “each” – while they do NOT tell us how to solve – are important context clues to help us decide whether each number given is a part or the whole.
I used the CUBES attack strategy to go with this. However, instead of boxing “keywords,” we boxed “context clues”. Again, those words are still important – they just don’t tell us how to solve. The words are important because they tell us which numbers are greater or less than other numbers, or if a certain number represents a group. All are important things to know in determining the parts and the whole.
Once students identify what each number represents, they are able to solve. I’ve found that students who were correctly able to determine the parts and the whole in a word problem were VERY successful in finding the answer.
Free Training for Word Problem Strategies
Want to learn more about how to effectively teach word problems? I’m hosting a FREE video training series that you won’t want to miss! It’s launching THIS MONDAY, 9/21, so make sure you join the waitlist so you don’t miss out. Upon signing up, you will receive my free 30-page e-book for how to differentiate word problem instruction in your classroom. CLICK HERE TO JOIN THE WAITLIST, or sign up using the form below.