Teaching math word problems is, well, a problem. Why? The issue here is that you aren’t teaching students to do a certain thing, you’re teaching them to think a certain way.
This is an infinitely more difficult thing to teach. Without the ability to get inside students’ heads and actually do the thinking for them, you’re left scrambling to help them make sense of real world problems, to get to the bottom of exactly what kind of math they even need to do.
Think about it, if you’re teaching an operation, like addition, there are various strategies you can easily teach. You can explain, demonstrate, provide a set of concrete instructions: do this, then this, then this, plug these numbers in here, input, output. With enough exposure and practice, students will eventually be able to replicate the process to solve most addition problems with decent accuracy. Word problems are not this. There is no formula you can teach to accurately solve word problems. Word problems are a synthesis of background knowledge combined with math skills (and a little bit of fairy dust) applied in a way that makes sense in a real world context. Teaching that to children is like trying to hold a rainbow in your hands. But you are not completely hopeless, dear math teacher. Here are 5 strategies you can employ starting right now to help guide your students to word problem mastery.
Tip #1: Math Talk All. The. Time
Remember, teaching word problems is not teaching students how to do, it's teaching them how to think. They can't hear your thoughts or the thoughts of their classmates (let's hope!), so how can they learn how to think about math? You can help your students develop powerful critical thinking and problem solving skills just by thinking aloud. It's that simple.
Whenever you solve a problem, think out loud. Explain how you are thinking about and making sense of the problem. Provide opportunities for students to share their own thinking aloud and to work with classmates. Encourage them to share their thinking with one another. This is often called "Math Talk" and it does take some practice. Thinking aloud doesn't come naturally to everyone. It can feel a little funny at first. Some thoughts are difficult to put into words. With ample opportunity to practice, you can foster this skill in your math classroom and it is invaluable in building minds that can make sense of word problems.
Let me illustrate this for you. It's "Math Talk" time in your math class. You get your students' attention and write this word problem on the board:
You read the problem aloud and then say, "I'm visualizing this problem like a movie playing in my head. I can see Monica and Diego and they are sitting in a canoe. I see Monica catch 5 fish." You draw 5 fish on the board. "Now they are eating lunch," you continue. "Maybe they brought some sandwiches with them. What happens next?" you ask your class.
"Monica catches 3 more fish," a student volunteers.
"That's right!" you say as you draw 3 more fish. "So how many fish did Monica catch then?" Someone answers: 8 fish. "How did you know that?" you ask the answerer.
"I added the 5 fish from before lunch and the 3 fish after lunch. 5 plus 3 is 8 fish."
"Great! So Monica caught 8 fish." You write Monica - 8 fish on the board. "What about Diego?" you ask. "Did Diego catch any fish?"
"Yes!" students affirm with enthusiastic head nods.
"But how many fish did Diego catch?" you ask. "Does it say how many fish he caught? I don't see any more numbers in this problem," you look truly puzzled and then call on someone.
"It says he caught half as many fish as Monica," a student explains, "so we have to figure out what half of 8 is because Monica caught 8 fish."
On the board you write Deigo - half of 8 fish. You ask students what half of 8 is. You call on a few to explain their thinking: "half of 8 is 4 because 4 + 4 is 8," "half of 8 is 4 because if you divide the 8 into two equal groups, they each have 4," "I looked at 8 fingers and saw that I had 4 and another 4 so half of 8 is 4," etc.
You erase half of 8 fish and write 4 fish next to Diego's name. "Ok great!" you say, "so Monica caught 8 fish and Diego caught 4 fish. But which of those numbers is the answer to this problem? What is the problem asking us to find? Monica? Diego?" you look puzzled again, then call on some students to share their thoughts. You let the students explain that you must add Monica's 8 fish and Diego's 4 fish together to find the answer: 12 fish.
Surprisingly, students LOVE math talk. If this sort of thing is not already part your daily math routine, it should be! You'll be amazed at how much students' critical thinking skills and problem solving abilities grow. It works well with a whole group and even better with a small group.
Tip #2: Make It Concrete
Part of what makes word problems so difficult is that they involve real word scenarios taken completely out of context. If you are in the canoe with Monica and Diego in the example from Tip #1, the answer is a no brainer. There are 12 fish in the canoe at the end of the day. But, alas, you aren't in the canoe. You're in a math classroom staring at a word problem with way more information than you can easily make sense of. I mean, you've only even been reading fluently for like a year! If you can make the theoretical scenarios presented in word problems real for your students, you will greatly increase their comprehension. No, I don't mean take them on a canoe fishing field trip. Instead, encourage them to use math manipulatives and drawings to help conceptualize what is happening in the problems.
It's easy to assume that students know what to do with base ten blocks, unifix cubes, and color tiles but the reality is that most do not. Show them how to use manipulatives to model math problems. Make it fun for some extra brownie points. Grab a bag of Swedish Fish candies and start modeling the fish from the word problem. Here are the 5 fish Monica caught before lunch. Add 3 more to it. Model dividing the 8 fish in half. Add 4 more fish... you get the idea.
Drawing is another invaluable way to make math word problems concrete. Students don't get manipulatives to use on standardized tests but they do get scrap paper. Model how you draw pictures to better understand word problems. Show them tricks for drawing math. I use symbols to represent base ten blocks. A square is a hundred block, a line is a ten, and a dot is a one. Show them efficient ways to draw fraction models. Draw division and multiplication problems, open number lines, area models. There is so much you can do with a pencil and a blank sheet of paper to make math concrete for your students but don't assume they already know how to do this for themselves. Actively teach your students how to use drawings to be better problem solvers by modeling these strategies often.
The best part about this tip is that it's actually pretty fun. I turned concrete modeling into a game I've named named "Mathtionary." Students draw a card to reveal a math fact, fraction, word problem, or geometric figure and have to either draw or model it (with play doh) while their partner tries to guess. It's so much fun no one will suspect they're actually building their conceptual understanding of math! You can find that game here if you want to check it out. My Equivalent Fractions Pizza Swap, Base Ten Block Structuresl, and Area and Perimeter Zoo are a few other ways I've sought to make concrete modeling fun for my students.
Tip #3: Tread Lightly With Key Words
Key words are every teachers go to when it comes to "teaching" word problems because they're the only teachable skill you've got. They're the only way to use rote memorization to kind of sort of teach word problems. But remember, word problems are not memorization. They are thinking not doing. They cannot be taught in this way. That's why my third tip is one you're not going to want to hear: tread lightly with key words.
I won't outright tell you to NOT use key words at all because I do think they have some value. After all, words like altogether, total, and sum do often suggest addition while difference, how many are left, and take away often correctly point students towards subtraction. It's okay to point these words out and have discussions about their meaning and which operations they are often associated with and why. But, do not, for any reason whatsoever, isolate the key words from the context of the problem! Don't just point out the word altogether and say "I don't even need to read the rest of the problem. I see the word altogether so I know this is an addition problem." NOPE. Read the problem, visualize it, concretely model it, talk about the word altogether and why it means you need to add in this particular problem.
I go as far as to scare my poor math students with trick key words. Evil but effective. Take the following problem for example:
If students are taught only to pull out the numbers (7 and 4) and the key word (total) they may assume that this is an addition problem when in fact it is a subtraction problem. Instead, if students are taught to read the problem, visualize what is happening, possibly even model it with manipulatives or draw the birds in the tree, they should realize that birds are actually leaving the tree, not joining. They should then realize that this is a subtraction problem. We have lost birds, not gained them.
Teach them key words, sure, but also teach them to think critically about the context of the problem. Show them trick key words and have discussions about them. Do not pull out numbers and key words and forget to make meaning of the rest!
(If you're a key word fan, you may like this Math Key Words Word Search I created)
Tip #4: Provide Low Stakes Opportunities to Practice
It's so easy to focus on operations and equations in math class and let word problems fall by the wayside. Let's be honest, they're sort of a nightmare for everyone. It's tempting to save yourself the trouble of having to help everyone comprehend and just hand out a worksheet of multiplication facts or problems nicely aligned and set up for the solving. But look at any standardized math test and what will you see? The vast majority of problems are word problems. Don't sugar coat your math class for your own convenience and leave your students completely unprepared for the literal book of word problems they will face on the next standardized test.
Provide ample opportunities for students to read, think about, discuss, and solve word problems during class when the stakes are low. No grades, no test scores, just chances to flex their critical thinking and problem solving skills. Use concrete modeling, think out loud, let them work with partners, provide real world scenarios. Do whatever you have to do to make word problems fun and approachable, not scary. That way, when they face that standardized test, it won't be a total shock. They'll have a bag of tricks to pull from and the critical thinking skills to make sense of those word problems.
Tip #5: Make Word Problems Accessible to All Students
For some students, you can do all of these things and they're still going to have a very hard time mastering word problems. Unfortunately, mastery doesn't just involve critical thinking skills and math strategies, it also requires reading ability, language comprehension, and background knowledge of the objects, customs, and situations included in the problems. You will have students who lack some or all of those requirements either because they have a learning disability and struggle to read fluently, they are an English Language Learner and don't fully comprehend English, or they come from a home life with different customs or limited exposure to the world that hasn't equipped them with the background knowledge to fully understand the context of the problems.
So, what can you do? Provide necessary accommodations as needed to make word problems accessible to these students. That might mean reading word problems aloud to them, including illustrations with the word problem, providing a list of key vocabulary or translating key words for them, and having discussions ahead of time about anything in the problem you anticipate being unfamiliar to compensate for a lack of prior knowledge.
Non-math related handicaps shouldn't keep a student from demonstrating their math ability. Do whatever you can to remove those handicaps, even if that means reaching out to support specialists like EC teachers, speech and language pathologists, and ESL teachers for help. Make it official if you have to. Request the IEP, the 504, whatever it takes to help your students be the best they can be in your class.