Let’s talk about word problem strategies. It can be a frustrating topic to teach because it feels more like a comprehension problem than a math problem at times. But here’s the thing, comprehending math situations is a part of math! There are a variety of different strategies you can try if you have students who are butting heads with the idea of word problems
There’s a few typical paths students follow when they are struggling with word problems:
- There’s the number plucker. The number plucker searches for numbers in the problem, plucks them out, and adds them together. The words in the word problem are irrelevant to your number plucker. They are there to pluck and add as quickly as possible.
- The key word hunter. The key word hunter is looking for the keywords they saw hanging on a poster a few years back. Altogether? ADD! Find the difference? SUBTRACT! There is no nuance or attempt at comprehension in the key word hunter’s strategy- they are on a hunt and solve tear!
Am I over simplifying in these descriptions? Surely I am. Are there students who are genuinely trying to comprehend and solve but are falling short? Absolutely. But in each of these descriptions along with the students who are simply struggling to comprehend there is a common thread- students are lacking understanding of the problem.
The strategies in this post are designed to help your students comprehend word problems, understand the action that is taking place and to be able to create a model that will lead to a calculation or solving strategy.
Make It Numberless
A numberless word problem is a story problem that doesn’t (yet) contain numbers. When teaching a sequence of numberless word problems you will start with a problem that contains no numeric information and no question:
- A fruit bowl has apples and bananas.
You will then discuss the information you see with your students. What is this problem about? What are you wondering about the fruit in the bowl? What *could* be the number of apples and bananas?
Slowly, you add more information to the context. Each step of the way you are asking your students “What do we know now? What are we still wondering?” along with other questions to probe their thinking.
- A fruit bowl has 7 apples and also some bananas.
- …. and then…
- A fruit bowl has 7 apples and 5 bananas.
Finally, you introduce the question in full and ask that your students model and/or solve the problem. Because you have front-loaded this exercise with activities and discussion intended to build understanding you will find your students will find more success than they would have if they had been presented the question in isolation.
- A fruit bowl has 7 apples and 5 bananas, how many fruits are in the bowl?
If you would like to read more about this strategy a blog post that goes into greater depth can be found here and a “Getting Started Guide” including question prompts and sample questions can be found here. If you’re ready to dive in, themed numberless word problem sequences can be found here.
Have a Discussion
Outside of numberless word problems, discussion can still be a powerful tool! Drawing your students attention to certain features of a word problem can help them to comprehend the context and to create a plan to model and/or solve.
- Ask who or what the story is about? What is the main subject of the problem?
- Ask what main action is happening to the subject. If the story is about a boy, what is the boy doing? If the story is about a length of ribbon, what is happening with the ribbon?
- Ask about the numbers in the word problem and what they are telling us. If there is a “5” in the story, what is that 5? 5 feet of ribbon? Is that all of the ribbon in the story or part of the ribbon? Is that ribbon being cut into pieces or being sewed to create a longer length?
- Ask about what the question is wondering. If we have 7 apples and 5 bananas in a bowl the problem is solved VERY DIFFERENTLY if we are wondering the total number of fruits vs. if we are finding how many more apples than bananas are in the bowl. Ask your students explicitly “What is this problem wondering?”
This discussion will help your students to comprehend the problem so that they are able to solve in a more meaningful way. What you don’t want to do is to turn this discussion into a procedure!
If you start asking your students to circle who or what the problem is about and underlining the numbers and highlighting the question your students will stop working to comprehend and, instead, will start working to hunt for these pieces of information. In the context of a word problem, a whole is greater than the sum of it’s parts. When we turn comprehending word problems into a hunt for who, what and how many students focus on the parts and miss the bigger picture.
Ask For a Model
If you have read any blog posts here before, you know that I am a fierce advocate for the concrete, representational, abstract approach to math instruction.
In this approach, we take a concept that is abstract like an equation or word problem and make it more visible and approachable for our students.
Shifting the focus from solving word problems to modeling word problems can help to make word problems more visual for your students so that they can have greater success in solving.
Present a word problem to your students and, instead of asking them to immediately solve, ask them to:
- Model the story with counting bears.
- Model the scenario with centimeter cubes.
- Model the story using base ten blocks.
- Draw a picture to illustrate what is happening in the story.
- Draw a number bond that matches the parts in the story.
- Draw a tape diagram that matches the word problem.
Write Your Own Word Problems
A strategy I am very fond of is asking students to write their own word problems to show their understanding of a topic. First, word problem instruction doesn’t need to be “separate from” your other math instruction. You can embed practice within the units you are teaching. Second, in writing your own word problem, students need to attend to the information required to make a problem solvable.
If you have been studying, for example, the part/whole relationship you can ask your students to write a story where two parts are being put together OR a story in which a whole is being taken apart. If you have been studying place value of 2-digit numbers, you could ask your students to write a story where some tens and some ones are being put together.
The best part? After your students write and solve their own problems you can use the strategies above (Make it Numberless, Have a Discussion or Ask for a Model) to solve the problems your students have created themselves. The fact that their classmates have written the problems makes them that much more engaging and will increase the motivation to solve as well!