Getting to the Heart of a Math Word Problem

Consider this math word problem:

Mario and Terrence have both been saving their allowance. Mario has saved $35 and Terrence has saved $52.

What math is the problem asking you to do?  If you said you don’t know, don’t feel bad! Without the question, there is no way to solve the problem, because it’s not really even a problem yet—just a collection of facts. Each of the following questions could be answered using the information given above:

  • How much more money has Terrence saved than Mario?
  • If the boys pool their money to buy a present, how much will they have?
  • If the boys combine their savings and buy a present for $78, how much money will they have left?

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In her book, Building Mathematical Comprehension, Laney Sammons writes that good readers use the structure of texts to make meaning. For example, the structure of a narrative piece is very different from a nonfiction text. She goes on to say:

“Students benefit from knowing about the structure of word problems—considered by some to be a unique genre.”

Sammons describes the structure by outlining three typical parts: the introductory information (beginning), the factual information (middle), and the main idea (end). Look back at the problem at the beginning of this blog post. You see two of the three parts. What’s missing is the main idea…the question…the part that tells the students the problem they need to solve.

I’ve been working with my 3rd Grade intervention group for the past two weeks to help them understand the importance of the question and analyze it for meaning. One strategy I’ve used that has been quite successful is to have students read through the problem once and then actually have them cover up the introductory and factual information and just analyze the question. The truth is, students are often blinded by the numbers. Taking the numbers out of the picture and having students concentrate on the question is a powerful comprehension strategy.

Having students write their own word problems is another way to improve comprehension. I have several easy versions that I like.

You Write the Story

Give students an expression and let them write a word problem that can be solved using the expression. This requires little or no prep as a workstation activity, and you get a lot of bang for your buck. Of course, students need to be familiar with the structure of word problems and you need to model the process of writing a problem before the students try it on their own.

You can differentiate the activity easily by giving students different expressions. For example, you see three different versions of an expression pictured below. Remember that the focus of this particular task is on understanding the structure of math word problems and generating math word problems to match the equation, not the actual computation.

writing math words problems

You can also use diagrams or models, instead of expressions, for You Write the Story. For example, students could write story problems based on the pictured diagram.

writing math word problems

The Answer Is

For this version, give students only the solution as shown in the picture below. This frees students up to use any operations and numbers they are comfortable with (even two-step problems) and will result in a wide range of story problems.

writing math word problems

You Write the Question

Give students just the information part of the word problem, without the question (similar to the way I started this blog post). Let them write a question that can be answered using the information. The problem pictured below comes from the workstations book I coauthored with Laney, but you can easily adapt word problems from textbooks or worksheets for this task.

writing math word problems

These three tasks can be used all year long! If students can write math word problems, they are likely going to be able to solve any word problems that are thrown at them.

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  1. Somewhere online a teacher had a great idea that I use. You give the students a setting, a character from a book, and two numbers and let them create the word problem. They love it!

  2. Great post. We need our kiddos to focus on meaning and the main idea, we can no longer focus on keywords. Thanks!

  3. I am going to implement this as stations this week! I have been having students read each word story problem three times. On the third time, they can pick up their pencils. My kiddos like to rush through them, and it has helped with that.

    1. That is an excellent idea, Niki! It’s a great way to establish the habit of reading carefully. I’m definitely going to use that with my kiddos!

  4. My students had 3 days of benchmarking this week. Day 2 they were done (except a few) and did not want to read (after the reading benchmark) so they started writing word problems on their desks with dryerase markers. I wanted to follow the rules and tell them to stop, but my math teacher brain let them continue and had them write it on paper for later use !!!! They used one the next day for warm up!

    1. It’s so hard to help students understand that faster is not better, Heidi. Anything we can do to slow them down will help!

  5. Great idea, and I love going at word problems from different angles. I would love to see a post on how you have them record their answers and how much work you require them to show. I get so much flack from both parents & students about my requirements, no matter the grade level I teach (I recently changed from 5th/6th grade math to 4th). They have to show their work (or at least the problem(s) they used) and answer in a complete sentence using all the words from the question. What do you require?

    1. This is where I really lean on the Mathematical Practices! Instead of telling students they have to show their work, I build on the idea that “mathematicians communicate their thinking in words and pictures.” I try to help them understand the purpose behind putting their thinking into writing–it’s helps other mathematicians understand their process. As the teacher, I am one of those mathematicians that needs to understand how they solved a problem. I can’t see what’s going on inside their head, so I can’t help them with errors unless they put their thinking into writing.

  6. We try to act out word problems first and then write the word problem from there. Seeing it as a real world situation really fosters comprehension.

  7. I like your idea of having the students cover the facts and just look at the question. I have been frustrated when some students just want to start doing something with the numbers but they haven’t considered the question!

  8. More of a question than a comment: my students see a word problem and almost immediately react with, “I don’t get it!” Any good techniques for helping get past that?

  9. I love the 3 reads strategy from Amy Lucenta and Grace Kelemanik. They have a book, Routines for Reasoning and a website , fosteringmathpractices.com where this strategy is laid out in more detail.

    Essentially, the first read, you try to summarizethe story/ connect in 3-5 words. Second read, you discuss what the question is. In the third read, you find the quantities and relationships between quantities: including implied quantities (such as conversion rates).

  10. To slow my kids down, I block out the numbers when I am projecting a story problem. They can’t rush to write a problem. They really need to make a plan. When they come up with a plan, I show the numbers.

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