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.
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.
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.
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.
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.