Tackling Tough Math Word Problems

There’s no doubt that our students are seeing tougher word problems on state math accountability tests. In Texas, our students take the STAAR test, and the current version is much more rigorous than previous tests. Specifically, it includes more problem-solving and process skills. Instead of:

What is the perimeter of the figure shown below?

Now we see:

Figure 2 is a square.  What is the difference between the perimeter of Figure 1 and the perimeter of Figure 2?

That’s a pretty big leap. And what about story (or word) problems? They are harder, too. More multi-step problems.

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Kids need attack skills—strategies that help them know how to tackle challenging problems. Staring at a blank page just won’t do it. Sure, there are plenty of problem-solving strategies—draw a picture, work backward, make a table, and so on—but I think it really comes down to visualizing the math that’s happening in the problem.

That’s why my favorite (and most successful) problem-solving strategy is drawing a model. You and I can picture the story in our heads, which helps us decide what math to do. But that visualization is a skill that develops over time, and our students need support learning how to draw models that show the math behind a situation. The more they draw, the more naturally they’ll begin to create those mental images on their own.

Yep, it’s that CRA connection again! Drawing pictures to visualize the math is the representational part of the process. While drawing a model won’t work for every problem, it’s especially powerful for problems that require students to decide which operation—addition, subtraction, multiplication, or division—to use.

So what does it look like? There are many ways to draw math pictures (or models). Probably the one most people are familiar with is Singapore model drawing. My process is a little less structured than that. Take this problem:

Susan is arranging flower vases for the Volunteer Appreciation Luncheon. She wants to put 4 roses in each of 12 vases. How many roses does she need to buy?

You probably read this and instantly saw multiplication in your head. Not so for a 3rd grader (who is just learning the difference between multiplication and addition) or a 4th or 5th grader who lacks comprehension skills.

In her book Building Mathematical Comprehension, Laney Sammons points out that most story problems follow a predictable structure. The first sentence is usually the setup—it provides the context or setting but often includes no information that actually helps solve the problem. Next comes the information—the important details students need to solve it. That information might be shown in a table, chart, or graph, or it might be embedded in the story itself. Finally, comes the question, which Sammons describes as the main idea of the problem.

The challenge is that by the time students reach the question, many have already decided what math they plan to do. Haven’t you seen that happen? They eagerly solve something—but it’s not the question that was actually asked!

So, in the problem above, the problem solving goes something like this.

• Read the problem all the way through. Write an answer statement from the question.
  How many roses does she need to buy?  She needs to buy ______ roses.

• Now go back and carefully read the first sentence. Susan is arranging flower vases for the Volunteer Appreciation Luncheon. Okay, interesting enough, but this just tells me the setting of the story. No math here.

• Read the next sentence. She wants to put 4 roses in each of 12 vases. Hmmm, what does that look like? Let me draw it. Well, there are 12 vases. Let me draw them (Yes, they look like rectangles. It’s not about creating art, it’s about seeing the math.).

• Okay, that sentence also says that she wants to put 4 roses in each vase. How can I add that to my picture?

• What kind of math does that look like (add, subtract, multiply, divide)? Why?

• Now do the math you see. I see the number 4 twelve times. Hmm, 12 x 4 = 48.

• Put your answer back into the answer statement to check for reasonableness.

  She needs to buy 48 roses.

Trust me on this—teach kids this process and it will build their mathematical thinking and their problem-solving ability. It’s all about breaking the problems down into manageable parts.

Grab a little cheat sheet showing the steps here. It’s sized so students can glue it into their math journal.