Rescuing Middle School Math Students From Keyword Traps

There was a time when I was a big proponent of keywords in the middle school math classroom.

I’m referring to when mathematics assessments primarily focused on computation, and it made sense to tell students that the word “left” implied subtraction. For example: Jaylen had $18. He spent some money and then had $5 left. How much did he spend?

This problem follows familiar patterns; the keyword “left” points students toward subtraction and gives them a place to begin.

But math standards have changed. Students are expected to do more than calculate. They need to read, interpret, justify, and explain. I noticed the switchover when I was teaching integers. The word “left” suddenly had multiple meanings depending on the context. On a horizontal number line, “left” describes a direction. In a math problem about money, “left” describes what remains after someone makes a purchase. The word sounds the same, but the mathematics are completely different.

I still see these issues in my classroom. Students look for keywords instead of reading the whole problem. Another common issue is when they assume that every math problem has only one right answer waiting to be found. Over the years, three simple strategies have helped my students move beyond both of these errors.

The Keyword Trap

The real danger of keywords is not that they are wrong, necessarily. It’s that they look so right. I call these keywords “false friends.” In mathematics, a false friend is a word that looks familiar but is being used differently than a student expects. False friends are pranksters. They trick students into looking at one thing, while the real answer is somewhere else entirely.

Take this example problem: Jaylen saved some money. After spending $14 at the store, he had $9 left. How much did Jaylen save?

The student sees the word “left.” They subtract: 14 minus 9. They write down “$5” with complete confidence, but they’re incorrect. The prankster did its job. The correct answer is $23, because Jaylen ended up with $9 after spending $14. The question is really asking about where Jaylen started. The word “left” describes the remaining amount and has nothing to do with which operation to use.

Reading in a mathematics classroom is a unique experience. The numbers and the words are equally important—they’re part of the same story. A student who scans for a keyword and ignores the situation around it is reading only half of the problem. Math teachers can help students read and analyze the entire problem.

3 Strategies That Help Students

Teach keywords as warnings, not commands. Instead of telling students what a keyword technically means, remind them to consider what’s actually being described in the math problem. When a student sees the word “left,” they shouldn’t immediately jump to the operation that “left” may or may not signal. Encourage them to examine the whole scenario with questions like these:

• “What does ‘left’ suggest here?”
• “Is there money remaining after a transaction?”
• “Is something positioned on a number line?”

The word is the same, but the situation determines the mathematics. To really get your point across, try showing students two problems where the same term requires different operations.

1. Sophia collected 18 cans on Saturday and 24 cans on Sunday. How many cans did she collect in total?
2. A movie ticket costs $12. A family bought 5 tickets. What was the total cost?

Both problems include the word “total,” but that’s where the similarities end. Let students discover that a keyword alone is not enough to solve a math problem. They need to understand the whole problem before choosing an operation.

Use open questions to build mathematical confidence. Open questions have more than one correct answer, which is great: A student can respond based on what they know, submit something completely different from the person sitting next to them, and get it right. I like to toss out confidence-builders such as these:

1. Write an equation in slope-intercept form that has a slope greater than -2 and a y-intercept less than 25.
2. The product of two factors is in the 20s. What could the factors be?

Both questions allow the class to come up with multiple correct answers. The tension in the room drops when students collectively realize there’s no single right answer. When open-ended questions are kept in the mix, students grow more emboldened about solving problems without teacher support. Open questions don’t lower learning expectations—they give students more chances to talk about math, share their reasoning, and learn from one other.

Use targeted tips so students do the thinking. Sometimes a student needs assistance, but not a full lesson. I call this a targeted tip. The student isn’t given the answer—they’re provided a small nudge that allows them to see the next possible step. These are some of my favorite targeted tips:

• “What changed?”
• “Where did you start?”
• “Compare the two ratios.”
• “Is the product positive or negative?”

One student in my seventh-grade class was working on a proportional reasoning problem with ordered pairs. She asked for a third sheet of scrap paper. I watched her treat each pair as an isolated fact rather than part of a relationship. She was looking for a whole-number pattern because a similar problem had produced a pattern. This problem, though, was not cooperating.

I walked over and said three words: “Try to simplify.” Then I walked away. I trusted her to take it from there, and she did. She divided each ratio, found the consistent relationship, and identified the constant of proportionality on her own. “I got it!” she told me.

She didn’t get it because I explained the answer to her. She got it because I gave her direction and trusted her to do the work. When students seem stuck, resist the urge to explain everything. A full explanation might help students finish today’s problem. A targeted tip helps them think through the next one. It keeps the thinking where it belongs: with the student.