The Problem with Key Words

Key words are taught in math classes around the country. Teachers have anchor charts posted around the room with "helpful" reminders that "in all" means to add and that "left" indicates you should subtract. This method has been reinforced by the overly simple and formulaic story problems (word problems for those of us who are old school) often found in textbooks. We often present the key word approach to problem solving with good intentions. We want our students to know when certain operations should be used, and we think the best way to help them understand is to provide words that are linked to those operations. In theory, this works. In practice, however, we quickly realize there are limitations to the magic of key words.

When students rely on key words, they cease to reason about or understand the situation posed within the story problem. The key word approach encourages children to ignore the meaning and structure of the problem and look for an easy way out. This is why our students end up using the incorrect operations and are inconsistent with their mastery of solving word problems. In short, key words are the bane of my teachering experience.

Let's examine a story problem together.

I had 5 apples in my basket on Monday. On Tuesday I increased the amount of apples so now I have 7 altogether. How many apples did I add on Tuesday?

If the student is using the key-word approach, "increased," "altogether," and "add" would indicate they need to add 5 and 7 together to get 12 apples. The key words here are misleading, and will not help our students understand or solve this problem.

So how do we approach story problems if key words are not the answer? Building models is an excellent alternative! These can be physical models built with manipulatives or graphics that the students draw.

The example to the right is a bar model, and can be created with strips of paper or drawn as it is here. By comparing the part (the 5 apples I have on Monday) to the whole (the 7 apples I now have on Tuesday) I understand I am adding onto 5 until I get to 7.

The example below models the same problem, but uses manipulatives instead. We start with 5 apples, add some amount, and end up with 7 apples. From there, we can determine the number of apples needed to complete the problem.


Both of these methods allow students to start making connections between addition and subtraction and they can start to see how they are the inverses of each other. Both of these examples also help lay the foundation for Algebra later on, and both methods can be extended to help students understand multiplication and division and the relationship they have to one another. This is something that simply using key words does not help our students understand.

Here are some questions that you can use in whole class discussions or have students answer on paper. Similar questions can be used for most problems:

• What is happening in this problem?
• What will the answer tell us?
• Do you think it will be a big number or a small number?
• What operation do you think you'll need to use to solve this problem? Why?

Requiring students to provide an explanation of their process is also important. The explanation can be an illustration or written sentences. If students choose to draw pictures, make sure you have a discussion with them about what makes a good drawing in mathematics: simple is good. While we want to encourage our students to be artistic, we do not want our students to lose sight of the mathematics they are trying to model.

How do you approach teaching word problems in your classroom? What has your experience been with your students using key words?