“Class, today we’ll work on word problems in math!” cheers Ms. Enthusiastic with a slight jump and rah, rah.

The class is filled with shouts of…

“No!”

“Ugh!”

“I just don’t get this.”

“Ms. E., I think I’m going to puke. Can I go to the nurse?”

“But…, I have a great new poster with key words…” Looking around the class Ms. E. sees heads drop and a few more students clutching their stomachs. Half heartily she continues, “These words will make solving word problems so much easier.”

Have you ever felt like Ms. E? I know I have. I’ve tried anything and everything to make problem solving easier for my students. I remember spending hours looking for the just right key word poster for problem solving. I knew if I could find just the right one, all my problem solving woes would be solved.

Well, they weren’t. In fact, in many ways my students became worse problems solvers then before. Here’s why I say, “No to key words for problem solving.” (Well at least some of the time.)

#### Altogether, Total and In All

These are common key words we use to signal students that it is time to add. Let’s look at two examples to see why they don’t always work.

###### Sam has 2 cars. He buys 5 more cars. How many cars does he have in all?

**Cars Sam Has**

**Cars Sam Buys**

Students see the key words in all. They think, “In all means to add, so I’ll add, 2 + 5 = 7.”

In this case the students have use the correct operation and find the correct answer. However, they probably didn’t think about the problem other than to look for the key words in all.

##### Here’s a similar word problem with the same key words.

###### Sam has 2 boxes. He puts 5 toy cars in each box. How many cards does he have in all?

**Box 1**

**Box 2**

Students who look just for keys words see in all and write, 2 + 5 = 7.

This is an incorrect answer.

Students are looking for the keys words instead of making sense of or visualizing the problem. When students seek to understand the problem instead of just looking for key words, they write a correct equation which in this case could be one of the following:

2 + 2 + 2 + 2 + 2 = 10

5 + 5 = 10

2 × 5 = 10

5 × 2 = 10

All of these equations would be considered correct and demonstrate an understanding of the word problem.

A question for a later discussion, is which of these equation if any are more correct than the other.

#### Each and Equal Groups

These key words apply to both multiplication and division. Let’s look at a couple of examples.

###### Beth has 5 boxes. She puts 2 toy cars in each basket. How many cars does she have?

Students who have been taught that each means division or multiplication might try the following.

**Might write **

5 ÷ 2 = What?

They might draw or visualize the picture below.

**Box 1**

**Box 2**

**Box 3**

Hold, it! I don’t have anymore cars.

**Box 4**

Now what do I do?

**Box 5**

I think I need to go to the restroom. Yeah, that’s what I should do.

As you can see the picture and the equation don’t match. So in the students’ mind the problem is well…going to the restroom might just be the best way to deal with the problem for them.

Without understanding the problem, students generally go automatically to multiplication. They didn’t move to multiplication because it is the correct operation but because division here just doesn’t make sense to them. Or division is too hard.

To understand this problem, students have to move beyond the key word/s and visualize or draw what is happening in the problem. In this case, it would be 5 boxes with 2 cards in each box. Like this.

**Box 1**

**Box 2**

**Box 3**

**Box 4**

**Box 5**

** **

Again correct equations could be:

2 + 2 + 2 + 2 + 2 = 10

5 + 5 = 10

2 × 5 = 10

5 × 2 = 10

Let’s try one more example. We’ll change up the numbers a bit.

###### Beth has 6 toy cars. She puts 2 toy cars in each box. How many boxes does she have?

Looking at just key words, students will likely write an addition or multiplication equation. (They’re easier for students.)

But when students seek understanding, they’ll visualize or draw 6 cars divide into groups of 2 until all the cars in are boxes.

**Box 1**

**Box 2**

**Box 3**

Then hopefully, they’ll write the following equation:

6 ÷ 2 = 3

And not 2 ÷ 6 = 3 (This is a problem for later.)

#### Take Away

Hang with me for just one more example of key words, take away. I know, take away is used so much for subtraction. It really doesn’t signal any other operation. It does, however, limit students’ understanding of subtraction.

I don’t automatically say no to take away, it is a natural way for little ones to start understanding subtraction. The problem is when take away continues to be used for subtraction. Students believe that subtraction only occurs when you “take something away” from a group and the group gets smaller.

Let’s look at a word problem to see why take away just doesn’t work.

###### Marco has 3 toy cars. Aja has 2 toy cars. How many more toy cars does Marco have than Aja?

**Marco’s Cars**

**Aja’s Cars**

This is a subtraction problem that requires comparing two groups. Nothing is taken away. Because nothing is taken from either group, students will decide to add. In fact, the word more causes students to think of addition or multiplication because it implies that a group is getting larger.

Students will often write 3 + 2 = 5 instead of 3 – 1 = 1.

Next week, I’ll look at better strategies for teaching problem solving other than key words.