I think it’s safe to say that most elementary school teachers don’t get into education because they love math (although there are a few). If you’re like most, you wanted to give children a love of reading, which is so important to learning about everything else, or you wanted to encourage wide-eyed little sponges who still have a sense of awe that learning is fun. If you struggled with math at all, or if you saw it as something getting in the way of exploring something more interesting, you might view teaching math as a chore. Math may seem like just a bunch of dispassionate numbers sitting on a page. You learned to manipulate them to get other dispassionate numbers, and later they threw letters at you and asked you to figure out what numbers they stood for! What does that have to do with anything meaningful?

How to Make Math Meaningful—Real-World Examples

Math is the language of many things we do care about. Like word language, it presents or underlies interesting or at least practical ideas.

• There is math in commerce, used every time you buy or sell something or get paid. 
• There is math in the kitchen, used when you measure ingredients or figure out when dinner will be ready.

• There is math in construction, used in everything from your kitchen table to your school to every road, water pipe, and stop sign.
• There is math in our daily schedules, used every time we look at a clock to plan our day.
• There is math in medicine, used to measure whether we are healthy or develop a cure if we are not.
• And there is math in science! Virtually every manufactured object on Earth has math involved in its creation, along with our ability to travel beyond Earth.

We tend to take math for granted when tasting an exquisite chocolate cake or driving across a beautiful bridge. Every time we need to know “how much,” we are just finding a missing part of our real-world story. We encounter many of these missing bits every day: how much the groceries will cost, how much time before the school bus arrives, how many eggs are needed to make 5 batches of cookies for the bake sale. These problems are not generally written out for us—they just arise. No one tells us, “This is going to be an addition problem” or, “You’ll have to calculate the total needed first and then subtract what you already have.” We figure this out from the context and information at hand. There are no shortcuts in our real-world stories.

Basic Steps to Help Students Solve Word Problems

So how can you guide your students toward figuring out what a particular problem requires to solve it? Remember these basics principles:

• Every problem is different; there is no single way to solve all problems.
• You need to put yourself in the picture to understand each situation.
• After you understand what is going on, you can figure out what you need to solve any problem in a math class or in real life.

Here are some simple steps for students to follow to solve math word problems:

1. Start by looking for the basic idea, reading the problem once to see what it’s about. Students should ask themselves, “What’s going on in the situation?”

Let’s use this problem: Erin wants to go to the county fair. A ticket costs $11.50. Erin has $2. She gets $4 for her allowance, and Aunt Vi gives her $5. Does Erin have enough money? The situation is about going to the fair.

2. Next, read the problem again more carefully: put yourself in the situation. Decide what you need to figure out. Students should ask themselves, “What is the goal of the problem?”

In our sample problem, it’s whether Erin has enough money. It’s very helpful at this point to draw a picture or diagram of the situation, especially for young learners, English-language learners, or those who are aren’t yet comfortable with abstract thinking. In the picture or diagram, each important number should be included and labeled, as well as the part you are trying to figure out. A student might draw a stick figure next to $2, $4, and $5 and a ticket saying $11.50.

3. Next, students should ask themselves, “What do these numbers have to do with each other?” The relationship of the numbers will help the student decide which operation(s) to use to help solve the problem. Note that some problems require multiple steps. Students should ask themselves, “What do I need to add, subtract, multiply, or divide? Do I need to figure out another number first?”

In our problem, a student would write “2 + 4 + 5 = 11” and “11 < 11.50.” Students should never stop after they’ve done the calculations. They should go back to their picture or diagram and think about the story with their answer in place. Students should ask themselves, “Does my response answer the question? Does it make sense?”

The Ideal Problem-Solving Practice Is Authentic

Solving problems, mathematical and otherwise, requires reasoning. The main purpose of word problems is to practice translating situations into mathematical language.

Ideally, problem-solving practice should include:

• authentic or engaging situations that students can relate to.
• problems written in a natural way describing the situation so the students can visualize it.
• opportunities for consistent practice.

Students should not rely on key words to provide clues to the appropriate operations. Such artificial clues deprive students of the visualization and analysis practice required to make sense of and solve actual problems. Shortcuts for approaching particular types of problems may appear to save time and effort, but they require a lot of memory in the long run, as there are infinite types of problems.

By supporting the higher-order thinking aspects of problem solving, you are not teaching the next generation how to just follow a recipe; you are teaching them how to cook!

 

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Kathy Jorgensen has been an educator most of her life, starting as a peer tutor in second grade and tutoring her way through high school and college. After teaching grades 2 through 12, she spent two decades editing standardized tests. Kathy happily returned to her teaching roots, providing instruction and practice in Evan-Moor’s math and science products. When she’s not polishing words on the page, Kathy is flitting down the dance floor indulging her passion for Scottish country dancing as a dancer, choreographer, and teacher.