Solving Math Word Problems

Ahhh… Math Word Problems! Quite possibly the these are the single most intimidating topic in mathematics for middle schoolers, high school students, and often… their parents, too.

Let me tell you why they are inherently difficult and give you some suggestions how to approach them more successfully.

Why are They so Confusing to Solve?
Math word problems are difficult because they are examples designed to represent how specific algebraic techniques could be applied.

The application of a skill is always much more challenging than practicing the skill in isolation.

So, if your child finds solving math word problems a challenge, that’s to be expected and quite normal.

The Best Approach to Solving Math Word Problems:
Here’s how to approach these problems in a step-by-step way.

• First, read the problem. That might sound like a silly thing to say because it’s so obvious, but actually, many students don’t read the problems carefully. They skim over them, or read them so sloppily, that they don’t understand what the given information is, and what is being asked.

  Pay attention to what the given information is, and what is being asked.

• The second step is to decide how to use variables, expressions or equations to represent the information and the question of the problem. This normally is what students find to be the hardest step.

Let’s consider a typical 7th grade math problem that your child might encounter in a prealgebra course as an example; and then I’ll explain the remaining steps:

The Word Problem: Boris has three times as many marbles as Natasha. Together they have 40 marbles. How many does each one have?

So first, we read the problem looking out for what the question is, which is how many marbles do they each individually have.

And we notice the given information, which is something about what they have together, and something about the relationship of their respective quantities.

Now, for setting up the problem with variables: Usually you can let X, the variable, represent whatever is the question. But in this case, there are two questions, Boris’ quantity and Natasha’s quantity.

So in that case you will let X represent Natasha’s number of marbles.

Why is that?

Because Boris’s quantity is defined in terms of Natasha’s, so if she has X and he has three times as much, we can say he has 3X.

Now we’ll write the equation: The problem said "together", and that suggests addition, so the equation is Boris’ number plus Natasha’s number=40, or…
3X+X =40

The Final Steps
The remaining steps in the problem are generally the downhill slope, the easier part.

• The third step will be just solving the equation.



• The fourth step will express our answer in terms of the question of the problem.



• The fifth step will be a check to make sure our answer makes sense and is correct.

What are the common mistakes in Solving Math Word Problems?
A very common mistake is to stop here, after solving for X. That is a mistake because we haven’t really answered the question! We are supposed to find out how many marbles each person has.

X represented Natasha’s number. To find Boris’ number, substitute 10 in for X in Boris’ expression, 3X becomes 3*10 which is 30.

Then to actually answer the question, we can say:
Boris has 30 marbles and Natasha has 10 marbles.

(Math teachers tend to be picky about answering word problems with words!!!)

The Final Step…Check your Answers:
As a last step, we can check to see that our answer really fits the words of the question. Does Boris have 3 times as many as Natasha?

Yes! Because 30 equals 3*10.

Do they have 40 together?

Yes, because 30+10=40.

We did it!

How to Get Proficient at Solving Math Problems:
There are many categories of math word problems, such as; rate problems, work problems, wind and current problems, problems about angles. These various traditional categories are all designed to illustrate the use of a specific algebraic technique. Normally, the teacher will present an example of each type as it’s encountered in the course.

If the student carefully works and reworks the class example, until the steps flow naturally, he or she should be able to do the problems in homework or one a quiz. That’s a very common mistake students make, that they don’t practice with the examples given in class from their notes, but jump right in to the homework questions and then find themselves stuck.

So if your child needs help with word problems, a good first step would be to go over the notes together working through the examples again and again until the steps are obvious. If your child is coming home without any notes from class, you need to tell him to start taking notes!

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