My Favorite Method for Teaching Percent Word Problems

Word problems involving percent can be especially difficult for students.  Various methods can be used to solve them.  Yet, just as students are gaining confidence at solving percent word problems, they often run across a problem requiring a different approach.  The abundance of situations that can be described, and what specific information is given can make word problems very confusing … not just for kids!

Here is an example of the sort of problem students REALLY struggle with!

A scarf costs $16.48 with tax included. If the tax rate is 5%, what is the selling price of the scarf?

 

After many years of teaching this topic, I’ve decided that the method I will explain here is the most successful of those I’ve tried.  This approach enables students to analyze and solve any word problem involving percents more confidently.

Too often, students identify the base number as the "total".  This leads to many misunderstandings.  The base is "the original amount", which is not always the total.  After this misconception is cleared up, the problem solving immediately becomes easier.  Identifying the base first, even if it is missing, gets students off to a strong start.

Once the issue of identifying the base is clarified, the next step is to determine what to use as the percentage and the rate.  The rate is a "percent" and the percentage is "part of the original amount".  This can be a bit tricky because the part can sometimes be more than the original amount.  For example, suppose you are given a price with tax included.  That price would be more than the original amount, but is the percentage because it is based on the original amount.

In my experience, the most difficult thing for students to understand is that the percentage and the rate must be in agreement.  For example, consider the problem below.

Eight percent of the students in a class of twenty-five are absent today.  How many students are present?

p = ___ number of students present
r = 92% present
b = 25

The base is 25 because that is the original amount of students in the class.  We want to find out how many students are present, and this would be the percentage because it is part of the original amount.  Although 8% can be used as the rate, it represents the percent of students absent.  To find the number of students present quickly, I would use 92% because it is the percent of students present.

This is an overview of this approach.  To become really good at analyzing information and solving a variety of word problems involving percents takes practice.  If you are interested in further support materials, they can be found here.