If your student has trouble with percentages, it is essential to troubleshoot the problem early, as future math concepts build upon prior knowledge. Learning the basics of percentages may begin as early as third grade and should play an important role through eighth grade, according to The National Council of Teachers of Mathematics. A student needs to understand the meaning of percent, its visual representation and its relationship to decimals and fractions.

## Understand the Term

Knowing that the "cent" part of the word "percent" means "100" can act as a starting point for understanding. Khan Academy recommends associating the 100 years in a century with this term. The “century” becomes the whole, and the “100 years” represents the parts of the whole. In other words, the word “percent” means "per 100." In addition, an NCTM Illuminations activity suggests that you relate percents to everyday events. A teacher could ask, "What does it mean to score 100 percent on a spelling test?" or "What does it mean to have 50 percent of a candy bar?" or "If 4 percent of 100 parking places should be available for people with disabilities, what does that mean? How many spaces would that be?” Questions like these can assess where students need to begin.

## Create Grids

By using grids of 100 squares to demonstrate percents, teachers can demonstrate the “parts” and the “whole.’ If the students color 15 small parts out of 100, they can visualize 15 percent. If they color in all 100 parts, then they have colored 100 percent of the grid or an entire large square. Christopher Scaptura and other mathematics instructors who collaborated at George Mason University, propose using the 10-by-10 grid as an artwork assignment. The students can devise their own designs by color and then compute the percentage of each color. The artwork engages the students and promotes understanding.

## Understand Percents Over 100 Percent

Often, a figure like 200 percent confuses students, because they might assume the value means 200 times more. By using two large squares, each divided into 100 parts, students can see what percents over 100 means visually. For example, filling in 100 parts of the first large square and 25 parts of the second square will equal 125 percent. If a student thinks the answer should be 125 out of 200, remind him that percent refers only to parts out of 100. Once a student fills in all 200 smaller parts, he will realize that he has filled in two large wholes. Therefore, 200 percent refers to two large squares, not 200.

## Apply the Concepts

Viewing an interactive visual model allows students to compare percents to other concepts. One Illuminations model allows students to experiment with percents, fractions and decimals. At first, the student can view the numerator and denominator 1/1 converted to 100 percent, a 1.0 decimal or one purple rectangle. As the student makes changes, moving the numerator to 2/1 or 200 percent, she will see two rectangles and a decimal of 2.0. If she moves to one-half, she will see half a rectangle and 50 percent or 0.5. Such experimentation can engage a student and encourage an interest in mathematics.

#### References

- National Council of Teachers of Mathematics: Math Standards and Expectations: Numbers and Operations
- Khan Academy: The Meaning of Percent
- National Council of Teachers of Mathematics Illuminations: Parking at the Mall
- George Mason: Masterpieces to Mathematics; Using Art to Teach Fraction, Decimal and Percent Equivalents; Christopher Scaptura et al
- National Council of Teachers of Mathematics Illuminations: Fraction Models

#### Photo Credits

- Peshkova/iStock/Getty Images