Introducing your students to the relationship between fractions, decimals, and percents, can be fun and educational. It’s important that your students understand that fractions, decimals and percents are different numerical ways of representing the same thing. For example, 1/10 = 0.1 = 10%. I’ve found that a great place to start when teaching how these mathematical concepts relate to each other is by using coins. All of your students know how much one quarter, two quarters, three quarters, and four quarters are worth. Let’s start there…..

On the whiteboard, I write the words, “Coins” “Fractions” “Decimals” “Percents” as the headings of four columns. I ask, “Who can tell me which one of our coins has a picture of George Washington on the front?” “A quarter!” someone yells out. I draw a circle with 25 cents inside it underneath the “Coins” heading. “Can anyone come up to the board and represent the quarter in fraction form?” I ask. Usually, a bunch of hands go up, and I call on someone to come up and represent a quarter in fraction form. “1/4! Very good!. Now for a tougher question…..why does 1/4 represent 25 cents ?” This question usually elicits some good discussion. Eventually, someone will say, “Because it takes 4 quarters to make a dollar, and we just have one of them.” “Exactly! The numerator (1) represents how many quarters we have and the denominator (4) represents the group of quarters needed to make one dollar.”

“Now let’s move onto the next column. Who can come up and represent our quarter in decimal form?” This is a tougher task for the kids. If only a few hands are up, I’ll say, “Think of how you write 25 cents using the decimal point.” More hands go up, and I’ll have someone come up to write a quarter in decimal form. “0.25! Excellent!” Once again I’ll ask, “Why does 0.25 represent 25 cents ?” There are a few different ways of correctly answering this question. One student says, “Because there are 25 cents in a quarter.” “Very good!” I respond. “The number “25” shows how much a quarter is worth.” A higher-level answer would be, “Because 0.25 means 25 hundredths, which is one quarter of 100.”

“We have one more column to go. Who can come up and represent our quarter in percentage form?” A brave soul will come up and give their answer. “25%! Fantastic!,” I say. “But, why does 25% represent 25 cents ?” This is usually the toughest question to answer. I have to remind my students that percentages are based on 100. “Remember, we use 100 parts to find percentage because percent means per hundred. For example, there are 100 years are in a century.” Eventually, the discussion leads the students to realize that 25% means the same thing as 0.25, and 1/4.

I continue this exercise using 2 quarters (2/4, 0.50, 50%) 3 quarters (3/4, 0.75, 75%) and 4 quarters (4/4, 1.0, 100%). By the time this mini-lesson is over, students are beginning to get more comfortable with converting between fractions, decimals and percents. Now, they are ready to get into the lessons below, which will give them a chance to deepen their understanding of how these concepts are related to each other.

## Fractions, Decimals, and Percents:

Coin Conversions

Students continue to use coins to help them deepen their understanding of the relationship between fractions, decimals and percents. This clever lesson has an excellent worksheet embedded in the plan which requires the students to use different combinations of coins to make 50 cents, and then leads them to discover the fraction, decimal and percent equivalents. The next lesson on Sports Math is meant to be used after this lesson has been done.

Sports Math

The world of sports is an excellent place for students to explore fractions, decimals and percents. Think of it……a basketball game has four quarters, the winning time for the 100 meters was 9.35 seconds, Peyton Manning completed 67% of his passes last season. This excellent lesson has terrific worksheets, attachments and websites that students can access to help them continue their exploration of the relationship between fractions, decimals and percents.

M&M Math

M&M’s to the rescue again! Students work together in pairs to calculate the fraction, decimal and percentage values for each color M&M found in their bag. For example, if your bag has 20 M&M’s, and 4 are red, the fraction of red M&M’s in the bag is 4/20 or 1/5…..which converts to 0.2 and 20%. I love math lessons that use M&M’s because the motivation factor (consumption of M&M’s can only happen once the work is correct!), never fails.

Comparing Fractions, Decimals & Percents

Students use a variety of websites embedded in this plan to review equivalent fractions and decimals and study how to convert a decimal to a percent. This selection would be appropriate for older students who are able to work independently, and have a grasp on the relationship between fractions, decimals and percents.