Fraction circles are colored circles divided into pieces representing halves, thirds, quarters, fifths, sixths, eighths, tenths, and twelfths. Through visual and hands-on learning, students can use fraction circles for a deeper understanding of fractions, mixed numbers, common denominators, comparing fractions, equivalent fractions, and adding fractions.

Some fraction circle providers also offer fraction rings that fit around fraction circles and display scales as fractions, decimals, percents, degrees, or time.

Virtual manipulatives, such as Brainingcamp's Fraction Manipulatives, make it fast and easy to work with virtual fraction circles that rotate and snap together. Fractions circle pieces can display their values as fraction, decimal, or percent labels. Brainingcamp's Fraction Manipulatives also includes fraction rings, fraction tiles, and a fraction wall.

Using Fraction Circles

Make complete circles with each type of color piece. Notice that a fraction is a number than compares a part (number of pieces) with a whole (complete circle). Find the circle that has 5 pieces and remove 2 of the pieces. The remaining pieces represent 3/5 of a whole. The denominator 5 represents the number of equal-size pieces in a whole, and the numerator 3 represents the number of pieces shown.

If a circle represents one whole, then model and label the fractions 1/3, 2/3, and 3/3. Think about what fraction comes next in the pattern. The next fraction is 4/3. A fraction where the numerator is greater than the denominator is called an improper fraction. Improper fractions can be written as a mixed number with a whole and a fraction. So 4/3 can be written as the mixed number 1 1/3.

To find the common denominator of 1/3 and 1/4 using fraction circles and fraction rings, place a 1/3 and 1/4 segment beside each other inside of a ring. Try various ring intervals until the segments align with tick marks on the ring. The 1/3 and 1/4 segments align with tick marks of twelfths because 12 is a common denominator of 1/3 and 1/4.

To compare 1/3 and 1/5, drag a 1/5 piece over a 1/3 piece to see which is greater. Notice that when fractions have the same numerator, the greater the denominator the smaller the fraction (1/5 < 1/3). Represent 2/3 by putting two 1/3 pieces together. Notice that when fractions have the same denominator, the greater the numerator the greater the fraction (2/3 > 1/3).

Place a piece that represents 1/2. Find two pieces that represent 1/4. Notice that the two 1/4 pieces represent the same part of a whole as 1/2, so 1/2 and 2/4 are equivalent. Experiment with other colors to find more fractions that are equivalent to 1/2.

To add 1/5 and 2/5, combine one 1/5 tile with two 1/5 tiles. There are three 1/5 tiles in total so 1/5 + 2/5 equals 3/5.

Model 1/2 + 1/3 by placing a 1/2 and 1/3 piece together. The common denominator of 1/2 and 1/3 is 6, so cover the 1/2 and 1/3 pieces with 1/6 pieces. Notice that there are five 1/6 pieces in total, so 1/2 + 1/3 equals 5/6. Using a fraction ring, place a 1/2 piece and a 1/3 piece inside of the ring. The 1/2 and 1/3 pieces align with tick marks of sixths because 6 is a common denominator of 1/2 and 1/3. The sum of the two segments equals 5/6, so 1/2 + 1/3 equals 5/6.

Fraction division can be modeled using fraction circles and a fraction ring. Division can be thought of as finding how many times the second number fits inside the first number. To find 1/4 ÷ 1/3, place a 1/4 piece and then place a 1/3 piece on top of it. Place a fraction ring around the pieces. The 1/3 and 1/4 segments align with tick marks of twelfths because 12 is a common denominator of 1/3 and 1/4. The 1/3 segment fits inside the 1/4 segment 3/4 of a time, so 1/4 ÷ 1/3 equals 3/4.