Fraction tiles are colored bars to represent the fractions: halves, thirds, quarters, fifths, sixths, eighths, tenths, and twelfths. These manipulatives are also called fraction bars and fraction strips. Fraction tiles provide a concrete and interactive way to understand fractions, mixed numbers, comparing fractions, equivalent fractions, and adding fractions.
Virtual manipulatives, such as Brainingcamp's Fraction Manipulatives, make it fast and easy to work with virtual fraction tiles by providing the ability to easily position and snap tiles together. Fractions tiles can display their values using fraction, decimal, or percent labels. Brainingcamp's Fraction Manipulatives also includes fraction circles, fraction rings, and a fraction wall.
Place a "whole" tile, and then place 1/5 tiles below it. A fraction is a number than compares a part (number of pieces) with a whole. It takes 5 pieces to make the whole, so each piece represents 1/5. Remove two of the 1/5 pieces. The remaining pieces represent 3/5. The denominator 5 represents the number of equal size pieces that make a whole, and the numerator 3 represents the number of pieces shown.
Place a "whole" tile and then below it model 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 compare 1/3 and 1/5, place a 1/3 fraction tile directly below a 1/5 fraction tile 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). Below the 1/3 fraction tile, place 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 fraction tile that represents 1/2. Below the 1/2 fraction tile, place two 1/4 fraction tiles. Notice that the two 1/4 pieces represent the same part of a whole as 1/2, so 2/4 and 1/2 are equivalent. Experiment with other fraction tiles to find more fractions that are equivalent to 1/2.
To add 1/5 and 2/5, combine one 1/5 fraction tile with two 1/5 fraction tiles. There are three 1/5 fraction tiles in total so 1/5 + 2/5 equals 3/5.
Model 1/2 + 1/3 by placing a 1/2 and 1/3 fraction tile together. The common denominator of 1/2 and 1/3 is 6, so below the 1/2 and 1/3 fraction tiles use 1/6 fraction tiles to make a length equal to 1/2 + 1/3. Notice that there are five 1/6 pieces in total, so 1/2 + 1/3 equals 5/6.
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 fraction tile and then place a 1/3 fraction tile below it. To see how many times 1/3 fits into 1/4, it can help to place 1/12 fraction tiles below the other fraction tile (because 12 is a common denominator of 4 and 3). The 1/3 fraction tile fits inside the 1/4 fraction tile 3/4 of a time, so 1/4 ÷ 1/3 equals 3/4.