In this activity, explore fractions with the help of virtual Cuisenaire® Rods—a collection of rectangular rods, each of a different color and length. In a set of actual Cuisenaire® Rods, the smallest rod (white) is 1 centimeter long; the longest rod (orange) is 10 centimeters long. Using these rods, students can readily visualize a fraction both as part of a whole and in relationship with one another. As students become more familiar with the use of Cuisenaire® Rods to represent fractions, they can use them to solve fractional problems.

To represent a fraction with Cuisenaire® Rods, a student places one length of rod directly above another. A simple demonstration would be to use an orange rod to represent the whole and to ask students to identify which rod is one-half its size. The student should then find the two equally sized rods (in yellow) that, when placed end to end with each other, make a “train” that exactly matches the length of the orange rod. Keeping one yellow rod in position above the orange rod, the student has modeled the fraction 1/2.

As students continue to model fractions with Cuisenaire® Rods, they should recognize that the numerator (top part) of each fraction is the number of equal parts being considered. That is, it’s the number of same-sized rods represented on the grid. The denominator (bottom part) of each fraction is the number of equal parts that the whole is divided into. This means it’s the number of same-sized rods that would be used if the train were equal in length to the given whole.

When students begin to understand the concept of a fraction by using the orange rod as one whole, they may use rods of different sizes to represent one whole and to make new equivalencies. For example, if a brown rod represents one whole, then one red rod would be 1/4 of a brown rod.

As students become comfortable using Cuisenaire® Rods, you may introduce simple operations, such as the addition of fractions, even if the fractions do not share the same denominator. For example, students can visualize that 3/5 plus 1/10 equals 7/10 by placing the fractions to be added in a train and then matching the train with other rods to find a length of rod equal to the length of the train.

Two fractions are considered equivalent when each one can be used to represent the same amount of a given object. Connecting this idea to the activity, lining up 10 white rods, each being one-tenth the size of the orange rod, equals the length of the orange rod. So 10/10 is equivalent to 1/1. As students progress with their understanding of equivalence, you can begin to draw their attention to part–part relationships. For example, five white rods (5/10) is equal in length to one yellow rod (or 1/2 the length of an orange rod). This means that five-tenths is equal to one-half, and the fractions are equivalent.

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