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Modeling Fractions with Cuisenaire Rods

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Interactive

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Source: Teaching Math Grades 6-8: "Modeling Fractions"

This asset is adapted from an activity from Annenberg Learner's Teaching Math Grades 6-8, a professional development course for teachers.

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This interactive activity adapted for grades 3–5 from Annenberg Learner's Teaching Math Grades 6–8 invites students to explore fractions using a virtual collection of rectangular rods, each of a different color and length, called Cuisenaire® Rods. The activity allows students to model fractions through stacking and connecting the rods and to understand how to perform comparisons and simple addition problems. As students begin to explore relationships among fractions, their early work solidifies their understanding of basic fraction concepts and facilitates their comparing and ordering fractions and working with equivalency.

Cuisenaire® is a trademark of ETA hand2mind.

Background Essay

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.

Connections

Connections to the Common Core State Standards

Number and Operations—Fractions

• Develop understanding of fractions as numbers.
• 3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
• 3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
• Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
• Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
• Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.
• Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, and < justify the conclusions, e.g., by using a visual fraction model.
• Extend understanding of fraction equivalence and ordering.
• 4.NF.1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
• 4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, and < and justify the conclusions, e.g., by using a visual fraction model.

Teaching Tips

Before the activity
Ask students to list some ways they use fractions in their daily lives. Examples may include pouring out half (1/2) a bottle of water to share with a friend, taking two-eighths (2/8) of a pizza at the dinner table, or adding three-quarters (3/4) of a stick of butter to other ingredients when baking a cake.

After the activity
Here are some discussion questions you might wish to use to check for understanding:

• What is the meaning of a fraction?
• Name the parts of a fraction.
• Explain the relationship between the parts and the whole.
• Discuss how students made equivalencies, how they compared fractions, and how they modeled and manipulated the fractions to perform operations.

Standards

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