Grades: 3‒6

Students use algebraic variables to build area models of equivalent fractions. For example, to create fractions equivalent to ^{1}/_{2} , students construct a model of ^{1}/_{2} as ^{n}/_{2n} and then vary the value of *n*. As they do, visual representations of ^{1}/_{2} , ^{2}/_{4} , ^{3}/_{6} , etc., appear on screen. Students also make fractions equivalent to ^{1}/_{3} , ^{1}/_{4} , ^{2}/_{3} , ^{3}/_{5} , and ultimately, any fraction whatsoever. Through this process, students learn that multiplying the numerator and the denominator of a fraction by the same variable can be used to create equivalent fractions.

Note: This activity is available in two versions—an area model that represents fractions as parts of a circle and an area model that represents fractions as parts of a rectangle.

OBJECTIVES

- Students will understand that multiplying the numerator and the denominator of a fraction by the same value creates an equivalent fraction.
- Students will use the concept of a variable to construct equivalent fractions.

COMMON CORE CONNECTIONS

Mathematical Practices

(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (5) Use appropriate tools strategically; (7) Look for and make use of structure.

Content Standards

3.NF3; 4.NF1; 6.EE2

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