Lesson 11

The purpose of this lesson is for students to generate equivalent fractions numerically, by using factors and multiples of the numerator and denominator.

In earlier lessons, students saw that one way to generate equivalent fractions is by grouping unit fractions on a number line into larger units. For instance, 12 twelfths could be put in groups of 3 to make 4 equal parts, each part being a fourth. Or they could be put into groups of 2 to make 6 equal parts, each part being a sixth, which means that \(\frac{12}{12} = \frac{4}{4} = \frac{6}{6}\). Some students may have related these observations to the fact that \(12 \div 4 = 3\) and \(12 \div 2 = 6\). These insights are formalized and generalized in this lesson.

Students have also generated equivalent fractions and verified equivalence by multiplying the numerator and denominator by the same number. In this lesson, they find equivalent fractions by dividing \(a\) and \(b\) by a factor \(n\) that is common to both numbers.

• Create a set of Fraction Galore cards from the blackline for each group of 3.

What evidence did you see of students choosing a method strategically as they generated equivalent fractions? For students who chose a fixed way regardless of the given fractions, what questions could you ask them to prompt them to be more strategic?