In an earlier lesson, students used visual representations to generate equivalent fractions. They did so by partitioning each increment on a number line into smaller equal-size parts. In this activity, they connect that action to a numerical process—one that involves multiplying both the numerator and denominator by the same factor. When students notice that they can multiply the numerator and denominator of a fraction by any whole number to get an equivalent fraction, they observe regularity in repeated reasoning (MP8).

• Select 1–2 students to share their equivalent fractions for  and their reasoning. Display their equivalent fractions as equations Examples:  , , , and .
• “Do these equations show the same patterns as the equations in the Warm-up? How are they alike or different?” (Alike: In all of the equations the numerators and denominators are multiplied by the same whole number. Different: In the Warm-up, each numerator and denominator was multiplied by 2. In these equations, each the numerator and denominator of the fraction is multiplied by different numbers each time.)

In this activity, students identify equivalent fractions. In the first problem, they use the numerical strategy they learned earlier to determine if two fractions are equivalent. In the second problem, they can use any strategy in their toolkit—which now includes a numerical method—to identify equivalent fractions.

Students encounter some fractions with unfamiliar denominators, such as 9, 16, 32, 40, and 80, but they will not be assessed on such fractions. These denominators are multiples of familiar denominators such as 2, 3, 4, 5, 8, or 10, and are included to give students opportunities to generalize their reasoning about equivalence.

• “Check your list of equivalent fractions with another group.”
• “Discuss any disagreement about a fraction until both groups agree whether or not it is equivalent to .”
• 3 minutes: small group work