The purpose of this activity is for students to use diagrams to reason about equivalence and to reinforce their awareness of the relationship between fractions that are equivalent.

Students show that a shaded diagram can represent two fractions, such as and , by further partitioning given parts or by composing larger parts from the given parts. Unlike with the fraction strips, where different fractional parts are shown in rows and students could point out where and how they see equivalence, here students need to make additional marks or annotations to show equivalence.

In upcoming lessons, students will extend similar strategies to reason about equivalence on a number line—by partitioning the given intervals on a number line into smaller intervals or by composing larger intervals from the given intervals.

In the first problem, students construct a viable argument in order to convince Tyler that of the rectangle is shaded (MP3).

• Select previously identified students to share their responses and their reasoning. Display their work for all to see. 
• As students explain, describe the strategies they use to show equivalence. Ask if others in the class showed equivalence the same way.

The purpose of this activity is for students to generate equivalent fractions, including for fractions greater than 1, given partially shaded diagrams. Students may use strategies from an earlier activity—partitioning a diagram into smaller equal parts, or making larger equal parts out of existing parts—or patterns they observed in the numerators and the denominators of equivalent fractions (MP7).

If students name a fraction based only on the given partitions, consider asking:

• “Cuéntame cómo llamaste a la fracción” // “Tell me how you named the fraction.”
• “¿Cómo puedes usar el diagrama para encontrar una fracción equivalente?” // “How could you use the diagram to find an equivalent fraction?”

• Select students to share their strategies for writing equivalent fractions for each diagram. Display the diagrams they marked or annotated.
• “¿En qué se diferenciaba el último diagrama de los tres primeros?” // “In what ways was the last diagram different from the first three?” (It shows 2 wholes. The shaded parts were greater than 1.)
• “¿Su estrategia para encontrar fracciones equivalentes en este diagrama fue diferente a la que usaron en los tres primeros? ¿Por qué sí o por qué no?” // “Was your strategy for finding equivalent fractions for this diagram different from the first three? Why or why not?” (No, it still involved making smaller equal parts. Yes, I partitioned the first 1 whole and the second 1 whole separately.)
• If no students mention for the last diagram, ask, “¿Pueden mencionar una fracción distinta a  y ?” // “Can you name an equivalent fraction other than and ?”