The purpose of this activity is for students to explore different ways to partition rectangles into halves and fourths. They notice that when they partition two of the same rectangle into fourths or halves in different ways, the resulting pieces may have different attributes. In the Activity Synthesis, students explain why the equal pieces of the same whole could look very different even though they have the same size, as long as the original shapes were split into the same number of equal pieces (MP3, MP7).

• Invite previously identified students to share their rectangles partitioned to make fourths.
• Display students’ work.
• “Cada uno de estos estudiantes piensa que partió el rectángulo en cuartos o cuartas partes. ¿Con quién están de acuerdo? Expliquen” // “Each of these students think they have split the rectangle into fourths or quarters. Who do you agree with? Explain.” (The pieces look different in each rectangle, but they all show fourths because each rectangle is split into 4 equal pieces.)

The purpose of this activity is for students to consider different ways to partition a circle or rectangle into thirds. Students continue to deepen their understanding that equal pieces of the same whole can look different. Monitor for the ways students reason that the equal pieces of the same whole may look different but are the same size, to share in the Lesson Synthesis (MP3, MP7).

• “¿En qué se parecen y en qué son diferentes las partes de pan de maíz de Diego y su hermano?” // “How are the pieces of cornbread Diego and his brother have the same and different?”
• “¿Ven alguna manera en la que podrían separar y volver a juntar la parte del hermano de Diego para que tenga la misma forma que la parte de Diego?” // “Do you see a way you could break apart Diego's brother's piece and put it back together so it's the same shape as Diego's piece?”

• Invite previously selected students to share.
• “¿Cómo puede ser que ambos estudiantes hayan coloreado un tercio si sus partes no se ven iguales?” // “How is it possible that both students have shaded a third if they don’t look the same?” (Their thirds might not look the same when compared to each other, but they each partitioned their shape into 3 equal parts and shaded 1 part.)