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).

MLR2 Collect and Display. Synthesis: Direct attention to words collected and displayed during the previous lesson. Invite students to borrow language from the chart as needed, and update it throughout the lesson.
Advances: Conversing, Reading

• Invite previously identified students to share their rectangles partitioned to make fourths.
• Display students’ work.
• “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).

• Invite previously selected students to share.
• “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.)