The goal of this activity is for students to draw diagrams that represent a unit fraction multiplied by another unit fraction in context. The macaroni and cheese context was introduced in the Warm-up to motivate students to draw a diagram to represent the pan. The focus in this activity is on the different diagrams students draw and how they represent the same situation (MP2). Some students may identify that Lin ate of the pan. Invite these students to share their observation at the end of the Activity Synthesis when they think about the diagrams in relation to the fraction of the whole pan of macaroni and cheese Lin ate.

Monitor for students who draw different diagrams to show of such as those shown in the Student Responses.

The approaches will later be displayed side by side to help students interpret representations of fractions of fractional quantities and how different diagrams can represent the same situation. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven’t shared recently.

• Invite previously selected students to display their work side by side without sharing their thinking.
• “Take a minute to look at each of these diagrams.”
• Connect students’ approaches to the learning goal by asking:
  • “How does the diagram represent  of of the pan?” (First, the rectangle or pan is divided in half and then a third of one half is shaded.)
  • “How are the diagrams the same?” (They all show the full pan cut in half. Then they show a half cut into 3 equal pieces and one of those pieces is shaded.)
  • “How are the diagrams different?” (One diagram cuts the pan in half horizontally and the other two cut it in half vertically. The other cuts into 3 equal pieces are also sometimes horizontal and sometimes vertical.)
• “How much of the whole pan did Lin eat?” (Students may say  or other fractions.)
• Record all responses and revisit this in the Lesson Synthesis.

Continuing the macaroni and cheese context from the previous activity, the purpose of this activity is for students to interpret diagrams showing a fraction of a fraction of the pan. Then students address what fraction of the whole pan the shaded piece of the diagram represents. Because the whole pan is not subdivided, students may need to add the extra divisions or think carefully to identify the fraction of the whole pan represented by the diagrams. To identify that the shaded pieces in the two diagrams have equal area students may:

• Cut out and compare the shaded pieces explicitly.
• Reason that they are each or of the same amount.
• Reason that they are each of the whole.

• Ask previously selected students to share in the given order.
• “How does each diagram represent of ?” (They each show shaded in the lighter blue and then of that half is shaded darker.)
• “How do we know the darkly shaded pieces are the same size?” (I cut them out to check. They are both of . They both represent of the whole pan.)
• If not already mentioned by students, ask: “How can we figure out how much of the whole pan of macaroni cheese the dark shaded piece represents?” (We can extend the lines in Diagram A and we can partition the rest of the square in Diagram B.)
• “ of is equal to how much of the whole pan of macaroni and cheese?” ( of the whole pan.)