The purpose of this activity is for students to solve a contextual problem about dividing a fractional amount by a whole number. Students draw a diagram to represent the situation and relate the diagram to a division expression. Because of earlier work in this unit, students may draw one of the familiar square area diagrams showing the product . Other students may make a diagram resembling the macaroni and cheese pan and divide it appropriately. The focus in the Activity Synthesis is on bringing out how the diagram shows and how it allows students to answer the question. The relationship between and will be brought out in later lessons. When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2).

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

• “Create a visual display that shows your thinking about the problems. You may want to include details such as notes, diagrams, drawings, etc., to help others understand your thinking.”
• 2–5 minutes: independent or group work
• 5–7 minutes: gallery walk
• “How does each representation show  a pan of macaroni and cheese?”
• “How does each representation show 3 equal pieces?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• “How do we know that each person got the same amount of macaroni and cheese?” (I divided the half into 3 equal shares.)
• “How much of the whole pan of macaroni and cheese did each person get?” ()
• “How do the diagrams show ?” (Each of the pan is divided into 3 equal pieces, so each of those pieces is of the whole pan.)

The purpose of this activity is for students to continue to solve problems about dividing a unit fraction by a whole number. The unit fraction in both problems is so that students will consider the relationship between the number of people sharing the macaroni and cheese and the size of the serving each person gets. When students connect the quantities in the story problem to an equation and a diagram representing the story, they reason abstractly and quantitatively (MP2).

• “How are the situations the same? How are they different?” (Both situations are about a pan of macaroni and cheese, but this one has more people sharing it, so each person gets less macaroni and cheese. When 4 people share, each person gets of the whole pan. When 5 people share, each person gets of the whole pan.)