The purpose of this activity is for students to draw a diagram representing the product of a unit fraction and a non-unit fraction. Then students use the diagram to represent the product with an expression and find its value. Students may draw many different diagrams that represent the situation. The context of sports fields was chosen to encourage students to divide the square in thirds, vertically or horizontally. Then students divide the two thirds that represent the sports in half, horizontally or vertically, to represent the part of the sports section that will be used for soccer fields. The Activity Synthesis focuses on the expressions and equations that represent the area for the soccer fields. Students reason abstractly and quantitatively throughout as they relate their diagram and the expression representing it to the park (MP2).

• “How can you adapt your diagram to show that  of the park will be used for sports?”
• “How can you adapt your diagram to show that of the part that is used for sports will be soccer fields?”

• Invite students to share their drawings of the soccer fields.
• Display the image from the student solution or use a student-generated image.
• “How does the diagram represent ?” (There are two vertical slices of the park on the left that are of the park.)
• Display expression:
• “How does the diagram represent  ?” (The top half of the left of the square is shaded darkly.)
• “How does the diagram represent how much of the whole park will be used for soccer fields, which is also the value of ?” (It shows 2 pieces that are each of the whole.)

The purpose of this activity is for students to relate expressions to a diagram in a situation where they represent the product of a unit fraction and a non-unit fraction. Students work with a diagram that represents a different park. Students write expressions, trade with a partner, and interpret their partner’s expressions and match them to a diagram. As students work together, listen for how they explain why the expressions represent the corresponding areas. While the activity focuses on relating expressions and parts of the diagram, in the syntheses students find the value of products and analyze equations in terms of the park (MP2). As students discuss and justify their decisions while looking through each others’ work, they share mathematical claims and the thinking behind them (MP3).

• Ask previously selected students to share their thinking.
• Display:
• “What part of the diagram does this equation represent?” (It represents the section of the park that is swings. We can see that the swings take up of of the park.)
• Display:
• “What part of the diagram does this equation represent?” (It represents the section of the park for grass, which is of of the park. It is also of the whole park.)
• Display:
• “What part of the diagram& does this equation represent?” (It represents the section of the park for the pond, which is of of the park. It is also of the whole park.)