The purpose of this activity is for students to write expressions for and find the area of shaded regions whose side lengths are a unit fraction and a non-unit fraction. Students look at a series of diagrams with an increasingly large shaded region so they can look for and make use of structure (MP7).

It is important to relate the work here to what students have already learned about the product of a unit fraction and a unit fraction. This is the goal of the Activity Synthesis. For example, students have seen that . Since is six s, the product will be six s or .

• Ask previously selected students to share the patterns they noticed in the table.
• Display the expression from the last problem: .
• “¿De qué manera el diagrama muestra ?” // “How does the diagram show ?” (The first row of pieces in a square is  of the square.)
• “¿De qué manera el diagrama muestra ?” // “How does the diagram show ?” (There are 6 pieces shaded and each one is of the row.)
• “¿De qué manera el diagrama muestra ?” // “How does the diagram show ?” (There is of a row shaded and that row is  of a square unit.)

The purpose of this activity is for students to write multiplication expressions to estimate the area of a shaded region. This builds on the Warm-up and the Activity Launches by asking students to write an expression for the shaded region in the image they considered in the Warm-up.

This work in this activity combines the skill of estimation with an understanding that the area of a rectangle relates to its length and width. So far, students have only calculated these areas as products of fractions when at least one side length is a unit fraction. Students may write products of two non-unit fractions. While they have not yet learned how to calculate these products and relate them to areas, these answers are valid when the estimates are reasonable and students will learn in the next lesson how to find the value of these expressions.

• Ask previously selected students to share their solutions.
• Display the first diagram.
• “¿Cómo nos ayuda pensar en  a estimar el área de la región coloreada?” // “How does thinking about help us estimate the area of the shaded region?” (We know the area is less than  because only part of is shaded.)
• “¿Aproximadamente qué fracción de  está coloreada?” // “About what fraction of is shaded?” (More than of . Maybe of or of .)