The purpose of this activity is for students to analyze area diagrams and use the properties of operations to interpret expressions. The diagrams are decomposed in different ways and the expressions all have a fractional part. On some cards the fractional part is written as a mixed number and on other cards the whole number and fraction are separated using the distributive property. This sorting task gives students opportunities to analyze diagrams and expressions closely and make connections (MP7).

• Display Diagram C and Expressions J and O.

• “How does each expression represent the area of the shaded region?” (There are 3 rows and each row has an area of square units.)
• Display Diagram B and Expression L.

• “How does the expression represent the area of the shaded region?” ( is the area of the full rectangle and then I take away the unshaded part, .)

The purpose of this activity is for students to write expressions that represent the area of shaded regions. Monitor for students who are writing a variety of expressions that represent the distributive property.

• Select 2–3 students to share their expressions for the first problem.
• If not mentioned by students, display:

• “How does each expression represent the first problem?” (There are 4 rows and each row has square units or square units.)
• “Did your approach change when writing expressions for the last diagram? If yes, how?” (It was easier to see the square units and apply the distributive property.)
• If not mentioned by students, display these expressions for the area of the shaded region in the last diagram: