The purpose of this activity is for students to consider situations and the operations involved in order to select reasonable numbers for each situation. Students are given a set of numbers which must each be used once in the statements. Students may find that their initial thinking does not work with the given constraints and they may need to revise their work (MP1). They also need to think carefully about the units involved and consider whether a number is representing a linear unit or a square unit. Students may solve these problems using several different strategies.

• “How can we use a diagram to represent the situation?”
• Draw a diagram to represent the rug situation. “What numbers might make sense for the length and width of the rug?”

• Ask previously selected students to share their solutions.
• “Which numbers did you think made sense for the width of the rug in feet?” (I thought any of the numbers 5, , or made sense.)
• “How did you decide which number to use for the width of the rug?” (The product had to be . So I tried a width of 2 feet and that was too small. Then I tried a width of 3 feet and that worked with feet for the length.)

The purpose of this activity is for students to match different diagrams and expressions representing the same product. In the previous several lessons, students have studied different ways to find products of a whole number and a fraction using arithmetic properties such as the distributive property. Earlier in the unit they learned about the connection between fractions and division. Students combine these skills as the expressions and diagrams they work with incorporate both the distributive property and the interpretation of a fraction as division (MP7). Students may match diagrams to expressions differently than the ways that are listed in the Sample Responses. Encourage students to match the expressions and diagrams in a way that makes sense to them, as long as they can accurately explain how the expression is represented in the diagram they chose.

MLR7 Compare and Connect. Invite students to prepare a visual display that shows their thinking about their favorite diagram and expression. Encourage students to include details that will help others understand what they see, such as using different colors, arrows, labels, or notes. If time allows, invite students to investigate each others’ work.
Advances: Representing

• Display Diagrams B and D. 
• “How are the diagrams the same? How are they different?” (They both have the same shaded area and the same divisions inside. The top one shows the length of the shaded rectangle. The bottom one does not have enough information to find the shaded area.)
• Invite students to share their favorite ways to find the product.