This optional activity prompts students to analyze a design problem that involves fractional measurements. Students determine which of the three designs from the Warm-up would fit on a folder that is 9 inches wide and 12 inches tall. To do so, they find the heights and widths of each design using addition, subtraction, multiplication, or a combination of operations.

• Invite a group to share their responses and their reasoning on each design. Display their reasoning, or record it for all to see.
• Ask others if they agree and if they approached it the same way.
• Explain to students that they will now verify their responses. Assign one design for each group to verify.
• Give 12 small sticky notes to each group. Ask students to use the sticky notes to create the design.
• Next, give each group an inch ruler, and ask them to measure to see if their design is less than 9 inches wide and less than 12 inches tall.

In this optional activity, students interpret and solve problems involving fractional measurements and operations of fractions in the context of distances on a map. First, students examine the measurements on the map and use them to answer questions. Next, they interpret given expressions and consider what the expressions might represent in the situation. Finally, they write a new problem, based on the given quantities and information. The work here prompts students to reason quantitatively and abstractly (MP2).

This activity uses MLR6 Three Reads. Advances: reading, listening, representing.

• Invite 2–3 students to share their responses to the last two problems.

In this optional activity, students hone the skills they have learned in this unit: multiplying a fraction by a whole number, adding and subtracting fractions with the same denominator (including mixed numbers), and adding tenths and hundredths. Students are each given a fractional expression. They evaluate the expression, find a classmate whose expression is different but has the same value (verifying that this is indeed the case), and write a new expression that also has the same value. (See Student Responses for the matched expressions.)

In addition to evaluating expressions, students who have Cards J, K, and L also will need to think about fractions that are equivalent to the value of their expression in order to find their matches. For instance, a student may reason that the value of Card K is or , but the match—Card 2—shows . Consider using these expressions to differentiate for students who could use an extra challenge.

• Ask students to display their work around the room.
• “Take a few minutes to walk around and look at the work of at least 3 other groups.”
• “As you study others’ work, pay attention to how the work is like and unlike yours.”
• 6–7 minutes: Gallery Walk
• “What is the same about the calculations that you saw? What is different?”
• 1 minute: quiet think time
• Discuss responses.