In this activity, students use their knowledge of feet and inches and the perimeter of a rectangle to solve problems in context. Given the perimeter and one length of a room, they determine its width, in feet, and the distance along two walls, in inches. Students could reason about each problem in a number of ways. As they interpret the quantities in the situation and represent them with expressions or equations, students practice reasoning quantitatively and abstractly (MP2).

• Invite students to briefly share their responses to the first problem, and then focus the discussion on the last problem.
• Select students, with different strategies to find the distance the ant walked, to share their reasoning.

This activity allows students to consolidate their learning from the past few units to solve problems about length measurements in a mathematical context.

First, students find the perimeter or unknown side length of various quadrilaterals. To do so, they apply what they know about adding and subtracting fractions and about rewriting certain fractions as whole numbers. Next, they determine which pairs of figures have a certain multiplicative relationship—for instance, which figure has a perimeter that is 9 times that of another figure. Because the measurements are in different units, students need to attend to the relationship between the units and perform conversions accordingly.

The activity can be done in the format of a Gallery Walk or by giving each group a full set of the diagrams from the blackline master.

• See the Lesson Synthesis.