In this activity, students consider possible side lengths for a rectangle with a perimeter of 12 inches, and visualize each rectangle. Students may notice many patterns as they find different rectangles (MP7) including:

• The sum of the length and width is 6 inches.
• The length and width can be exchanged to give a length and width pair.
• When the length is a fraction so is the width, and vice versa.

• Invite students to share a set of side lengths.
• Record responses. This table will be used in the next activity.
• If students do not offer fractional side lengths as an option, consider asking students to consider a pair of side lengths that includes fractions.

In this activity, students build rectangles, with a perimeter of 12 inches and varied side lengths. Then they reason about the side lengths of rectangles, the perimeters of which are multiples of 12.

If students show they may be confusing the idea of perimeter with that of area, consider asking:

• “How did you determine the length and the width of the rectangle?”
• “How could you draw or use the chenille stems to represent the perimeter?”

• Invite students to share their responses to the last two problems and their reasoning.
• “How did you know that 5 chenille stems were used in the last problem?” (60 is 5 times 12.)
• “How did you know that the side length of the last square is 15 inches?” (The perimeter of a square is 4 times its side length. )
• Consider displaying a table as shown here to highlight the relationships between the number of chenille stems used, the perimeter of the square, and the side length of the square.

  number of chenille stems	perimeter (inches)	side length of square (inches)
  1	12	3
  2	24	6
  5	60	15

In this activity, students continue to think about the relationship between side lengths and perimeter by drawing (on grid paper) rectangles when given the perimeter, one or both side lengths, or the relationship between two rectangles. They apply what they learned in an earlier unit about comparing quantities multiplicatively.

• See the Lesson Synthesis.