The purpose of this activity is for students to understand that rectangles with the same area do not necessarily have the same perimeter. The work here reinforces the idea that area and perimeter are two separate measures of shapes. An area of 24 was chosen because it has many factors and is a familiar number to students.

• Invite students to share the rectangles they drew and to explain how they knew the area was 24.
• “How did you decide what rectangles to draw?” (I thought about what numbers could be multiplied to get 24, like 6 times 4, and made those the side lengths of the rectangle.)
• “We just showed that rectangles with a certain area do not always have the same perimeter.”
• “How would you explain to someone how to draw rectangles with an area of 30 square units but different perimeters?” (Think about pairs of numbers that multiply to 30, use those numbers for the side lengths, and find the perimeter of each.)

The purpose of this activity is for students to draw rectangles with the same area and different perimeters. Students draw a pair of rectangles for each given area, then display their rectangles and make observations about them in a Gallery Walk.

• “As you visited the posters, what did you notice? What did you wonder?”
• Discuss observations or questions that can reinforce the connections between side lengths, perimeter, and area of rectangles.
• Consider asking: “What area did you and your partner choose to work with when you could choose your own area? Why did you choose that area?”