The purpose of this activity is for students to understand that rectangles with the same perimeter do not necessarily have the same area. In the Activity Synthesis, students begin to consider how to systematically draw different rectangles with the same perimeter.

• Select students to share their rectangles and to explain how they knew the perimeter was 16 and how they found the area.
• “We just showed that rectangles with a certain perimeter do not always have the same area.”
• “How would you explain to someone how to draw rectangles with a perimeter of 30 that had different areas?” (Choose a length for two of the sides, like 10, and then double that to get 20. There’s 10 left for the other two sides, so each side will be 5. Split 30 in half to get 15. The two different side lengths need to add up to 15, so we can use different pairs of numbers with the sum of 15.)

The purpose of this activity is for students to draw rectangles with the same perimeter and different areas. Students draw a pair of rectangles for each given perimeter. Then they display their rectangles and make observations about them in a Gallery Walk.

Students may notice new patterns (MP7) in the rectangles with the same perimeter (for instance, that as two sides each increase by 1 unit, the other two sides each decrease in length by 1 unit). They may also notice that, so far, all the perimeters are even numbers. Students may wonder if it is possible for a perimeter to be an odd number. If these observations arise, consider discussing them in the Activity Synthesis.

• “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 perimeter did you and your partner choose to work with when you could choose your own perimeter? Why did you choose that perimeter?”