Third Grade · Math · week 30

Same area, different perimeter

Explore how rectangles with the same area can have different perimeters.

Here is a surprise: two rectangles can have the SAME area but DIFFERENT perimeters. A 1-by-12 and a 3-by-4 rectangle both have area 12, but their fences are different lengths.

Long skinny rectangles have bigger perimeters; boxy (square-ish) rectangles have smaller perimeters for the same area. Farmers and builders care about this a lot.

📋 For the teacher
Teach it (10–15 min):
  • Build several same-area rectangles with tiles and measure each perimeter.
  • Connect to factor pairs — the side lengths must multiply to the area.
  • Ask a real question: least fencing for a 12-square garden?
  • Let them discover the boxy-is-shorter pattern themselves.
Talk about it:
  • Can two shapes share an area but not a perimeter?
  • Which shape has the smallest perimeter for a fixed area?
  • How do factor pairs help you list rectangles?

Mastery looks like: They generate same-area rectangles and compare their perimeters, explaining the pattern.

Common stumbles: Assuming same area forces same perimeter; using side lengths that do not multiply to the area.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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