5.SS.1: Design and construct different rectangles given either perimeter or…

Fence It, Fill It: Area and Perimeter Grades 3–4

Which mat is really the biggest? Does the same fence always hold the same garden? Can the same rug need more edging? Four lessons where students tile, stretch rope and chalk the schoolyard to find out that area and perimeter measure different things.

• Does the same fence always hold the same garden? 50–60 min

  Teams stretch the same 12 m rope loop into different rectangles in the schoolyard and find that a fence of the same length can hold 5, 8 or 9 square metres. Students find perimeter by adding the sides, find area by multiplying, and recommend a shape for a school garden.

• Can the same rug need more edging? 45–60 min

  Teams build every rectangle they can from the same 24 square tiles and find that the edging around them runs from 20 to 50 tile edges. Students explain that the same area can have different perimeters, and use length × width = area to find a missing side.

• How much turf for an L-shaped playground? 50–60 min

  Teams chalk a real L-shaped playground in the schoolyard, split it into rectangles to find its area, and discover that cutting a corner off a rectangle takes away area but leaves the perimeter exactly the same. Then they design their own playground to a set of criteria.