8. Perimeter and Area

One of the more powerful ways for young students to understand the meaning and distinction between perimeter and area is to get a lot of string and a lot of square foot tiles. Then, demonstrate that, with a fixed perimeter (i.e., a fixed length of string) different areas can be enclosed, and vice versa (i.e., a fixed area can have different perimeters).

As first efforts, you might take 8 square foot tiles. In a 2-by-4 arrangement, the perimeter is 12 feet, but in an L-shaped arrangement of 3 and 5 tiles, the perimeter is 16 feet.

Conversely, with 12 feet of string, a 2-by-4 rectangle can be roped off, and the area is 8 square feet. But a stack of 1, 2, and 3 tiles constitutes only 6 square feet even though its perimeter is also 12 feet.

Later, teams of students can be handed different rectilinear shapes and then asked to determine their perimeters and areas using mathematics (formulas or measurements). Their answers can be empirically verified by cutting the appropriate lengths of string (determine whether it fits the perimeter) and collecting the appropriate amount of surface area (determine whether it covers the region). Here you should use paper square foot tiles so that they could easily be cut into smaller pieces.

Clearly we have:

Q. an obvious question, “Determine the perimeter and/or area of a given rectilinear region.”

R. The answers are obtainable via measurement and formulas.

V. The results are verifiable by actually surrounding the periphery with the suggested length of string and/or tiling the region with the suggested amount of material.

Collaborative School Activities for the Teaching and Learning of Mathematics