When teaching basic geometry concepts, such as perimeter and area, you will save yourself quite a bit of grief if you start by making clear the difference between units and square units. Our common abbreviations for these, such as cm and cm², look deceivingly similar to each other and are easily confused by students who don’t have a thorough understanding of their meanings.
I address this problem in two ways. First, I equate units with a string and square units with a tile. To illustrate, I draw this:
We also do activities in the classroom where we actually measure perimeters of figures with strings and areas with some handy little one-inch square tiles I found buried in a cabinet one year.
Secondly, I require younger students to write out “square cm” instead of using the abbreviation, at least until sixth grade when they’ve had some more experience with exponents.
When we begin working with volume, I go through the same routine with the addition of a centimeter cube, and the younger students write out the label “cubic cm.”
Time spent on cementing this concept clearly and solidly will pay big dividends in the long run!