What are some hands-on ways to teach perimeter to third graders?

String. Have them make shapes with string, then they can straighten out the string and find out the total perimeter of each shape.

When I was in fifth grade, my teacher gave us each one index card and scissors and asked us to cut the card so we could fit our head through it. If that’s too tricky, you can just ask your kids to cut the card so it has the greatest possible perimeter. The main lesson here is that a shape can have the same area (since cutting the index card doesn’t change the amount of paper) but the perimeter can get arbitrarily long.

I did this with fourth graders when I was a teacher, and then taped their paper strands to the ceiling, and tried to see if any could reach the floor. We didn’t measure the perimeters exactly, but the kids could tell which had the greatest perimeter pretty easily.

In response to finkelitis’s point, there’s a way to cut an index card so that you can step through it. Here’s a link that shows how, although I wouldn’t suggest having the kids do this. You could make this one and then challenge them to see how big they can make it.

[note about the link they actually cut off a strip of paper in the third step, however you can avoid this by just cutting along the fold, instead of below the fold]

Maybe this is obvious and boring, but you could also have them use a measuring tape and use it to measure the classroom, hallway, etc. Whoever is holding the end of the measuring tape should be able to tell what the perimeter is. String and index cards are way more fun though.

One of my favorite activites is in the Marilyn Burns book, About Teaching Mathematics (which by the way if you don’t already own you should DEFINITELY get, not just for perimeter lessons but for every area of math – I find it indispensable). In this lesson the kids trace their own foot onto a piece of centimeter-square graph paper. They look at their foot tracing and estimate the perimeter. Then they lightly tape a piece of string along the tracing line, then unstick the string and measure it. The use of the kids’ own feet adds a great hook for their interest and attention to the meaning of perimeter.

Incidentally, once you start studying area, the foot tracings again come in really useful. The kids can shade in each square unit and keep count as they go (it’s great to have them debate the best ways to keep track of how many they have shaded – in groups of 1, 5s, 10s, 100s, etc). Then they can also shade in the partial square units, looking for pieces that together make a whole square unit. This activity is fun, meaningful, and has the added benefit of being good practice for those questions on the standardized tests that ask them to estimate the area of a circle, or some other shape where they need to visualize partial units adding together to form whole units.

PS – I have found I need to do a short lecture before either of these “foot” activities about keeping one’s comments about other people’s feet (or socks, or shoes) to oneself, with some sort of strict consequence, such as not being allowed to do the activity, for those who break this rule. Otherwise comments about size/smell/etc. can lead to hurt feelings.

PPS – You keep your socks on. :-)

(or you could use hands)