What if someone challenged you to cut a hole in an index card big enough to squeeze your entire body through the hole? Believe it or not, it’s possible and all you need is an index card, scissors, and a hefty dose of critical thinking and creativity.
Fold the notecard in half the long way.
Use the scissors to make a cut about 1 cm from one end of the notecard. The cut should start at the fold and end just before the edge of the notecard. Be careful not to cut all the way through!
Repeat step 2 on the other end of the notecard.
Unfold the notecard. Use the scissors to cut along the crease of the large middle section. Do NOT cut through the slits on each end that you created in the previous steps.
Fold the notecard once again.
Start on one end of the notecard. Make a cut about 1 cm away from your first cut. Start on one side and go almost to the edge on the other side but do not go all the way through.
Make another cut about 1 cm away from your cut in step 6. This time, however, start your cut from the opposite side of the card. Again, go almost to the edge on the opposite side.
Continue moving along the card making cuts about 1 cm apart. Each time, alternate which side you start the cut from and do not cut all the way to the other side.
Once you have cut to the other end of the card, carefully unfold the notecard and gently pull it open.
You should have a giant ring which you can step through and maybe even squeeze your entire body through!
A standard 3×5-inch index card has an area of 15 square inches and a perimeter of 16 inches. No big deal, right?
But here’s the twist: cut that card into a 1/4-inch chain and the area stays put at 15 square inches. The perimeter, however, jumps to an astonishing 120.5 inches! The surface area of the card never changes, so the width of the ring directly impacts the length.
So what’s the lesson here? You can dramatically change the perimeter without touching the area. It’s a fantastic, hands-on way to get kids thinking about the difference between area and perimeter. Turn that humble index card into a math adventure.
Remember… by carefully cutting the index card in the pattern above, you are redistributing the entire surface area across the length of the ring, all while keeping the surface area connected. The closer together you make your cuts, the longer the ring will be.
This isn’t just a one-hit-wonder of a lesson. Kids also get to play with the concept of relative size. That tiny index card can stretch out to be a big ol’ chain that you could practically hula hoop through. How big of a circle could you make using a standard sheet of typing paper (8.5×11)? On the other end of the spectrum, how big of a circle can you cut using a business card or an old playing card?
What if we told you that you can fit a quarter through a dime-sized hole in an index card? Would you believe it was possible? […]
