• A bag of gumdrops (If you can't find gumdrops, try using bits of rolled-up clay, mini-marshmallows, or partly-cooked beans. Be creative!)
• A box of round toothpicks

Start with 4 toothpicks and 4 gumdrops. Poke the toothpicks into the gumdrops to make a square with a gumdrop at each corner.

Poke another toothpick into the top of each gumdrop. Put a gumdrop on the top of each toothpick. Connect the gumdrops with toothpicks to make a cube. (A cube has a square on each side. It takes 8 gumdrops and 12 toothpicks.)

Use more toothpicks and gumdrops to keep building squares onto the sides of the cube. When your structure is about 6 inches tall or wide, try wiggling it from side to side. Does it feel solid, or does it feel kind of shaky?

Start with 3 gumdrops and 3 toothpicks. Poke the toothpicks into the gumdrops to make a triangle with a gumdrop at each point.

Poke another toothpick into the top of each gumdrop. Bend those 3 toothpicks in toward the center. Poke all 3 toothpicks into one gumdrop to make a 3-sided pyramid. (A 3-sided pyramid has a triangle on each side. It takes 4 gumdrops and 6 toothpicks.)

Use more toothpicks and gumdrops to keep building triangles onto the sides of your pyramid. When your structure is about 6 inches tall or wide, try wiggling it from side to side. Does it feel solid, or does it feel kind of shaky?

You can make a very big structure out of squares and cubes, but it'll be wiggly and will probably fall down. If you try to make a structure out of only triangles and pyramids, it won't be wiggly, but you'll probably run out of gumdrops and toothpicks before it gets very big. A 4-sided pyramid has a square on the bottom and triangles on all 4 sides. When you make a structure that uses both triangles and squares, you can make big structures that are less wiggly.

Build a square, then poke a toothpick into the top of each corner.

Bend all 4 toothpicks into the center and connect them with one gumdrop, to make a 4-sided pyramid.

What other ways can you use squares and triangles together? How big a structure can you make before you run out of gumdrops?

Stretching and squashing -- some basic principles

Even though your gumdrop structures are standing absolutely still, their parts are always pulling and pushing on each other. Structures remain standing because some parts are being pulled or stretched and other parts are being pushed or squashed. The parts that are being pulled are in tension. The parts that are being squashed are in compression.

Sometimes you can figure out whether something is in tension or compression by imagining yourself in that object's place. If you're a brick and someone piles more bricks on you, you'll feel squashed�you're in compression. If you're a long steel cable attached to a couple of towers and someone hangs a bridge from you, you'll feel stretched -- you're in tension.

Some materials -- like bricks -- don't squash easily; they are strong in compression. Others -- like steel cables or rubber bands -- don't break when you stretch them; they are strong under tension. Still others -- like steel bars or wooden toothpicks -- are strong under both compression and tension.

What's the big deal about triangles?

As you've probably already discovered, squares collapse easily under compression. Four toothpicks joined in a square tend to collapse by giving way at their joints, their weakest points. A square can fold into a diamond, like this:

But if you make a toothpick triangle, the situation changes. The only way to change the angles of the triangle is by shortening one of the sides. So to make the triangle collapse you would have to push hard enough to break one of the toothpicks.

If you want to, you can use your gumdrops and toothpicks to build some strong structures that are made by combining triangles and squares. The pattern on the left is one that's similar to some used in modern bridge design.

Looking for other triangles in structures around you may give you ideas for other designs you can build with gumdrops and toothpicks.

Published by Owl Books,
Henry Holt & Company, New York,
1996 & 1997

ISBN 0-B050-4536 & ISBN 0-8050-4537-6 ,
$12.95 each