There are many adaptions of this concept.
Clay and stick sculpture
I have found this simple one quick to assemble and sturdy enough to stay together.
Push the toothpick into a small piece of the clay, then push the skewers into the same piece of clay on each side of the toothpick (see first photo).
Add additional blobs of clay at the ends of the skewers.
Stand the toothpick on your finger, the table, or other surface.
If pushed to one side, it will right itself.
Encourage students to experiment with various configurations of the materials and see how their new models balance, or not.
(e.g. what happens if you remove one skewer, what happens if you change the position of the skewers, does it work without the clay at the end of the skewers?...)
Quick to set up.
Try and balance the small end of a grape on your finger. It's pretty much impossible.
Add some mass below the grape, using forks, or other heavy objects, stuck into the grape at an angle.
If the forks are heavy enough an apple will work too.
A banana with a curve can be balanced on your finger if it curves downwards, as the curve puts some mass below the balance point, making it more stable.
Explanation in terms of force
The sculpture balances because most of the mass is low down underneath the balance point. When gravity pulls on these masses, the force pulling down on the balance point effectively comes from underneath it.
If the sculpture is tipped to one side, gravity pulls the weights back down to the lowest position.
Explanation in terms of centre of gravity/mass:
The exact position of the effective force on the toy is in midair underneath the balance point, and is called the centre of gravity/centre of mass. As long as the centre of gravity is below the balance point, the sculpture is stable. If the sculpture is tipped in any direction, the centre of gravity is raised. This results in gravity pulling it back towards an upright position, and returning it to its upright position.
Applications of this concept:
Engineers try to design a sports car's centre of gravity as low as possible to make the car handle better.
When high jumpers perform a "Fosbury Flop", they bend their body in such a way that it is possible for the jumper to clear the bar while his or her centre of mass does not.
When balancing on a beam, we stretch out our arms and move them around, to keep our centre of mass over our feet.