Kids can test whether an egg is hard-boiled or raw by spinning it on a tabletop or other hard surface. Hard-boiled eggs will spin quickly, while the liquid inside a raw egg will damp its motion and cause it to turn much more slowly. Prepare the experiment by boiling a few eggs ahead of time and cooling them so that the temperature doesn't give away which is which. Let preschoolers spin the eggs to test them --- making sure they don't accidentally spin raw eggs off the surface --- then open a few eggs to verify the results.
Eggs are more dense than fresh water but less dense than very salty water. Dissolve four tablespoons of kosher salt in two cups of water and pour the resulting solution in a tall glass or other transparent container. Carefully pour one to two cups of fresh water down the side of the glass to create two layers of water with different densities. When you place an egg gently into the water, it should sink to the boundary between the layers, then float at that level.
This experiment must be performed by an adult, but the results are dramatic enough to interest preschool-aged spectators. Wet the rim of a bottle whose lip is a little bit narrower than the diameter of an egg. Peel a hard-boiled egg and prepare to place it on top of the bottle to form a seal. Light a scrap of paper on fire and drop it into the bottle, then place the egg on top. As the fire consumes oxygen, it should create a slight vacuum and suck the egg into the bottle even though the egg looked too large to fit.
The substance that makes an egg shell hard is calcium carbonate, the same substance that hardens human bones. If you soak an egg in vinegar, the acetic acid in the vinegar will dissolve the calcium carbonate in the egg shell, creating carbon dioxide as a byproduct. Let preschoolers place an egg in about a cup of vinegar and observe the tiny bubbles of carbon dioxide that form. After about a day, when the bubbles stop forming, remove the egg carefully and observe that the shell has become soft.