Let's use a different way to color the eggs for this Easter.

For this experiment, we are placing each raw egg in a container, pouring enough vinegar to fully cover the egg's surface and finally putting some food paint in it. Repeat this process for as many eggs as you like using different colors of food paint. Let the eggs rest in these mixture containers for 2 days.

The result is squishy and more transparent eggs.  

Let your child experiment with these transformed eggs, compare them to usual raw egg. They will touch, feel their elasticity and try to break. Using a flash light you can show the increased transparency of these eggs.

Finally, we use this opportunity to draw parallels between the tooth (enamel) and the egg shell, and also vinegar's resemblance to the acid that is the result of anything we eat. Brushing teeth regularly will help remove this acid from mouth protecting our tooth (enamel).

More science behind what's going on

Vinegar contains acetic acid and this acid breaks apart the solid calcium carbonate crystals that form the egg shell into their calcium and carbonate parts.

If you use a glass/transparent container, you may observe a lot of bubbles. So what causes those bubbles?  Breaking apart calcium carbonate occurs by detaching electrons from the calcium which renders calcium missing electrons; calcium ions that float free. These detached electrons are attached to the carbonate creating carbon dioxide, that is, the bubbles you see.