ooey gooey science-y
But it's inevitable isn't it? I do recall getting slime out of gumball machines as a kid. On purpose. It seemed to the thing to do at the time. There are two main varieties of slime: polymer and non-Newtonian fluid. So if your little grossologist must have slime, here's how to do it.
Polymer slime aka borax and school glue (pictured above):
Polymer Slime instructions
Note: This is my favored slime. It's not all that slimy, it keeps for a while in a baggy or my least favorite plastic storage container, and it generally cleans up and behaves itself.
Non-Newtonian slime aka cornstarch/corn flour(UK) and water:
Instructions plus science
A page with lots of silly cornstarch slime vids
Note: This stuff is a menace. When it's being a liquid, it gets everywhere, it feels disgusting, and will destroy plumbing quick as anything. When you clean up, use a bucket, outside if possible. You need to thin the cornstarch/corn flour to nothing before it ceases it's starchy mayhem.