(pre meaning from able to sit up to able to write circles and lines)

By far the cheapest game for teaching I have ever played is 'clean up' I am serious, cleaning up is sooo educational, and can be more educational if you want it!

Take a toy, any toy you have been playing with. ask your kid to 'sort' as you pick up. Whatever you ask for don't get mad the first billion times when your kid doesn't get it (eventually they will, and will ask you for the toys!)

Now you know your kid wont start out having a clue what sort means, so we start with simple questions:

"can I have the short skinny block?"
"the square block?"
"the doll with brown hair?"
"with blue eyes?"
"all the big trucks"
"all the green dinosaurs"
"the A piece/book"
"the number 5"

If you allow more than one toy out at a time back up to 'all the blocks' or 'all the cars' move on to more specific when the room has only one type out (or only a few).

Kids are like sponges, they soak up information whether you want it or not, we can only chose what information is available.