1. Put the numbers in order
I've been working a lot with L or putting the numbers 1-5 in order (forwards and backwards), so this task provided good reinforcement. Depending on your child's level, you could start with a random number and ask them to find the numbers that go before and after it, or arrange them by skip counting (by 2s, 5s, etc..). It might be fun to play 'complete' the pattern with older kids and arrange them in all sorts of interesting sequences.
2. Magic Wand Number Tap
When I asked the girls to tap the correct cup with a (magic) spoon as I called out the number, they were very excited (who would have thought!). This is a great exercise in number recognition. It would have been fun to place a coin on top of the correct cup as well.
3. Number Swiper
I didn't get a picture of this one, but we arranged a subset of number cups in order and then I asked the girls to close their eyes while Swiper the Fox (character from Dora the Explorer, played by Mommy) removed one of the cups. They had to figure out which one was missing.
4. Hidden Treasure
Nothing gets Preschoolers more excited than a little
-What number comes right before/after seven?
-What is the smallest/largest number (from the available set)?
-If you have four cookies and you give two to your sister, how many will you have?
This is where (in my opinion) math starts getting fun because you get into problem solving, not just memorization.
5. Role Reversal
Let your kids make up some problems for you to solve. This proved really tricky for my 3-year-olds who absolutely loved hiding a treat under one of the cups for Mommy, but had a really hard time saying the number on the cup without pointing at it. Older kids can probably come up with some good word problems.. we'll have to continue playing this to see if my kids start getting more creative.
6. Free Play
A side note: There are probably a dozen more things to do with these cups if you combine them with other manipulatives, but I intentionally tried to avoid counting exercises (i.e. put the correct number of objects in the cup) because we've been doing a lot of that lately, and I want the kids to be able to work with just the numeric representations of those quantities..
UPDATE: I was so inspired by how much my kids enjoyed early math "games" that I created the La La Logic Critical Thinking Curriculum for 3-6 year olds, which includes online brain challenge games, printable worksheets, enrichment activities and more!