I have an older son who is really into math/science/engineering. He also learned to count to twenty by the time he was 18 months. He learned how to count three objects because I had a rule that he could't eat more than three pickles in a sitting. I never tried to teach him anything because I thought this was normal but right before he turned three (I remember because his baby brother had just been born) a fire truck passed us and he said, "there are four tires on the truck, so if there are four on the other side, it has eight tires!" I was shocked because I'd never taught him any addition or subtraction. After this, he started talking about it all the time. In the bathtub, he would sit and just calculate "Four plus two is six! Five minus three is two!" Soon after that it became clear that he could do small multiplication and division (he hasn't memorized the times tables, he can visualize it in his head). All this is to say that I'm not sure that you need to teach it. Your child will probably intuitively grasp basic addition and subtraction.
My husband is a mathematician and he is mostly focused on instilling a love of math in our kids so he doesn't teach any math but they talk about interesting concepts together and we read books about math ideas and mathematicians. Through these discussions, my older son has developed a sophisticated grasp of advanced mathematical concepts even if we haven't really focused on teaching any basics.
My second son, who is now 2.5, is similar. He is obsessed with those little counting bears that schools use to teach kids counting. I bought a set with matching cups and they have been his favorite toy for at least four months. He sorts them by color, arranges them in shapes or letters (he tries to spell his name), he makes beds for them and carries them around in a box. I think they are great to play with but also imagine they help him to develop a real understanding of quantities. There are a ton of activities you can find online or in books if you want to use the bears to teach specific concepts. I just let my younger son play with them for now.
Both of my sons love to cook with me and they learned about fractions and measurement this way. I also let them play with measuring cups in the bathtub. My 2.5 year old loves to carry a measuring tape around and measure things and loves to read a book called "Me and the Measure of Things." There is also a similar one about time.
There is a toy called inchimals that are blocks with numbers and animals on them and they also function as rulers. They are fun to build with, play with and also to measure and do some math if your son is interested.
My 2.5 year old loves his numbers place mat. It has numbers from 1-1,000,000. His babysitter (a preschool teacher) was shocked that he can identify numbers up to 100 but he learned them by staring at this place mat and playing games where he insisted that we cover a certain number with a bean or strawberry. This sounds simple but I was shocked a few months ago to discover that my 5 year old's classmates cannot identify numbers up to 100. Again, I thought that was normal behavior.
Finally, let your kid play with lots of blocks and Legos and building toys.
