As I mentioned a few posts back my daughter Marie and her husband Erik are doing an amazing job helping their son Lachlan learn the intricacies of counting and other aspects of maths They don't force it on him, make him complete math activities, or even call it maths. They just make him aware of the quantitative and geometrical aspects of his life as he interacts with the world around him. Currently, he is coming to terms with the oral number name sequence up to twenty. He nearly has it except some of the teen numbers are a bit random.
Quite remarkably, at two and a half, he also is beginning to develop a sense of cardinality. This is when you put quantities to the number names, Right now when hes says, "one, two, three, four" etc he is just saying a sequence of words, a little like reciting the alphabet. He has cardinality with two; he can identify two objects that are the same. This is an important idea because you cannot count rationally unless you know what you are counting. He can identify two fingers or two tractors or two people. The fingers, tractors and people are the referents of the counting words, the things to which "two" refers. In early rational counting the identification of the referent is important because we can develop the idea of counting as the process of "one more"; three is two and one more altogether. The word "three" now refers to the objects which were two and one before they were joined together to make three.
This is not as easy as it sounds because there is also the ordinal and nominal use of number. The ordinal use of number, first, second, third really doesn't come into play at this point in the learning to count process. But the nominal use of number, using numbers to name things, does. In the picture above the numeral 1 appears above a single tomato, as do 2,3 and 4. It's easy for a young child to name each tomato as 1,2,3 or 4. This would be a good activity for teaching the numerals once they had been learned orally. But to teach rational counting, or the cardinal use of number, you would need a picture with one tomato next to the 1, two tomatoes next to the 2 and so on so that the numeral becomes a number associated with that many.
Making maths a part of everyday life for young children is easy if you know what you are doing. Bedtime Math is a wonderful resource I have mentioned before.