I have mainly infants and toddlers, they range from 10 months to a new 3. I do weekly themes and we work from that. I also do circle time, for those who are interested. We talk about all that you mentioned, sing, count, do finger plays, read, etc. The older children usually sit and participate and the younger ones come join as they please. The 2 year olds like to do circle time!
I also do a lot of play based "teaching". I talk a lot with them and introduce concepts as we play. For instance "J, you have a yellow star" or just randomly start singing or counting toys.
You will be surprised at what the younger children pick up! One day, I was doing circle time and one of the younger kids was sitting and playing across the room from us and all of a sudden he was holding up fingers and counting (in his baby/toddler talk, he was only 1)! Another child just started saying the ABC's randomly while playing.
They are always listening!
