To learn about animal classification, we tried two simple games with my toddler. These Montessori-like Animal Classification Games included classifying the animals based on their type and classifying them based on where they live, geographically.
For the first game, I arranged some toys on a line: one wild animal, one domestic animal, one bird, one reptile. My son also included an insect. I wanted to include fish, but he was dead set against it. Under each of these groups, my son as supposed to put a line of picture cards of animals, belonging to that group. Obviously, prior to playing, we had to go over what it means for something to be a bird or to be a domestic animal, etc.
For the second Animal Classification Game, I pulled out a map. My toddler knows all continents and oceans, so firstly we went over these. Then, I asked him which animals live on which continent and he put picture cards of animals onto the right continents.
My son just turned three, so I had to be nearby in order to hep, assist and correct. This game helped him learn the basics of science and geography. We used the cards from Pick Up Pairs Game. However, any Montessori animals cards or other printable animal cards would be fine.