In the early months of school, we present the children with many opportunities to play with many different materials. We create invitations to explore mathematical concepts, without explicitly teaching "the right way". A basket full of mixed rocks placed in the middle of a table with two smaller, empty baskets invites a child to sit down and sort the rocks. She is in JK, and does this quickly and efficiently. The teaching team takes note of this, knowing that she may benefit from more challenging sorting provocations in the future (e.g. buttons of many kinds).
Another very young JK child plays with a set of farm animals. I approach him and tell him about our farm and how we keep the same types of animals together. The chickens are in the coop, the ducks are at the pond, and the ponies are in the barn together. He absorbs this for a moment, then finds some long blocks. He creates stalls, and begins to sort the animals by type. He pauses when he picks up the spotted pig. He sets it with the Holstein cows, looks at it for a moment, then places it with the other pig. Once again, I take note and marvel at the knowledge this young child brings with him to Kindergarten.
Patterning emerges in many areas of the classroom in these early weeks of school. I hear the SK students saying, "Look at the pattern I made!", and a few days later, I hear a JK student use the same words.
I confess, in my first years as a Kindergarten teacher, I "covered" curriculum in a way that made sense to me. I explicitly taught the children about patterns and sorting, spending lots of time creating "activities" for them to do to "prove" to me that they could do it, and checking this off my list of expectations as each child "performed" the task I'd set for them.
It turns out you can teach an old(er) teacher new tricks.
As we set out enticing, open-ended materials with no real expectation of what will be "covered", we uncover what the children already know. We keep note of children who are not yet sorting and patterning, and make a point of sitting down with them wherever they play to introduce the concepts to them in a playful, informal way.
Without teaching the whole group at the same time, we meet each child's needs in a way that respects their previous mathematical understanding and provides "next steps" to deepen their understanding.