Our formal math lessons are still working through addition and subtraction. We’ve covered up through the 7′s, I think. I don’t present more advanced math concepts usually because I want to make sure we follow an orderly progression that helps develop strong numeracy. Sometimes, though, dd figures things out on her own (which is fine).
A week or so ago she told me that she really preferred numbers that had two in them, like 4, which had two 2′s, or 6, which had 4 and 2. After we talked about this a bit, I told her about even and odd numbers. She was able to explain the difference in the result when you add two even numbers versus two odd numbers or one of each.
Another night in the car she asked me what half of 2 was. We talked about that and how to figure it, and she went on to tell me what half was for all the even numbers up through twenty. Then she asked about half of 9, so we talked about why we couldn’t do half of 9 without using a number in between 4 and 5. I didn’t bring up whole numbers as a concept.
DH surreptitiously asked me if we had covered this stuff in school, and I told him we had not. Sometimes these concepts come up while we are doing other things, so it’s not as though we never discuss them, but we aren’t formally learning them. For instance, dd offered up the fact that 16 and 16 are 32. Well, upon questioning her, I learned that she got that fact from a lullaby on a CD they listen to at night sometimes. I knew that but had forgotten, and she took that lyric and filed it away in her math facts.