This is an American thing... as far as I know we don't talk about "Common Core Math" up here in the great white North. However, the math curriculum changes as often as the seasons (okay, that's a bit of an exageration) and it's hard for teachers to keep up with it, let alone parents (I'm sure, I'm not a parent).
Anyways, I came across this article a while ago and the example in the photo stumps me
As far as I know, where I live we are required to teach our students a variety of strategies for solving problems. BUT, what I tell my students is that once they find a way that they like and that they are good at, they should stick with it. I won't ask them to do an addition question a certain way on a test, they can choose the way that works best for them... hopefully they will find a way that works best for them.
Anyways, if you are confused by all these new fangled math ways you are not alone!
Confession I taught my students this way to multiply this year
None of them use it (hardly any of them used it after I taught it, probably because I didn't devote enough time to it which is likely part of the problem with this common core math)
But if your children are coming home with confusing multiplication homework... maybe that will explain at least one strategy?