I googled it and did some light research, so that makes me more or less an expert on this topic now.
From what I can tell, it's basically just a way of doing addition and subtraction with a focus on tens as landmarks so that you don't have to carry over the ones or replace tens with nines like what is normally taught. It looks something like this image I put in. In more complex problems (multiplication, division, etc.) they basically just use light algebra (distributive properties).
For example: 13 x 5 would become (10 + 3) x 5 and then (10 x 5) + ( 3 x 5 ).
In reality, teachers already teach this **** (and the students intuitively pick up on this) in order to explain the "old way" in the first place. Even if they don't, they'll learn it at around 7th - 9th grade in Algebra 1. It's a cumbersome and somewhat strange process, especially once more digits are being accounted for (try using this method with something like 1,256,471 - 302,468 and it'll take a lot longer than the "old way").
Regardless, this is still early math skills, and anyone who has enough mathematical knowledge to design a building is already plenty good enough at simple addition and multiplication that they can do it in their head (or maybe even a ******* calculator, something that exists nowadays).
Therefore, it's ridiculous to attribute the design of this house to Common Core, since it's more reliant on Physics rather than simple math. More likely, the designer probably had a coincidental history of being taught Common Core and then made this. It's the classic mix-up between coincidence, correlation, and causation.
TL;DR, Common Core probably didn't even have anything to do with this house.
With my experience with common core math it's not so much something you can teach, but moreorless a thought process you learn naturally over time.
I was never taught it but I use it alot for multiplication. If i have a large number such as 102 and i'm multiplying it by 9, it's much easier for me to multiply 9 by 900 and then 9 by 2, then add the two sums together, than to perform the classical method of multiplication.
All in all, i feel like common core, as most things, have at least one use. To teach it to cover every aspect of mathematics, however, is greatly exxaggerating its very limited usage.
I took math in BC Canada and I luckily was a year ahead so when the wave of curriculum changes came, I didn't have to take part in the ensuing ******** ; apparently the new curriculum was designed in part by people brought in from California. I ended up doing some tutoring in my last year of high school and met up with this system they called "Algebra squares". It took me a bit to learn the procedure, and I've honestly already forgotten it already, but I remember that it was a massive hindrance to students who understood algebra fine.
The mandatory practice of these simplifying methods might bring up some kids who were struggling before, but it definitely stood as an obstacle for kids who found it intuitive. They should be given to teachers as tools to help struggling students open their mind to think in new ways, but students who had the fortune of being taught to think mathematically from a young age do not need this; it wastes the school's time and money, as well as the students.
I tutored younger kids for a number of years, and having that time one on one with kids to see how their minds works was incredibly beneficial at my place of work, and while I can understand that public school teachers don't have that luxury all the time, this method of teaching is not a substitute for lower class sizes.