If you haven't heard of Clothesline Math, it's a concrete way of building number sense by hanging numbers on a literal clothesline, and it can apply from elementary all the way up.
I went to one short session on it at TMC and saw solving equations, fractions, logarithms, geometry problems and more.
I'm still not confident in using it myself but I did use it once last year and never blogged about it.
I made pieces of characteristics of mathematicians and had them put the pieces in order on a clothesline.
Of course this went differently in each class and doesn't have a correct answer. I would say that they started with what I expected like getting answers quickly but through their own discussion started to move things around and highlight the things I don't want...copying others, sitting silently, and watching others do math.
My favorite part was just them explaining why they thought things should be moved aka why they think certain characteristics make a good mathematician.