TOAST is an acronym that stands for "Time Owed After School Today." It's a very simple and non-punitive consequence that we implement for students who don't follow the rules: 1) Respect all people, property, and ideas; 2) Follow directions the first time; 3) Be prepared. I make it very clear at the beginning of the year that TOAST does not mean I'm mad at you or that you're a bad person; however, there are consequences for your actions that are not consistent with our community expectations. Paying with time and doing some community service or making a plan to change student actions have been effective ways to turn negative student behavior into a positive.
During Live Investigation and Task sessions (both teacher-led), I often use a whole group discussion format just like a traditional classroom. Blended or not, there is no substitute for discussion.
The core ideas of my classroom are big ideas and themes that run through almost every lesson I teach. They are good math values, work values, life values. Whenever they come up during a lesson, I always explicitly make the connection. Next year, I plan on using a graphic for each value (some kind of eye graphic for core idea #1) to show, in my lessons, where the ideas come up.