I would be so grateful for your insight: the initial lesson check… what does that look like? How do you-without wasting classroom time-create those groups in real time?
The initial lesson check is 1 or 2 quick questions that address the "verb" of the lesson objective. Each groups work is predetermined. You can post the activities for each group on the board. For example , purple, green, and yellow groups. List what each group should do. Then as you are assessing the lesson check, assign a color on the spot, based on performance. Once you give them a color, they can look to the board and know what to do next.
I don't have one recorded, but I'm ela, the principle is the same. Get them used to working in groups before incorporating content. Then base the content on their data-proven ability.