Here's something I copied off a classroom wall at Mission HS.
Imagine it a lot prettier with stick figure examples.
I don't differentiate between these three very well (at all) with my students. The always insightful Grace also pointed out to me that it helps the teacher differentiate the three types of activities. Often a teacher calls something "group work" but what it really is just students working in parallel. It's one of those "no duh" moments I always have when I walk into someone else's classroom.
Addendum: Something I forgot to mention in my last post. Mission HS is experimenting with Geometry for every 9th grader regardless of whether or not they even took Algebra in 8th grade. During the class they emphasize the algebra components within geometry, mainly working with the coordinate plane, graphs, and solving equations. As sophomores, students then go back to either taking Algebra or Advanced Algebra.
They had a whole bunch of interesting reasons. They felt students could use a fresh start and didn't need their math history to haunt them into high school. Geometry itself is so different that perhaps students who hadn't had success in math would find something in geometry. Their freshman courses were heavily skewed along racial lines. The standard math sequence is screwy anyway since you'd be better off doing Advanced Algebra (Alg II) immediately after Algebra instead of having a year off with Geometry.
I'm curious to follow up next year. Last year I wrote about how inspiring the group of math teachers are and nothing I saw changes my opinion. I really don't know if Geometry for all ninth graders is a good idea. Someone in California politics thought Algebra for every 8th grader was a good idea. But they're willing to stick their necks out and experiment and do what they believe is the right thing.
PS - Mission is the school featured in the article Everything You've Heard About Failing Schools is Wrong.