If you are used to the tried and true "talk a lot at the whole room for a while" method of math teaching, you aren't alone. Tons of people do it, it's marginally effective, and the kids have been institutionalized the accept it. Plus, it prepares them for college. But then you get a glimpse at the teacher who has the nice square desks that can be arranged so easily. Then you hear things about "stations" and "partner activities" and posters start popping up on the walls in your hallway. Lots and lots of literature says groups are the most effective way to engage kids with math, and they do it in science class all the time. But if you're the new teacher that knows nothing or the old standard who has done this way for years, how do you get started?

I've started experimenting and having kids in predetermined groups all day every day really lets some nice things happen. Mainly, there's a lesson or two in every curriculum that begs to be done in groups (for Algebra II it's typically linear regression models). Planning the lesson is tricky enough, but then you have to split the kids up. How do I know the right way to split them? How do I make sure one group won't just talk about nothing the entire time? Where do the strugglers go? Well if you assigned groups from the start, it's settled. One less thing to worry about. And since you know you have the groups ready to go, any lesson can become a group lesson. No need to explicitly think about how you want to divide them. And no fielding complaints about how a student isn't with their friends. Once you get comfortable you can start getting really methodical with the pairings. I have an intention that by the end of the year my high achievers will be paired up and given more challenging work. Strugglers with strugglers so I can focus my attention on one set of them and not hop around finding all of them and re-explaining things.

Basic structure of my class:

- warm up exercise on the board, 6 problems written in 6 colors with instructions to complete the matching color; alternatively, give instructions to complete the exercise matching their number (my room has six color groups with desk 1-5)
- introduce a concept, show examples, provide a sample set for the class to do with either 4 problems that everyone does with random sharing, or mimic the warm up exercises dividing by color or desk number
- for a deeper concept, create packs of index cards with exercises on them, have the kids divide responsibility but require them to complete the whole set
- assess the groupwork by questioning each group informally, or have the whole class share; the method you choose varies depending on whether all the groups had the same exercises or the groups had unique assignments

Observations:

- running through warm ups goes faster
- kids are willing to do 1 measely warm up problem
- in the past it could take 30 minutes to cover a 5 problem warm up, and most of the time no one got to number 4 or 5 anyway
- dividing a warm up "shrinks" the class as when you hit on a particular colored/numbered problem, the odds a kid gets called on rises to 1 in 5 or better
- kids from other groups will chime in with questions on a problem they didn't have to do
- high-achievers will want to know about a technique present in another group's problem
- while working, the kids know immediately what neighbors to look at for help
- kids within a group will help a member who gets called on but struggles
- during index card activities, some groups will figure out your little game and share the answers realizing it's faster than every kid for themself (which is a good thing!)
- if the colored problem set exercises have multiple steps, you can hop around the entire group to share the steps
- interesting example (needs tweaking as it was a little long, but has tons of potential): we were working on multi-step equations, each color was given a unique exercise. When I arrived at particular color, I hopped from member to member to get all the steps. Every single kid in the room had to say something aloud, in a room of 28 in one case. How often do you get that to happen?
- answering one question will spur progress in 5 kids, you repeat yourself less, kids near the one you're talking to will lean in to hear the explanation

The other day we tackled lines. I created a set of 5 index cards that were identical for all of my groups. On one side was an equation they had to graph. On the back was an unrelated line for which they should determine the equation. Every group member had to end the activity with 5 pictures and 5 equations. I've done similar sets for inverses and transformations. Where's the write up sheet or the worksheet or whatever? That's why you make them buy notebooks!