I'm going to be teaching small (< 10 students) but very mixed group of middle schoolers (US system, ages 11-13) who have had varying amounts of pre-algebra and algebra instruction thus far. I need to give a placement test so that I know who has mastered which topics, to plan appropriately. I will probably then split the group into two subgroups, and also have enrichment activities available for students who have "tested out" of a topic the rest of their group needs to cover.
The problem is, they will show up on the first day of school rusty and not remembering much of what they learned last year. How can I quickly "de-rust" them to the point where I can get reasonable results on a placement test, preferably within one or two 45-minute sessions (with homework in between if helpful).
I'm thinking the homework might be a sample of problems like the ones they will see on the placement test, that they can hopefully remind themselves how to do. These are mostly above-average math students, but mostly lacking a parent who remembers algebra who could help remind them of what to do. So, if I could come up with (or find pre-made online) some kind of quick reference of pre-algebra and algebra topics (preferably not more than a couple of pages) that I could give them as a reference to refresh memories, that would probably be helpful.