what we do
6th grade:
we have a list of what concepts our students need to master in math (as gaged by proficiency on state assessment) we do 1 of 2 things:
if we have enough information from the previous state assessment, we use that--like we have a subtest for geometry so didn't pretest there--we divided kids into 3 groups--top, middle, lowest--3 teachers (+1 resource who took the lowest and IEPS--unless one of the IEPs happened to be strong in an area, and we move that kid into appropriate class) we also use professional judgement--like if a kid scores high, but we know that group will be too fast-paced, we'll bump him down...
if a unit we're working on (all 3 of us are on the same unit at the same time) doesn't have a subtest on our assessment (like fractions--that's in computation and number sense), we make a pretest using all the skills that the assessment covers for that unit. (IE: multiples, factors, reducing, comparing fractions...) Then we use that information to group the students.
it sounds like your group doesn't want to do this, though. i'm not sure why--it makes it way easier to differentiate when a majority of the kids are in the same place with the same amount of knowledge--the whole group can work slower or easier, with no one getting frustrated (especially the teacher!)
with my fraction concept group, (of course, this is 6th grade), i did item anlaysis with the pretest and the students who already knew the concepts received a more challenging assignment on those days--they joined the class to work with me on the days they hadn't mastered skills. this led into our next unit: fraction operations (add, mult, div....) Since many of them had fraction concepts down, i knew they would know how to add and subtract fractions--we didn't regroup after this unit, just keeping our original fraction groups--so i gave my own pretest (with all the fraction operation skills represented) and used item analysis on a grid to show who knew what. (i'll attach that.)
last year for this unit, i had students work through independent packets to get what they missed (also working with me) and then they got to move on to challenge/enrichment work of their choice (advanced algebra or geometry, logic...) I did NOT have the energy to do that this year, so they are working on independent fraction work (and working with me) for the concepts they don't have down and then they all have the same enrichment packet--with bits of everything--and they get to choose from it what pages to do. these advanced students LOVE it! (and i know the slower students like working at a pace that works for them without the stress of being rushed.)
good luck!
