I just finished 10 years in the classroom and I have switched grades or classroom every single year. Yes, I know! It's a lot. Having moved grades or classrooms every year, I have learned to not use the storage in my classroom as much and invest in my home. It makes it easier to move every year. I'm not a big fan of file cabinets so I resulted to using a binder.
I store the buckets in the cabinets in my classroom until we get to the unit. Once we get to the unit I pull the bucket and keep it in the math area. That way when I finish with different centers and activities I can put them right back in the bucket instead of sitting it somewhere.
Any centers, games or materials that I had not used at the end of the unit goes into my sub tub or guided math bucket for review or RTI.
Works like a charm!