Walls and Ceilings - Fire blocking codes

I framed a 2x4 wall that runs perpendicular to the ceiling joists in my basement. Since walls in the basement are not load bearing walls, I used single (rather than double) top plate which was nailed directly to the parallel ceiling joists. The outer side of the framed wall is spaced from 1/2 inch to 1 inch from the cement wall surface. I'm thinking about a way to install fire blocks to meet Codes in Virginia where I live. So far, I cannot think of any good way. I think I can nail 2x4 pieces extending between adjacent vertical studs to the bottom surface of the top plate and extending outwardly into contact with the cement wall surface. But there are still a lot of small gaps formed between adjacent ends of adjacent 2x4 pieces, the outer surface of the associated stud and the cement wall surface. According to Codes, I can use wool insulation to block these gaps, but I cannot find any wool insulation in my area. Please help me if you can think of a way to do it. Thanks in advance.

where I live you can use something called rotten cotton. call you local lumber yard

Ask the county inspector. Filling with fiberglass insullation may be OK. Another method is to fasten 1 inch of drywall to the inside bottim of the top plate extending to snug against the wall. Great use for small scraps.

Codes tend to vary from area to area. You need to check with your local building inspector regarding permits, codes, and inspections.