sieve, sift, screen
篩 centers on separating fine material from coarse: a sieve or screen used for sifting. The meanings all relate to the action or tool for filtering particles by size.
篩 combines 竹 (bamboo) with 師, which likely contributes the sound. Bamboo was commonly used to make sieves, so the character suggests a bamboo sieve.
The top 竹 is bamboo, and the bottom 師 looks like a master or expert. Imagine a master craftsman weaving a bamboo sieve to sift flour perfectly.
For シ, picture a sieve sifting fine sand at the sea (シー): sea -> シ, and the sieve separates the grains.