I am not 100% sure on this, but it looks very like a diatom. These are a range of very diverse unicellular algae found world-wide in soil and water environments (salt and fresh). There are a huge number of species (also genera, families etc.).
The reasons I think that this is a diatom are that it has what appears to be a thick transparent wall (photos 2 and 3) and has a "cut in half" shape - where the word diatom comes from ( _dia_ divided, _tomos_ I cut). Diatoms are usually between 20 and 200 micrometres long, so 250-400x observation fits fairly well.
I think what you have here is a pennate diatom (see images under "classification"). Some pennate diatoms are motile
There's an image of one that resembles yours here (see second image)