The correct word for the material is "plastics". Originally "plastic" is an adjective and means "deformable". Over time people have used "plastic" to mean "plastics". Unfortunately DL still does not accept "a cup made of plastics" as the correct answer. As a plastics engineer (not a plastic engineer! and apparently not very formable ;o) ) I will continue to provide the DL-wrong answer. Eventually I assume DL will catch on.
Even if it's technically so, we're teaching a language as it's spoken. So, in this case, dictionaries count more than a specific industry. (I'm also an Engineer and I notice some differences too, but I cannot demand that everyone speak as if they were engineers)
In general language, "plastics" is used to show "types of plastic materials" or "plastic materials as a whole". It's natural that industries and professionals work with "plastics", because they're supposed to know it all. You're a plastics engineer because you work with all kinds of plastics.
For all examples of a single material, they use plastic, as in "made of plastic", "piece of plastic", etc.
We cannot go against these major dictionaries. Also, "cup made of plastic" brings 32.000 google results, while "cup made of plastics" brings back 8 results.