Despite what many people say, Chinese isn't actually that difficult a language. What it is, however, is different. Sure there are funky weird things like having tones or a non-alphabetic representation but it makes up for this by a dead simple grammatical structure, a lack of tenses, and a fairly logical way of constructing words.

Just as we have Anglo-Saxon root words that mean things on their own but which aren't used on their own, Chinese also has roots. Each individual character in Chinese generally has an independent meaning but most Chinese words are bigrams made up of two characters.

窗帘 Window + Curtain = Curtains
门帘 Door + Curtain = Door covering
草帘 Grass + Curtain = Grass mat used to insulate a greenhouse
水帘 Water + Curtain = Waterfall

超市 Great + Market = Supermarket
菜市 Vegetable + Market = Vegetable Market
市场 Market + Place = Marketplace
城市 Fortification + Market = City
上市 Up + Market = Go on the market / be listed on the stock exchange

As in English, there are still contractions with "obvious" parts of words being dropped. This mostly isn't a problem for communications unless the "obvious" part is only obvious to one half of a conversation.

On the 2012 trip, on my way out of Beijing, I deliberately planned my route to go past Laoshan Velodrome in the hopes of stopping by and saying hi to one of the coaches I knew from working at the Tour of Hainan and Tour of Qinghai Lake. Coach Li turned out to have just returned to Hainan and Coach Fu (from the People's Liberation Army Cycling Team) couldn't meet with me because, even though he was nearby, and even though the nearby place was a place I planned to bike through, he was "跟车队一起在训练". This had me very confused until I realized that instead of saying he was "out training with the bike team" he actually meant he was "out on training maneuvers with a military convoy". 

Since I only knew him in the context of being a bike coach, I was assuming that 车队 Vehicle + Squad = Bike Team when it actually meant something else very very different.

With the Tongwan City Ruins, I saw that the name was 统万城遗址 and assumed that it was Tongwan + Fortification + Ruins and that it was either the ruins of one of the forts on the Great Wall or that it was part of the Great Wall. However, in this case, the 城 in the name wasn't a contraction of 长城 (Long + Fortification = Great Wall) but was instead a contraction of 城市 (Fortification + Market = City).

The names of the three nearby villages 白城则村 (White + Fortification + Near + Village), 边城子 (Alongside + Fortification + Place), and下城子 (Below + Fortification + Place) only served to further convince me that this was related to the Great Wall (长城) rather than it being some other 城.