The other day W told me that sometimes one plus one equals one. I was a little skeptical, but I've been helping him understand addition by showing him that it is a process of putting things together. I've been emphasizing the process of addition because I don't want math for him to be what it mostly was for me and most children: meaningless manipulation of symbols. I remember some half-hearted attempts at making math meaningful in school by making us solve contrived word problems or insisting upon units. One teacher would become upset if the class answered "what is 3 pigs plus 3 pigs?" with "6" instead of "6 pigs".
In any case, I asked W when it might happen that one plus one equals one. He replied that when he attaches one toy to another toy, he has one toy. I liked that example. I suggested another by taking two glasses of water and pouring them into a third glass, showing that one glass of water plus one glass of water can equal one glass of water. The best example was then suggested by Beth: if you add one herd of sheep to one herd of sheep, then you have one herd of sheep. I was happy to see W developing an understanding that our answer depended on how we performed the addition, as well as what we were interested in counting.
So there you have it. Sometimes one plus one equals one.