There are dozens (maybe thousands) of websites that explain what triangular numbers, square numbers, etc. are. I'm searching for a printed book that includes this material, preferably at a level that would be appropriate for an elementary school-aged student (i.e., someone 11 or younger). It's not typically found in elementary school textbooks or other curricula, so this would probably need to be a "Cool Math"-type of extracurricular book. Does anybody know of such a source?
There is a publication in the ERIC archive called Recreational Mathematics*, authored by William L. Schaaf, that is a bibliography of books and journal articles about recreational mathematics, organized by topic. A search in this document for "triangular numbers" yields quite a few results, for example, a page of books about "number curiosities":
A specific book that treats triangular numbers is Martin Gardner's Mathematical Carnival, which starts from Pascal's Triangle and shows the different sorts of numbers that can be extracted from it. As Gardner puts it, "the pattern is so simple that a 10-year-old can write it down."
I suggest a search through ERIC for some more recent references, or a search through the Internet Archive for some possibly older ones, may result in a list of suitable books. Some of the "out of print" books may have been revived in an affordable Dover printing.