If math is about measurement, then Mathletics may have your child's number. Much like games that post the best scores of players, the Mathletics SOAP API makes student scores accessible to programs as well as its website.
Google has just introduced a new Enterprise Service, "Google Maps Coordinate", a web and mobile application that helps businesses manage and improve the efficiency of their mobile workforce. You can check out the Google Coordinate API here.
The prevalence of mashups on the web is probably thanks to the Google Maps API and other mapping APIs. It remains the most popular type of mashup, more than three times the second-most, photos. The ubiquity means maybe map mashups have lost some of their luster.