In this paper, we discuss the way of calculations of Σ^^n__<k=1>k^p in Wasan from the view point of mathematical activities. Wasan is the mathematics which was studied until the Edo period in Japan. In Wasan, calculations were based on the number of bamboos in a bunch, as described in "kuchizusami in Japanese" which is one of the oldest mathematical books in Japan. We have considered the calculation of Σ^^n__<k=1>k^p which is called "houda in Japanese". We introduce "shyousahou in Japanese", elementary methods by Yasumoto Okayu (1794〜1862) who was a mathematician in the Edo period, and the method using diagrams and "suida in Japanese" which is a very important formula. And from the view point of mathematical activities we introduce the way of teaching calculations of Σ^^n__<k=1>k^p in the high school mathematics.
