In addition, the extension sections of the Shanghai syllabus also enabled Shanghai students to develop
new and innovative mathematical ideas through investigation, history of mathematics and projects. Some
examples of innovative topics were as follows: a) history of number (grades 1 to 2), b) foreign exchange
of currency (grades 4 to 5), c) puzzles and cultural mathematics such as “The Nine Chapters Arithmetic”,
d) mathematical proof such as why √2 is not a rational number (grades 6 to 7), e) the use of optimization
theory in industrial production and human management (grades 8 to 9), and f) projects involving
probability in daily life problems (grades 8-9).