The work presented in this chapter focuses on numeration and the calculation of arithmetical operations through mechanical instruments that have partially automated them. The sequence is based on the careful observation of two pin wheels calculators filmed in ad hoc videos. The machines are a “Lightning calculator” adder and an Odhner type “Brunsviga 20” multiplier.
These machines being at the same time mathematical and technological objects by nature, the activities carried out with them logically achieve objectives in the two disciplines, and beyond, as it were, through the linking of both of them. More specifically, working with these machines is designed to lead to a concrete, in-depth understanding of their operating principle which in turn, sheds new light on the mathematical objects and concepts involved in the operations they perform, like numeration basis and orders, carry-over, multiplier, quotient, divisor and remainder and also associativity and distributivity.
After presenting the machines and their historical context, the teaching sequence is detailed. Implementation in class is then presented and pupil productions are exhibited, illustrating the way the above objectives are achieved. The chapter ends with paths to go further in mathematics, in technology and in the history of science and technology.