This paper summarizes the contents of our workshop. In this workshop, we presented and discussed the « Greek » multiplication, given by Eutokios of Ascalon in his commentary on The Measurement of a Circle.

We discussed part of the text from the treatise of Eutokios. Our basic thesis is that we think that this historical method for multiplication is part of the algorithms friendly to the user (based on the ideas that the
children use in their informal mental strategies). The important idea is that the place value of numbers is maintained and the students act with quantities and not with isolated symbols as it happens with the classic algorithm. This helps students to control their thought at every stage of calculation. We also discussed the Russian method and the method by the cross (basically the same as « Casting out nines ») to control the
execution of the operations.