In this paper, we describe the skeleton of two teaching units, based on a Model for teaching mathematics, Context Orientated Teaching (COT). The first teaching unit concerns the proof of a mathematical proposition, while the second one concerns the solution of an open problem. Both are taught in the 10th grade, under the specific conditions of the Greek educational system. We conclude that the model can assist in outlining the progression of activities in the classroom, making it easier for the teacher to locate where individual students had difficulties and what those difficulties were, and helping students organise their thoughts.