# 9 Outline lesson plan for Episode 2

Episode 2 focuses on distinguishing the necessary and sufficient logical conditions for a shape to be a roof. (Some PGCE mathematics teachers, unused to applying their own fresh logic, have found this challenging.)

Episode 2, act lathe teacher models to the class how a set of four numbers can be used in a given order to draw a roof-shape on the grid; then that another set of four numbers makes a non-roof.

Episode 2, act 2: the class work in pairs/groups on the worksheet, to find out what makes a set of four numbers produce a roof. The teacher circulates and observes, suggesting counter-examples where groups have begun to formulate a rule.

Episode 2, act 3: the teacher lists different pair/group observations and generalisations in single sentences before going back over them, sifting and checking validity and similarity, and refining or combining them, focusing on those rules that not only apply to all roof-shapes, but are necessary and cover others, then asking ‘what are the least rules necessary?’