SACone

	Proving the Surface Area of a Cone
	Description/Aim
		In this activity students are given minimal data about a cone and asked to build it from card. In doing so students have to consider Pythagoras theorem, arc lengths and sector areas as well as deducing the net of a cone. Having done this, students use their discoveries to deduce and prove algebraicaly the surface area of a cone. Its practise of skills in the context of problem solving and presents an engaging challenge! There are 2 attached files, one for the activity itself, then one with some related challenges
	Teachers Notes - Why? How? What?
	*Why* we like this activity …. This can be a wonderful example of learning by doing! The end goal of a physical cone provides the incentive to solve the problems they encounter along the way. Students have to use what they have learned about sector areas and arc lengths to work out the relationship between the sector that makes the curved surface area and the circular base. the ensuing discussions are excellent practise of the skills. The discovering the net of a cone by testing theories with paper and cone is fun to watch! In short this activity can bring out the best of students problem solving skills. It is fun and fruitful How this activity be used …. I have used this with a top set group of 14 year olds grouped into threes. My input was minimal and limited to probing questions when I felt a group needed an injection. My colleague suggested 'Hint Cards' that could be requested every so often to make the activity more accessible to other groups of students. Obviously it becomes more accessible the more information you give, but it is important to leave the element of discovery. We did proving the formula together. What to expect when using this activity – from our experience The biggest hiccup I had was not having the means to draw large circles and then not having good enough materials to stick the cones together. I would reccomend tape and staplers! Theorywise, students were thrown by the curved surface area being the minor sector rather than the major one - as was I, I must admit *Extra Notes*