I like to encourage students to discover rules and formulae for themselves. It’s important that students understand where the maths comes from so they can apply their skills effectively. They also don’t have to rely on remembering a rule (which they may forget when they are stressed).
Image credit: http://www.ck12.org/geometry/Surface-Area-and-Volume-of-Cones/
This resource is a neat and effective way to investigate the surface area of a cone through measuring circles and creating a 3D shape. Students get a physical feel for how the dimensions fit together. Throughout the lesson I let students choose their degree of accuracy in cutting, measuring and calculating. Of course, when we discussed the ‘solution’ at the end of the session it was impossible for me to put one correct answer on the board. So I generalised using a and b for the radii – explaining that everyone could check their method in general terms. The lovely ‘penny drop’ moment happened when my a’s and b’s suddenly became a general rule. I’d conned the class into using algebra because of the accuracy issue.
Download the worksheet and answers here: Surface_area_of_a_cone
Hint: Copying onto coloured paper or card makes this activity stand out in their notes.