This task is designed to introduce students to the ideas of calculus – in particular, finding the volume
of a complex shape (a lemon).
The design of the task incorporates a principle learned from research –
students are more interested in new knowledge if it helps them solve a problem, and they see a need
for the knowledge (Schwartz & Bransford, 1998). When students see that knowledge is important, their
brains become more primed to learn it. The task helps students see the need for important principles
in calculus. Students are asked to come up with their own ideas for finding the volume of a complex
shape – a lemon. Instead of being told a method for finding the volume, they are invited to think deeply
and creatively, using their own intuition and mathematical ideas they have already learned. Later on
they can be taught concepts such as limits, which will help them solve the problem.
In order to help students solve the problem, we provide students with a range of resources that might
help them investigate the volume of a lemon.