Double Your Popcorn, Double Your Pleasure

This problem applies and extends skills and knowledge in several directions; estimation, measuring both linear and mass, construction, surface area, proportion, methods of calculating the volume of different shapes ... Part of the benefit of such a question is that it sends a loud message about how we use mathematical vocabulary and how precisely it describes concepts. What does it mean to double something? If we are referring to a three dimensional object, which surfaces do we have to double? What are the implications for the increase in size?

Presenting this problem as it is on the site will be further helped by having all the likely resources for making containers readily available.

Tell me about the amount of popcorn this container will hold.

The last part of the problem gives an idea for a possible extension.

Some pupils will benefit from someone to one work with using cuboids made from unit cubes and talking about the volumes.