Three Cubes
Why do this problem?
This problem presents a series of three-dimensional challenges which encourage the learner to visualise a solid and then use two-dimensional representations to help them to reach a solution. On the way to a solution, there are opportunities to practise using trigonometry and Pythagoras, as well as formulas for volume.
Possible approach
Each part of this problem could be tackled by small groups who could then present their solution to other groups. For each problem, it is best to take some time to visualise what is being asked, and then draw some diagrams to see what calculations will be necessary.
The third problem is about volume and surface area. In order to work these out, learners will have to calculate the dimensions of a tetrahedron cut from the corner of a cube.
Key questions
What two-dimensional diagrams can be drawn to help to solve the problems?
Possible support
Learners who have not met or are not confident with trigonometry and Pythagoras could solve parts of the problem using scale drawing.
Possible extension
The Spider and the Fly gives another opportunity to visualise a problem in three dimensions.
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