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Optimal Cuboid

Sunday 13 November 2011

Optimising understanding with 3D shapes - A quick idea for playing with cubes and cuboids

This blog post is just a quick way of sharing an idea that is developing. I love it when ideas pop in to your head as you are teaching and you just go with them. Its a risk, but some times brilliant things happen and great ideas are born. I tried this in class this week and it got me thinking about a series of questions and challenges that could be really engaging and help students to get to grips with 3D shapes.


  • For students to play with different nets for a cube.
  • For students to explore the nets and thus the surface area of cuboids.
  • For students to consider what is an appropriate measure of 'bigness' and thus consider the idea of volume.
  • Students think about 'Optimisation'.

The Task

  • Students are given a piece of A4 card from which they must do the following;
  • Draw the net, cut out and make a cube 5cm by 5cm by 5cm
  • From the card that remains, students must draw the net, cut out and make the 'biggest' cuboid that they can!

The thinking!

The following are some of the thoughts and observations related to this activity that came out as we did it. They are in no particular order!

  • Students straight away wanted to know if their nets had to be a single piece - i answered yes so as to stick with the definition of a net and make it more of a challenge. I was pleased that students seemed to recognise a key point early on.
  • Students had to think about the different nets for a cube so they could choose one that left a maximum area of card for the cuboid. 
  • What does 'biggest' mean? And so surface area and volume are born as ideas!
  • There is no substitute for building 3D shapes for understanding how the nets work and which sides have to correspond.
  • Students are thinking about optimisation at an early age! A super concept to introduce.
  • Most importantly, students were engaged from start to finish with solving the problem and all of the objectives listed above.
  • On a technology note - I had just had a new document camera delivered to my room and it was perfect to be able to use it to show the class all the cuboids up close so we could decide which one was the biggest.
  • The ensuing debate was terrific.

The more I think about this, the more possibilities I see and I want to go away and devise a series of questions involving more complex shapes! Watch this space - I plan to post a resourced activity on this idea in the future! Thoughts and suggestions welcome!

Tags: quick idea, geometry, challenge, 3D, cubes, cuboids,


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