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Next Size Up

The challenge for you is to make a string of six (or more!) graded cubes.

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More Pebbles

Have a go at this 3D extension to the Pebbles problem.

Cylinder Cutting

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Why do this problem?

This activity would be perfect to give to a very high-attaining pupil.  It offers a starting point that can lead to a hugh variety of avenues to pursue.

Possible approach

Present the pupil with a kitchen roll (or similar) tube and introduce the activity as suggested.  If the learner is not accustomed to exploring mathematically, you might consider encouraging them to look at all the angles involved (both of the required shape and the pieces cut off the $A4$). If s/he still needs more prompting then you might consider suggesting they explore these angles further.
 
There are further suggestions in the hints.

Key questions

Tell me what you have so far.
Which direction do you want to go in now?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.