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Bundles of Cubes

Age 7 to 11
Challenge Level Yellow starYellow star
  • Problem
  • Getting Started
  • Student Solutions
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In this challenge, we will be making 'bundles' of cubes.  

We are going to start by making bundles of four cubes.

In the animation below, we start with one bundle and add an extra cube on its own, making five cubes altogether.
See what happens as we have more bundles and still keep just one extra cube:
 
 
What do you notice?
Can you explain your noticings?

We could then look at using a bundle of a different size. In the pictures below we see the same idea with bundles of six cubes and eight cubes:


 

The images above stop at 'four lots' but you could try going much further, maybe up to sixteen lots.
What happens when the bundles are of five, seven or nine cubes?

When you've done some exploring and got some results, then compare your results for the different sizes of bundles.
What do you notice?
Can you explain any of your noticings?

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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