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The Third Dimension

Age 5 to 11
Challenge Level Yellow starYellow starYellow star
Primary curriculum
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Lots of you sent us excellent solutions for The Third Dimension. Chris and Michael from Moorfield Junior School, and Lily and Ruth from Brecknock Primary School in Camden managed to find eight arrangements altogether, including the one which we drew in the question. Lily explains how she systematically looked for them all:

To do this problem I used unifix cubes to help me. First I started with a long block, then I took one cube off and moved it to different positions making sure I didn't do the same one twice. I kept the cube in the middle and moved a second cube from the end to make a square. After that I moved this brick into further positions.

Here is Ruth's drawing which shows these arrangements very clearly:
eight arrangements of four cubes joined together

Ciara (from Bristol) explained her strategy:

First I built a tower with multilink where all four blocks were in a row. I called this 'The Tower'. Then I kept three in a row and moved one block into other possible positions. I gave them both names and this helped me with spotting if I'd done any repeats.

When I'd found all of these, I tried versions where there were no more than two blocks in a row. The names were really useful especially with the 'Staircases' as I realised there were two different ways of building the staircase.

In total I found 8 different possibilities for arranging four cubes.


Thank you for these good solutions. Well done !

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Make a cube out of straws and have a go at this practical challenge.

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How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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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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