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3D Stacks

Age 7 to 14
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This activity may be used as a follow-on for those who have successfully worked at Doplication.

 
Let me help you visualise this representation of a 3D situation.
In this example of a 2 by 3 by 4 we see in the red balls, as two layers of 3 by 4.

 new6
These two layers together can also be viewed as representing 6 cubes.

 
 
In the top picture the centre of each cube is shown with a light/dark brown ball.
 

In Doplication you would have had;
 
 axitate version
which we called $4$ ? $3$.
 
In this activity it would be called something different involving $4, 3, 2$. Just for now I am going to use @, so the diagram above represents $4$@$3$@$2$.
 
I invite you to explore many such arrangements and find a way of recording your results.
You might like to just look at the arrangements that are like cubes - $3$@$3$@$3$ , $4$@$4$@$4$, $5$@$5$@$5$, etc.
 
As with most mathematics it's good to compare so maybe compare the results for squares in Doplication and cubes in 3D Stacks.
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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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