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 Post subject: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 8:02 am

Joined: Mon Jul 08, 2013 2:32 pm
Posts: 192
My Ds seems to be struggling with 3d cubes, questions such as which cube cannot be made from...?
We have a rubiks cube and he places post-its on each side so he can get an idea of whether the sides match the cubes represented on the multiple chioice selection and using this method he gets it, however without the rubiks cube hes getting the majority of 3d cubes wrong.

Has anyone got any ideas? As apart from taking the cube in the exam with him with a million post-it notes i can't really think of any ideas and how likely has 3d cubes come up in the CEM exams in the past?

All replies greatly appreciated.

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 8:15 am

Joined: Mon Aug 22, 2011 8:20 pm
Posts: 1706
Location: Warwickshire
Get him to start by looking at the shapes on the cube:
Are there any (there usually are!) which have an order of rotational symmetry of 1, in other words can only face one way, such as the 'J' if the shapes on the cube are letters?

Focus on this shape and imagine unfolding the cube to create a net? What is on the left/right/below/above your key shape?

This should help to eliminate at least some of the possibilities.

Also look at shapes which are next to each other on the 3d cube you are given. If they are next to each other on the cube, they can't be two apart on the net - either on opposite sides of a strip of 3 or 4, or separated by another object if they are in a strip of 3 or 4.

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 8:32 am

Joined: Sat Mar 06, 2010 11:39 pm
Posts: 2080
This came up recently:
viewtopic.php?f=2&t=33078&p=388078&hilit=Nets#p388078

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 10:14 am

Joined: Mon Jul 08, 2013 2:32 pm
Posts: 192
Thanks Okanagan and KS10, he usually loves nvr but becomes really disheartened when cubes come along, i'm going to try the rotational symmetry and the previous post that KS10 kindly suggested cutting the cube out on paper and folding it up himself.

Thanks

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 10:18 am

Joined: Sat Jan 05, 2013 5:34 pm
Posts: 49
Just as in KS10's link I printed cube nets from the internet and cut them out. I asked my DS to pick one each time we worked as a fun warm up or if I was marking his work.

I would give him colouring pencils and get him to colour edges that would join together in the same colour, and then decorate faces on the cube that would be opposite with the same symbol/picture. Then he made the cube to see if he was right or not. Sometimes I asked him to colour each set of 3 corners that would join together as fast as he could.

We would discuss afterwards how it spot easily which edges and corners join and which faces are opposite. We talked about which edges would "sew" together. I think it helped him to get faster at mentally building the cubes from nets in his mind or taking them apart. Later we looked a little at direction of the symbols on the sides and how they move around. Anyway - it was quite fun and more light relief than working through books or problems!!!

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 11:20 am

Joined: Mon Jul 08, 2013 2:32 pm
Posts: 192
Hi Sanna, forgive me but did you give him a cube that was already made into a cube and then he coloured it in and then made the same cube again?
Or did he colour in the cube but it wasn't made and then he made the cube?

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 12:21 pm

Joined: Sat Mar 06, 2010 11:39 pm
Posts: 2080
And don't forget IronMikeTyson's rules:

when you have the 3 squares going across, the 1st and 3rd are opposites in the cube.
When you have 4 squares going down 1 +2,,3+4,2+3 will be next to each other. 1 + 3,2 &4 will be opposite

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 1:19 pm

Joined: Mon Jul 08, 2013 2:32 pm
Posts: 192
Thanks KS10
Lots of cube making tonight.

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 1:29 pm

Joined: Sat Jan 05, 2013 5:34 pm
Posts: 49
Hi Catwoman, I don't think my explanation was at all good! Let me try to be clearer.

I printed out some flat unmade net shapes for cubes from the Bond online resources (you have to sign in) where they have the 11 types of nets for cubes ready to print out.
https://www.*** Advertising Censored ***.co.uk/nt-bond/fr ... 0Cubes.pdf

I cut each of them out keeping them them flat and not made into 3-d cubes. I would ask my DS to pick one and then:
- try to work out which pairs of sides would join together if the cube were made and colour along each pair of sides with a different coloured pencil
- try to work out which pair of sides would be exact opposites to each other when the cube is made up and on each pair draw/colour a quick picture/symbol
- try to work out which sets of 3 corners would join together when the cube is made up and mark each set of three with a different colour

After he had a go (and sometimes I timed him so he would work fast) he was then able to fold the shape and make it into an actual 3-d cube, and we would see if his colour coding worked or not.

It helped him to really understand how to spot opposite sides quickly (which can help rule out options) and to be much faster at figuring out which sides would be adjacent etc.. You can also draw arrows on sides and see what happens when the cube is made up - how the arrows change directions.

I guess if any child is not a natural at it you could start the other way round as you suggest and make up a blank cube, get them to colour it and see what happens when it is pulled apart. This might be a more gentle way to introduce the concepts! We didn't try it this way round.

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 Post subject: Re: 3D CUBES NVR ?Posted: Wed Oct 09, 2013 1:47 pm

Joined: Mon Jul 08, 2013 2:32 pm
Posts: 192
Thanks Sanna
Yes thanks for the clarification that really helps i'm going to print out your suggestion with the cubes and start on it tonight

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