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 Post subject: Dulwich College paperPosted: Wed Jun 29, 2016 3:39 pm

Joined: Thu Mar 12, 2015 4:11 pm
Posts: 171
Hi all,

This is a question from an old Dulwich College paper that I can't now find anywhere online (so no URL I'm afraid). There is a picture of large cuble 3cm x 3cm x 3cm which is made up of (27) 1cm cubes. I would be grateful for help with c) and d). I must admit I'm struggling to understand what they mean by these questions.

20. A cube with sides 3 cm is made from smaller cubes of side 1cm as shown.

a) How many small cubes are used in making the bigger cube?

b) If the bigger cube is painted blue all over, how many small cubes will have
three blue faces?

c) How many small cubes share a face with 5 other small cubes?

d) How many small cubes share a face with exactly 2 other small cubes?

Thanks

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 Post subject: Re: Dulwich College paperPosted: Wed Jun 29, 2016 3:56 pm

Joined: Thu Mar 12, 2015 4:11 pm
Posts: 171
Actually I think just got it....

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 Post subject: Re: Dulwich College paperPosted: Thu Jun 30, 2016 12:24 pm

Joined: Mon Jun 13, 2016 11:43 am
Posts: 10
I must admit it's not an easy one for a 11 year one.

Is it 4 for c and 0 for d?

Is there a technique to solve it or child is expected to draw and then visualise?

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 Post subject: Re: Dulwich College paperPosted: Wed Jul 06, 2016 6:42 am

Joined: Tue Jan 21, 2014 5:50 pm
Posts: 38
(a) 27 small cubes are used in making the bigger cube.
(b) 8 cubes on the vertices will have three blue faces.

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 Post subject: Re: Dulwich College paperPosted: Wed Jul 06, 2016 9:09 am

Joined: Fri Oct 11, 2013 8:55 am
Posts: 500
What do they mean by 'share a face' in parts c) and d)?

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 Post subject: Re: Dulwich College paperPosted: Wed Jul 06, 2016 12:39 pm

Joined: Wed Jan 18, 2012 11:41 am
Posts: 4584
Location: Essex
What do they mean by 'share a face' in parts c) and d)?

I assumed 'have the whole of one of their flat bits touching the whole of a flat bit of another small cube'? So the one right in the centre will 'share a face' with six other small cubes. The fewest shared faces any cube can have is three (the ones on the vertices, which have the most faces showing to the outside).

_________________
Outside of a dog, a book is a man's best friend. Inside of a dog it's too dark to read.Groucho Marx

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 Post subject: Re: Dulwich College paperPosted: Wed Jul 06, 2016 12:56 pm

Joined: Fri Oct 11, 2013 8:55 am
Posts: 500
What do they mean by 'share a face' in parts c) and d)?

I assumed 'have the whole of one of their flat bits touching the whole of a flat bit of another small cube'? So the one right in the centre will 'share a face' with six other small cubes. The fewest shared faces any cube can have is three (the ones on the vertices, which have the most faces showing to the outside).

I thought perhaps that, but seemed a bit of a strange question.

So if that's what it means then I guess c) would be 6 (the 6 small cubes whose face is at the centre of each face of the the large cube) and d) would be zero?

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 Post subject: Re: Dulwich College paperPosted: Wed Jul 06, 2016 1:00 pm

Joined: Wed Jan 18, 2012 11:41 am
Posts: 4584
Location: Essex
What do they mean by 'share a face' in parts c) and d)?

I assumed 'have the whole of one of their flat bits touching the whole of a flat bit of another small cube'? So the one right in the centre will 'share a face' with six other small cubes. The fewest shared faces any cube can have is three (the ones on the vertices, which have the most faces showing to the outside).

I thought perhaps that, but seemed a bit of a strange question.

So if that's what it means then I guess c) would be 6 (the 6 small cubes whose face is at the centre of each face of the the large cube) and d) would be zero?

I guess so

It may just be an odd way of phrasing it, but I think most children would be able to work out what they meant.

_________________
Outside of a dog, a book is a man's best friend. Inside of a dog it's too dark to read.Groucho Marx

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 Post subject: Re: Dulwich College paperPosted: Wed Jul 06, 2016 1:26 pm

Joined: Thu Mar 12, 2015 4:11 pm
Posts: 171
Those are the answers I got to: c=6 and d=0.

I think people who write papers should refrain from questions that are not clearly understandable. 'Share a face' isn't a clear enough expression. If they can't think of a better one they should scrap the question altogether. eg. 'Share a face' could mean that the small cube has a face that is part of a face of the large cube.

My DD almost got there when I explained to her what the question was meant to say.

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 Post subject: Re: Dulwich College paperPosted: Wed Jul 06, 2016 1:41 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11934
'Share a face' is very imprecise terminology and not one I've ever heard a specialist maths teacher use.

The words have no place on an exam paper when children are under pressure anyway.

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