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 Post subject: Dulwich College paper
PostPosted: Wed Jun 29, 2016 3:39 pm 
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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?
Answer: __________________ [2]

b) If the bigger cube is painted blue all over, how many small cubes will have
three blue faces?
Answer: __________________ [2]

c) How many small cubes share a face with 5 other small cubes?
Answer: __________________ [2]

d) How many small cubes share a face with exactly 2 other small cubes?
Answer: __________________ [2]

Thanks


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PostPosted: Wed Jun 29, 2016 3:56 pm 
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Actually I think just got it....


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PostPosted: Thu Jun 30, 2016 12:24 pm 
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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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PostPosted: Wed Jul 06, 2016 6:42 am 
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(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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PostPosted: Wed Jul 06, 2016 9:09 am 
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What do they mean by 'share a face' in parts c) and d)?


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PostPosted: Wed Jul 06, 2016 12:39 pm 
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Proud_Dad wrote:
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).

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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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PostPosted: Wed Jul 06, 2016 12:56 pm 
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ToadMum wrote:
Proud_Dad wrote:
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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PostPosted: Wed Jul 06, 2016 1:00 pm 
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Proud_Dad wrote:
ToadMum wrote:
Proud_Dad wrote:
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.

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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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PostPosted: Wed Jul 06, 2016 1:26 pm 
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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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PostPosted: Wed Jul 06, 2016 1:41 pm 
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'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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