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 Post subject: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 11:21 am

Joined: Fri Apr 23, 2010 9:08 am
Posts: 93
Does anyone know which three squares need to be shaded in question 20?

Is it a trick question? Doesn't seem possible at first glance.

http://fluencycontent-schoolwebsite.net ... 2016-p.pdf

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 11:34 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13044
It's very poorly worded - what do they mean by 'line'?

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 11:36 am

Joined: Fri Apr 23, 2010 9:08 am
Posts: 93
Yes, there are the two diagonals and then the horizontal and vertical ones

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 11:37 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13044
A line of reflection can be anywhere!

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 11:44 am

Joined: Fri Apr 23, 2010 9:08 am
Posts: 93
If the diagonals are the only lines meant, then there are just 3 squares needed

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 11:49 am

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13044
The question should say diagonal lines if it means that.

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 12:24 pm

Joined: Mon Mar 02, 2015 11:15 am
Posts: 131
In order for the shape to be symmetrical about a line of reflection, the line of reflection must bisect the shape into two halves of exactly the same size. If one were to imagine a vertical line of reflection (with two and a half squares to the left/right) then I can't see a way to make the shape symmetrical about that line by shading just three squares; the same is true if you imagine a horizontal line of reflection (with two and a half squares to the top/bottom).

Many candidates would get confused at this point and 'burn' time trying to figure it out. The more able candidates would immediately realise that there are two possible diagonal lines of reflection and either one could form a line of symmetry, if the correct squares are shaded. There are multiple solutions (depending upon which of the two diagonals is chosen).

I suspect that they intentionally didn't point out the option of diagonal lines of reflection.

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 12:51 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 13044
No, goodheart, with respect, I totally disagree.

It's a poor question - it does not make it clear it has anything to do with the symmetry of a square - a line of reflection can be anywhere.

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 1:14 pm

Joined: Mon Mar 02, 2015 11:15 am
Posts: 131
Guest55 wrote:
...it does not make it clear it has anything to do with the symmetry of a square - a line of reflection can be anywhere.

I think the fact that the question says, "Shade exactly three squares so that the shape has reflection symmetry about any line" should give the reader at least a hint that it's a question about symmetry. I agree that the question isn't terribly clear.

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 Post subject: Re: St Albans High School for Girls maths questionPosted: Tue May 31, 2016 6:21 pm

Joined: Mon Jun 18, 2007 2:32 pm
Posts: 7065
Location: East Kent
Goodheart wrote:
Guest55 wrote:
...it does not make it clear it has anything to do with the symmetry of a square - a line of reflection can be anywhere.

I think the fact that the question says, "Shade exactly three squares so that the shape has reflection symmetry about any line" should give the reader at least a hint that it's a question about symmetry. I agree that the question isn't terribly clear.

If a question can spark off such a debate between competent mathematicians, how on Earth was a child supposed to instantly pick up the nuances?

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