St Albans High School for Girls maths question

[ontarget]

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.

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[Guest55]

It's very poorly worded - what do they mean by 'line'?

[ontarget]

Yes, there are the two diagonals and then the horizontal and vertical ones

[Guest55]

A line of reflection can be anywhere!

[ontarget]

If the diagonals are the only lines meant, then there are just 3 squares needed

[Guest55]

The question should say diagonal lines if it means that.

[Goodheart]

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.

[Guest55]

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.

[Goodheart]

...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.

[yoyo123]

...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?