Maths marking scheme workings - are alternatives allowed?

[PurpleDuck]

DS was doing some past maths GCSE papers and we were checking the answers against the marking scheme. On one of the questions, his workings out looked a bit different to what was shown in the marking scheme. Given that there may be more than one way of arriving at the same answer in maths, should the marking scheme be interpreted as the only ‘approved’ way of doing things, or will any method do, as long as it’s logical and makes sense?

The particular question in this case was this:

The equation of a line L is x + 2y = 6 . Find the gradient of L.

DS calculated the gradient as -1/2 (written as a 'normal' fraction, not with a slanted line), using these workings:
2y = -x + 6

y = -x/2 + 3

According to the marking scheme, 3 marks were to be awarded for the following workings out:

2y = 6 - x

y = 3 - x/2
or
y = (6 - x)/2

Gradient: -1/2

NB. In all cases, there was a 'normal' fraction presentation, not a slanted line; I managed to type it properly in Word, just can't get it to show here.

To my mind, DS’s and ‘official’ workings out are equivalent, although visually I prefer his version as it follows the 'y = mx + c' format I am used to.

Would full marks for this question be given only if the workings out were shown exactly the same as in the marking scheme or would DS's version be acceptable?

Thanks in advance for any thoughts on this.

[Proud_Dad]

I would be shocked if your DS didn't get full marks for his answer. His working is virtually identical to the official answer anyway other than the order of the terms.

Like you said its conventional to write this sort of equation as y = mx + c.

Regardless of that the order shouldn't really matter as both are logically correct.

[Guest55]

The working is fine - did he actually state gradient is -1/2?

Just rearranging to gradient-intercept form is not enough.

[Thereason for 'their' order is so the negative is 'seen' by markers]

[PurpleDuck]

Thank you Proud_Dad and Gues55, that's a relief.

Yes, he did write the gradient as -1/2 in the space for the answer, so that was fine.

It's just that the marking scheme showed marks for workings out and I wasn't sure whether a different order of terms in the re-arranged formula would be accepted. I'm glad that would be fine; maybe I need to stop panicking.

Guest55 - when you say "so the negative is 'seen' by markers" - do you mean to avoid a risk of someone not noticing the minus sign when it's in the front of the equation and perhaps it's not written very clearly? That would make sense to me.

[Guest55]

Yes - a quick glance might miss a negative sign near an equals sign. There is a convention that a positive term is written first in an equation but in this case I would tend to write in 'y = mx + c' format. I would ensure a gap and a clear negative sign.

Never chnage a sign by crossing out/altering it - always rewrite the equation. All exam papers are scanned these days so writing does have to be clear.

[PurpleDuck]

Thank you, that's very helpful, indeed.