When I told her I had successfully graded the pattern in question to a size 6 she was interested to know how I did it.
So, here are some pictures of another pattern I was grading anyway - I hope it will give her and maybe someone else the general idea on how to grade a pattern.
It's not failsafe and there are probably many other ways to do it, but this is how I learned and it gives you a place to start - make adjustments as needed.
Also this works only on patterns where all sizes are stacked on the page.
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I start by drawing straight lines through all corners, marks and notches on the pattern piece.
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Then I measure the distances between the sizes - sometimes the distance between sizes vary a lot. Take into account how much you need to enlarge by.
I find it is easier to grade a size at a time instead of doing it all in one go. But that's up to you.
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In this particular pattern the distance between all sizes were 1/4" and that was about the amount I needed to get in my finished garment too. (1/4" on each side of a front and back pattern piece will give you 1" all around).
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When you get to a corner you should get the lines to meet nicely along the line unless you have graded to add lots more in width than in length - or the other way around. Then you'll need to even out the line a bit.
If you grade on a curve try to follow the curve of the previous sizes - sometimes it helps (if you're not drawing on the actual pattern paper like I usually do) to set a start and end point of a curve then slide the original pattern piece so that it aligns and use the curve in your new size.
This is all a very basic way of doing it I guess. I'm sure there are lots of more scientific ways to do it but it works for me.
If you grade several pattern pieces - like in a blouse you have front, back and a sleeve, make sure you add the same amount on all sides so that you don't end up with a ungraded sleeve to sew into an enlarged bodice.
Toiles may be a good idea. (I guess some call them muslins).
Trial and error is the motto of the day.