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In the Half Blood Prince during the chapter where Harry finds the Potions book inscribed with the aforementioned title, Professor McGonagall states:

"Take Charms and I shall drop Augusta a line reminding her that just because she failed her Charms O.W.L., the subject is not necessarily worthless."

I instinctively assumed this was because she was a teacher when Augusta was a student but then their respective ages would not make sense or do they or are they incorrect? Maybe my alternate question is, what age is Neville's grandmother? I will be so disappointed if the answer to my original question is, she just knew! Thanks.

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    I assumed it was because they were near the same age and thus, peers in school on some level. Like Harry reminding Hermione in 50 years that she dropped Trewlaney's class – NKCampbell Jan 18 '18 at 20:59
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    @AdrianMann You can self-answer. It's actually encouraged. – T.J.L. Jan 18 '18 at 21:06
  • @T.J.L. its officially encouraged and i support it and encourage the OP to do it just like you. But it's worth just conceding that some individuals have something against it. It's nowhere required, but I think it's kind of good etiquette to let others have a fair crack for a few hours before giving the answer and you should make sure before you award yourself the tick that you're sure your answer is best. in all cases, the Q & A should appear in good faith. If the question is trivial or tedious it will leave a nasty taste of rep farming and cheapening the site. None of that applies here tho! – Au101 Jan 18 '18 at 21:48
  • It could be that as the head of Transfiguration, Deputy and sometimes Acting Headmistress, she merely has access to those records – Au101 Jan 19 '18 at 15:35
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Professor McGonagall knew Mrs Longbottom from Hogwarts.

It's less clear whether she knew her in the capacity of a teacher or as a fellow-student. However, Professor McGonagall has been at Hogwarts for a long time, potentially long enough to have taught Mrs Longbottom as a student.

How long have you been teaching at Hogwarts?" Professor Umbridge asked.
"Thirty-nine years this December," said Professor McGonagall brusquely, snapping her bag shut.
(Order of the Phoenix, Chapter 15, The Hogwarts High Inquisitor).

If she wasn't a teacher at the time then Minerva McGonagall still would've come across Mrs Longbottom at Hogwarts, unless Mrs Longbottom is very old indeed. There was only a two year period where McGonagall was not at Hogwarts.

Though a most efficient and gifted employee, and fond of her much older boss, Elphinstone Urquart, Minerva was unhappy in London, and found that she missed Scotland. Finally, after two years at the Ministry, she was offered a prestigious promotion, yet found herself turning it down. She sent an owl to Hogwarts, asking whether she might be considered for a teaching post. The owl returned within hours, offering her a job in the Transfiguration department, under Head of Department, Albus Dumbledore.
(Pottermore, "Professor McGonagall").

We don't have a canon statement on Augusta Longbottom's age, as far as I'm aware, which makes pinning down when she was at Hogwarts quite tough. We know that her son, Frank, was a fully trained Auror by the time he was tortured into insanity around 1981. This would mean that he was in his late teens at the earliest, although he could've been much older. Since McGonagall started teaching in 1956 she would almost certainly have taught Frank. Whether she taught Augusta depends on Augusta's age, which we can't pin down as far as I'm aware.

It would be surprising for McGonagall to know Mrs Longbottom's Charms results if they weren't at Hogwarts together. We can't be definitive, I'm afraid, but I think McGonagall's confident assertion is proof enough that her time at Hogwarts overlapped with Augusta's at some point, whether as student or teacher. She wouldn't be privy to that information otherwise.

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    If Frank was a trained Auror by '81, he must have had at minimum 7 years of Hogwarts and 2(?) years of Auror training, meaning that he was at least 11 in '72. Thus he would have been born in 61 at the latest, and so (barring very early teen pregnancy), Augusta would not have been a student of McGonagall. If McGonagall graduated from Hogwarts in 1962, then there's plenty of room for Augusta to be up to six years older than McGonagall (i.e. she had Frank between 17 and 23), while having met McGonagall at Hogwarts when the latter was a younger student. – Adamant Jan 19 '18 at 15:16
  • @Adamant I screwed up the dates. 39 years from 1995 gives a start date for McGonagall of December 1956. I agree that Frank couldn't have been born any later than 1961 or 62. If Augusta had him fairly early in life (which we don't know) then she could still have been a student of McGonagall's between 1956 and 1961. It seems more plausible that McGonagall would remember her Charms results because she was a teacher at the time. If she was a fellow-student it's less likely she would take that information on board. – The Dark Lord Jan 20 '18 at 0:08
  • I think it's entirely plausible that McGonagall, as a fellow student, could have known Mrs. Longbottom's Charms poor O.W.L. score if the latter had made a fuss of it, which the dialogue suggests did happen. – Kevin Jan 20 '18 at 1:17
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    There's also a little more room to move, where dates are concerned, considering J.K.Rowling is bad at maths. – Gnemlock Jan 20 '18 at 3:54
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    Belatedly accepted. – atw Jan 3 '20 at 16:11

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