He is so instantly tempted to try to introduce this one to that charming Gryffindor girl from yesterday who was also emitting Potions Prodigy In Progress at three hundred yards. Unfortunately if he recalls correctly - and when attempting to collect credit for introducing talented people to each other, he flatters himself that he usually does - that one was Muggleborn, and the young Slytherins are currently rather... a way.

Well. Perhaps he will invite them both to the junior Slug Club anyway. If they make friends Dumbledore will be terribly pleased with him and if they studiously ignore each other no one will notice the missed opportunity except Slughorn.

In any event, as much as it would probably be fun to spend the whole class answering the thousand questions this child clearly has, he does have a whole class to teach, so he instead smiles at her and says, "If you have any additional follow-up questions please feel entirely free to visit my office hours, Miss - ?"

(The office hours are prominently posted on the classroom door; he gestures expansively in their general direction while he's saying this.)

"Prince, Professor.  Ophelia Prince.  Would you be so kind as to return the favor?  The Professors' names were unaccountably omitted from our schedules, and I hardly want to erroneously assume."

It had not occurred to him this would be necessary in this particular class. Usually only the Muggleborns don't know that Horace Slughorn has been the Potions Master at Hogwarts for forty years; Slytherin doesn't have those these days, and the Hufflepuffs usually give theirs an enthusiastic rundown within thirty seconds of the Sorting to help them feel included. Nevertheless, he rallies affably: "Ah, my apologies. Horace Slughorn, at your service, Miss Prince. I look forward to seeing more of you in my classroom. Now! Enough of me blathering on, let's start brewing!" 

Slughorn's philosophy of teaching is that he will slowly meander the room like a sort of ponderous friendly bullfrog, peering over everyone's shoulders as they work, and comment helpfully, whilst they practice the subtle and exacting art of potion-making. He is aware that this stresses the self-conscious ones out but he doesn't know a better way to catch dangerous mistakes, which while rare inside the heavily enchanted potions lab do not occur at a zero rate.

The instructions are reasonably straightforward. "My mum told me," says Ed conversationally to Ophelia, as he turns his textbook pages and peers at the list of ingredients, "always read the whole thing before you start," and begins identifying various things out of his potions kit, tapping their containers with a fingertip as he reaches each item on the list but not touching the actual ingredients, humming jauntily to himself. They each have their own cauldron and seem to be expected to share the classroom tools that are assigned to each two-cauldron table (various knives, measuring spoons, etcetera).

How is she to be certain that Hogwarts did not suddenly acquire a new Potions professor last year, Professor Slughorn?  Potions experiments have a habit of exploding!

Anyway.

"Your mother is wise."

Ophelia is doing much the same with her own kit, laying out the ingredients and tools precisely.  She has even brought little bits of index card to annotate the instructions upon the lab table more directly.

"Make sure to inspect your tools as well; it would be unpleasant should improperly handled residue from some other student's work impact your own."

(She is, in fact, carefully examining the common tools herself, including their cauldrons; should anything seem amiss she intends to alert the professor - Muggle chemistry of the science lab sort is usually well-solved with running water and a good scrubby brush, but she does not know enough of Potions to be sure the same techniques hold true.)

The tools are, on inspection, so pristinely clean it's realistically not possible students are responsible for cleaning them. The classroom is mostly of a state of cleanliness better in line with occasionally being scrubbed by resentful detention-goers, but the tools are supernaturally perfectly shiny.

Ed nevertheless gamely inspects a fair half of them, nodding agreeably at the explanation, and reports that he does not think any of these tools have any residue on them "but it's very sensible of you to want to check I think!"

"The moment you assume something is safe to handle is the moment you pour concentrated acid into the sink, where it promptly gets everywhere and causes much suffering.  Much like -" an almost unnoticeable pause - "being careful to keep your hand off your wand when pronouncing an unfamiliar word."

"Concentrated... acid? ... why is that a thing that there would be in a potions lab, I mean you're absolutely right that being careful with potions materials is important for that reason but what a specific example of - oh, I suppose probably it's an ingredient for acid pops, like you use concentrated vanilla extract to make cookies?"

"I suppose it must be; there's a sort of acid that all the citrus fruits produce - though I was thinking of much harsher substances."

What a charmingly Ravenclaw person this Slytherin is. Ed likes her. (Ed likes everyone but this doesn't mean he doesn't have reasons every time!)

Anyway, does she have any other things she wants to do before they get started? They're not terribly behind schedule, they have all class period to do something that, judging from Slughorn's reported lesson plan, normally takes half that long at worst.

She is quite ready to begin.  In fact, she has already begun.  Carefully.  There are graduated cylinders involved, and sifting devices (so as to ensure that no fragments of snake fang are unground).

(There's also a metronome.  And a (mechanical) kitchen timer.  Those, however, come later in the process.)

Ed is just going to put his snake fangs in the mortar and grind them with a pestle according to the gently animated picture in the textbook like a normal person but he will watch Ophelia's process with delighted interest while he's doing it. 

Slughorn does not ask Ophelia what on Earth she is doing because it seems likely that she is one of those people who if you ask them a question they will speak unless interrupted for, like, an hour, but he does, when he is not busy answering various questions (such as how to operate the cauldron burners, where to find the measuring glasses, whether this porcupine quill is enough of a whole to count as one and not three-quarters of one...) stand interestedly over her shoulder a bit, as he's taking it in turns to do with everyone, and occasionally nod approvingly.

"Professor, a question: When...measuring...measures, is it more important that they be allocated in the same action or series of actions, or of equal resulting volume?"

(A measure, as Ophelia has learned from the textbook, is a fraction: when the instruction says "four measures of ground snake fang," it means, "divide your ground snake fang into four parts." This is not what it means in standard mundane English, but what do wizards care if they have vocabulary collisions with Muggles?)

"The value of this standard is twofold, Miss Prince: most potions which ask you to divide your ingredients into measures do so both because they do not want you to add too large a volume quite all at once, which is what you'd get if you had too few measures, and because they do not want you to add it so slowly that it is, as you say, no longer part of the same action, which is what you'd get if you had too many. Does that answer your question?"

"That is the exact opposite of an answer to my question, unfortunately; it has in fact given me more questions.  If it is as you say the rate of addition that matters, then why is the process not accomplished by use of a funnel or similar flow-restriction device?  I had been expecting that the probable rationale of a 'measure' or portion was numerological significance, not a matter of volatility."

"Ah, well, yes, if you try to use a funnel instead you do eventually run into problems caused by numerology but that sort of thing is normally beyond the scope of a first-year Potions class. I would gently advise against getting into the habit for this reason, if you wish to progress beyond OWL-level Potions someday, but if it would help you while you are learning I will not stop you."

This kid is going to get twelve awards before she even takes her OWLs and he's going to get to proudly shake hands with the Minister about it, it's going to be awesome.

She nods.  "I see.  We return to my original question of whether it is more important that the portions be equal or singular, then."

"What do you mean by 'singular'?"

"Divided in the same act and then not further mixed or mingled."

"Ah! No, it is much more important that they be of equal volume. It is under the vast majority of circumstances safe to separate them approximately and then weigh them and adjust, for example, and you'll be specifically warned if it isn't."

While he's saying this, and distinctly not using the phrase 'perfectly safe', he gestures in the direction of a banner over the blackboard, which reads in elaborate glittering multicolored calligraphy PERFECT SAFETY IS JUST A DANGER YOU HAVEN'T NOTICED YET. It was a gift from one of his NEWT students a few years ago who was really into magical ink and is now a professional signmaker.

"Thank you, Professor."  And she can, with that sorted, portion her snake fangs!

"...Of equal volume or of equal mass?"

"Oh, mass, of course."

(Slughorn, not being either a historian or much into Muggle studies, doesn't know this, but wizard academics actually noticed that weight and mass are not the same thing sooner than mundanes, on account of the number of materials they regularly interact with which levitate.)