Slughorn explains, when everyone is assembled, that alchemy with an egg is actually where phoenixes are speculated to originate; but no one has the recipe any more and there haven't been new phoenixes for centuries. They will not be making living things today. But the eggshell is a good base from which to appear lots of possible objects; alchemy doesn't like to conjure things into existence in plain sight but is quite willing that new things appear inside eggshells, cocoons, geodes, and similar. Their eggs have been pre-drained of their interiors for this purpose, although some recipes use full eggs.
As last week, they are invited to come up with recipes on paper for review by the professor before trying anything. Known possible results available with this set of ingredients include wooden, decorated eggs nested inside the shell; a shellful of small sharp teeth (the commonest source of hens' teeth, as they have encountered once or twice in potions); successively smaller eggshells the smallest of which holds a blob of mercury; and a perfectly hardboiled egg which can be arbitrarily flavored by exact details of the process. But they are welcome to aim at another result as long as their procedure looks safe.
"And from what I saw of the dynamics I'm not sure Arens listens to anyone other than Astoria, if he even listens to her, so maybe it's faster to decide."
"Well, last year I think Hufflepuff won, and before the war Harry Potter was part of the team, but apparently before he joined Slytherin used to win most of all Houses."
"But they might have been using different strategies, they'd have had all different captains in that time."
"Yeah, and I'm on the team this year so there's an obvious confounder for which strategy's best."
The following morning, Sadde arrives at the Ravenclaw table and says, "Good morning! Guess who's the newest Beater for the Slytherin Quidditch Team?"
"My, I wouldn't know, but whoever it is I'm sure the newest Beater for the Ravenclaw Quidditch Team will have no trouble dealing with them!"
"Us civilised people don't hit other people, we make other things hit other people, or we hit other people indirectly."
"Anyway," she says, looking at Miranda. "D'you wanna practice Patronuses today during free period?"
"I didn't really get much more than mist but the last time I tried was last year, and maybe there's something to do with age, or I could try some new memories."