Beulah buttoned her spring jacket and clutched her lunch bag in her hand as she surveyed the schoolyard. Both Effie and Nell and were absent and Minnie was inside working on math. Beulah hoped that she would see someone sitting by herself, but all the other girls had tight knots of friends gathered around them. The largest group gathered around Winifred Waldfogel, and even some of the boys stood close by her.
Great names there. But too many of them for the top of a scene. Each will take attention away from the reader getting to know the main character. What's important? It's lunchtime. Beulah is alone. We don't need to know why she's alone. What we need to know is how it makes her feel. So Get rid of Effie et al. Mention them later, as needed.
Beulah buttoned her spring jacket and clutched her lunch bag in her hand as she surveyed the schoolyard.
This does a good job of identifying the character and providing enough info that we know the situation: School. Lunch. Spring.
You don't need "in her hand." You only need to add more to "clutch" if the whatever is being clutched in something other than her hand (her teeth, for example).
Now to make the buttoning of the jacket more important (so it doesn't just seem like a way to get action in there), think about adding something that hints at why she's buttoning. Like if it's early spring and still chilly, maybe she buttons it "tight" or "up to the neck" or she buttons "every button."
Blocking is important here because you have two actions that require hands. You can clutch using only one hand, but it's hard to button using only one hand. It can be done, but more likely you'd put down whatever is in your hand and button using both hands and then pick up the whatever again.
That might be more description than you want for a relatively unimportant action. So think about a substitute action that accomplishes the same sort of thing, but without hands. Maybe, if you want to show that it's cold, she can "hunch her shoulders against the wind" or stick her free hand in her pocket or use that hand to pull up her hood.
Beulah hoped that she would see someone sitting by herself, but all the other girls had tight knots of friends gathered around them.
Hmm. This is okay, but I wonder if you can make it more active, not just a sort of static hope, but something that shows this in motion? You're designing the scene, so you can do almost anything. :) I'm thinking of something like Beulah seeing a classmate sitting alone and starting over there, but before she can get there, a knot of girls emerges from the school and heads to gather around the bench.
The largest group gathered around Winifred Waldfogel, and even some of the boys stood close by her.
Again, this is fine, and I love the name. But think about putting Beulah in motion. She starts towards the one bench, where there's only one girl, but then the other girls beat her there. She turns (she does need somewhere to sit to eat lunch!), and is looking right at Winifred and sees that the group around her is even larger.
I like that "even some of the boys" because it tells me subtly that this isn't high school yet because it's unusual for boys to be hanging around girls, and it's a testament to Winifred's attractiveness that they're hanging around.
Just think about showing Beulah's hope and disappointment in action. It's not a big deal; the emotion is really what matters. And actually, if this is for children, especially middle-grade or lower, you might want to state the emotion out (Beulah hoped) as the younger reader might not be experienced enough to interpret the action as "hope and disappointment".