Weights are a contract

The syllabus says: homework 20%, quizzes 20%, midterm 25%, final 35%. Most people read that as a recipe for the end of the term. It's more useful to read it as a contract that is being executed continuously — because at every moment it has already decided part of the grade, and the part it hasn't decided has a known size.

Banked, and in play

Every graded category contributes weight × score ÷ 100 course points, and those points are banked: nothing that happens later can remove them. Everything ungraded is in play: worth its full weight, from 0 to all of it.

Take the syllabus above with homework at 92 and quizzes at 85:

• Banked: 20 × 0.92 + 20 × 0.85 = 18.4 + 17 = 35.4 points
• Still open: midterm 25 + final 35 = 60 points

Two numbers fall out, and they're the two that matter:

$\text{floor} = \frac{35.4}{100} = 35.4\% \qquad \text{ceiling} = \frac{35.4 + 60}{100} = 95.4\%$

That's the window. The term will end somewhere between 35.4 and 95.4, and nothing outside it is reachable any more. On day one the window was the full 0–100; every grade you enter narrows it from one side or the other, and it never widens again.

What the window is good for

The window answers questions that a current average can't:

• "Can I still get an A?" Only if 90 is inside the window. Here it is — barely.
• "Am I safe?" Only if the floor is already above the cutoff you care about. At 35.4 nobody is safe yet.
• "Does this assignment matter?" Its weight is the answer. A 5% category can move the outcome by at most 5 points — which is either decisive or noise depending on how wide the window still is.

Notice that a current grade — the weighted average of what's graded so far — is a different number with a different job. Here it's 88.5% over the 40% of the course that's been graded. It's the best estimate of how the student is doing. It is not a prediction, and treating it as one is how a student walks into a final believing they have an A when they have a window.

When the weights don't add to 100

Real syllabi are often partial — you've entered three categories out of six, or the department leaves 10% for participation you haven't defined. The honest move is to compute over the weights that actually exist rather than pretending the missing ones are zeros, and to say so. A grade over 65 declared points is a real, useful number; the same grade reported as if it covered 100 is a lie of omission.

The part that's on you

The contract cuts both ways, and the teacher's half is rarely stated: a weight you assign is a promise about how much a piece of work can matter. Put 35% on a final and you have promised that a bad semester is recoverable and a good one is not yet safe. Put 5% on it and you have promised the opposite, whatever the syllabus says about its importance.

If those promises don't match what you tell students in week one, the weights win — they're the part that executes.

Run it

Open the grade calculator with exactly this syllabus loaded — homework and quizzes in, midterm and final still open:

1. Read the landing strip: solid teal is banked, the lighter band is still in play. Confirm the window against the arithmetic above.
2. Enter a midterm score. Watch the window close from both ends at once — a good score lifts the floor, a bad one drops the ceiling.
3. Set the final's weight to 5% and look at the window again. Same student, same work so far, and a completely different set of futures.