Solve it backwards, and say it early

Every student who has ever asked "what do I need on the final?" was asking you to run the contract in reverse. It's one line of algebra, and the answer is often a number nobody wants to say out loud.

The inverse

Forwards, the grade is banked points plus whatever the open work earns. Backwards, you fix the target and solve for the score:

$\text{needed} = \frac{\text{target} \times \text{total weight} - \text{banked}}{\text{open weight}}$

Homework 20 at 92, quizzes 20 at 85, midterm 25 at 78 — banked 18.4 + 17 + 19.5 = 54.9 points, with the 35-point final open. For a 90:

$\frac{90 - 54.9}{35} = \frac{35.1}{35} = 100.3\%$

An A is gone. Not "unlikely" — arithmetically gone, by three tenths of a percent on a final that only goes to 100, and no amount of effort changes it. The calculator doesn't print 100.3; it reads the same result and says out of reach — even 100% falls short, which is the sentence you'd have to say anyway.

The same formula produces the three other verdicts worth knowing:

• Above 100 → out of reach. The target died before the exam.
• Between 0 and 100 → an actual number to work toward.
• At or below 0 → already secured. Even a zero on the final gets there, which is information a stressed student deserves just as much as the bad news.

The number nobody computes: when it died

A calculator tells a student where they stand today. It cannot tell them the thing that matters most: the moment the door closed.

Follow the ceiling — the best grade still reachable — for a different, weaker student on the same syllabus. It starts at 100 and falls every time a below-target score arrives. Homework at 60 drops it to 92. Quizzes at 55 drop it to 83. A midterm at 48 drops it to exactly 70.

At that instant, a C requires a perfect final. One more point lost on that midterm and a C was mathematically impossible — in week eight, for a course that ends in week fifteen.

Nothing in a normal gradebook surfaces that. The student sees a percentage that is bad but not obviously terminal, and keeps attending a class whose outcome was decided a month earlier.

What you owe, and when

This is the ethical payload of the whole course, and it's arithmetic rather than opinion:

If a target has become unreachable, that is information the student has a right to have on the day it happens. Not at the final. Not in an end-of-term email. On the day, because on that day their options are still real: withdraw, change the plan, negotiate a retake, or decide deliberately to take the lower grade for reasons of their own.

Three habits, none of which take a policy change:

1. Check the ceiling, not the average, whenever you enter a big grade. The average tells you how it's going; the ceiling tells you what's still possible.
2. Say the number. "You'd need 100% on the final for a C" is specific, checkable, and impossible to misread as a mood.
3. Say the good version too. "You've already secured a B" is the same computation and it changes behavior just as much.

A grading system that can answer "what do I need" and never volunteers "nothing will work" is a system that only speaks when the news is good.

Run it

Open the grade calculator with the midterm now entered:

1. Read the "for 90% you need" line: out of reach — even 100% falls short. The window above it says why — it tops out at 89.9%.
2. Read the letter table under it. B and C come back as reachable numbers; that's the conversation to actually have.
3. Now load the student from the figure — 60, 55, 48 — and read the top of the window: exactly 70.0%. A C needs a flawless final; anything less and the course is already decided. Then ask the real question: in your own gradebook, this term, who is already past a door they don't know closed?