{"id":"study-related-rates-hint-questions","audience":"college","category":"studying","technique":"constraints","track":"study","title":"Get hints on a related rates problem without the solution","free":false,"task":"You're stuck on a Calculus I related rates homework problem and want to work it out yourself. Get exactly 3 numbered hint questions, under 60 words total, plain text, with no equations solved, no derivative written out and no final answer. The first question should point you to what stays constant, and all must be about this problem.","materialLabel":"The problem and your attempt (attached to your prompt automatically)","material":"MATH 1210 - Calculus I - HW 3.9 Related rates - #8\n\nA 10-foot ladder leans against a wall. The bottom slides away from the wall at 2 ft/s. How fast is the top sliding down when the bottom is 6 feet from the wall?\n\nMY ATTEMPT:\nx = distance from wall to bottom, y = height of top\nI wrote x² + y² = 10², then took the derivative and got 2x + 2y = 0, so... nothing works.\n(I know something's off with my derivative but I don't see it.)\n\nProf. Lindahl's related-rates steps:\n1. Draw it and label what CHANGES and what stays CONSTANT.\n2. Write an equation connecting the variables.\n3. Differentiate with respect to TIME (every changing variable gets a d/dt).\n4. Plug in numbers only AFTER differentiating.\n\nThe answer is in the back but I covered it.\nQuiz on 3.9 Wednesday. Office hours Tues 1-2.","rules":[{"type":"numberedItems","count":3},{"type":"maxWords","max":60},{"type":"plainText"}],"mistakes":[{"title":"Asking it to solve","why":"The AI's default is to work the whole problem, so you copy instead of learning.","fix":"Say: \"Don't solve it. Only ask me questions.\"","checks":["r0","r1"]},{"title":"Not saying how many questions","why":"The AI picks its own number, and it usually picks more questions than you need.","fix":"Be exact: \"Exactly 3 numbered questions.\"","checks":["numberedItems"]},{"title":"Trusting the AI to count words","why":"AI is bad at counting. Ask for a total and it often lands 20% over.","fix":"Cap each one: \"each question under 15 words.\"","checks":["maxWords"]},{"title":"Not saying where to start","why":"The AI may open with a general calculus tip instead of the first step your professor teaches.","fix":"Add: \"The first question should ask what stays constant.\"","checks":["r2"]},{"title":"Forgetting where it will be read","why":"AI formats for a screen, with bold and headings that show up as stray symbols in your notes.","fix":"Say: \"Plain text, no bold, no headings.\"","checks":["plainText"]}],"promptHints":[{"label":"Says how many questions","patterns":["\\b(3|three)\\b.{0,25}question"]},{"label":"Says not to give the answer","patterns":["(don't|do not|never|no).{0,25}(answer|solution|solve|tell me|give)","only (ask|question|hint)"]},{"label":"Points to the first step","patterns":["constant","changes","first question"]},{"label":"Sets a length limit","patterns":["\\d+\\s*words","word (limit|count)","under \\d+"]},{"label":"Asks for plain text","patterns":["plain","no bold","no markdown","no formatting","no headings"]}],"hint":"A tutor asks, they don't tell. Ask for questions only, say how many and how short, and say what the first one should make you look at.","rubricLabels":["Contains only questions: no statements, explanations or worked steps before, between or after them","Never writes out the correct derivative (such as 2x dx/dt + 2y dy/dt = 0), the value y = 8, or the final rate","The first question points the student to what stays constant (the ladder's 10-foot length) or what changes, and all questions are about this ladder problem"]}