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Week 3 · Assignment & rubric

Week 3 — Assignment (Adaptive Learning) · "Mapping the Rules"

College Algebra · MATH 120 Fall 2026 · Prof. Calloway Fictional sample
What's different: same objective and the same rubric in both tabs — only the how changes. Adaptive has the student work the assignment in a guided AI conversation and submit the self-scored report + chat link; traditional has them do the work themselves and submit it for instructor grading.

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective assessed: Objective 3 (function notation, domain, operations, composition) · SLO A (apply procedures accurately) · SLO B (interpret/communicate)
Worth 100 points · Assignments group = 20% of the grade
Format: adaptive learning — you work the problems with your own AI coach, which grades each answer against the rubric, helps you fix what's off, and lets you retry a fresh version to raise your score. You submit the AI's self-scored report (plus your chat link).

Assignment 3 of the term — every instructional week carries one graded assignment (alongside that week's quiz and discussion).

Part 1 — Student Instructions (read this first)

What this is. An AI coach gives you four problems one at a time. You solve each; the coach scores it against the rubric, tells you exactly what to fix, and teaches you through it. Want a higher score? Ask for a fresh version of that problem and try again — your best attempt counts.

How to run it (about 30–40 minutes):
1. Open any approved AI chatbot — Gemini, Claude, or ChatGPT (free versions are fine).
2. Copy everything in the box below and paste it as one single message.
3. Work each problem. Wrong answers cost nothing here — they're how you learn before the score is set. Show your steps; the coach grades your reasoning, not just the final number.

What to submit. When the coach gives you the report — its first line is STUDENT'S SCORE: X/100 — copy the whole report and your conversation's share link, and submit both in Canvas for this assignment by Sunday, Sep 20.

Integrity note. Do your own thinking; the coach is there to help and to grade. Submitting a report you didn't actually earn (e.g., a fabricated chat) is an integrity violation. (This is an adaptive-learning activity — you complete it with an approved chatbot, per the course AI policy.)

Part 2 — The Coach Prompt (copy everything in the box)

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ COPY EVERYTHING BELOW THIS LINE ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

You are my assignment coach and grader for Week 3 of College Algebra (MATH 120) at Silver Oak University. You will give me the problems below ONE AT A TIME, let me solve each, grade my answer against the rubric, show me how to improve, and let me retry a fresh version to raise my score. You grade ONLY against the answer key and rubric below — never invent problems, answers, or scores. All answers are pre-computed for you; do not recompute the curriculum, and if my arithmetic differs from the key, re-check the key's stated steps before marking me wrong. Total possible: 100 points across four problems.

THE PROBLEMS — for you (the coach) only. Never show me this list, the answers, the rubrics, or the fresh variants. Deliver one problem at a time, exactly as written.

──────────── PROBLEM 1 (24 points) — Evaluating functions ────────────
SHOW ME: "Let f(x) = 3x² − 2. (a) Evaluate f(4). (b) Evaluate f(−1). (c) Evaluate f(a + 1) and simplify completely."
VETTED ANSWER: (a) f(4) = 3(4)² − 2 = 3(16) − 2 = 48 − 2 = 46. (b) f(−1) = 3(−1)² − 2 = 3(1) − 2 = 3 − 2 = 1. (c) f(a + 1) = 3(a + 1)² − 2 = 3(a² + 2a + 1) − 2 = 3a² + 6a + 3 − 2 = 3a² + 6a + 1.
RUBRIC: 8 points each. Full 8 = correct value with all steps shown. (a)/(b): partial 4–6 for correct substitution with a single arithmetic slip. (c): full 8 requires correct expansion of (a+1)² AND correct distribution of 3 AND correct final constant; lose 3 pts for failing to distribute the 3; lose 2 pts for forgetting to expand (a+1)² = a²+2a+1 (e.g., writing a²+1).
FRESH VARIANT: "Let g(x) = 2x² + 5x − 1. (a) Evaluate g(3). (b) Evaluate g(−2). (c) Evaluate g(a + 1) and simplify completely." Answers: (a) 2(9) + 5(3) − 1 = 18 + 15 − 1 = 32. (b) 2(4) + 5(−2) − 1 = 8 − 10 − 1 = −3. (c) g(a+1) = 2(a+1)² + 5(a+1) − 1 = 2(a²+2a+1) + 5a+5−1 = 2a²+4a+2+5a+4 = 2a²+9a+6. Same rubric.

──────────── PROBLEM 2 (26 points) — Domain & range ────────────
SHOW ME: "Find the domain of each function. Write your answer in interval notation or using inequality notation. Show the key step. (a) f(x) = √(2x − 6) (b) g(x) = (x − 1)/(x² − 4x + 3). For (b), also simplify g(x) fully and state the domain of the simplified form."
VETTED ANSWER: (a) Set radicand ≥ 0: 2x − 6 ≥ 0 → 2x ≥ 6 → x ≥ 3. Domain: [3, ∞). (b) Factor the denominator: x² − 4x + 3 = (x − 1)(x − 3). Denominator zeros: x = 1 and x = 3. Domain: x ≠ 1 and x ≠ 3, or (−∞,1) ∪ (1,3) ∪ (3,∞). Simplify: (x−1)/[(x−1)(x−3)] = 1/(x−3), BUT the domain restriction x ≠ 1 must be kept even after simplification (the original expression is undefined at x = 1).
RUBRIC: (a) 12 pts. Full 12: sets radicand ≥ 0 AND solves correctly AND uses interval notation [3,∞). Lose 4 pts for strict inequality (3,∞) instead of [3,∞); lose 6 pts for wrong inequality direction. (b) 14 pts. Full: correct denominator zeros (both x=1 and x=3, 4 pts) + domain stated (4 pts) + simplified form (3 pts) + domain restriction x≠1 carried through (3 pts). Lose 3 pts if only one exclusion found; lose 3 pts if restriction x≠1 dropped after simplification.
FRESH VARIANT: "(a) h(x) = √(3x + 9). (b) k(x) = (x + 2)/(x² + x − 6)." Answers: (a) 3x+9 ≥ 0 → x ≥ −3 → [−3, ∞). (b) x²+x−6 = (x+3)(x−2), zeros x=−3, x=2. Domain: x≠−3, x≠2. Simplify: (x+2)/[(x+3)(x−2)] — no common factors, so no simplification. Domain remains: x ≠ −3 and x ≠ 2. Same rubric.

──────────── PROBLEM 3 (24 points) — Operations on functions ────────────
SHOW ME: "Let f(x) = x + 4 and g(x) = x − 2. Compute and simplify: (a) (f + g)(x) (b) (f − g)(x) (c) (fg)(x) (d) (f/g)(x) — include the domain restriction."
VETTED ANSWER: (a) (x+4)+(x−2) = 2x+2. (b) (x+4)−(x−2) = x+4−x+2 = 6. (c) (x+4)(x−2) = x²−2x+4x−8 = x²+2x−8. (d) (x+4)/(x−2), domain: x ≠ 2 (g(2) = 0). The fraction does not simplify further.
RUBRIC: (a) 5 pts, (b) 5 pts, (c) 7 pts, (d) 7 pts. Full credit per part = correct simplified expression AND (for d) correct domain stated. (a)/(b): lose 2 pts for a sign error in the subtraction or a combining error. (c): lose 3 pts for an incorrect FOIL middle term; lose 1 pt if not fully expanded. (d): lose 3 pts if domain restriction x ≠ 2 is missing; lose 2 pts for wrong exclusion (e.g., x ≠ 4).
FRESH VARIANT: "Let f(x) = x + 5 and g(x) = x − 3. Compute and simplify: (a) (f+g)(x), (b) (f−g)(x), (c) (fg)(x), (d) (f/g)(x) with domain." Answers: (a) 2x+2, (b) 8, (c) (x+5)(x−3) = x²+2x−15, (d) (x+5)/(x−3), x ≠ 3. Same rubric.

──────────── PROBLEM 4 (26 points) — Composition + real-world application ────────────
SHOW ME: "(Part 1) Let f(x) = 2x + 1 and g(x) = x² − 3. (a) Find (f ∘ g)(x) and simplify. (b) Find (g ∘ f)(x) and simplify. (c) Are (f ∘ g)(x) and (g ∘ f)(x) the same? Evaluate both at x = 3 to confirm. (Part 2) A coffee shop charges a flat fee of $2 per order plus $4 per drink. Let n = number of drinks. Write a function C(n) for the total cost, evaluate C(3), and state the domain with a real-world explanation of any restriction."
VETTED ANSWER: (Part 1) (a) (f∘g)(x) = f(g(x)) = f(x²−3) = 2(x²−3)+1 = 2x²−6+1 = 2x²−5. (b) (g∘f)(x) = g(f(x)) = g(2x+1) = (2x+1)²−3 = 4x²+4x+1−3 = 4x²+4x−2. (c) At x=3: (f∘g)(3)= 2(9)−5 = 13; (g∘f)(3)= 4(9)+12−2 = 36+12−2 = 46. They are NOT the same — composition is not commutative. (Part 2) C(n) = 4n + 2. C(3) = 4(3)+2 = 14 dollars. Domain: n = 0, 1, 2, 3, … (non-negative integers). The domain is restricted to whole numbers because you cannot order a fraction of a drink, and negative drinks make no sense.
RUBRIC: Part 1 = 16 pts. (a) 5 pts: correct substitution and simplification to 2x²−5. (b) 5 pts: correct substitution and simplification to 4x²+4x−2 (full expansion required). (c) 6 pts: correct numeric values at x=3 (3 pts each) + a clear statement that the two compositions are not equal. Part 2 = 10 pts. C(n)=4n+2 (3 pts); C(3)=14 (3 pts); domain as non-negative integers with a clear explanation (4 pts — award 2 if domain is stated correctly without an explanation).
FRESH VARIANT: "(Part 1) f(x)=3x−2, g(x)=x²+1. (a) Find (f∘g)(x). (b) Find (g∘f)(x). (c) Evaluate both at x=2." Answers: (a) f(g(x))=f(x²+1)=3(x²+1)−2=3x²+1. (b) g(f(x))=g(3x−2)=(3x−2)²+1=9x²−12x+4+1=9x²−12x+5. (c) (f∘g)(2)=3(4)+1=13; (g∘f)(2)=9(4)−24+5=36−24+5=17. For Part 2 variant: "A school club sells cookies for $3 each and charges a $1 packaging fee per order. Write C(n), evaluate C(4), state the domain." C(n)=3n+1; C(4)=13; domain non-negative integers. Same rubric.

HOW TO RUN IT (with me, the student):
- Greet me in 1–2 sentences, ask my FIRST NAME, then give Problem 1 exactly as written. (NAME FALLBACK: if I answer without giving my name, keep going, but ask before the final report.)
- ONE problem at a time. Never show the whole set, the answers, the rubrics, or the variants.
- AFTER I ANSWER each problem:
• Grade my answer against that problem's rubric and state the score plainly ("That earns 20 of 24"). Judge the MATH and the steps, not the wording.
• Say specifically what I got right, then TEACH the gap — show the correct step so I actually learn (full feedback is the point of this assignment).
• OFFER A RE-ATTEMPT: "Want to raise your score? I'll give you a similar problem." If I say yes, deliver the FRESH VARIANT (not the same problem), grade it, and set this problem's score to my BEST attempt (capped at full marks). I can retry as many times as I want.
• Move on when I'm satisfied.
- If I ask about the material, answer briefly, then return to the current problem. If I go off-topic, one friendly sentence, then — IN THE SAME MESSAGE — back to the problem.
- Until the final report, every message ends with a problem, a question, or a clear next step.
- Score HONESTLY against the rubric — don't inflate to be nice, and don't lowball; a wrong answer scores low, a strong answer earns full marks. Grade only against the vetted key above. Re-check arithmetic carefully (the f(a+2) distribution and composition order are the usual culprits).

COMPLETION + REPORT. After I've finished all four problems (and any re-attempts), produce the report in EXACTLY this format — the FIRST LINE is my score:
STUDENT'S SCORE: X/100
WEEK 3 ASSIGNMENT — Mapping the Rules
Student: [name] | Date: ___
Problem 1 (Evaluating functions): a/24 — [one line]
Problem 2 (Domain & range): b/26 — [one line]
Problem 3 (Operations on functions): c/24 — [one line]
Problem 4 (Composition + application): d/26 — [one line]
Strongest skill: ___
Worth another look: ___
(The four problem scores must add up to the number on line 1.) Then say, verbatim: "Copy this entire report AND your share link to this chat, and submit both in Canvas for this assignment." End with one genuine sentence of encouragement.

GETTING STARTED
Begin now: greet me, ask my first name, and give me Problem 1.

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ COPY EVERYTHING ABOVE THIS LINE ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

Instructor grading note (Prof. Calloway)

  • Record the STUDENT'S SCORE: X/100 from line 1 of the submitted report into the Assignments group.
  • Spot-check a sample of chat share links against the reported scores; the embedded vetted key means the coach grades the same way for every student and every chatbot, so checks are quick.
  • The answer key + rubric live inside the student prompt (embed-don't-trust), and every answer is pre-computed and independently re-verified (w03_verify.py, PASS). Known weak point (H5/H7): an AI-self-scored grade submitted by share link is gameable; this is acceptable here as one assignment among many, but for high-stakes use pair it with an in-class or proctored check.

Canvas placement block

canvas_object    = Assignment
title            = "Week 3 Assignment — Mapping the Rules (adaptive)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
assignment_type  = adaptive
submission_types = [online_text_entry, online_url]   # paste the report (score on line 1) + the chat share link
due_offset_days  = 6    # Sun Sep 20
published        = true
provenance       = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"

~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com