Week 2 — Assignment (Adaptive Learning) · "Solving Is the Move"

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective assessed: Objective 2 (linear equations, inequalities, absolute-value) · 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 2 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 13.

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 2 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) — Solving linear equations ────────────
SHOW ME: "Solve each equation. Show every step. Identify any equation that is an identity (infinitely many solutions) or a contradiction (no solution). (a) 2(x + 4) − 3 = x + 9 (b) x/3 + x/6 = 5 (c) 5(x − 2) = 3(x + 4) (d) (3x − 1)/4 = (x + 5)/2"
VETTED ANSWER: (a) 2x+8−3=x+9 → 2x+5=x+9 → x = 4. Check: 2(4+4)−3=13=4+9 ✓. (b) LCD=6: 2x+x=30 → 3x=30 → x = 10. (c) 5x−10=3x+12 → 2x=22 → x = 11. (d) multiply by 4: 3x−1=2(x+5) → 3x−1=2x+10 → x = 11. (Note: (c) and (d) happen to give the same numerical answer x=11 — each is a different equation with a unique solution.)
RUBRIC: 6 points each. Full 6 = correct value with all steps shown (or identity/contradiction correctly named with reasoning). Partial 3–5: right method, one arithmetic or distribution slip. 1–2: wrong method or just a guess. 0: missing.
FRESH VARIANT: "(a) 3(x − 1) − 2 = x + 7 (b) x/4 + x/8 = 3 (c) 4(x + 2) = 2(x + 8) (d) (2x + 3)/3 = (x + 5)/2". Answers: (a) 3x−3−2=x+7 → 2x=12 → x = 6; (b) LCD=8: 2x+x=24 → x = 8; (c) 4x+8=2x+16 → 2x=8 → x = 4; (d) multiply by 6: 2(2x+3)=3(x+5) → 4x+6=3x+15 → x = 9. Same rubric.

──────────── PROBLEM 2 (26 points) — Linear inequalities + interval notation ────────────
SHOW ME: "Solve each inequality. Write the solution in interval notation and show every step, including where you flip the inequality sign. (a) 4x − 3 > 9 (b) −3x + 6 ≥ 0 (c) −5 < 2x + 1 ≤ 7"
VETTED ANSWER: (a) 4x>12 → x>3 → (3, ∞). (b) −3x≥−6 → x≤2 (flip: dividing by −3) → (−∞, 2]. (c) Left: −5<2x+1 → −6<2x → x>−3; Right: 2x+1≤7 → 2x≤6 → x≤3. Combined: −3<x≤3 → (−3, 3].
RUBRIC: (a) 8 pts: 4 for correct direction + sign, 4 for correct interval notation. (b) 9 pts: 4 for flipping the sign correctly + writing x≤2, 5 for correct notation (−∞,2] with bracket). (c) 9 pts: 4 for solving both sides correctly, 5 for the compound interval (−3,3] with correct bracket placement. Lose half credit for any sign-flip error or wrong bracket/parenthesis.
FRESH VARIANT: "(a) 3x + 2 < 11 (b) −2x + 4 > 0 (c) −4 ≤ 3x − 1 < 8". Answers: (a) 3x<9 → x<3 → (−∞, 3); (b) −2x>−4 → x<2 (flip) → (−∞, 2); (c) Left: −4≤3x−1 → −3≤3x → x≥−1; Right: 3x−1<8 → 3x<9 → x<3. Combined: −1≤x<3 → [−1, 3). Same rubric.

──────────── PROBLEM 3 (24 points) — Absolute-value equations and inequalities ────────────
SHOW ME: "Solve each. Show the full setup for every case, and use interval notation for inequalities. (a) |3x + 2| = 11 (b) |x − 4| = −2 (c) |2x − 1| < 5 (d) |x + 3| ≥ 4"
VETTED ANSWER: (a) Case 1: 3x+2=11 → x=3. Case 2: 3x+2=−11 → 3x=−13 → x=−13/3. Solutions: {−13/3, 3}. (b) Right side = −2 < 0 → no solution (∅). (c) −5<2x−1<5 → −4<2x<6 → −2<x<3 → (−2, 3). (d) x+3≤−4 or x+3≥4 → x≤−7 or x≥1 → (−∞, −7] ∪ [1, ∞).
RUBRIC: (a) 6 pts: 3 per correct solution (must show both cases). (b) 6 pts: full credit only if student identifies the right side is negative and writes "no solution" — zero credit for x=±2. (c) 6 pts: 4 for correct compound inequality setup, 2 for correct interval. (d) 6 pts: 3 for "or" (two cases), 3 for correct values and notation (brackets required at −7 and 1).
FRESH VARIANT: "(a) |2x − 3| = 9 (b) |x + 1| = −4 (c) |3x + 2| < 8 (d) |x − 2| ≥ 5". Answers: (a) 2x−3=9 → x=6; 2x−3=−9 → x=−3. Solutions: {−3, 6}. (b) Right side = −4 < 0 → no solution. (c) −8<3x+2<8 → −10<3x<6 → −10/3<x<2 → (−10/3, 2). (d) x−2≤−5 → x≤−3; x−2≥5 → x≥7. (−∞,−3] ∪ [7,∞). Same rubric.

──────────── PROBLEM 4 (26 points) — Real-world application and interpretation ────────────
SHOW ME: "(Part 1) A car rental company charges a flat fee of $25 plus $0.20 per mile. You can spend at most $49. Write an inequality for the number of miles m you can drive, solve it, and write the answer in interval notation. (Part 2) In one or two sentences that a classmate could follow, explain what your solution means in plain English — including whether the endpoint is included or excluded and why."
VETTED ANSWER: (Part 1) 25 + 0.20m ≤ 49 → 0.20m ≤ 24 → m ≤ 120 → [0, 120] (also accept (−∞, 120] with a note that negative miles make no physical sense; ideal answer uses [0, 120] and acknowledges context). (Part 2) Accept any clear interpretation such as: "You can drive between 0 and 120 miles, including exactly 120. The bracket at 120 means driving exactly 120 miles would cost exactly $49 — within budget."
RUBRIC: Part 1 = 14 pts (5 for correct inequality setup 25+0.20m≤49, 4 for correct algebra steps to m≤120, 5 for interval notation [0,120] or equivalent). Part 2 = 12 pts (6 for explaining the meaning in context, 6 for correctly explaining why the endpoint is included — i.e., ≤ means the boundary value is allowed). Half credit in Part 2 if the explanation is correct but unclear or incomplete.
FRESH VARIANT: "(Part 1) A plumber charges a $30 visit fee plus $25 per hour. You have a budget of $105. Write an inequality for the number of hours h the plumber can work, solve it, and write the answer in interval notation. (Part 2) Explain what your solution means in plain English, including what happens at the endpoint." Answers: (Part 1) 30+25h≤105 → 25h≤75 → h≤3 → [0, 3]. (Part 2) e.g. "The plumber can work between 0 and 3 hours inclusive; exactly 3 hours would cost exactly $105, which is right at budget." 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 (sign-flip and absolute-value errors are the usual culprits this week). Special watch: for Problem 3(b), if I write x = ±2, the rubric gives zero — the correct answer is "no solution" because the right side is negative.

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 2 ASSIGNMENT — Solving Is the Move
Student: [name] | Date: ___
Problem 1 (Solving linear equations): a/24 — [one line]
Problem 2 (Inequalities + interval notation): b/26 — [one line]
Problem 3 (Absolute-value equations & inequalities): c/24 — [one line]
Problem 4 (Real-world application & interpretation): 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 (w02_verify.py, PASS) so the score is consistent across Gemini / Claude / ChatGPT. Key watch point this week: Problem 3(b) — if a student submitted "x = ±2" (wrong) and the report scores it anything other than 0, the chat link should show whether the coach applied the rubric correctly.

Canvas placement block

canvas_object    = Assignment
title            = "Week 2 Assignment — Solving Is the Move (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  = 5     # 5 days after module start (module starts Tue Sep 8)
published        = true
provenance       = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"

Traditional variant — for comparison. This sample course is configured adaptive learning, so its actual Week-2 assignment is the AI-coached, self-scored version in I-assignment-and-rubric-week-02.md. This file shows the same Week-2 skills built the traditional way — the student completes the work and submits it, and the instructor grades against the rubric — so you can see both formats side by side. (Choosing assignment_type = traditional at course setup generates this style instead.)

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective assessed: Objective 2 (linear equations, inequalities, absolute-value) · SLO A (apply procedures accurately) · SLO B (interpret/communicate)
Worth 100 points · Assignments group = 20% of the grade

The Assignment

This week is about the most important mechanical move in algebra: solving. In four parts, you'll show you can solve linear equations (including with fractions and variables on both sides), write inequality solutions in interval notation, handle absolute-value equations and inequalities, and apply these skills to a real-world problem. Show all your steps. Submit your work as a document upload or text entry in Canvas. Read the rubric before you start.

Part 1 — Solving linear equations (24 pts). Solve each equation. Show every step. For any equation that is an identity or contradiction, say so explicitly and explain why.
(a) 2(x + 4) − 3 = x + 9 (b) x/3 + x/6 = 5 (c) 5(x − 2) = 3(x + 4) (d) (3x − 1)/4 = (x + 5)/2 (e) 4(x − 1) + 2x = 6x − 4 (f) 3x − 7 = 3x + 2

Part 2 — Linear inequalities + interval notation (26 pts). Solve each inequality. Write the solution in interval notation and show every step. If you multiply or divide by a negative number, say "FLIP" at that step.
(a) 4x − 3 > 9 (b) −3x + 6 ≥ 0 (c) −5 < 2x + 1 ≤ 7 (d) 5 − 2x ≤ 11 (e) −4 ≤ 2x + 2 < 10

Part 3 — Absolute-value equations and inequalities (24 pts). Solve each. Show the full case setup for equations. For inequalities, write the solution in interval notation.
(a) |3x + 2| = 11 (b) |x − 4| = −2 (c) |2x − 1| < 5 (d) |x + 3| ≥ 4

Part 4 — Real-world application and interpretation (26 pts). A car rental company charges a flat fee of $25 plus $0.20 per mile. You have at most $49 to spend.
- (Part 1) Write and solve an inequality for the number of miles m you can drive. Show your algebra steps and write the answer in interval notation.
- (Part 2) Explain in one or two sentences — in plain English that a classmate could follow — what your solution means. Say whether the endpoint is included or excluded and why.

Integrity & AI note. This is your own work, submitted for grading. You may use an approved chatbot (Gemini, Claude, or ChatGPT) to help you think — check a rule, test an idea — but submitting AI-generated answers as your own is not allowed; if AI helped you think, add a one-line note of which tool and how. (Note: this is the traditional format. In this course's actual adaptive assignment, you work the problems with the chatbot and submit its self-scored report — see I-assignment-and-rubric-week-02.md.)

Rubric — 100 points

Levels describe observable differences so grading stays fast and consistent. (This same rubric is what the adaptive variant embeds for the AI to grade against.)

Instructor answer key — REMOVE BEFORE PUBLISHING TO STUDENTS

(All values pre-computed and independently re-verified — w02_verify.py, PASS.)

• Part 1: (a) 2x+5=x+9 → x=4. (b) LCD=6: 2x+x=30 → x=10. (c) 5x−10=3x+12 → 2x=22 → x=11. (d) 3x−1=2x+10 → x=11. (e) 4x−4+2x=6x−4 → 6x−4=6x−4 → 0=0 → identity (infinitely many solutions). (f) 3x−7=3x+2 → −7=2 → contradiction (no solution, ∅).
• Part 2: (a) 4x>12 → x>3 → (3,∞). (b) −3x≥−6 → x≤2 (flip) → (−∞,2]. (c) −6<2x<6 wait: −5<2x+1≤7 → −6<2x≤6 → −3<x≤3 → (−3,3]. (d) 5−2x≤11 → −2x≤6 → x≥−3 (flip) → [−3,∞). (e) −4≤2x+2<10 → −6≤2x<8 → −3≤x<4 → [−3,4).
• Part 3: (a) 3x+2=11 → x=3; 3x+2=−11 → x=−13/3. (b) Right side =−2<0 → no solution (∅). (c) −5<2x−1<5 → −4<2x<6 → −2<x<3 → (−2,3). (d) x+3≤−4 → x≤−7; x+3≥4 → x≥1 → (−∞,−7]∪[1,∞).
• Part 4: 25+0.20m≤49 → 0.20m≤24 → m≤120 → [0,120] (physical context: miles ≥ 0). Explanation: "You can drive up to 120 miles. The bracket means exactly 120 miles is allowed — that costs exactly $49, which is right at your budget."

Canvas placement block

canvas_object    = Assignment
title            = "Week 2 Assignment — Solving Is the Move (traditional)"
assignment_group = "Assignments"
points_possible  = 100
grading_type     = points
assignment_type  = traditional
submission_types = [online_upload, online_text_entry]
due_offset_days  = 5     # 5 days after module start (module starts Tue Sep 8)
published        = true
rubric_ref       = "week-02-assignment-rubric"
provenance       = "~ Prof. Calloway's edition · Fall 2026 · built with thecoursemaker.com"