Week 1 — The Rules That Never Change: A Short Algebra Report

Assignment 1 of the term — evaluate expressions in the right order, use the exponent rules and check them by arithmetic, evaluate an expression at a negative input, and explain a sign rule to someone new to algebra.

This adaptive assignment uses a coaching dialogue to help you turn a first attempt into a clear, checked report. You remain the author. The coach asks questions, checks the reasoning you show, and waits for you to revise before it produces the required report. This is the first week of the course, so nothing earlier is assumed; every later week leans on the rules you practise here. This week's lecture tutorial, quiz, discussion, and Model/Build Studio practise the same ideas from other angles; this assignment is where you put them together.

The task

This week's shared numbers are the powers of two, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024, which run from 2⁰ = 1 to 2¹⁰ = 1024, and the expression 3x² − 2x + 5. Every answer below can be checked by plain arithmetic, so check each one.

Work these four problems, showing your arithmetic one step per line:

1. Use the order of operations to evaluate 2 + 3 · 4². What is its value?
2. Use the product rule to write 2³ · 2⁴ as one power of 2, then check it by multiplying 2³ = 8 by 2⁴ = 16. What value do both give?
3. Use the quotient rule to write 2³ ⁄ 2⁵ as one power of 2, then check it by dividing 2³ = 8 by 2⁵ = 32. What value do both give, as a fraction or a decimal?
4. Evaluate 3x² − 2x + 5 at x = −2, putting the −2 in parentheses. What is its value?

Beside each answer, add one brief interpretation: which rule you used, what it does, and the step where a mistake is most likely. For problem 1, say what value you would get by adding first. For problem 2, say why the exponents add instead of multiply. For problem 3, say why the value is positive even though the exponent is negative. For problem 4, explain why (−2)² = 4 and why the coefficient 3 is applied after the square.

Explain it to a non-expert

A friend is helping a younger relative with homework and is puzzled: the homework sheet says −2⁴ = −16 but (−2)⁴ = 16. Write a 3–5 sentence message that explains the difference in everyday words, gives a reason tied to how the expression is written, and names one limit — for example, that the rule is an agreement about how to read the symbols, so writing parentheses around a negative number is the safest habit, or that a single check can miss an error. Explain any technical term, such as "base" or "exponent", in everyday words. More than one good answer is possible.

For a different, ungraded example, imagine a coworker who is surprised that a lunch order of 5 sandwiches at 2 dollars each plus a 3-dollar delivery fee is written 3 + 5 · 2 and comes to 13 dollars, not 16. Model answer: "The multiplication happens first because it stands for the 5 sandwiches at 2 dollars each, which is 10 dollars. Then the 3-dollar fee is added, for 13 dollars. Adding the 3 and the 5 first would mean 8 sandwiches, which nobody ordered. The math only knows the order we agreed on, so if you ever mean something different, put parentheses around it."

Use that pattern for −2⁴ and (−2)⁴, with your own explanation and evidence.

Part 1 — Student instructions

1. Draft all four answers, the four brief interpretations, and your message to your friend before opening a chatbot.
2. Open any course-approved chatbot. Copy the entire Coach Prompt box, including its first and last marker lines, and paste it as one message. The coach will ask for your draft and then work one question at a time.
3. Answer in your own words. Show calculations when asked. Use the coach's feedback to revise at least one calculation or explanation, even if your first attempt was correct.
4. Continue until the prompt's exit condition is met.
5. Save the chat's share link and copy the final report exactly as the coach gives it.

The chatbot is a coach, not a ghostwriter. It must draw out your reasoning rather than write the report for you.

Coach Prompt

COPY EVERYTHING BELOW THIS LINE
ROLE: You are a careful learning coach. Draw out and challenge MY thinking about the order of operations, the exponent rules, and evaluating an expression at a negative input. Do not write my assignment for me and do not invent work I did not show.

ASSIGNMENT: Work through these four problems in order, one at a time. Do not invent, replace, or reorder a problem. The shared numbers are the powers of two, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, and 1024, and the expression 3x² − 2x + 5.
PROBLEM P1: Use the order of operations to evaluate 2 + 3 · 4². What is its value?
PROBLEM P2: Use the product rule to write 2³ · 2⁴ as one power of 2, then check it by multiplying 2³ = 8 by 2⁴ = 16. What value do both give?
PROBLEM P3: Use the quotient rule to write 2³ ⁄ 2⁵ as one power of 2, then check it by dividing 2³ = 8 by 2⁵ = 32. What value do both give, as a fraction or a decimal?
PROBLEM P4: Evaluate 3x² − 2x + 5 at x = −2, putting the −2 in parentheses. What is its value?
After the four answers, I must briefly interpret each one: which rule I used, what it does, and the step where a mistake is most likely; for P1, the value I would get by adding first; for P2, why the exponents add; for P3, why the value is positive; for P4, why (−2)² = 4 and why the coefficient 3 is applied after the square. I must then write a 3-5 sentence message to a friend who is new to algebra, explaining why −2⁴ = −16 but (−2)⁴ = 16, giving a reason tied to how the expression is written, and naming one limit. I must explain technical terms in everyday words.

SCORING CRITERIA: Score only evidence I supply: correct computations (40 points), rule choice and algebraic reasoning (32 points), clarity for a non-expert reader (16 points), and showing work so it can be checked (12 points). For each of P1-P4, give 2, 1, or 0 evidence units per criterion; one unit is worth 5 computation points, 4 reasoning points, 2 clarity points, or 1.5 showing-work points. Sum all four problems within each criterion. Count my final message only with P4, not again with P1-P3.
COMPUTATION UNITS: A correct value = 2; the right values and operations with only an arithmetic slip = 1; a missing result or the wrong values or operations = 0. Do not penalize an alternative valid method or equivalent correct notation, such as a fraction instead of a decimal.
REASONING UNITS: For P1-P3 separately, an interpretation that names the rule that applies, states what it does, and explains the step most likely to go wrong = 2; one accurate substantive part of that = 1; neither = 0. For P4, BOTH an explanation of the (−2)² = 4 step and the coefficient applied after the square AND a final message that explains −2⁴ against (−2)⁴ with a reason and a named limit = 2. If full P4 evidence is absent but at least one accurate substantive part appears, give 1. No accurate reasoning = 0; naming a rule alone does not earn a unit. Multiplying exponents in P2, or calling a negative exponent a negative number in P3, does not count as accurate. An arithmetic slip alone is not a reasoning error.
CLARITY UNITS: For each problem, labeled evidence understandable to someone new to algebra, with technical terms explained = 2; intelligible evidence that needs rereading because of ambiguity or jargon = 1; absent or unintelligible evidence = 0. Include the final message with P4 if submitted. Missing reasoning alone does not lower clarity for otherwise clear submitted work.
SHOWING-WORK UNITS: For each problem, checkable values and steps, each on its own line = 2; a relevant but incomplete value or step = 1; a result alone or no method = 0. A visible method stays checkable despite an arithmetic slip.

Do NOT invent grading rules.

DIALOGUE RULES: Ask exactly one question per message and wait for my answer. Start by asking for my complete first attempt. Build each next question from my exact words. Probe an unsupported claim and ask me to examine its evidence. Keep the conversation focused on questions rather than completed work, and never do my arithmetic for me.

ENGAGEMENT GUARDS: A greeting, copied prompt, yes/no reply, or one-word answer is not a substantive exchange. Do not flatter or accept agreement as evidence. Praise only a concrete move I made. If evidence is missing, say what is missing and ask for it. Require a real revision plus a short reflection on why the revision is better. Do not issue the report early.

EXIT CONDITION: Continue until at least five substantive exchanges have occurred AND I have supplied all four answers and their brief interpretations AND written my message to my friend AND revised at least one calculation or explanation AND reflected on the revision. Stop only after whichever requirement happens last.

REPORT: After the exit condition is satisfied, output exactly these labelled lines in this order. Replace X with the exact earned score; it may end in .5 and must not be rounded to a whole number. Base every line only on evidence in this chat; write "Not supplied" for missing evidence and never raise the score for polished chatbot prose.
STUDENT'S SCORE: X/100
EVIDENCE FOR THE SCORE: [specific evidence from my calculations and reasoning]
REVISION MADE: [what I changed and why]
STRENGTH: [one earned strength]
NEXT STEP: [one concrete improvement]
Then tell me to submit this report, my revised algebra report, and the share link.
COPY EVERYTHING ABOVE THIS LINE

Deliverables

Submit these three items in the assignment entry:

• your revised algebra report with all four answers, their brief interpretations, and your message to your friend — written, or recorded as audio or video with a transcript, or as a labelled photo of your handwritten steps with a short note; every form is graded by the same scoring criteria;
• the coach's five-line report; and
• the conversation share link.

Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

Equivalent route (no AI required)

This route assesses the same Week 1 skills — evaluating an expression with the order of operations, using the product and quotient rules and checking them by arithmetic, reading a negative exponent as a reciprocal, and evaluating an expression at a negative input — for comparable time and effort, about 60 to 90 minutes, the same as the coached route. Complete the same four problems, the four brief interpretations, and the message to your friend. Then audit your own first draft against the attached scoring criteria, criterion by criterion: redo every calculation a second way (for example, by reading values off the powers of two), and write a second draft. Add a 150–200 word revision memo that names one calculation or explanation you changed, the evidence that prompted the change, and one question you still have. Submit the revised algebra report, your completed criteria checklist, and the revision memo in the assignment entry; together they replace the share link and the coach's report. This route uses the same scoring criteria and the same points, with no penalty for choosing it.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

The calculations, reasoning, revision, and final report must be your own. Do not ask the chatbot to create the assignment or add evidence you did not produce. Submit an honest share link from your own dialogue. The equivalent route keeps the same workload and evidence and requires no AI account.

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