Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Module: Week 1 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 1 — Simplify algebraic expressions using the properties of real numbers, the order of operations, and the rules of integer exponents.

This file holds two pieces: (A) the Module 1 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 1 meeting Tue Sep 1 and Thu Sep 3, and end-of-week work due Sunday Sep 6, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 1 Overview — Start Here

Welcome to Week 1: Real Numbers, Exponents & Algebraic Expressions

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

This week is the bedrock the whole course is built on. Before we ever solve an equation or graph a function, we lock down the rules that never change — the ones that let you rewrite any expression without changing its value. You've used them since grade school; now we make them explicit so they keep working when the numbers are unknown letters.

The week's big question

"What are the rules that never change — the ones that let us rewrite any expression without changing its value?"

By Friday you'll evaluate any expression in the correct order (and never again be tricked by whether −4² is −16 or 16), apply the exponent rules without swapping "add" and "multiply," and simplify a messy expression like 5x − 2(3x − 4) with confidence.

By the end of this week, you can…

Use this as a checklist. If you can do all four, you're ready for the quiz.

• [ ] Classify a number into the real-number sets — natural, whole, integer, rational, irrational — and explain why √16 is rational but √2 is not.
• [ ] Evaluate with the order of operations (PEMDAS as two left-to-right pairs), including the −4² vs (−4)² trap.
• [ ] Name and apply the properties of real numbers — commutative, associative, distributive, identity, inverse.
• [ ] Apply the integer-exponent rules (product, quotient, power, zero, negative) and simplify expressions by distributing and combining like terms.

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, and then you judge its work. Chatbots routinely fumble these — they'll call −3² equal to 9 (it's −9) or add exponents they should multiply. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Lead with the idea, not the notation. Every rule this week is a plain-English idea first (commutative = you can reorder; a negative exponent means reciprocal). The symbols come after the idea clicks.
• Memorize the two traps. −4² = −16, but (−4)² = 16 (the negative is squared only inside parentheses), and x²·x³ = x⁵ (add), but (x²)³ = x⁶ (multiply). These two cause most Week-1 lost points.
• Use the one-question test for irrational numbers. Does the number simplify to a fraction or whole number? If yes → rational. Only non-ending, non-repeating decimals (√2, π) are irrational.
• Show every step when you simplify. Distribute first (to every term, watching the signs), then combine like terms. Most errors are a dropped negative, not a deep misunderstanding.
• Treat the chatbot as a smart intern, not an oracle. It drafts; you check. That habit is the whole semester in miniature.

You don't need much background for this week — just a willingness to slow down and respect the signs. See you Tuesday.

(B) Welcome Announcement — Module 1

Release setting: post on the module's start day (offset = 0 days), i.e., Tue Sep 1, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Tue Sep 1."

Subject: Welcome to Week 1 — the rules that never change 👋

Hi everyone, and welcome to College Algebra!

Quick question before we start: have you split a bill, doubled a recipe, or worked out a tip recently? You were doing algebra — applying a rule to numbers you didn't know in advance. This whole course is about doing that correctly and confidently, and Week 1 is the foundation everything else stands on.

This week — Real Numbers, Exponents & Algebraic Expressions — we tackle the big question: What are the rules that never change? By Friday you'll evaluate expressions in the right order, apply the exponent rules without mixing up "add" and "multiply," and simplify a messy expression without losing a sign — and you'll never again be fooled by whether −4² is −16 or 16. (It's −16. Ask me Tuesday.)

Three things not to miss:
1. Lecture Tutorial 1 — work through the week's ideas with one approved chatbot (Gemini, Claude, or ChatGPT) and submit the share link. You'll catch the model's mistakes, not just trust it. Due Sun Sep 6.
2. Quiz 1 (no AI on quizzes) and Discussion 1 — "Find the Flaw" also close Sun Sep 6 — the discussion is a quick AI dialogue you summarize and post, so start early and leave time to reply to classmates.
3. Assignment 1 — four AI-coached problems with a self-scored report; due Sun Sep 6.

One promise: this is a course about thinking clearly and respecting the rules, not about being a "math person." We lead with plain-language ideas every single week; the notation comes second. Slow down, show your steps, and the algebra takes care of itself.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring a pencil and a willingness to argue about whether −4² is positive. See you Tuesday.

See you soon,
Prof. Calloway