Week 1 — Readings & Resources · Real Numbers, Exponents & Algebraic Expressions

Course: College Algebra (MATH 120) · Silver Oak University (fictional sample) · Prof. Calloway
Objective covered: Objective 1 — Simplify algebraic expressions using the properties of real numbers, the order of operations, and the rules of integer exponents.

How to use this page

Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded.

This week's load is deliberately light: ~4 short readings + ~3 short videos, grouped by the four ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 40–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① the real-number sets → ② order of operations (and the −4² trap) → ③ properties of real numbers → ④ exponent rules & simplifying expressions.

A habit to start now: the AI tutorial this week ends by having you catch a chatbot's mistake. Keep that posture as you read — the tool drafts, you check.

① The Real Numbers and Their Sets

Maps to Lecture Segment 2. Every number this term is a real number; the smaller clubs (natural, whole, integer, rational, irrational) are how we describe it.

Reading — "Real Numbers: Algebra Essentials" (OpenStax, College Algebra 2e, §1.1)
🔗 https://openstax.org/books/college-algebra-2e/pages/1-1-real-numbers-algebra-essentials
Why it's assigned: the cleanest tour of the real-number sets and the properties, with the same classification examples we did in class (including why a simplifying square root like √16 is rational). Read the "Classifying Real Numbers" part.
⏱ ~9 min

② The Order of Operations (and the −4² trap)

Maps to Lecture Segment 3. PEMDAS is two pairs read left-to-right, not six steps — and the exponent binds tighter than a negative sign.

Video — "Order of operations: PEMDAS" (Khan Academy)
🔗 https://www.youtube.com/watch?v=piIcRV2dx7E
Why it earns the click: a worked, multi-operation example done in the exact order we used — exponents before multiplication, multiplication before addition.
⏱ ~6 min

Video — "Introduction to order of operations" (Khan Academy)
🔗 https://www.youtube.com/watch?v=ClYdw4d4OmA
Why it earns the click: makes the point of the convention clear — why we need one agreed order so an expression has a single meaning. A good first watch if PEMDAS feels arbitrary.
⏱ ~5 min

③ Properties of Real Numbers

Maps to Lecture Segment 4. Commutative moves the order, associative moves the parentheses, distributive breaks the parentheses open.

Reading — "Real Numbers: Algebra Essentials" (OpenStax, College Algebra 2e, §1.1 — "Using Properties of Real Numbers")
🔗 https://openstax.org/books/college-algebra-2e/pages/1-1-real-numbers-algebra-essentials
Why it's assigned: the second half of the same §1.1 section lays out commutative, associative, distributive, identity, and inverse with clean examples — and warns about the subtractions/divisions that are not commutative.
⏱ ~7 min

④ Exponent Rules & Simplifying Expressions

Maps to Lecture Segments 5–7. The lesson that sticks: multiplying adds exponents, a power-of-a-power multiplies them, and a negative exponent means reciprocal.

Reading — "Exponents and Scientific Notation" (OpenStax, College Algebra 2e, §1.2)
🔗 https://openstax.org/books/college-algebra-2e/pages/1-2-exponents-and-scientific-notation
Why it's assigned: every integer-exponent rule we used — product, quotient, power, zero, and negative exponents — with worked examples, in the order we taught them.
⏱ ~10 min

Reading — "Integer Exponents" (Paul's Online Math Notes — Algebra)
🔗 https://tutorial.math.lamar.edu/classes/alg/IntegerExponents.aspx
Why it's assigned: a tight, example-driven page that nails the two rules students swap — x²·x³ (add) vs. (x²)³ (multiply) — and shows how to clear negative exponents. A great second pass.
⏱ ~8 min

Video — "Studying Exponents and Order of Operations" (Professor Leonard)
🔗 https://www.youtube.com/watch?v=NKrxqWhf01Q
Why it earns the click: an unhurried, full-length walkthrough of exponent rules and the order-of-operations sign traps, worked at the board — ideal if you want to see every step.
⏱ longer lecture (skim to the parts you need)

Optional one-stop reference (free online)

If you'd like one optional reference to return to all term, Paul's Online Math Notes — Algebra keeps a full, free set of notes online, and Professor Leonard's College Algebra playlist has full-length lectures for every topic in this course.
🔗 Paul's Algebra notes: https://tutorial.math.lamar.edu/classes/alg/alg.aspx
🔗 Professor Leonard — College Algebra / Trigonometry playlist: https://m.youtube.com/playlist?list=PLDesaqWTN6ESsmwELdrzhcGiRhk5DjwLP
Why they're here: reputable, currently-available references you can come back to in later weeks — entirely optional this week.

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these and you'll be ready for the quiz:
1. Read OpenStax §1.1 — Real Numbers (groups ① and ③).
2. Watch Khan Academy — Order of operations: PEMDAS (group ②).
3. Read OpenStax §1.2 — Exponents (group ④).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Calloway and use the Paul's Online Math Notes reference above in the meantime.