Week 1 — Readings & Resources

Your primary reading is Chapter 1 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 12 items (6 readings and 6 videos). Allow 84–104 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (17–20 min total)

• What is the order of operations? Why do we need it? — Purplemath
• Introduction to Exponents — The Organic Chemistry Tutor

① Which family is this number in? The real-number sets

Chapter 1, Section “Sort the real numbers: name each number's family” · Session 1, Segment 1, “Classifying real numbers” · Remember: evaluate a number first, then name the smallest family it belongs to.

• Identifying Sets of Real Numbers — Mathispower4u — a short walk through sorting numbers into natural numbers, whole numbers, integers, rational numbers, and irrational numbers, one example at a time. (video, 7 min) (captions: creator)
• Common Number Sets — Math is Fun — a one-page picture of how the number sets fit inside one another, with the letters N, Z, Q, and R. Use it while working through the Week-1 module overview. (reading, 3–5 min)

② What comes first? The order of operations and the minus-sign trap

Chapter 1, Section “Follow the order of operations: two left-to-right passes” · Session 1, Segment 2, “The order of operations” · Remember: an exponent binds before a leading minus sign, so check whether the minus sign sits inside the parentheses.

• The Order of Operations, Example 1 — Patrick J — one expression worked from start to finish, saying each step of the order out loud. (video, 4 min) (captions: automatic)
• Negative Numbers and Exponents Explained — TabletClass Math — a close look at why a minus sign outside the parentheses waits until after the power, the same trap as −4² against (−4)². (video, 7 min) (captions: automatic)
• What is the order of operations? Why do we need it? — Purplemath — a friendly explanation of why the order exists and how the memory aids work; read it for the reasons behind each step. (reading, 6–9 min)

③ Which swaps are safe? Properties of real numbers and like terms

Chapter 1, Section “Use the properties of real numbers: why the shortcuts work” · Session 1, Segment 3, “Properties of real numbers” · Remember: the distributive property reaches every term inside the parentheses, and it is also what combines like terms.

• Properties of Real Numbers — Mathispower4u — the commutative, associative, distributive, identity, and inverse properties, each named on a short example. (video, 8 min) (captions: creator)
• Combining Like Terms Using The Distributive Property — The Organic Chemistry Tutor — many short examples of distributing and then combining like terms; pause after each one and try it first. Stop here before solving equations; next week takes that up. (video, 12 min) (captions: automatic)
• Properties of Real Numbers — Regents Exam Prep — the commutative, associative, distributive, identity, and inverse properties, each stated as a rule and then shown on small numbers, such as 7 × 43 worked as 7 × 40 plus 7 × 3; read from the commutative property through the inverse property, skipping the example that multiplies two binomials, which comes in a later week, and stop before the closure property. (reading, 8–11 min)

④ How do exponents combine? The integer-exponent rules

Chapter 1, Section “Build the exponent rules on the powers of two” · Session 2, Segment 4, “The exponent rules” · Remember: multiplying powers adds the exponents, and a negative exponent means a reciprocal, never a negative number.

• Introduction to Exponents — The Organic Chemistry Tutor — a steady start-from-zero tour of what an exponent counts and how the basic rules follow. (video, 11 min) (captions: automatic)
• Positive, Negative, & Zero Exponents in Algebra — Regents Exam Prep — the zero exponent explained by halving down the powers of two (8, 4, 2, 1), a negative exponent shown to be a reciprocal that never makes a number negative, the same −2⁴ against (−2)⁴ trap as the chapter, and three worked simplifications; the closing questions repeat the same points as review. (reading, 8–12 min)
• The Laws of Exponents — MathBootCamps — the product, quotient, and power-of-a-power rules, each followed by a short why-does-this-work that writes out the factors and counts them; the closing list adds the zero exponent and warns that an exponent does not distribute over a sum. (reading, 5–8 min)

Optional one-stop reference (free online reference)

• Desmos Graphing Calculator — Desmos — the free calculator this course uses all term; type any expression you have worked by hand and compare the value it shows, using parentheses exactly as the expression has them. (reading, 5–10 min)

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the reference above in the meantime.

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