Week 1 — Real Numbers, Exponents & Algebraic Expressions

Welcome to your Week 1 Start Here page.

Why this matters

The same few rules let a nursing student check a dosage calculation and a small-business owner split costs and add a tip. Learn them once, and you can check every answer yourself.

In plain language

Algebra runs on a short list of rules that never change, and this week you learn them. You will sort numbers into families, such as the integers (the whole numbers and their negatives) and the irrational numbers (numbers whose decimals never stop and never repeat). You will learn the agreed order for doing arithmetic, so everyone who works a problem gets the same answer. You will learn the shortcuts for exponents (the small raised numbers that count repeated multiplication). Most of all, you will learn to check your own work, so you never have to wonder whether an answer is right.

• This week: the language of algebra — the kinds of real numbers, the order of operations, the properties of real numbers, the exponent rules, and simplifying and evaluating expressions.
• How they connect: this chapter is the foundation, so there is no earlier week to lean on; every later week uses the rules you build here.
• Where we're going next: Week 2, Linear Equations & Inequalities, uses these rules to find the number that makes a statement true.

Focus

What are the rules that never change, and how do you check that you used them right?

By the end of this module, you should be able to:

• [ ] sort a real number into its family
• [ ] evaluate an expression in the right order, and tell −4² from (−4)²
• [ ] simplify with the six exponent rules and check by arithmetic
• [ ] distribute, combine like terms, and evaluate at a negative input

To-do

Plan your week

1. Read Chapter 1 (about 40 minutes), then the lecture and the slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: evaluate 3x² − 2x + 5 at a negative input and check one exponent rule on the powers of two.

You've got this

Every later week builds on these rules. Take it in order, and ask your instructor early if a step snags.

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