Chapter 8
Introduction to Algebra
You hand over a twenty dollar bill for a sandwich and eight dollars come back. Arithmetic works when every number is already on the table, but this question hides one and tells you only what it has to do. That gap is where algebra begins. A letter can hold the place of an amount nobody has told you yet, so the relationship can be written down before it is worked out. Then comes the harder question: how do you get from that written line to the number itself?
What You'll Explore
5 lessons.
- Variables and Expressions
Why would anyone write a letter where a number belongs? Here you meet the idea that a symbol can hold an amount that is not fixed, and what changes when a phrase in ordinary words gets rewritten in letters, and what that writing is worth once the letter is given a value.
- Evaluating and Simplifying Expressions
Two expressions can look nothing alike and still give the same answer for every number you try. This lesson pulls apart the two things you can do to an expression, putting numbers into it and tidying it up, and asks what makes the tidying safe.
- Solving One-Step Equations
Picture a balance scale with a hidden weight in one pan. You cannot see the weight, but you can see that the scale is level, and that alone turns out to be enough. This lesson asks what it means to solve an equation, and how a hidden number can be uncovered without ever guessing.
- Solving Two-Step Equations
Suppose two operations stand between you and the unknown instead of one. Peeling them off one at a time still sounds easy, but the order you choose changes how much work you make for yourself. This lesson asks which layer comes off first, and what decides that.
- Inequalities
Not every question has a single answer. A sign saying you must be at least forty eight inches tall is satisfied by a whole stretch of heights, not one. This lesson looks at what it means to solve a statement like that, and at one move that behaves in an unexpected way.