Chapter 2
Integers and the Number Line
An elevator can go below the ground floor. A bank account can be spent past empty, leaving you owing money rather than holding it. In both, zero is not the smallest amount but a chosen starting point, with the quantity on the far side of it. Counting numbers stop dead there. Negative numbers let the line carry on the other way, which raises three questions worth chasing. Which of two of them is the larger? What happens to arithmetic once numbers point two ways? And what is left of a number when you stop caring which way it points?
What You'll Explore
4 lessons.
- Negative Numbers and the Number Line
Which is colder, three degrees below zero or twelve degrees below zero? Once the numbers continue past zero on both sides, even deciding which of two is larger needs a second look. You will build the line these numbers live on and see what a position on it tells you.
- Adding and Subtracting Integers
Adding usually makes a total larger and subtracting makes it smaller. Neither stays true once negative numbers join in, and a subtraction can even leave you with more than you started with. Here you will trace what each operation does to a position on the line, and ask whether the two are as different as they look.
- Multiplying and Dividing Integers
Multiplication began as repeated addition, and three groups of a loss is clearly still a loss. But what could it possibly mean to take a negative number of groups of something? This lesson follows that question until the sign rules for multiplication and division stop looking like a chart to be memorized.
- Absolute Value
Thirty meters below the surface and thirty meters above it put a diver and a kite on opposite sides of sea level. Some questions care only about how big a quantity is and not which way it points, and this lesson gives that idea its own name and its own notation.