Rational Exploration: Numbers and their Opposites

Introduction

Hot, cold, wet, dry, off, on... Are you thinking about opposites yet? We see and use opposites in the real world every day, but what about numbers? Do numbers have an opposite? Have you ever thought that about the fact that the number system includes more than just numbers we can actually count? What is the opposite of positive? Negative! We will be working with and using positive and negative numbers in this unit and applying it to how we look at direction and distance.

Essential Questions

What are positive and negative numbers used for?
How are rational numbers represented on a number line?
How are coordinates graphed on a coordinate plane?
How do you order and arrange rational numbers?
What does the absolute value of a rational number represent on the number line?
How does absolute value differ from a statement about an order?

Key Terms

The following key terms will help you understand the content in this module.

Absolute Value: The distance between a number and zero on the number line. The symbol for absolute value is shown in the equation |−8| = 8.
Coordinates: An ordered pair, (, ), that locates a point in a plane.
Inequality: Any mathematical sentence that contains the symbols > (greater than), < (less than), < (less than or equal to), or > (greater than or equal to).
Integers: The set of whole numbers and their opposites {... − 3, −2, −1, 0, 1, 2, 3, ... }.
Negative Numbers: The set of numbers less than zero.
Opposite Number: Two different numbers that have the same absolute value. Example: 4 and −4 are opposite numbers because both have an absolute value of 4.
Ordered Pair: A pair of numbers, (, ), that indicates the position of a point on the Cartesian Plane.
Origin: The point of intersection of the vertical and horizontal axes of a Cartesian plane. The coordinates of the origin are (0, 0).
Positive Number: The set of numbers greater than zero.
Rational Number: The set of numbers that can be written in the form where a and b are integers and b ≠ 0.
Sign: a symbol that indicates whether a number is positive or negative. Example: in −4, the (−) sign shows this number is read as "negative four."
X-Axis: The horizontal number line on the Cartesian coordinate plane.
X-Coordinate: The first number of an ordered pair; the position of a point relative to the vertical axis.
Y-Axis: The vertical number line on the Cartesian coordinate plane.
Y-Coordinate: The second number in an ordered pair; the position of a point relative to the horizontal axis.

IMAGES CREATED BY GAVS