GRN - Graphing Rational Numbers Module Overview

Graphing Rational Numbers

Introduction

We will continue our work from the Rational Exploration: Numbers and their Opposites module to work with and use positive and negative numbers in this unit and apply it to how we look at direction and distance. We will focus on the location of points in all four quadrants of the coordinate plane and the use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

Essential Questions

  • What is the distance between two coordinates that have the same first or second coordinate?
  • How can we use graphical reasoning to connect the location of rational numbers on the horizontal axis and the vertical axis to locations in all four quadrants of the coordinate plane? 
  • How can we solve relevant problems involving the application of algebra through geometry as we work with polygons to find the distance between points on a coordinate plane? 

Key Terms

  • Cartesian Coordinate Plane: Also called the Coordinate Plane, this contains two perpendicular axes. X is the horizontal axis and y is the vertical axis, They intersect at a point called the origin, which is at (0,0).
  • Coordinates: An ordered pair, ( , ), that locates a point in a plane.
  • Origin: The point of intersection of the vertical and horizontal axes of a Cartesian plane. The coordinates of the origin are (0, 0).
  • 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).
  • Polygon: A two-dimensional figure with at least three straight sides. Some examples include triangles, quadrilaterals, pentagons, and hexagons. The name tells how many sides the shape has. 
  • Positive Number: The set of numbers greater than zero.
  • Quadrants: The coordinate plane is divided into 4 sections we call quadrants. The top right is quadrant 1 and has a positive x value and a positive y value. The top left is quadrant 2 and has a negative x value and a positive y value. The bottom left is quadrant 3 and has a negative x value and a negative y value. The bottom right is quadrant 4 and has a positive x value and a negative y value. 
  • 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. 

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