Lesson 23 — Activity 1: Working in the First and Second Quadrants Using Ordered Pairs


Getting Ready


Have you ever done a connect-the-dot exercise at some point in your life?

One way you can create a connect-the-dot exercise is to use a series of coordinates to create the original picture. What are coordinates? Coordinates are ordered pairs.

Here's an example of a connect the dots page.

Workers in the forestry industry often spend time in remote areas of the forests of Alberta. A Global Positioning System (GPS) helps people keep track of their exact location. Pilots and air traffic controllers also rely on GPS and other technology to keep track of where planes are flying.

Maps and sections of maps use grids to identify specific areas and locations. Grids are used to identify integers and ordered pairs and to display data.

A coordinate plane is used to help mark locations. A coordinate plane is a two-dimensional surface with locations identified using x and y coordinates (x-axis and y-axis). Coordinates are similar to latitude and longitude.

(Adapted from K&E Studio.)
The grids on this map identifies specific areas on an island.
Images courtesy of www.imagesgoogle.com

An ordered pair consists of two numbers. The first number represents how far you will move left to right, or horizontally. It is known as the "x-coordinate."

The second number represents how far you will go up and down, or vertically. It is known as the "y-coordinate." Wherever these two numbers intersect, or meet, you place a dot.

For example, let's say you have been given the ordered pair (12,5). First you move 12 places across. Then you will move 5 places up. Place a dot where 12 across and 5 up intersect. It has been done for you on the coordinate plane below with a star instead of a dot.

This image shows a graph with ordered pairs.

You can also graph using negative numbers. In order to do that, the graph paper has to be drawn in a different way than what you may be used to. It is divided into four different quadrants. The information below shows how the new graph paper looks.


 Single Part of a Four Quadrant Grid


  • A quadrant is a simple Set of Axes (called "axes" because there are two axes: the x-axis and the y-axis).

  • x can go from 0 onwards and is always positive. y can go from 0 upwards and also is always positive.


  • We call this the first quadrant:

                       This image shows the first quadrant.


Showing a Four Quadrant Grid


  • As noted above, in the first quadrant, x is positive and y is positive.

  • In the second quadrant, x is negative and y is positive.

  • In the third quadrant, x is negative and y is negative.

  • In the fourth quadrant, x is positive and y is negative.

                        This image shows a four quadrant grid.


How to plot the coordinates:



This image shows coordinates plotted on a graph.

This is the coordinate (4,4).

  • The x coordinate is always first.

  • The y coordinate is second.
  • Go along 4, and then go up 4, and then "plot the dot."
  • It is easy to remember, in the alphabet, x comes before y, so the first number must be the x coordinate.


This image shows the plotting of negative numbers.

This is much the same as before except where there is a negative number:

  • Go backwards for x or down for y.
  • For example, (–4, 4) means: go back along the x axis 4, and then go up 4.
  • And (–4, –4) means: go back along the x axis 4, and then go down 4.


While all of the information talks about all four quadrants, you will only be working in the first and second quadrants.


Digging Deeper

Watch this video, which gives you more information about graphing using ordered pairs.