The Coordinate Plane

Contributor: Marlene Vogel. Lesson ID: 11239

Can math really be fun? Yes, if you have the right tools! Coordinate planes don't take off, but you can fly through this lesson to learn how to plot coordinates by playing printed and online games!

categories

High School

subject
Math
learning style
Kinesthetic, Visual
personality style
Beaver, Golden Retriever
Grade Level
High School (9-12)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

Audio:

Have you ever enjoyed the game "Twister"? You know, the one where the person who is spinning spins the arrow and tells the other players what to do. Examples include right hand red, left foot yellow, and right foot green. Are you also familiar with the game "Tic-Tac-Toe"? You remember, the goal is to get three of your X's or O's in a row. This lesson includes an activity that combines both Twister and Tic-Tac-Toe. The name of this game is "Dots-In-A-Row."

Before playing the game, you will need to learn the basics of how to use a coordinate plane.

Let's start with some basic vocabulary (All definitions can be found at Mathwords.com. Don't forget to write them down!):

  • coordinate plane
  • quadrant

This lesson will discuss what the coordinate plane looks like, the four quadrants in the coordinate plane, how to place a point into the coordinate plane, and how to label the position of a point already located in a coordinate plane.

Above is an illustration of a coordinate plane. As you can see, there are two axes that divide the coordinate plane into 4 sections. These 2 axes are the x-axis (which is horizontal) and the y-axis (which is vertical). See below:

The four different sections of the coordinate plane are referred to as quadrants and are labeled in a counter-clockwise manner. See below:


Each quadrant is unique.

Notice the numbers located on both the x-axis and the y-axis. The place on the coordinate plane where the x-axis and the y-axis intersect is known as the origin and is labeled with the number "0." Not every illustration of a coordinate plane includes the 0 label. If that is the case, feel free to write in a 0 if you desire.

  • In Quadrant 1, you will see the part of the x-axis to the right of the 0 and the part of the y-axis above the 0. Both of these parts of the axes contain positive numbers. This means, if given an ordered pair with two positive coordinates, such as (5, 7), you know that the corresponding point will be located in Quadrant 1.
  • In Quadrant 2, you see the part of the y-axis above the 0 and the part of the x-axis to the left of the 0. The part of the y-axis seen in this quadrant contains positive numbers, but the part of the x-axis seen in this quadrant contains negative numbers. This means, if given an ordered pair with a negative coordinate and a positive coordinate, such as (-5, 7), you know that the corresponding point will be located in Quadrant 2.
  • In Quadrant 3, you see part of the x-axis to the left of the 0 and the part of the y-axis below the 0. Each axis in this quadrant contains negative numbers. Therefore, if you are given an ordered pair of two negative numbers, such as (-5, -7), you know that the corresponding point will be located in Quadrant 3.
  • In Quadrant 4, you see part of the y-axis below the 0 and part of the x-axis to the right of 0. The x-axis portion in Quadrant 4 contains positive numbers but the y-axis portion in Quadrant 4 contains negative numbers. Therefore, if given an ordered pair with one positive number and one negative number, such as (5, -7), you know that the corresponding point will be located in Quadrant 4.

So, what is an ordered pair? An ordered pair is a pair of numbers located in a set of parentheses and separated by a comma. For example, (5, 7) is an ordered pair. The first number in the set of the parentheses always refers to the x-axis, and the second number refers to the y-axis. In order to place the point that corresponds with the ordered pair onto the coordinate plane, you need to locate the positive 5 on the x-axis and the positive 7 on the y-axis. Once you have completed this step, use your fingers to draw an imaginary line up from the 5 on the x-axis and use another finger to draw an imaginary line to the right from the 7 on the y-axis. See below:

The place where the two imaginary lines intersect is the place where you will place the point. See below:

This is how to graph a point on the coordinate plane when given an ordered pair. The most important point to remember is that the first number in the set of parenthesis refers to a place on the x-axis, and the second number refers to the place on the y-axis. Also, pay close attention to the sign of each number in the ordered pair so you graph the point in the correct quadrant.


The last skill you need to know about working with a coordinate plane is the ability to locate a point in the coordinate plane and write the ordered pair.

Below is a coordinate plane with four points graphed on it. To be able to list the ordered pair that coincides with the point's position on the coordinate plane, you will need to find the x-axis and y-axis positions of the point. See below:

To locate the coordinates of the point on a coordinate plane, place your finger on the point and bring it up or down to the x-axis. Use the green point for this example. Put your finger on the green point and bring it down to the x-axis. You will land on -9; that is your x value for the ordered pair. Now put your finger back on the green dot and move it to the right until you reach the numerical value on the y-axis. You will land on 8. That is the y value for the ordered pair. Now you can write your ordered pair as (-9, 8). Practice with the other three points on the coordinate plane and see if you can write the ordered pair for each point.

  • Did you get (4, 3) for the blue dot, (-2, -3) for the pink dot, and (6, -6) for the yellow dot? Fantastic!

The following Got It? section offers activities for you to practice your new geometry skills. You can choose to complete one or both of the activities.

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