The Coordinate Graphing System

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In this lesson, you will be learning about how perpendicular number lines are used to define a coordinate graphing system.

Perpendicular Lines are lines that cross to form four right (90º) angles.

Number lines are lines which have been divided into equal parts which are numbered at regular intervals, in the same way as a ruler is divided and marked.

Integers are all the positive whole numbers, their opposites (the negative values of each number), and zero.

Learning Outcomes

By the end of this lesson, your children will have a basic understanding of how a coordinate graphing system is arranged, and be able to identify its parts using the correct mathematical terminology.

Warm Up

Coordinate graphing is an area where algebra and geometry overlap one another. Since most students tend to identify more with one of these areas than the other, coordinate graphing is often a subject of shared interest among students.

Those who enjoy algebra more appreciate the functions and the visual display of patterns. Those who enjoy geometry more seem to understand the patterns better by plotting points and drawing lines to create the coordinate graph. Since this is an area of overlap, it is especially important to understand how the coordinate graph system is arranged, and what all the various parts are called.

Understanding the academic vocabulary involved in particular math concepts helps make sure that all mathematicians share a common, basic understanding. Take the Pre-Test below. If you score 10 or more, you are ready to go on to the lesson.

Pre-assessment worksheet

Have your children take the Pre-Test below to see if they are ready for this lesson. If they get 9 or less correct, review number lines and types of lines with them before continuing on to the lesson.

Main Lesson: Coordinate Graphing System

The coordinate graphing system is formed by a pair of perpendicular number lines. The two lines intersect, or cross, to form four right angles.

coordinate grid showing four quadrants with origin highlighted

The number lines are both marked with the set of integers. They intersect each other through zero on each line. This intersection point is called the Origin.

four quadrants of graph with x and y axes highlighted

Each of the two number lines is called an axis (pronounced "ack-sis"). The plural form of axis is axes (pronounced"ack - sees").

The horizontal axis, the one that goes across from side to side, is called the X axis.

The vertical axis, the one that goes up and down, is called the Y axis.

Points can be drawn, or plotted, on the coordinate graph using specific coordinates. These coordinates are written using an ordered pair of numbers. These numbers are written inside parentheses and are separated by a comma.

A point is always plotted from the starting point of the origin, where the lines intersect through the number zero. The first number in the ordered pair shows how far left or right to move from zero on the x axis. The second number in the ordered pair shows how far up or down to move from zero on the y axis.

coordinate grid with (4,5) and (-6,-3) plotted

The coordinates of point B are (4,5) because it is located 4 units to the right of zero on the x axis, and 5 unit up from zero on the y axis. It is plotted where the two lines cross.

The coordinates of point C are (-6, -3) because it is located 6 units to the left of zero on the x axis, and 3 units down from zero on the y axis. It is plotted where the two lines cross.

Graph Quadrants

If you look at the coordinate graph, you can see that when the x and y axes cross, they form four sections. These sections are called quadrants. That's why you will sometimes hear a coordinate graph be called a four-quadrant graph. The quadrants are numbered using Roman numerals, starting with the top right quadrant, and moving around in a circle to the left.

The quadrant the plotted points will fall in depends upon whether the numbers in the ordered pair are positive or negative integers.

If both the x and the y number are positive, the point will be in quadrant I. If the x number is negative, but the y number is positive, the point will be in quadrant II. If the x and y numbers are both negative, the point will be in quadrant III. If the x number is positive, but the y number is negative, the point will be in quadrant IV.

coordinate grid with four graph quadrants shown

 

Remind your children that the x axis coordinate is listed first in the ordered pair, followed by the y axis coordinate. The numbers in every ordered pair will follow the (x ,y) format.

Work through the five questions below with your children to help them recall what they have learned in this lesson.

 

1. What kind of lines form a coordinate graphing system?

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2. What is the vertical line called?

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3. What is the horizontal line called

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4. How do you know whether to go right or left from zero on the x axis?

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5. What are the numbers that give the coordinates of a point called?

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Note: You might find this printable graph paper generator handy.

Recap

  • The coordinate graphing system is formed by the intersection of two perpendicular number lines marked by integers.
  • The lines are called the x and y axes.
  • The x axis is horizontal.
  • The y axis is vertical.
  • The origin is the point at which the lines intersect.
  • The intersecting lines form four sections, called quadrants, numbered with Roman numerals.
  • The coordinates are written as an ordered pair.
  • The ordered pair is always written in the (x, y) format.
  • Always begin at the origin when plotting a point.

Test Questions

Review the above recap points with your children and then print out the Post Test that follows.

At least 8 out of 10 correct will show that your children have completed this unit with sufficient understanding to move on to the Coordinate Graphing of Real-World Situations.

 

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