Math Background

Lesson: Ordered Pairs
Introducing the Concept

Your students encountered ordered pairs last year, but it will be worthwhile to review with them how to graph points on the plane. Relating the x- and y-axes to a number line will help your students find ordered pairs when graphing.

Materials: overhead transparency or poster paper

Preparation: Draw a coordinate grid on a transparency or poster paper. Use Learning Tool 20 in the Learning Tools Folder.

Locate a point on a wall of the classroom a few feet in from the left side of the wall and a few feet up from the floor. Tape a paper plate or circular cutout to the wall to indicate the point.

Prerequisite Skills and Concepts: Students need to understand positive and negative numbers and how to locate points on a number line.

  • Say: Look at the point on the wall. Pretend I can't see it. Who can tell me how to locate it?
    Lead a student discussion about the need for a place to start and directions to get to the point— for example: Start at the bottom left side of the wall. Move about 6 feet to the right and 3 feet up.
  • Say: When we are locating points on a plane, we need the same kind of information — namely, a place to start and directions for getting there. Point to the coordinate grid. On the coordinate plane we start at the origin. Where is the origin?
    Some students will say it is where the two lines intersect. Others will say at zero or (0, 0).
  • Say: We use the numbers on these two lines to describe locations. What are these lines called?
    The horizontal line is called the x-axis. The vertical line is called the y-axis. Relate the points on the axes to points on a number line.
  • Say: An ordered pair of numbers tells us where to move on the axes. The first number tells us how to move on the x-axis and the second number tells us how to move on the y-axis. Let's find point (3, 4) on the plane. Where will we start? (the origin) How many units will we move on the x-axis? (3) How many units will we move on the y-axis? (4)
  • Mark point (3, 4) on the coordinate plane. Elicit from students that we move right on the x-axis and up on the y-axis for coordinates that are positive. Provide students with other ordered pairs that have positive x- and y-coordinates and have them tell you how to locate the points on the coordinate plane.
  • Say: Some ordered pairs have negative coordinates. Tell me how to locate point (-5, -4).
    Students should know that they move left on the x-axis and down on the y-axis for coordinates that are negative. To locate point (-5, -4), start at the origin, move 5 units to the left on the x-axis and 4 units down on the y-axis. Have students tell you how to locate points (-2, 3) and (6, -1). Provide additional examples if necessary. See Operations With Integers.
  • Say: Points directly on the x-axis have a y-coordinate of zero. Mark points (2, 0); (5, 0); and (-3, 0) on the coordinate plane. This point is (2, 0). This one is (5, 0). This point is (-3, 0). Where is the point (-6, 0)?
  • Do a similar presentation for points on the y-axis; for example, (0, 4) and (0, -7).

Houghton Mifflin Math Grade 5