Math Background

Lesson: Ordered Pairs
Developing the Concept

Now that students have seen you graph points on the coordinate plane, it is time for them to try it. Be sure to have students use the proper vocabulary in explaining what they do.

Materials: overhead transparency or poster paper; grid paper and rulers for students

Preparation: Draw a coordinate grid on a transparency or poster paper.
Pass out grid paper with points A to H marked on them as shown on the grid below. (There are two points in each quadrant.) Put a transparency with the same grid on the overhead for the students to see. Point to points A and F as you ask the questions below.

  • Ask: What are the coordinates for this point? Explain how you found the coordinates.
    After doing this for both points A and F, have the class find the coordinates for the other six points. Have students explain how they found the coordinates.
  • Ask: Where is the point (0, -4) on the plane? Explain.
    Repeat for several other points found on either the x- or y-axis.
  • Say: Plot on your graph the following points: (-3, 2), (3, -1), (2, 2), and (-4, -6). Have a volunteer plot the points on the overhead after students have plotted them at their desks.
  • Say: Look at the points in the first quadrant. What can you tell me about the x- and y-coordinates for those points? (They are both positive numbers.) Now look at the points in the second, third, and fourth quadrants. See if you can tell me anything about the x- and y-coordinates for those points.
    After students have told you about the x- and y-coordinates in each of the quadrants, ask questions like the following.
  • Ask: In what quadrant would you find a positive x-coordinate and a negative y-coordinate? (IV) In what quadrant would you find a point with a negative x-coordinate and a negative y-coordinate? (III) Where would you find a point with a zero x-coordinate and a negative y-coordinate? (lower half of the y-axis) What ordered pair corresponds to the origin? (0, 0)
  • Ask: Who can summarize the information about the signs of the coordinates in the first quadrant? (They are both positive.) Second quadrant? (xis negative; yis positive.) Third quadrant? (They are both negative.)Fourth quadrant? (x is positive; yis negative.)What about the points on the two axes? (Zero coordinates are neither positive nor negative.)
coordinate grid

Wrap-Up and Assessment Hints
Provide students with coordinate grids (Learning Tool 20 in the Learning Tools Folder) and have them work with a partner to locate points on the grid. Encourage them to challenge each other by providing pairs of x- and y- coordinates that alternate between positive and negative signs — for example (3, -5) and (-3, 5). Have students label the points on their grids. Circulate to spot-check their answers.

Houghton Mifflin Math Grade 5