Math Background

Lesson: Finding the Length of a Line
Developing the Concept

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Materials: poster paper or a transparency and overhead projector for demonstration; straightedge; Coordinate Grid (PDF file) Worksheet or Learning Tool 51 in the Learning Tools Folder, and a straightedge for each student

Preparation: Draw a coordinate grid on poster paper or a transparency. Label the x- and y- axes from 0 through 10. Make copies of the grid for students.

Prerequisite Skills and Concepts: Students should know about ordered pairs and locating points on a grid. They should also be able to recognize and interpret an equation.

  • Say: Earlier we saw how you can find the length of a line segment on a number line and on the x- and y-axes. Today let's try finding the length of line segments in other locations on a grid.
  • Draw (6, 2) and (1, 2) on your grid. Connect them with a horizontal line segment.
  • Ask: Who can count how many units long this line segment is?
    Have a volunteer count the units using the grid squares or along the x-axis.
  • Say: That's right, but did you know there's a quicker way to do that? Who can tell me the x-coordinate of this point? Point to (6, 2). And the x-coordinate of this point? Point to (1, 2).
  • Write the two x-coordinates on the board.
  • Ask: What is the difference between these two numbers? (5) Is that the same as the number of units we counted? (yes) So you can find the length of a horizontal line segment by subtracting the x-coordinates.
  • Give students several horizontal line segments to graph, connect, and find the length of.
  • Then add the point (6, 5) to your grid and connect it to (6, 2) with a vertical line segment.
  • Ask: Can anyone predict how we might find the length of this segment?
    Then follow the same steps as before, but use the y-coordinates rather than the x-coordinates.

Wrap-Up and Assessment Hints
Reinforce the idea that these techniques only work on horizontal and vertical lines. As you assess students, make sure they are using the correct coordinates for each kind of line. One way to provide some additional help for students having difficulty is to use inch-ruled grid paper and provide students with rulers. Let them measure the line segments with the ruler and compare the results to the answer they get.

Houghton Mifflin Math Grade 4