Lesson: Finding the Length of a Line
Introducing the Concept
Finding the length of a line segment by subtracting its coordinates is an important skill for your students to master now. In the next few years, they will learn more about graphing lines. To do that, they need to have a solid understanding of these basic concepts.
Your students have probably had experience with number lines at prior grade levels. Use that experience to introduce finding length on a grid.
Materials: poster paper or a transparency and overhead projector for demonstration; straightedge
Preparation: Draw a coordinate grid on poster paper or a transparency. Label the x- and y-axes from 0 through 10.
Prerequisite Skills and Concepts: Students need to be very familiar with locating ordered pairs on a grid.
- Draw a number line on the board that goes from 0 to 10. Put a vertical arrow at 1 and a vertical arrow at 5.
- Ask: How can I find the number of units between the two points?
Some students may suggest counting units from 1 to 5. Others may suggest subtracting 1 from 5. If students don't suggest subtraction, mention it to them. - Say: Five minus one equals four, so we know it's four units from the first point to the second point. Count the units to check.
- Now mark points at (1, 0) and (5, 0) on a coordinate grid for the class to see. Connect the points with a line segment.
- Ask: Who can tell me how to find the length of this line segment?
Students should realize that the axis is like a number line, so they can count the number of units between the points, or subtract. - Now mark (0, 1) and (0, 4) on the grid.
- Say: This axis is like a number line that goes up and down instead of left and right. Who can tell me the length of this line segment?
Encourage students to understand that the process works the same whether the line is vertical or horizontal. Only the coordinates change.