Math Background

Lesson: Graphing Integers
Developing the Concept

Now that students have been shown how to graph a linear function, it is time for them to try it. Be sure to stress the use of correct mathematical vocabulary. Also stress that the equation, table, and graph are different representations of the same function.

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

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

  • Say: Earlier we learned how to make a table and graph for a linear equation like x + 2 = y. Today you will have the opportunity to practice this on your own. If you want to graph x + 2 = y, what should you do first?
    Students should respond that they need to make a table.
  • Ask: What should you do in order to make this table?
    Students should say that they need to pick some different values for x and substitute them into the equation and solve it for y. Give students a few minutes to make a table. Stress that students should pick both positive and negative values for x to substitute into the equation.
  • Ask: Great, now what should you do?
    Students should say,“I need to graph the ordered pairs I found,” or something equivalent.
  • Say: Using your graph paper, plot the ordered pairs.
    Give students time to plot the points. Have someone graph the points on the overhead transparency grid.
  • Ask: What do you notice about the points? (They seem to lie in a straight line.) Good, now draw a straight line through the points. Put arrowheads on both ends of the line to indicate that it goes on indefinitely.
  • Say: Let's make a list of the steps we need to follow to graph an equation. What is the first step?
    Students should respond that they need to create a table. Write this as Step 1 on the board. Have students copy the steps in their math journals.
  • Ask: What is Step Two?
    Students should say they need to select x-values, substitute them into the equation, and find the corresponding y-values. Then they need to record the values in the table and write the ordered pairs.
  • Ask: What do we do next?
    Students should say to graph the ordered pairs and draw a straight line connecting them. Be sure to have students put the arrowheads on the ends of the lines.

Give students two more equations to graph on their own, while you walk around the room helping individual students.

Wrap-Up and Assessment Hints
Students should be aware that they can also use a graph to complete the table of data for a function. Write the equation x = 8 − y on the chalkboard. Have students find two ordered pairs for the equation—for example, (7, 1) and (5, 3)—and locate them on a coordinate grid. (Use Learning Tool 20 in the Learning Tools Folder.) Tell them to connect the two points with a straight line. Then have them list other coordinates that the line passes through and verify that those coordinates also satisfy the equation.

coordinate grid

Houghton Mifflin Math Grade 5