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Math Lesson: Functions / Grade Level: 7
Lesson Summary: Students graph a variety of linear equations using data from input/output tables. Graphs will be displayed and discussed to determine common characteristics and differences. Advanced students will be introduced to the y = mx + b form and graph equations without using an input/output table. Struggling students graph direct variation equations.
Lesson Objectives:
The students will know…
· that linear equations can be graphed in the coordinate plane.
· that linear equations have common characteristics.
The students will be able to…
· graph linear equations in the coordinate plane and recognize characteristics of linear functions.
Learning Styles Targeted:
x / Visual / x / Auditory / Kinesthetic/Tactile
Pre-Assessment:
Use this quick assessment to see if students understand how to plot points.
1) What is the location of each point in the coordinate plane?
Whole-Class Instruction
Materials Needed: PowerPoint Presentation*, square poster paper, coordinate grid
Procedure:
Presentation
1) Explain that just as points can be graphed, so can values for functions. Demonstrate the process for y = 2x –1.
2) Draw an input/output table. Choose values for x and find corresponding y-values. Explain that any values for x can be chosen, but it will be helpful to choose consecutive values and x = 0.
3) Plot the input/output pairs as ordered pairs.
4) Students will see that the points are in a line. As the line is drawn, explain that students can use test points to prove that the graph is continuous.
Guided Practice
5) Have students work in groups to graph a linear equation on poster paper so that the graphs may be displayed and compared. Assign the following equations: y = 2x, y = 3x, y = 4x, y = 2x + 1,
y = 2x + 2, y = 3x + 1, y = –2x, y = –3x
6) Display the graphs and discuss what students notice.
· Some graphs have the same steepness (slope), and some are steeper.
· All of the graphs rise to the right except for y = –2x and y = –3x.
· Some graphs go through the origin, some cross the y-axis at the same point.
7) It is not necessary to use terms such as slope and intercept at this point. The purpose is for students to see that the graphs are linear, and to see the common characteristics.
Independent Practice
8) Have students play a game using the PowerPoint Presentation.
Closing Activity
6) Ask students for input and output values for y = x2. Plot the points and discuss that not all equations will graph as a line. Is there a way to tell which equations will be linear?
Advanced Learner
Materials Needed: coordinate grid, and pencils
Procedure:
1) Ask students to analyze the graphs displayed from the Guided Practice and to look for common characteristics.
2) Students will have made some observations from the Guided Practice discussion, but direct them towards more specific conclusions, leading to the y = mx + b form.
· The point where the line crosses the y-axis has an x-coordinate that is the same as b (If there is no b, such as y = 2x, then the line passes through the origin).
· The steepness of the graph, or slope, is determined by m.
3) Have students choose random equations, in the y = mx + b form, and graph them without using an input/output table.
4) Discuss student results and strategies. What did they need to know to graph the equations (the y-intercept, and the slope)?
5) Ask students if they could look at the graph of a linear equation and determine the equation (yes, because they would know the slope and y-intercept).
Struggling Learner
Materials Needed: grid paper and pencils
Procedure:
1) Model with students how to graph y = 5x. First, have students make an input/output table with x-values from 0 to 5. Then, have students draw the first quadrant of the coordinate plane on grid paper.
2) Have students graph y = 6x, y = 7x, y = 8x, y = 9x, and y = 10x, on the same grid paper sheet, following the steps above.
3) Discuss anything students notice:
· The graph always goes through the origin.
· The graph gets steeper as the number x is multiplied by gets larger.
4) Ask students what the graph for y = 20x would look like.

*see supplemental resources