Lesson plan
|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. |
|What is the location of each point in the coordinate plane? |
|[pic] |
|Whole-Class Instruction |
|Materials Needed: PowerPoint Presentation*, square poster paper, coordinate grid |
|Procedure: |
|Presentation |
|Explain that just as points can be graphed, so can values for functions. Demonstrate the process for y = 2x –1. |
| |
|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. |
| |
|Plot the input/output pairs as ordered pairs. |
| |
|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 |
|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 |
| |
|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. |
| |
|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 |
|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: |
|Ask students to analyze the graphs displayed from the Guided Practice and to look for common characteristics. |
| |
|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. |
| |
|Have students choose random equations, in the y = mx + b form, and graph them without using an input/output table. |
| |
|Discuss student results and strategies. What did they need to know to graph the equations (the y-intercept, and the slope)? |
| |
|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: |
|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. |
| |
|Have students graph y = 6x, y = 7x, y = 8x, y = 9x, and y = 10x, on the same grid paper sheet, following the steps above. |
| |
|Discuss anything students notice: |
|The graph always goes through the origin. |
|The graph gets steeper as the number x is multiplied by gets larger. |
| |
|Ask students what the graph for y = 20x would look like. |
*see supplemental resources
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