The document defines slope as the steepness of a line and the vertical rise over the horizontal run. It provides the formula for calculating slope as change in y over change in x. It discusses relating slope to ski slopes by considering which of three staircases would be the steepest and least steep. It also discusses factors to consider when setting up a ladder, such as the angle placed at and where it should start and end on the ground.
7. Definition of a Slope A. Definitions 1. Slope is the steepness of a line. 2. Slope is the vertical rise over the horizontal run. 3. Slope = change in y (rise) change in x (run)
10. Relate this lesson to a ski slope. Of the three calculated staircases, if they were a ski slope, which would be the most difficult to ski and which the least and why? When you look up the stairs, is this an example of a positive or negative slope? When you look down the stair, is this a positive or negative slope?
11. Given the following problem, come up with some solutions: When you arrive home from school one day, you realize that you do not have your house key, however, you can get into the garage where there is an extension ladder stored. You notice that the top window is open, so despite your fear of heights, you proceed to get the ladder. What are some of the factors that become important when you set up the ladder? Possible solutions-Look for ideas about the angle at which you place the ladder, where on the ground it should start, where it needs to end, etc.
12. Notes for slope The students should discover how changing the coefficient of x changes the steepness of the line, including making the line steeper, less steep, or horizontal. The students should also discover how to manipulate the coefficient of x so that the line can be made to go up from left to right or to go down from left to right. Students should make other discoveries, including how the y -intercept appears in a linear equation
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