In this lesson, students evaluate and compare slope of a line in different ways. Students will use the formula for slope, similar triangles, and grade percentage to evaluate and compare slope of a line. Students will plan for a wheelchair accessible ramp and determine the percent grade of a mountain during this lesson. Students will learn about ADA Guidelines and safe mountain driving for truck drivers during the lesson.
Students come to understand that greater rates of change are indicated by steeper slopes on graphs in the coordinate plane. Also students will be able to compare positive and negative slopes.
At the end of this lesson, students will be able to:
evaluate the slope of a line using the slope formula.
compare slopes to determine which has a greater rate of change.
determine the rise and run based on a grade percentage.
use similar triangles to explain why the slope is the same between two points on the line.
Student Target
“I can…
evaluate the slope of a line using the slope formula by finding the slope of lines drawn on a coordinate plane."
compare slopes to determine which has a greater rate of change by comparing the slopes of the lines from the Extra Practice Sheet and putting them in order from least to greatest."
determine the rise and run based on a grade percentage by completing the Slope and Grade Percentage activity."
use similar triangles to explain why the slope is the same between two points on a line by comparing the points in the two dimensional drawing in the Extending Activity."
CCR Focus Standards
Algebra and Functions - Level D
Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. [Also see 7.RP.2b]
Supporting Standards
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.* [NOTE: See modeling conceptual categories ]
Standards for Mathematical Practice
Model with mathematics. (MP.4)
Attend to precision. (MP.6)
Look for and express regularity in repeated reasoning. (MP.8)
KYAE Employability Standards
E.3 Model compliance of workplace policies and procedures.
E.6 Identify and effectively use skills and materials needed for a particular task.
E.7 Accurately analyze information and respond appropriately.
