Course Guide - USAID Teacher Education Project

c) Youngsters need to connect the concept of "rise" to the vertical distance on the y-axis and "run" to the horizontal distance on the x-axis in order to understand theconventional formula for finding slope (shown below). However, teachers oftenassume that students can translate this "rise over run" into the formula "delta y overdelta x."Youngsters are usually confused as to what "delta" means, and how delta relates to thechanges in y and x in the conventional formula for calculating slope:3. What is essential to know or do in class?a) Introduce the concept of slope by having students work with the Stairs Accordingto Code problem.b) Have students discuss the features of their graphs that involve slope.c) Clarify the difference between a graph’s steepness and its slope.d) Introduce the term "coefficient" and point out its role in indicating slope (m) in y =mx + b.e) Introduce three ways to talk about slope:1) Rise over run2) Change in vertical versus horizontal change, and3) The formula:f) Introduce several equations in y = mx + b format that have a positive slope, anegative slope, and a negative y-intercept.4. Class Activities:a) Begin by distributing copies of the Stairs According to Code problem. Havestudents follow the directions, first by creating a graph, then making a table of values,and finally developing an equation in y = mx + b format. (Again, do not giveparameters for the graph so students will create graphs with different scales that canbe used for comparison.)b) Once students have completed the assignment, have them discuss their graphs ininformal terms, noting that the ratio (slope) between any two points is 7 "up" versus10 "over," or 7/10. (It is important that students realize that the same 7 to 10 ratioexists between any two points on the line, not just two adjacent points.) Have