Course Guide - USAID Teacher Education Project

Unit 2 AlgebraWeek 3, Session 2: Linear Relationships and Slope1. What are the important concepts?a) Slope is a characteristic of linear functions, the constant rate between twovariables.b) In a linear equation in the form of y = mx + b, the slope is the coefficient "m."c) Slope is informally described as "rise over run." It can be more formally thoughtof as "the vertical change divided by ('over') the horizontal change" or expressed bythe following formula:d) Slope implies steepness, but the same slope on graphs scaled differently may lookdifferent.e) The slope of a line can be positive (going "up"), negative ("going down"), or 0 (ahorizontal line where there is no change).2. How do children think about these concepts?a) In many textbooks, slope is introduced via a "rise-over-run" visual on a graph.Although the following diagram may seem self-explanatory to adults, it is too abstractto be useful in introducing slope to middle grade students.Youngsters eventually will need to interpret this visual explanation of slope, but it hastoo many terms and symbols to be an effective introduction to the concept.b) Although students usually interpret slope as a measure of "steepness," the scale ofa graph can be misleading. Graphs with different scales will present different visualimages of steepness. This also true of most graphing calculators where the cell on thegraph is rectangular, not square. The rectangular cell means that a line with a slope of1 does not go up at a 45-degree angle to match the graph that a youngster created ongraph paper where the cells are square.