Course Guide - USAID Teacher Education Project

Unit 2 AlgebraWeek 3, Session 1: Linear Functions1. What are the important concepts?a) There is a connection between the various representations for linear functions.b) All linear functions have certain characteristics in common: a straight line graph, aconstant difference on a table, and an equation written in the form of y = mx + b.c) The "b" in y = mx + b is the y-intercept on a graph.d) You can recognize a linear function simply by looking at a graph, a table, or anexpression.e) Differences in the appearance of a graph showing the same data points are due to adifference in scale.2. How do children think about these concepts?a) When introducing linear relationships, textbooks often present the formula y = mx+ b, give a table of values, and ask youngsters to create a graph.In this course, we take the opposite approach:1) Learn about a table of values by creating what is called a T-chart2) Create a graph by using the table of values.Only when these two skills are in place do we introduce symbolic notation. Thissequence of events helps students make sense of the equation for a linear function:y = mx + bb) When presented with a linear function problem where the y-intercept is not 0,middle grade students are often surprised or confused. This is because the emphasisin their prior work may have been with situations where graphs began at (0, 0).c) Similarly, if youngsters have worked only with first quadrant graphs, they willneed the teacher’s help so that they can envision the entire coordinate plane. This iswhere their integer work in the Number and Operations unit with horizontal andvertical number lines can help them connect with a four-quadrant graph.3. What is essential to know or do in class?a) Introduce a linear function problem where the y-intercept is not 0.b) Have students create a table, graph, and symbolic expression to represent faresover various distances.