Course Guide - USAID Teacher Education Project

Unit 2 AlgebraWeek 2, Session 1: Variables and Coordinate Graphs1. What are the important concepts?a) Variables are symbols (often letters) used to represent patterns of change. Theinput variable is called the independent variable; the output variable is called thedependent variable.b) Variables are used in "pattern rules" (later called functions) to indicate arelationship and a rate of change between variables.c) Patterns of change can be represented on a coordinate graph that is created fromdata collected on a T-chart.d) The coordinate plane is divided horizontally by the x-axis (for the independentvariable) and vertically by the y-axis (for the dependent variable). This is why thecolumns of a T-chart are often labeled with the variables x and y.2. How do children think about these concepts?a) Usually a youngster is first introduce to algebra by being asked to find the value ofx as the unknown, a unique "answer" for a given equation. However, x is not only"the unknown," it can also represents a variable, as where there are infinite answersfor the expression x + 1. The distinction between these two meanings for x isimportant for teachers to understand so that they can communicate this difference tothe youngsters in their classrooms.b) When setting up a graph, students need to create a scale on each axis with aconsistent interval between each cell on the grid. Youngsters often "scale the data,"by using the numbers, which may not have a consistent interval between them, fromtheir T-chart.c) Youngsters have a tendency to connect the points they have plotted on their graph.When changes are continuous (as for the circumference of a circle), the points shouldbe connected to show that continuous change is happening between the data points.In other cases, often involving counting objects, there is no change between the datapoints and the student should not connect the points. This kind of graph is termed adiscrete graph.3. What is essential to know or do in class?a) Introduce variables, what they are and when and how they are used.b) Remind students how to set up a first quadrant coordinate graph.c) Have students collect data, record it on a T-chart, and then transfer thatinformation to a coordinate graph.