Course Guide - USAID Teacher Education Project

Unit 1 Number and OperationsWeek 4, Session 3: Introduction to Rates11. Maths Concepts to be studieda. Constant rates of change are ratios that show a relationship between an independent anddependent variable. In real life situations, this might be the unit price per loaf of breador kilometres (km) per hour.b. For example, if I drive at a constant speed (the independent variable), I can calculate thedistance I drove for various lengths of time (the dependent variable).c. Note that the word “per” separates the two units in the rate.d. Multiple Representations: When working with rates, it is important for students to seevarious ways change can be represented: table, graph, and equation. In the km per hourscenario, a table would show the following distances:Rate: 50 km per hourt: Time in hours (x) d: Distance in km (y).5 251.0 501.5 752.0 1002.5 1253.0 1505.0 250n50nThe graph of this scenario would look like this:Notice that the graph shows a straight line, indicating a constant rate of change, and thedistance traveled for any particular hour (or fraction of an hour) on the x-axis can befound by the line’s location relative to the y-axis.The third representation would be an equation, in this case d = 50 t where d is thedistance and t is the time. Note that if the time and distance were known we could usesimple algebra to discover the rate: d/t = 50.• Understanding constant rates of change will become important later in algebra wherethey will be linked to linear equations and slope.