Course Guide - USAID Teacher Education Project

c) Have a whole class discussion that brings out similarities and differences betweenthe taxicab problem and the recipe problem from last week.d) Introduce the conventional format for linear equations, y = mx + b.4. Class Activitiesa) Begin the session by distributing copies of Taxicab Fares and ask students to workin pairs to create a table, chart, and symbolic expression to represent fares overvarious distances.Note how students set up their graph. Do they scale the y-axis in whole numberamounts? What interval did they use for distances, which are expressed in “one-fifthof a mile” units? To how many miles did they extend their table of values?It is important that pairs of students make these decisions independently, and that youdo not give them specific requirements. This is to illustrate later that the same datacan look different when plotted on graphs that are scaled differently.When students have finished the assignment, begin a discussion about the “look” ofeach graph. Are they all the same? If not, how are they different? Why is this so?Have students recall the recipe problem from last week, asking how the taxicabproblem is similar to it.Students should note that the pulse graph showed a straight line, the table showed aconstant first difference, and the expression was in the form of mx.Ask how the two problems differ.Continue by discussing that because there is an initial fee, the graph begins at 2.50 onthe y-axis. This is different from most graphs they have encountered, which begin at(0, 0).Tell students that there is a special name for the place where a line crosses the y-axis:the y-intercept.Ask how this is represented in the expression they wrote. Remind students of theexpression they wrote for the recipe problem last week, that it was in the form of y =mx.What is the form of the taxicab problem's expression? Ask if there is a connectionbetween the y-intercept on their graph and the 2.50 in their expression.Note that in the recipe problem the graph started at 0, so the expression could bethought of as mx + 0. However in the taxicab problem, the expression is mx + 2.50.Tell students that the conventional notation for all linear equations is y = mx + bwhere b is a constant and represents the y-intercept.5. Assignments (to be determined by instructor)