Course Guide - USAID Teacher Education Project

For example, a taxicab in New York City imposes an initial cost for the ride. Then acost is added for each fraction of a mile travelled:• $2.50 upon entry into the cab• $0.40 for each one-fifth of a mile travelledThis can be modeled by a linear equation where the "starting cost" (the y-intercept) is2.50, to which is added 0.40x with x being the number of "one-fifths of a mile"travelled.Although there are certain problems, such as tiling the pool, that lend well todiagrammatic representations, the taxicab problem is more likely to be solved bytalking through it and then representing it in a table and graph before coming up withan equation.This taxicab problem, like the recipe problem, is an introduction to linear functionsset in a real life context to which adults like pre-service teachers can relate. Findinglinear function problems that relate to middle grade students can be challenging.However, it is important that pre-service teachers begin to understand linear functionsmore deeply by solving problems that are meaningful to them as adults.Session 2 will emphasize how linear equations in the form of y = mx are related toslope. The idea of "first difference" mentioned earlier will become important, since itrelates to the conventional formula for slope, which is expressed as the “difference iny related to the difference in x.”Your mentioning "first difference" in last week's session sets a foundation for studentsunderstanding how subtraction in the following symbolic representation is related tothe first differences they noted on their chart.Session 3 begins by looking at the conventional order of operations in arithmetic andthe use of clarifying devices such as parentheses when evaluating more complexalgebraic expressions. As usual, this will be approached not by presenting a series ofrules, but by giving students an arithmetic problem requiring several operations thatmay perplex them, resulting in more than one answer. When discussing theiranswers, students will be introduced to the conventional order of operations, and thenmove to discover how algebra uses additional notation to make the order of operationsmuch more clear.