Direct variation is one of the topics in algebra that represents a particular situation of a linear function. Direct variation may be used in modeling different situations in the real world. Essentially, direct variations are exhibited in situations where two quantities increase or reduce at a similar rate. Such quantities may be pay and hours or time and distance. Usually, the ratios between quantities in direct variations are constant which implies that one set of quantity doubles as the other set of quantities doubles as well.
How Direct Variation applies in Different Situations
For instance, in a situation where a mechanic is remunerated on an hourly basis understands that the longer he works the more money he makes, then he tends to extend his working hours and automatically his pay increases. This is because the amount he earns varies depending on the amount of hours he works and an increase in the number of hour works directly translates to an increase in the paycheck. On the other hand, if a driver of a racecar knows that completion of 100 laps prior to taking a pit stop is a better decision than taking a stop after completing 80 laps, then he or she will tend to drive longer and cover more distance. This is due to the fact that the distance is proportional to the amount of time spent when the driver’s speed is constant.
Importance of Direct Variation in Curriculum
Teaching direct variation as part of Algebra in schools is aimed at developing the student’s ability to use functions and patterns to model, analyze and represent different types of relationships and phenomena in real world and mathematical situations. The use of graphing calculators and computers to generate graphical representations and conduct complex calculations enable students to focus on the use of functions to develop quantitative patterns. Students need to have ongoing interactions with modeling situations in the form of equations like those that relate to side lengths and other shape parameters. Other curriculum sections such as estimated lines of fit and scatter boxes help in modeling data set trends.