Car racing is a captivating sport for many of us. It is very interesting sport for kids as well and that fact can be used to motivate some important concepts in mathematics. Car racing track, with its irregular shape, dictated by urban projects requirements and geography, can be used to introduce calculus, integration, rational, irrational numbers, finding the length of the curve of arbitrary shape, finding the surface area enclosed by racing track, which is also of an arbitrary shape. Kids would be more interested in math if they can be shown the applications in things they are interested in.
Examples you can use. Speed of Formula 1 cars (256.78 km/hr), time of arrival, fuel consumption (72.59 L/km), engine temperature (985.23 C), laps counts (2.5), tire rubber temperature, pit time (58.5 sec), randomness of pit times (probability distribution, average, expectation), track length (10.25km), compare tire diameter, volume with the length of the track.
When talking about racing car related concepts, care should be taken to explain the existance of logic and functional relationship between objects that will be, possibly, quantified later. This approach is important when using any real world example for mathematics. For instance, it should be signified that business, social, geographical, financial analysis was done before a race track is built. Hence, business, social, geographical, financial analysis dictated a number that you will obtain later by measuring the length of the track. In this framework, student should be shown that there are non mathematical relationships that dictates the shape, size, volume of objects that can be quantified later.
Looking at a number of cars that participate in a race, a function, as a mathematical concept, can be introduced. Moreover, functions of several variables can be introduced considering that each car travels different path, with different speed, uses different amount of fuel, engines have different temperatures, drivers change gears different number of times per minute, pit stops are of different length, and drivers complete the race at different times. Winning a race can be shown to depend on several mathematical parameters too, plus the skill of the driver. Randomness that is present in some of these measurable parameters can be used to introduce probability concept, stochastic processes, statistics.
But, when the driver of a racing car drives the car, he is generating quantifiable entities. He is dealing with objects and events that has mutual quantitative relations in addition to other relationships, like mechanical for instance, or spatial, or temporal. He is generating numbers, giving initial and boundary conditions for a number of PDEs and IDEs in mechanics, thermodynamics. He may be not aware that he is generating numbers. He does not think too much mathematically while driving a car, nor thinks about physics laws that take place every moment. The drivers is involved in the specification of physical initial and boundary conditions for those physics laws. Pressing the gas, accelerator pedal, steering the wheel, using the breaks. The driver knows what the output will be for his inputs. There is of course, a feedback from the car measurements system, providing him with certain important numbers, like fuel gauge, speed dial, temperature, tyre pressure. Given the context of race, and driving the car, these numbers will influence his decision about physical inputs to the car system, like slowing down perhaps, or accelerating.
It should be shown to students that numbers generated in a car race can come from different sources, and can be generated in different ways. They can be a product of driver's decisions, physics laws, random events, and should be shown that mathematics accepts all those numbers in the same way, as numbers only. It is us who keep track where the numbers come from, when, and why, as I have written about that in my previous posts.
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