SPARK Magazine | PILOT 2017
22 KUMON STUDIES
by looking at the peak. Using the distance from the sextant to the peak and the angle of the peak, we can calculate the height accurately.
Architects, sculptors, satellite engineers and even mountain climbers make extensive use of trigonometry.
Both of the examples above are governed by several complex equations dealing with volume, time, radius, turbulence, and viscosity of the fluid. One such equation is Poiseuille’ s equation:
Differential Equations( Levels L, N, O)
Differential equations and integrals study rates of change. Whether this rate of change is velocity, compound interest, or volume, integration gives us a very important tool for exploring relationships, often in relation to time.
Flow is a complex— but easy to visualize— rate of change relationship. Flow, often of a liquid or gas through a tube, represents a fascinating challenge to engineers and doctors alike.
Hydroelectric power, for instance, is currently the world’ s largest renewable source of electricity, accounting for 6 % of worldwide energy supply, or about 15 % of the world’ s electricity.
Hydroelectric power is generated when water flows downhill and pushes a turbine. The power output can be calculated as the volume of water flowing through the turbine over a certain period of time.
Another example of flow is how the human body acts very much like a plumbing system with veins and arteries acting like pipes. Consider how a kidney dialysis machine temporarily removes the blood from a human body in order to support the function of failing kidneys. Too much or too little pressure could be fatal.
Three Gorges Dam, the world’ s largest hydroelectric dam.
Although there are a variety of physical principles at play, it would be easy for a math student in Level L to understand that we are differentiating volume( V) with respect to time( t), and a Level O student may even understand that the shape and radius of the circular tube are relevant as well.
L 179b
Velocity and Distance
O 152a
Applications of Integrals 3
Undoubtedly, a strong learning attitude is necessary to reach Level J and beyond, but there is always room to grow. As the worksheets become more challenging, ongoing development of learning attitude can help develop excellent students and ultimately program completers. There are many more examples of real world applications that relate to math program subjects, which can help build curiosity and push students closer to program completion. ■
A special thanks to Instructors Geoff Brown, Lise Boileau-Ness, Mia Collados, Gandhi Dorairaj, Farhana Munim, Linta Lai-Tong, Noopur Pandya, Raj Srinivasan and all the other participants in our higher-level Math study group who continue to uncover new insights and strategies in the higher level worksheets every month.