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 .