One Year 10 group has been studying functions. Functions can be applied to a wide variety of mathematical situations and are used extensively to model real-life situations. The students have studied simple functions before, but they are now learning new language and notation. They have learnt how to write functions algebraically, the concepts of domain and range, and can relate these concepts to the graphs of the function. Soon, they will move onto composite and inverse functions.
One of our Year 11 classes is looking at the topic of graph sketching and graph transformations. With graphic display calculators and computer packages to aid them, students have been mastering what is, conceptually, a quite challenging topic. It is important for students to discover for themselves: why graphs look the way they do, the effects that transformations can have, why asymptotes are where they are, and the general shapes of graphs of similar forms.
The students were set the challenge of firstly discovering the rules of graph transformations for themselves, sketching curves by hand without the graphing technology and looking for patterns in their results. They quickly picked up the rules for f(-x), -f(x), f(x+c), f(x)+c, cf(x) and f(cx). Forced to think through the effects of the transformations, the students pick up a deeper understanding of the reasons for it.
The next few lessons will involve learning how to sketch more curves and students will have to ponder the infinite as they discover the rules that govern the vertical and horizontal asymptotes.
Mr Clem Parrish
Head of Mathematics