Thursday, 1 February 2018

On Exponential growth and decay


This sequence of learning activities, designed with the development of students’ mathematical maturity in mind, is intended for use by secondary teachers to strengthen and deepen students’ understanding of compound interest, move into exponential growth and decay, and gently via iteration onto the exponential function.

Piggybacking learning on an interrogation of the bank balance of a 20th century pizza guy who finds himself in 31st century New New York after a cryonics lab accident (Futurama clip below), via a paper-folding journey across the observable universe and a mathematical modelling of the potentially memetic spread of Random Acts of Kindness, we end up at Euler’s number, e.

Four one-page outlines of learning activities are provided below (and as png images at the end of the post), each centred on a particular theme or hook — i.e. Futurama, Paper folding, Pay it Forward, Euler’s number — and each containing key questions and links to video and other online provocations, prompts, etc.  Resources such as student practice tasks are also provided on each outline in the form of hyperlinks or QR codes to scan, to facilitate fuss-free downloads or projections onto a screen as desired.  Note that all the following downloads are provided in pdf format, unless shown otherwise.


Each one-page outline does not necessarily correspond to one lesson — the sequence in full typically takes me 10-12 hours teaching time.  Neither are the outlines intended for teachers to follow prescriptively; should a teacher use the ideas and resources presented here, they should of course adapt them in terms of where their own students' learning is currently situated, and where they are aiming to get to.



Work on the activities presented in this sequence focuses learning on the following aspects of the National Curriculum Mathematics Programmes of Study for key stage 4 in England:
  • Ratio, proportion and rates of change: Solving and interpreting answers in growth and decay problems, including compound interest and work with general iterative processes.
  • Algebra: Recognising, sketching and interpreting graphs of… exponential functions y = kx for positive values of k.  Plotting and interpreting graphs (including… exponential graphs)… in real contexts

2 comments:

  1. I'm someone who has lived a life seemingly in the background, I must say this final indignity I have suffered almost too much to endure. You see, I have been sickly and weak since the day I was born and doomed to go through all my life a weakling. I seemed to have always suffered from one illness or another and could never play with the other children as I so desperately wanted to. Mother always made such a big fuss over me, also, making the situation worse as the other boys teased me mercilessly after they saw it. I was browsing  the internet searching on how i could be transformed into a powerful when i came across the email of a man named Lord Mark. who was a VAMPIRE so I told him that I has always dreamed of becoming a  VAMPIRES, All i did was just to follow the procedure that i was been told, and i bet you that procedure I took change my entire life to something i ever desire, freedom, sickness free, pains free, fame, influence, connections and even more that i can. Thanks to Lord Mark. Do you want a life full of interesting things? Do you want to have power and influence over others? To be charming and desirable? To have wealth, health, and longevity? contact the vampires creed today via email: Vampirelord7878@gmail.com

    ReplyDelete