Order to…Chaos / Patterns in …Randomness
The Order to …Chaos theme consists of five sections covering formulae and equations, graphs and number operations to build up some ideas relating to fractals. The key idea is colouring in a square based on some numerical calculation. This develops, at a simple level, the idea of chaos in mathematics and the notion of fractal.
Visualising graphs – visualising 2-D graphs and using physical representations of 3-D graphs.
Graphs in colour - uses colour to represent a third dimension, uses the modulus function and flow charts.
Really long curves – exploring the notion of increasing the length of a curve and thus introducing the notion of a fractal.
Are you sure? – using calculator functions to explore iteration and how this leads to proof.
Towards chaos – an explanation of what the colours represent when drawing fractal pictures. There follows a history of the subject and several pictures of the Mandelbrot Set and other fractals.
There follows help, hints and more ideas for each section
Patterns in …Randomness contains four sections which look at how, with enough data, you can begin to make prediction about things which are random. The work in this section covers the mathematical areas of averages, frequency tables and charts, percentages, probability, ratio, data collection and analysis.
Reaction times - experiments to measure reaction times for a variety of stimuli.
Matching birthdays – experiment to discover the chance of two people in a class having the same birthday.
The colour machine - making a machine which generates random colours. This activity is based on software ‘one-armed-bandit’.
This dice is unfair!- discovering if a die is biased. This activity is based on software which simulates a loaded die.
There follows help, hints and more ideas for each section.
This book is part of the Century Maths series.