I have several references in various places on this blog to some great visualizations.
Time to put them all together!
From Jeffrey Ventrella this wonderful Composite Number Tree – I have used this successfully with many students. It makes a great starter. Students can work out themselves how the tree is being formed and comment on any patterns they notice.
Another excellent visualization, animated factorization diagrams comes from Data Pointed. And here is Stephen Von Worley’s blog post, Dance, Factors, Dance which tells the tale of the animation. Noting his reference to Brent Yorgey’s factorization diagrams led me to Brent’s own later post, More factorisation Diagrams. I love Brent’s use of colour here. If you want even more on these great diagrams he has more information and links on this page on his blog, The Math Less Traveled.
Statistics – thinking about large data sets which we will need to for the new A Level specification – for an amusing large data set, how about the Furbles?! The images generated here are from the original 2003 version which is still available on Alec McEachran’s ptolemy.co.uk. Talk to students about summarising this data, perhaps ask for their impressions as to which colour is the most or least common. Data can be presented as a bar chart or a pie chart and you can choose to categorise in various ways. It is also possible to vary the number of Furbles, the maximum and minimum number of eyes and sides. The illustration here show the largest data set possible.
Returning to the factorisation theme, note that Alec McEachran’s ptolemy.co.uk is also home to the Primitives application. As you can see from his site, you can read Alec’s article he wrote for the ATM magazine Learning About Primes.