Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Label this plum tree graph to make it totally magic!
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
The 'difference of two squares' is a key algebraic transformation and problems like this can lead students into a deeper appreciation of that form through a further visualisation.
The problem of writing the number $105$ as the difference of two squares becomes a problem about factor pairs that make a product of $105$.
Draw out from the students how this transformation helps [we now seek factors of $105$ rather than guessing squares and calculating differences].
For $105$ (and then for $1155$) how many ways might there be, and why do you think that ?