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
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
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 ?