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?
Start with a formula that has only multiples of n, nothing added
or subtracted, for example : $2n$, $3n$, $4n$ or $5n$
Look at the sequence of blue numbers and notice the pattern -
explain why it happens.
When you can explain what happens, switch to a formula where
something is subtracted.
Interactive Number Patterns 2
Do you see a connection between Difference 2 and the formula?
Change the formula to check that you were right about the
Finally, use those numbers in the bottom half of the screen to
help you explain why the connection you discovered in Difference 2