Age 11 to 14
Do you notice anything about the solutions when you add and/or
subtract consecutive positive numbers?
You could start by considering four consecutive positive numbers before moving on to
consider four consecutive negative numbers.
If you have looked at several sets of consecutive numbers and
noticed some similarities in the solutions, you may be wanting to
explain why they occur. An algebraic representation of the
situation might help you with this:
if $a$ is your smallest number, the four consecutive numbers are
$a$, $a+1$, $a+2$, $a+3$