nth term patterns

providing students with just one or two examples enables discussion about what the next and previous shapes are/could be










agreeing what the 'growth' rule is, identifies the structure of the pattern, prior to establishing the nth term rule

four examples where just the third pattern in a sequence is shown
















what is the growth rule?

how many (sticks) are added on each time?

what will the 'start' shape be (when n = 1)?

several examples (below) where students are encouraged to discern the nth term 'growth' rule by identifying the extra ("what you would add on") 'bunch' going from one shape to the next in the sequence

and what you would have as well ("what is left over") as this 'bunch' in the 'starting' (n = 1) arrangement