This type of activity is known as Rule. Please read the guidance notes here, where you will find useful information for running these types of activities with your students.

Over the years I have taught many students who struggled with algebraic proof. This is perhaps not too big a surprise as it can be a pretty challenging concept, involving questions that require all sorts of algebraic manipulation. What I want to do with this sequence of examples is to isolate the algebraic manipulation from the interpretation of the final expression. I believe these two skills can – and should – be taught separately. Specifically, here we are to imagine that a student has arrived at a final expression and is asked to decide, given the nature of n, whether the expression is always positive, always negative, or could be either. The formate of the Rule activity lends itself really well to this – students can reflect on what has changed, form an opinion themselves, discuss with their neighbour, and then reflect on the answer. Something similar could be done for odd/even numbers, factors/multiples, squares/cubes etc. Hopefully someone will take up the mantle and write them!