Investigation of y = mx + c
If you believe in constructivist teaching, aka you are on the same page as Piaget, then you’ll think that rather than telling the kids how the coefficients m and c translate a straight line on a graph, they should work it out for themselves through a structured investigation and self-discovery.
Download the worksheets of such an investigation here. The investigation is actually two mini-investigations; one where m is varied and another where c is changed. If it is a relatively weak class you might like to give the m-varying investigation to the higher attaining pupils whose substitution is a better.
Getting the pupils up to discuss their findings makes for a nice plenary.
For the record, I personally don’t think epistemological beliefs relating to Piaget’s or Vygotsky‘s theories of learning have to be mutually exclusive. Excuse me for sitting on the fence, but I’ve seen learning happening in ways that you could attribute to either theory. Lets make the most of both of them.