Why does graphite conduct electricity while diamond doesn't?

I'd start by asking the student what they knew about the structures of diamond and graphite, and asking them what they understood by the keyword "allotrope". If they were able to draw/ describe the diamond/graphite structures that'd be great, if not I'd show them an image of them. I'd then ask them to find carbon on a periodic table that I show on the screen and to tell me how many valence electrons carbon has (I would guide them towards this if they were unsure of any terms or how the group number links to the valence electron count). We'd refer back to the structures of diamond and graphite and we'd observe that each carbon has 4 covalent bonds in diamond but only 3 covalent bonds in graphite. I'd then ask them how many electrons were left over on each carbon atom (0 for diamond, 1 for graphite) and where they think these electrons might go. I'd guide them toward thinking about these electrons as free or delocalised electrons, meaning that these electrons can move through the structure. As electrons are charged this means that charge moves through the structure and so graphite conducts electricity while diamond does not. As a further question to cement their understanding if they seemed to be understanding this well, I would show them the structure of another allotrope of carbon that they might not have seen before (bukminster fullerene) and ask them to predict with reasons whether this would conduct electricity or not.