Thinking up new diagrammatic representations for grammatical concepts is excellent fun. I try not to worry about super-scientific accuracy, as the goal is to give the student a visualisation of a concept, but I do like to get them consistent and meaningful. Venn diagrams, mind maps, tree structures, flowcharts and graphs, all wonderful things. I enjoy the element of thinking on my feet, as a grammar rule emerges, finding a clear and accurate representation on the fly. My students aren’t really picking up any science as such with this one, but I think of it as training for when I start slipping in equations.
Many students need to practice reading out and writing down numbers over the phone, but I find it a little boring to always ask for phone numbers, or to get them to make up numbers, so in the last minutes of a lesson I sometimes set simple maths puzzles, or we calculate Pi together, work out some statistics among the class, the percentage of students who live in Berlin, converting it into a fraction, the probability of getting the right answer to a grammar question by just guessing, anything like that. Whatever fits with the situation. I find it pretty easy to come up with simple statistical or probability questions, regardless of the theme. It gets them to practice using numbers in a real world setting, and they may even pick up a bit of nerdy number love on the way!