I’ve started focusing on this a bit differently recently (ie. not just saying what a negative and fractional index does, getting them to use what they already know) so I have produced this to support that. It is supposed to get students thinking forwards and backwards rather than just getting into a mathematical rut regarding these.

Find the regions that Santa is yet to deliver presents to using inequalities. There is a worksheet and a PowerPoint presentation with this as well as answers.

Calculate the distance between baubles and the angle at which the tinsel is hung using Pythagoras and trigonometry.

Answer the indices questions, link them to the letters then unjumble the anagram produced to find out what Santa left in my stocking this year. This covers basic indices, fractional and negative.