Towards the end of the year 8 course we ran an introduction to surds. Over the course of about 3 lessons (which I virtually mirrored in year 9 classes as well), we introduced the concept, did some number crunching and some games/activities.
Much inspiration came from Andrew Stadel’s blog about rational-irrational war. I also used the hotmaths website as a resource for the introduction and some worksheets to practice adding and subtracting surds and working with them on calculators. Links to the resources for the activity can be found on Andrew’s site and are also directly linked below.