I could not believe this prompt was true when I first saw it. The equation comes from Rachael Read, a teacher I worked with in 2006-07 on a national programme run by the Leading Edge schools (UK). One of her year 10 students had stumbled across it. We can only wonder at the levels of enthusiasm and excitement that must have been generated in a lesson that gives a student the freedom to 'stumble' upon something like this. The prompt that I have subsequently developed has caused many audiences (students and adults alike) similar doubts to mine. Typical responses start with, "It can't be true ... can it?"
This prompt is suitable for students with high prior attainment in years 10 and 11. In the classroom, students are quickly hooked in to the prompt, particularly when one of them claims it 'works' after
checking on a calculator. My classes have usually selected the regulatory card "Ask the teacher to explain", thereby inviting the teacher to instruct them in how to manipulate surds. The inquiry might then follow one of two pathways. Either students opt to practice the manipulations in order to become fluent or, if confident, they will explore the peculiarities of the prompt in order to produce more examples of the same type (see mathematical notes below).