This task has been in the back of my mind to put together for a while. I’ve regularly written versions of it up on the board, in class, over the years. I was inspired by @bucksburnmaths who shared a “back of an envelope version” of the task on Friday. I decided to get this typed up. Just as I had done this he emailed me with his version, which he has kindly agreed to share. Both files can be dowloaded below. His task also incorporates some Don Steward.

Some might question the purpose of the diagram. It’s not about pupils using this to find the lcm. It’s about a visual reinforcement to guard against misconceptions. Pupils often, naively, add the denominators and numerators. The inclusion of the diagram serves to provide a mental image to fall back upon.

Credit: @chrismcgrane84 / @bucksburnmaths