I had an idea for a visual metaphor for irrational numbers, that I would like to use to help students understand these mysterious numbers. First, I would ask students to imagine that there are an infinite number of videos on youtube (more on this later). Then I would ask student to pick out their favorite music video. I want them to call this video "1" and write "1" on a piece of paper.
Student will then click the 1st link on the sidebar. They will call this video "2", and write it on a piece of paper. They will then click the 1st link on the sidebar of this video. This third video will be "3". Students will continue this process for 25-50 videos.
When students are finished, we will discuss whether their video sequence fell into a looping pattern, or whether all the videos of their sequence were different. I would compare a video sequence that "loops" to a rational number - all rational numbers have a pattern of decimal digits that eventually repeats itself. I would then compare a sequence that never repeated itself to an irrational number, which never contains a repeating pattern of digits.
I would then tell students that it is impossible for a video sequence on youtube to be "irrational", because there is a finite number of videos on youtube, so eventually any sequence must fall into a loop.
What do you think?