> > If I explain 1/2 and 2/4 using pie or pizza slices and ask you how "much" pizza did you get, I think the equivalence idea clears up quite nicely. > Sort of

> > If I explain 1/2 and 2/4 using pie or pizza slices and ask you how "much" pizza did you get, I think the equivalence idea clears up quite nicely. > Sort of. But childhood me would have just told you that, no, in one case I got one big piece and in the other case I got two smaller pieces. Why are we using pizza pies in the first place? I vaguely remember being taught something about pie as well. Instead how about this: You have a piece of string 1 m in length. You cut it into 2 equal pieces. We can denote the length of one piece as 1/2 m. You have a piece of string 2 m in length. You cut it into 4 equal pieces. We can denote the length of one of these pieces as 2/4 m. These pieces of string are the same length, therefore 1/2 m is the same as 2/4 m. Although in my head this feels more like a nice way of demonstrating they are the same, I'm not so sure if it helps a lot with reasoning about fractions. But that's fine, like the article said it's good to be able to explain something in multiple ways. Personally that's one of the things that absolutely fascinated me about arithmetic when I was young; That you can play around and have multiple ways of arriving at the same answer, and that if you follow the rules of math right, they always end up as the same answer, sometimes even unexpectedly so (for young me).