Fractions are just division. When kids learn division, it's about splitting into equal groups.
Fractions are a bit different though - you're splitting a single thing into equal chunks. Hence, slices of pie.
Multiplying by 1/5 is really dividing by 5. Introduce that first. We already know how to do this. You split your 1/3 slice into 5 equal slices.
Do the same to the other 2/3 slices, count all the slices, and you have 15. Hence, 1/15.
As an aside, common core math is amazing. They gave my daughter a model for the distributive property that can be used to show how to do long multiplication.
There's a difference in type of thinking in moving from operations on numbers (basic whole number math) to operations-on-operations-on-numbers (anything with fractions).
Suddenly, you need to begin to understand the rules around operators, sequencing, and what operations are legal and illegal.
Absent that understanding, even...
1/4 x 2/5
... gets very complicated trying to reason with physical analogs.
So it's the point at which math becomes "pure" rather than strictly physically-mapped.
IDK, I did fine with them and find thinking in them natural (I think of fractional division as division, in fact, though I certainly understand the multiplication analogy); I’ve just known enough people who lost track of math at fractions that I doubt it’s coincidence.
I’m not saying I don’t get it, I’m saying others have told me that they found the explanations and instructions they were given nonsensical.
Have you tried dumping all the sockets out of a socket set and putting them back in order? Do you find it's easier to order the metric ones than the imperial ones which have a lot of different denominators on adjacent sizes? I certainly do but I'm not American so maybe it's my background limiting me.
Just to save you some time: the numbers written on the sockets indicate the size of the socket. So you don't even need to read them, just put them in order of size and you'll have them in order of number automatically.
Fractions are a bit different though - you're splitting a single thing into equal chunks. Hence, slices of pie.
Multiplying by 1/5 is really dividing by 5. Introduce that first. We already know how to do this. You split your 1/3 slice into 5 equal slices.
Do the same to the other 2/3 slices, count all the slices, and you have 15. Hence, 1/15.
As an aside, common core math is amazing. They gave my daughter a model for the distributive property that can be used to show how to do long multiplication.