Consider the following problems:
A) You have 20 problems for your math homework this week, and you want to do 1/5 of them today. How many problems do you need to do today?
B) You need to read a 20 page book this week, and you want to read the first 1/5 of the book today. How many pages do you need to read today?
C) You need to run a total of 20 kilometers this week, and you want to run 1/5 of that today. How many kilometers do you need to run today?
Are these problems conceptually different enough that an educator needs to carefully deal with each of these scenarios, or will a child that can (actually) solve one of these problems also be able to solve the others?
To explain why I consider these problems different:
A) You have 20 problems. You can create 5 groups with 4 problems in each.
B) You have 20 pages. You can create 5 groups with 4 pages in each. However, in this case there is an implied order of the pages. This feels more like a scaling of a discrete set, than placing objects into groups of equal size.
C) The kilometers are not really objects and so it doesn't really make sense to group them. One could of course imagine them as "objects", but arguably we are really performing some kind of scaling operation.