Children investigate halves of shapes, including by halving a quarter and quartering a half.
They explain they are named eighths because they are an eighth as big as 1. They explain that they folded their quarter in half, so an eighth is half as big as a quarter, and that they quartered a half so an eighth is quarter as big as a half.

Children investigate halves, quarters and eighths of groups related to the 2 ways to divide by 2, by 4 and by 8 – into ‘groups of 2’ or ‘groups of 4’ or ‘groups of 8’ (quotative) and into ‘2 equal groups’ or ‘4 equal groups’ or ‘8 equal groups’ (partitive).  Partitive division is related to halving and quartering and eighthing.