"Le chapeau des garçons est grand."
Yes the plural is chapeaux, but here it is assumed that they only have one each, which does not apply to the English translation proposed.
Well. It doesn't make no sense to say 'The boys have a hat'. But if you say 'Chaque garcon a un chapeau' it makes more sense
There is a French style of singular/plural that doesn't translate very well to literal English. For instance, "our hearts" (hearts is plural, because there's more than one of us) is "notre coeur" (NOT "nos coeurs" -- the plural form).
In other words, in French, you say "the performance touched our heart" (singular!). It sounds crazy in English, but to use the plural is equally crazy-sounding in French.
It's hard to get used to, and the chapeau sentence does "feel" incorrect. (I'm still suspicious of it, at any rate.)
I translated it as the boys' hat is big . Unless you mean a group of boys are sharing one big hat this doesn't make sense in English. However that is what the French words mean.
Duo accepted it as correct.
On any of the straight translation exercises that Duo gives I wouldn't have used such a strange construction.
I can see I'm not the only one having a little difficulty with French/English plural usage.
No, it does not translate "the boys' hats are big".
"Le chapeau de garçon" would mean the hat designed for boys (as opposed to a hat designed for girls) and it would be a descriptive of the nature of the hat, like for example "le manteau de pluie" (raincoat)