From singular to plural
Let us look at the singular noun stuk (piece).
The word has a single, closed vowel: a short vowel word.
To turn it into a plural noun, we add -en:
stuken
To determine whether the newly formed plural noun has maintained its short vowel, we divide it into syllables:
stu-ken --> the first syllable ends in a vowel
Recall that a vowel at the end of a syllable is always a long vowel.
Apparently, we turned the short singular vowel into a long plural vowel. Because short vowel words must stay short, regardless of any changes (e.g. from plural to singular), we have to make sure that the plural is short too.
In order to establish this, we simply add an extra consonant (k in this case) to the end of the first syllable:
stuk-ken
The syllable now has a single, closed vowel. In other words: it is a short vowel word.
From plural to singular
Now we will do it the other way around.
We have a short-vowel plural noun:
katten (cats)
To turn it into a singular noun, we have to subtract -en:
katt
Recall that a word (or even syllable) never ends in two identical consonants.
Therefore, we simply subtract one of the consonants (t) and we get:
katt -> kat
Questions? 
