Here is a playful way of listing words and noticing how they are formed.
Make a list of words and phrases in which the last section of each becomes the first part of the following word or phrase. It could be that there are whole words within compound words:
pigtail – tail end – endpaper – paper cut – cut out – outside …….
Or syllables, or even smaller parts of the word. Be inventive. This is about playfulness, sound and meanings.
puppet – pet shop – shop window – window box – boxed set – set off – offspring …….
It is not always easy. You have to think ahead. But it does make you notice how words are constructed and how they work together.