The sentence fragment is a clause masquerading as a complete sentence. It may contain a verb (a doing word) but the verb does not set the action in time, i.e. it does not tell us when or if an action was, is being, will be or might be performed. Such verbs are called 'driving verbs', 'main verbs' or 'finite verbs'. These terms - driving, main or finite - are interchangeable. To be complete, a sentence needs a main verb.

Examples of fragments:

Working together to study volcanoes.

'Working’ is not a main verb. It is a style of verb called a gerund, i.e. a verb working as a noun. It does not power the sentence by telling us when the action was, is, will, or could be performed.

So that you can win an environmental prize in the future.

‘Can’ is a verb but the sentence leaves the reader hanging in mid air because it lacks a main clause telling us what must be done 'so that you can win ...'

I blame political speech-writers. They love fragments. In Tony Blair's 1998 oration to the Labour party, there were over a hundred fragments. He is often laughed at for this, but fragments have their uses: they make perfect soundbites.

'So that no child is left behind.'
'Education, education, education.'

For certain types of writing, including novels and journalism, fragments are very useful. In engineering reports, however, sentences need to be complete.

Here is an easy way of identifying fragments:

Pretend your sentence is the only sentence on the page.
Read it aloud.
If it leaves you feeling as though there is something missing, or it makes no sense without another sentence beside it, it is probably a fragment.

How to correct a fragment

Correcting a fragment is not hard. Often, the fragment just needs joining up to the sentence of which it clear forms a part:

The earth scientists from Glasgow University and Edinburgh University joined forces. Working together to study the environmental importance of ponds. (one sentence, one fragment)
The earth scientists from Glasgow University and Edinburgh University joined forces, working together to study the environmental importance of ponds. (one sentence)

N.B. Do not imagine that all short sentences are fragments.

That was nonsense.

This is not a fragment. It has a subject - that - and a main verb - was. To understand it fully, you may need to know what ‘that’ stands for, but if you replace ‘That’ with a noun, the sentence can stand alone.

His excuse was nonsense.

In a true fragment, it is not just a question of replacing ‘that’ with a noun, it is a question of adding a driving verb.