Final answer:
The correct completion for the tag question is 'don't they?', creating a tag question that complements the positive statement.
Step-by-step explanation:
The complete tag question, based on the given statement, is: 'The children need to be able to read to make their way through this education system, don't they?'
When constructing tag questions, you take the auxiliary verb from the main sentence ('need' in this case, which acts like 'do' for the present simple positive statements), turn it into the negative form ('do' becomes 'don't'), and match it to the subject ('The children'). Since the main statement is positive, the tag must be negative.