You can give an extension for a task or activity to one or more students rather than changing the deadline for the whole class.
First log in to the Teacher Dashboard and go to the Allocation tab.
Click through to the class to which your students belong. Click on the task in the Task or activity column, or the date in the Due column.
In the window that appears, tick the box next to Student name to deselect all the students in the class. Tick the box next to the names of the students to which you would like to give an extension. Click on the calendar in the To: field of the Select dates section, select the new deadline and click Update to save the changes.
You will then see two versions of the task on the class screen: one with the new deadline for your chosen group of students, and one with the original deadline for everyone else.