Students can be moved between Classes in a Subject at any time.
A student can only be enrolled in one Class within each Subject. You may want to move them for the purpose of differentiation, if the student has changed from your Class to another teacher's Class in a shared Subject, or to archive their work if they've left midway through the year. Their work moves with them, so it will appear under the new Class in your Markbook.
Moving the student is a simple drag-and-drop action.
On the Students page, select the Class that the student is currently in (not the one they should be in) and find them in the list of students.
Hover over the student's name and the cursor will become a directional arrow.
Click and drag the student into the desired Class in the left column of the page. A notification will appear on the right side of the screen to confirm the move.
If you have trouble dragging the student into the new Class, then you can click the 3-dots button to the far right of the student's name and select their new Class from the options listed.
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