A: Whenever possible, it's best to invite anyone who witnesses the ceremony to celebrate with you afterward, so you may want to rethink excluding your students from the reception. That said, if you still want to invite the class, rather than sending formal invitations, give them a casual note to take home. In it, explain to parents that the entire class is welcome to attend the ceremony. State the time it begins, and when it's expected to end, and give directions. You can't tell them not to bring a gift, but under the circumstances, most parents should get the message that the invitation is informal and a present isn't necessary or expected.
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