The best way to separate out responses from different classes who will be using the same TED-Ed Lesson quizzes is by making a new copy of your lesson for each new group of students (i.e. different class or new school year etc.) You can make a copy of a lesson by "customizing" it.
The "Customize this lesson" button can be found on any lesson page. It's a red button in the lower right corner beneath the section where you find "Think" or "Dig Deeper." It looks like this:
Customizing a lesson (whether a boilerplate TED-Ed lesson, another user-created lesson, or one of your own) allows you to keep it entirely intact (or make changes if you'd like), but will generate a new shareable link to make it possible to keep responses from different classes separated.
If you don't see the "Customize This Lesson" button on your lesson, then you did not select "Customizable" when you originally published the lesson. Here's how to activate customization:
1. visit ed.ted.com and mouse over the "Manage" menu
2. choose Lessons
3. find the lesson you want to copy and click Edit under its thumbnail
4. in the lesson editor, click the ON/OFF toggle for "Customizable" on the right side of the page
5. in the window that opens, select "Make my lesson customizable" as shown below:
6. click Save
7. you will need to Unpublish, and then re-publish your lesson
8. You should now see the red "Customize this lesson" button on your lesson page, allowing you to make a copy for your new class