Citing Math Lesson Plans
Do I need to cite the various websites I use for my work?


It depends on the work your are referring to. In your case, it is math lessons. One ought to cite for one or of the following reasons. Let's look at whether these points apply to you.


To show you've done enough research. You wouldn't have to prove to your students that you've done enough research; the study content should be sufficient.
To give credit for the source of the work. Is your work publicly available? Would it anyhow increase the citation count of the author you intend to credit? If so, it would be up to you.
To avoid plagiarism. You are not plagiarizing as you are not claiming the work to be your own; you are teaching what is established.
To allow readers to track the sources for further information. Do you feel that your students would have the need to go through the sources you've referred? If so, you wouldn't have to cite all of them, but only the ones you feel are important.



  Whether I do or do not cite, can I have my name on the lesson plans? 


Yes, as long as you don't claim the work to be novel in any way (which you obviously won't be doing). It would be better to add a disclaimer as you stated in your post like "This work has been collected and combined by name".


  Can I create a work-cited page and put all my references on that page, or do I HAVE to put in-text citations?


That would be actually useful, a work-cited page can be referred by avid students who would want to receive more information on the topic. But in-text citations would be have to be a matter of preference, that depends on the utility of the majority of your students.