For students who I knew would need extra scaffolding, I created an adapted version of the quiz, where there were less questions, and where the questions had a more structured response section to guide students step-by-step in solving the problem.
For the whole class, I also introduced the idea of hint cards. I told students that if they were completely stuck on a question, they could ask for a hint- I would then give them a hint card, and it would be stapled to their quiz. To students who asked about how the hint card would affect their mark, I replied, "Don't worry so much about your mark. I will take everything into account, but I want you to be able to show your learning as best as you can. Definitely try the question before you ask for a hint card. But I would rather that you solve the question with the hint card, than leave the question blank without it."
For the students whom I knew would need and enjoy the extra challenge, I also created bonus question cards, which were available to anyone who wanted to attempt it.
For the quiz, I had setup the marking structure so that students were rewarded points not just for the right answer but also for showing their work. I discovered that one student got all the answers correct but did not show most of the work. He would have barely passed. But I decided to give him an opportunity to demonstrate his learning orally. I spoke to him about his reasoning behind the answers, and it was clear that he understood the concepts very well. Due to this new evidence about his understanding, I decided to give him most of the credits for explaining his work.
These are the files mentioned above. Any feedback is welcome!