Target group

To whom do you aim the problems you are using to teach the lesson?
This question assumes that you teach by asking interesting questions and allowing students to figure out the math. If you do not teach in this mode, I am not sure this question applies. I am also not sure I have much to offer, because I think good teaching starts by recognizing that our job is to ask interesting questions and to help students figure out the math behind the questions. I think a teacher helps by watching, listening and letting the students do the work. Telling a student how it works does not work.
But I have talked about that before. This idea is new, I think. P.J. reminded me of this yesterday so I thought I would write about it before he did.

The problem should almost always be aimed at the top group of kids, say the top 25%. There is a myth that says teach to the middle. Do that, and over half of your students learn nothing. The ones above the middle already know it so you are wasting their time.

The problem needs to be accessible to everyone, but difficult enough, challenging enough, that no one can just solve it. That means it needs to be designed so the middle kids and below always have to stretch a lot, while the best kids are still challenged.

One thing to consider is that the top 25% one day will be a different group of students another day. The problems should not be aimed at a specific student but rather at a specific level of challenge. Problem solving has to happen for every student every day, or students will not learn how to solve problems.

"Oh, but students will give up, because it will be too hard for them," you say. I say, you are with them, you are walking around watching them work, and listening. You can push them in the right direction if they have a good thought, and redirect them if they don't. If everyone is about to give up, you will know it, and you can immediately fix it by intervention.

Differentiation does not mean make it really easy. It means teach students how to think. Good teaching means helping students learn what to do when they don't know what to do. That can only happen face to face in your classroom.
It is our job.