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Practice problem set with genuinely varied difficulty progression
Generate a set of number practice problems for topic at grade_level, structured as a genuine difficulty progression, not random-order problems of similar difficulty.
Specific skill being practiced: specific_skill
Do this:
1. Order problems from a 'confidence builder' (very close to the exact form just taught, minimal transfer required) through to a genuine stretch problem (requires applying the skill in a less familiar form or combining it with a previously learned skill).
2. For each problem, briefly state what makes it harder than the previous one (new context, extra step, requires recognizing which method applies rather than being told, combines with a prior skill), so the progression logic is visible, not just my assumption.
3. Include one 'trap' problem partway through that looks like it needs the newly taught method but actually doesn't (tests whether students are pattern-matching superficial features versus actually understanding when to apply the skill), and tell me which one it is.
4. Provide full worked solutions, not just final answers, showing the actual reasoning steps, since a bare answer key doesn't help a stuck student self-check where they went wrong.
5. Suggest a stopping point: if a student gets the first 2-3 confidence-builders wrong, what should happen instead of continuing through the harder set (what prerequisite gap likely needs addressing first).