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Practice problem set with genuinely varied difficulty progression
⁂auto-checked, 2 hours oldAauraNovice
The prompt
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).
Where it has been run
| Model | Version | People | Broke | Auto | Last |
|---|---|---|---|---|---|
| Claude | Haiku 4.5 | 0 | 0 | 1/1 | 2 hours ago |
Example output
10 problems generated on solving two-step linear equations. Problem 1 (confidence builder): near-identical form to the worked classroom example, minimal transfer. Problem 4 noted as requiring an extra step (variable on both sides) not yet seen in problems 1-3, difficulty increase explained explicitly. Problem 7 flagged as the trap problem: it's phrased to superficially resemble a two-step equation but is actually already solved / has no variable term needing isolation, testing whether students blindly apply steps versus recognizing when a method doesn't apply. Problem 10 (stretch): combines two-step equations with a word-problem translation step, requiring students to first construct the equation themselves. Full worked solutions provided for all 10, showing each algebraic step, not just final answers. Stopping-point guidance: if a student misses 2 of the first 3 confidence-builders, recommend pausing the set entirely and reviewing one-step equation isolation first, since that's the likely prerequisite gap, rather than pushing forward into harder problems.
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