Generate a practice worksheet that actually ramps in difficulty instead of scattering easy and hard problems randomly

Create a practice worksheet on one specific skill, with problems that genuinely ramp in difficulty rather than being randomly ordered at similar difficulty.

SKILL TO PRACTICE
Finding the area of composite shapes made of rectangles and triangles

GRADE OR COURSE LEVEL
6th grade math

NUMBER OF PROBLEMS
12

SPECIFIC ERROR PATTERN TO TARGET
Students forget to subtract the cut-out triangle's area and just add all the shape areas together

Divide 12 problems into three difficulty bands of roughly equal size: foundational (tests the core mechanic alone, nothing else), applied (the core mechanic embedded in a slightly more realistic or multi-step context), and stretch (combines the skill with one adjacent skill or requires noticing an exception to the usual pattern). Within the applied and stretch bands, deliberately include at least one problem specifically engineered to trigger Students forget to subtract the cut-out triangle's area and just add all the shape areas together — not by making it a trick question, but by presenting a normal-looking problem where the shortcut a student would use if they have that misconception gives a visibly wrong answer, so getting it wrong is diagnostic rather than just unlucky. Label each problem's band inline in a way a teacher could strip out before printing for students (e.g., a bracketed tag) but leave visible in the version I'm looking at now.

Then produce a separate answer key. For every problem in the applied and stretch bands, show the worked steps, not just the final answer — a final-answer-only key doesn't let anyone check where a wrong answer went wrong. For the problem(s) targeting Students forget to subtract the cut-out triangle's area and just add all the shape areas together specifically, add one line in the answer key explaining what the wrong answer would look like if a student made exactly that mistake, so a teacher grading by hand can recognize it instantly instead of having to re-derive it.

WHAT NOT TO DO
Do not make the stretch band so difficult it requires content outside 6th grade math — stretch means harder application of what's already been taught, not new material.

OUTPUT FORMAT
1. The worksheet, problems grouped and labeled by band.
2. The answer key with worked steps, and the diagnostic note on the targeted-mistake problem(s).