Bring ideas together without being told which method to use. Show the reasoning that makes your result valid.
Suggested session length: 40 minutes, as an unvalidated planning estimate. This collection contains 2 tasks; choose a manageable set and return for further sessions. Completing the whole collection may take substantially longer. This is a unit assessment, not a full course or AP examination.
Show the model assumptions, domain, units and intermediate calculations.
Record a prediction before inspecting a new measurement; explain what the result does and does not establish.
Written work needs rubric review; completion does not certify modeling proficiency.
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0 of 2 tasks have recorded responses. No overall mastery score is assigned.
A square sheet has side 12 cm. Cutting corner squares of side x and folding gives an open box. Derive its cubic volume model and physical domain. A different proposed model adds 0.2x(x−1)(x−2)(x−3) to the volume, with coefficients interpreted in compatible centimeter units. Both agree at cut sizes 0,1,2,3, where x=0 is the limiting flat-sheet value, not a nondegenerate box. Compare their predictions at x=1.5 and explain which model has a geometric derivation rather than only a finite fit.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Run cubic and quartic fits for synthetic calibration pairs (−2,−1),(−1,1),(0,6),(1,6),(2,7),(3,29), in sensor units. Keep a fresh check at x=0.5 with output 3.7 separate. Record transformations, equations, training SSEs and residual evidence, then predict before comparing with the check. Accept predictions and SSE within 0.002 of reference. The model must also join a preceding stage continuously at x=0 where its value is 4. Recommend a candidate using validation and this joining condition; state the calibration domain and a next independent action.
Structure your argument and preserve revisions
These optional planning fields save locally. Recording your response saves an immutable copy of the argument and these fields. Older records may contain only first/latest responses; missing intermediate revisions are not reconstructed.
Each field allows 2,000 characters. Keep a specific claim, state where it applies, cite the facts you use, and explain what still needs checking. Blank fields are allowed and are not evidence of mastery.
Review and revisit
Use each rubric to identify a valid argument, a missing condition or a step to revise. For independent evaluation, ask a teacher or reviewer to examine the complete reasoning. Self-review and recorded responses are not verified assessment results.
Coverage and targeted lesson returns
A square sheet has side 12 cm. Cutting corner squares of side x and folding gives an open box. Derive its cubic volume model and physical domain. A different proposed model adds 0.2x(x−1)(x−2)(x−3) to the volume, with coefficients interpreted in compatible centimeter units. Both agree at cut sizes 0,1,2,3, where x=0 is the limiting flat-sheet value, not a nondegenerate box. Compare their predictions at x=1.5 and explain which model has a geometric derivation rather than only a finite fit.
Run cubic and quartic fits for synthetic calibration pairs (−2,−1),(−1,1),(0,6),(1,6),(2,7),(3,29), in sensor units. Keep a fresh check at x=0.5 with output 3.7 separate. Record transformations, equations, training SSEs and residual evidence, then predict before comparing with the check. Accept predictions and SSE within 0.002 of reference. The model must also join a preceding stage continuously at x=0 where its value is 4. Recommend a candidate using validation and this joining condition; state the calibration domain and a next independent action.
