Academic purpose and safe learning
Students compare linear x=b+mt with quadratic x=b+mt+ct² using supplied synthetic data. They compute signed residuals, training RMSE and a holdout prediction, then select a plausible explanation with justified limitations. These lessons support the quantitative modeling and scientific inquiry practices of the broader HS-PS2-1 physics unit; they do not individually claim to fulfill all Newton's-law performance expectations.
Prerequisites: Week 02 coordinates and displacement, Week 03 velocity/acceleration, slope, graph axes and algebra; Week 04 also uses introductory sine/cosine; Week 05 uses squaring and means. Differentiation: provide a partially labeled diagram and pre-calculated table for foundation learners; use the full simulator for core; ask extended learners to critique simplifying assumptions.
Monday · The Curved-Graph Mystery
Target: Distinguish a linear motion model from a quadratic one using shape and rate changes.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: Does a curved graph necessarily prove an unchanging acceleration?
Tuesday · Residuals: The Difference Matters
Target: Compute signed residuals and explain why patterns diagnose model mismatch.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: Why can a model with smaller training RMSE still be a poor prediction model?
Wednesday · Fit a Line or Fit a Curve?
Target: Compare least-squares linear and quadratic models, RMSE, and holdout prediction.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: Why is a lower training error not the only acceptable model-selection criterion?
Thursday · Motion Model Detective Lab
Target: Test two preloaded synthetic datasets, examine residual graphs and make defensible model selections.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: How would one noisy holdout point affect your confidence in your model choice?
Friday · Capstone: Defend the Motion Model
Target: Construct a coherent CER using parameter estimates, residuals and prediction limits.
Suggested pacing: 8 minutes phenomenon and prediction; 17 minutes explicit reading and worked example; 15 minutes data/interactive investigation; 10 minutes written reasoning; 5 minutes correction and exit prompt.
Suggested check: What extra evidence would you gather before asserting that a force caused the observed acceleration?
Worked reference answers
For x(t)=1+2t (m), a=0 and x(3)=7 m. For x(t)=1+2t+0.5t² (m), modeled acceleration a=1 m/s² and x(3)=11.5 m. A signed residual is observed minus predicted position, for example xobs=5.3 m, xpred=5.0 m → +0.3 m. RMSE=√(Σ residual²/n) for the training points in meters. The studio fits the first five synthetic records and reserves the sixth as a holdout. The quadratic has more parameters and usually smaller training residuals; explain why holdout performance, mechanistic plausibility and uncertainty also count.
20-point CER review rubric
- Claim · 4
- Scientific answer limited by defined system and assumptions.
- Numerical evidence · 4
- At least two valid calculations or observations with units and data provenance.
- Interpretation · 4
- Accurate residual, RMSE, model coefficients or holdout interpretation.
- Reasoning · 4
- Correct physical equation and logically connected explanation.
- Limitations · 4
- Fair counterclaim, potential uncertainties and a useful next experiment.
Teacher review target: 16/20 (80%). Allow revisions and preserve evidence of initial work separately.
Common misconceptions and extension
- A curve automatically proves constant acceleration. — have students locate the invalid assumption and supply a correction.
- The quadratic is always the best model because it has more parameters. — have students locate the invalid assumption and supply a correction.
- A residual is predicted minus observed rather than observed minus predicted. — have students locate the invalid assumption and supply a correction.
- RMSE has no physical units. — have students locate the invalid assumption and supply a correction.
- One holdout point guarantees general predictive accuracy. — have students locate the invalid assumption and supply a correction.
Public open-book practice items and browser-local evidence are not secure, supervised final examinations. Teacher-verified assessments require a separate educator-controlled process.
Offline resources and portfolio
Preserve existing `khae_high_science_evidence_v1:` browser-storage keys and dormant STOS assets. New standalone lesson notes use separate namespaced keys and JSON export/import. No cross-device cloud synchronization is claimed.