Learning objective: Construct a coherent CER using parameter estimates, residuals and prediction limits.
45–60 minutes · Offline-capable · Public practice, not a supervised examination
Read and reason
What counts as a good claim?
A good claim does not say 'quadratic fits best because it looks curved.' It names the specific dataset, the time range and why the chosen model is a reasonable explanation. An example: 'For the synthetic acceleration dataset from t=0 to 5 s, the quadratic model is more physically plausible than a uniform-velocity model because its rate changes with time and its residual pattern better matches the data.'
Use calculated, labeled evidence
Include at least two fitted parameters or residual statistics with units. A quadratic coefficient c has units m/s² when x is meters and t seconds; modeled acceleration would be 2c m/s². RMSE and individual residuals have meters as units. Check held-out error separately from training RMSE. A correct equation and a numerical error comparison make a claim clearer and more falsifiable.
Engage a fair counterclaim
Another model may predict a short interval almost as well, or a single unusual datapoint may distort the fit. Measurement noise, an unrecorded direction change, or changing acceleration can make both models imperfect. A good report identifies which additional points, times or conditions would best distinguish the candidates. Do not infer force causes from position data alone without additional dynamics evidence.
Practice and responsible reporting
The Friday quiz randomly selects ten questions from a twenty-question open-book bank. Students are encouraged to retry after corrections toward 80% practice mastery. Public questions and editable browser records cannot substitute for separate authenticated exams or human-reviewed science evidence. Export your CER, model runs and a brief explanation of any mathematical mistakes you corrected.
Vocabulary in context
claim
A falsifiable statement matching the investigation question.
quantitative evidence
Specific numerical observations with units and provenance.
mechanistic reasoning
Explanation tying model structure to the expected physics.
counterclaim
A plausible alternative hypothesis deserving evaluation.
revision
A documented improvement made after studying evidence.
Use every term in a short original sentence or model explanation.
Worked example
Example: a quadratic fit x≈1+2t+0.5t² has c≈0.5 m/s²; interpreted a≈1.0 m/s² under the stated model. Compare its numerical residuals and holdout error with the linear model, and explain why a constant-acceleration model is a reasonable hypothesis—not a proven fact.
Show substitutions, signs and SI units in your own notebook.
Interactive laboratory & resources
Make a prediction first, change one parameter, record numerical evidence and explain model limitations.
Submit a complete CER with one model equation, two numerical pieces of evidence with units, a quantitative limitation, competing model, corrections, and a proposed additional test.
Your work stays in the local browser when possible. Export your notebook for backup.
Weekly mastery practice · ten of twenty randomized questions
Open-book practice with feedback and an 80% correction target. Randomized answers do not constitute a confidential official exam.
Continue
Select an artifact for your evidence portfolio. Explain what it supports and one factor it cannot establish.