Question: Which discrepancies matter, and what can they not tell us? Kit: B, model/data aid. 35 = 3 + 7 + 12 + 8 + 5.
- 0–3: Retrieve model predictions 160,80,40,20,10 and invented values 160,80,44,26,20.
- 3–10: Teacher models a row-wise residual
record − prediction: 0,0,+4,+6,+10. Say this is a numerical discrepancy, not a known instrument error or cause. - 10–22: Learners complete a two-series table or dot plot, label units arbitrary, and describe the growing gap at n=2–4. They ask whether paper differences, sensor position, ambient light or another factor was controlled; B does not tell us.
- 22–30: Peers challenge the sentence “more layers prove exact half-transmission.” Revise it to fit B. Routes: plot with large tactile dots on a supplied axis; compare paired number tiles; write or dictate a residual table and claim audit.
- 30–35: “Can this table tell us why the n=4 value is 20?” Key: no; B lacks controlled-method detail and independent repeat. Response move: if learner names a cause as fact, convert it to a testable question.
Another domain: Apply the same residual method to fictional theatre curtain readings, with no real acoustic/light claim. Home: invent two short prediction/record columns and mark their difference.