Level 1 · Foundations teaching kit · Grades 8–9
Measurement, uncertainty, and evidence
Use the learner record during the live investigation, then use the instructor guide to facilitate comparison, address misconceptions, and assess evidence-bounded reasoning.
Learner lab record
Correlated uncertainty investigation
How does shared movement between two inputs change the uncertainty of a combined result?
Setup
Use the live uncertainty composer. Change one control at a time, keep a record of every setting, and treat correlation as a declared relationship rather than a guess.
Predict first
- 1. Predict the result when ρ=0.
- 2. Predict whether positive or negative correlation makes the combined interval wider.
| Variable | Role | Unit |
|---|---|---|
| Input uncertainty σx | independent | chosen measurement unit |
| Input uncertainty σy | independent | same unit as σx |
| Correlation ρ | independent | unitless |
| Combined uncertainty σ | dependent | chosen measurement unit |
Observation columns
Analyze
- 1. Which run reproduced ordinary quadrature?
- 2. Which pair of runs isolates correlation?
- 3. What assumption would make your comparison invalid?
- 4. State the result with units and an uncertainty interval.
Conclusion frame
When ___ stayed fixed and ρ changed from ___ to ___, combined uncertainty changed from ___ to ___ because ___.
Instructor guide · 35–45 minutes
Teach the investigation, not the interface
Learning target: Learners distinguish independent quadrature from correlated uncertainty and defend a comparison using controlled variables.
Prepare
- • Open the uncertainty composer on every device.
- • Choose one familiar unit such as centimeters.
- • Prepare one deliberately flawed comparison for critique.
Facilitation moves
- • Ask which variable changed before discussing the number.
- • Have pairs reproduce one another's recorded setting.
- • Require units in every spoken conclusion.
Accessibility and participation
- • Read every Greek symbol aloud and pair it with its plain-language name.
- • Allow keyboard arrow control of every slider.
- • Offer the observation table before learners begin changing values.
Evidence of learning
- • A controlled two-run comparison
- • Correct use of units
- • A conclusion that names the role of correlation
Misconception checks
More measurements always remove uncertainty.
Repeated independent noise may shrink; shared bias and correlation do not disappear by repetition.
Negative correlation means bad data.
It describes opposing co-movement and can reduce a particular combined uncertainty.
Extension
Build a three-input budget and identify which covariance term dominates the output.