Source-linked investigation inventory
These cases extend the existing eight-unit skill ladder, not an empty course. Foundation typically supports grades 7-8; Core and Extension are chosen by readiness and the named prerequisites. This is not a college-credit claim. Select a level and accessible response format before teaching; supplied-record analysis and observed practical evidence are distinct.
These are supplied-data and paper investigations, not laboratory procedures. An educator must approve any actual practice, materials, location, supervision, accessibility and emergency plan beforehand. Do not grow or open unknown cultures, handle unknown spills, use hazardous apparatus, test hygiene on people, or collect personal health disclosures. Paper work does not certify unobserved practical skill. Public worked answers are nonsecure practice, not private assessor items. Sources below are method references or retrospective accounts. No new table is presented as real historical data. Use the preserved denominator/rate exercise before interpreting the historical comparison.
SM-U1: Who did the sample leave out?
Question: How does the sampling frame change the claim we can make about open-flower counts in this fictional garden?
Prerequisites: Count and add whole numbers, divide for a mean, and distinguish a description from a proposed explanation; use counters or a read-aloud table if needed.
Sources: UC Museum of Paleontology, Understanding Science: How science works; OpenStax Introductory Statistics 2e, 1.2: Data, Sampling, and Variation in Data and Sampling; UC Museum of Paleontology, Understanding Science: Testing scientific ideas. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: garden-frame; garden-draw; garden-transfer.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use the supplied garden-frame, garden-draw, garden-transfer records, assigned source sections, calculator and an accessible graph or diagram. No physical apparatus is required.
Variables: Record quadrat ID, location, common area and open-flower count. Location is observed, not manipulated; watering and plant type are unmeasured.
Controls: Use equal quadrat area, the same open-flower definition and observation time. An observational comparison cannot hold every natural condition fixed.
Sampling / replication: The spatial units are twelve quadrats; adjacent quadrats may be correlated. Recounting a quadrat is a counting check, not a new independently located quadrat.
Analysis: Compare census, convenience and random-sample means; propose a documented sample before seeing results and distinguish selection uncertainty from a causal explanation.
Uncertainty: Repeatedly inspecting path quadrats reduces counting mistakes there but cannot repair omission of the interior. Random sampling addresses selection from a population; random assignment distributes treatments among experimental units. Neither makes a small sample representative by guarantee. Weather, watering, plant type and observer rules remain possible explanations for a location association.
Record: Retain the synthetic label, frame, draw order, counting definition, arithmetic, source section/date, first explanation, revision and transfer. An educator signs only evidence actually reviewed.
Instructor review: An educator reviews prerequisites, source interpretation, reasoning and accessibility before assessment. A paper response does not certify unobserved practical technique; approved hands-on work requires a separate record.
SM-U2: Repair a record without inventing a measurement
Question: Which claims can a second reader reconstruct from an incomplete notebook, and which corrections are justified by a source?
Prerequisites: Read decimal lengths and times, compute a mean, and explain the difference between an observation and a remembered reconstruction.
Sources: Columbia University / ORI, Data Acquisition and Management: Foundation Text. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: notebook-ledger; notebook-transfer.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use the supplied notebook-ledger, notebook-transfer records, assigned source sections, calculator and an accessible graph or diagram. No physical apparatus is required.
Variables: Track source length, copied length, source availability and version of the calculation. No experimental treatment is assigned in this document audit.
Controls: Keep card IDs, centimeters and chronology stable across versions. Never rewrite source values to make a calculated mean look consistent.
Sampling / replication: Four cards concern four fictional strips, with only three verifiable initially. Recopying the same card creates no new measurement or independent replicate.
Analysis: Audit every row before calculating. Justify inclusion by source availability, compute the verified-only mean, then revise it when the missing source arrives.
Uncertainty: The cards are readable to 0.1 cm, but that does not establish true length accuracy. Excluding an unverified value from the verified-only mean must be disclosed; three available cards may not represent the missing one. Reconstructing a supplied record is not evidence of real-time recording during an actual practical.
Record: Retain all supplied cards, review date, collection times, visible N2 correction, N3 gap and recovery, calculation versions and reviewer questions; label the work as an audit of synthetic records.
Instructor review: An educator reviews prerequisites, source interpretation, reasoning and accessibility before assessment. A paper response does not certify unobserved practical technique; approved hands-on work requires a separate record.
SM-U3: Many digits do not make a balance accurate
Question: Which claims about an unknown mass survive checks of resolution, repeatability and calibration model?
Prerequisites: Add decimals, find a mean and range, convert g to mg; honors requires rearranging a line equation and discussing model assumptions.
Sources: JCGM VIM, 4.14: Resolution; JCGM International Vocabulary of Metrology (VIM), 2.13: Measurement accuracy; JCGM VIM, 2.39: Calibration. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: balance-checks; balance-settings.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use the supplied balance-checks, balance-settings records, assigned source sections, calculator and an accessible graph or diagram. No physical apparatus is required.
Variables: Reference value and indicated mass are the paired variables; object identity, display step and check date remain explicit in the record.
Controls: The supplied scenario holds instrument, object placement and conditions fixed within a repeat set. A changed date can reveal drift rather than a treatment effect.
Sampling / replication: Three readings per object assess repeatability of that object, not three independent reference masses or three balances.
Analysis: Calculate offsets and spread, compare a constant-offset model with a two-point line, and use the new dated check as counterevidence to stability.
Uncertainty: Resolution is not accuracy. The unknown indications span 0.2 g; that observed range is not the total uncertainty or a confidence interval. Reference uncertainty, zero drift, nonlinearity and loading method remain. Two reference points can define a line, but cannot validate it between or beyond the points; use additional approved checks before accepting a calibration model.
Record: Retain source section/date, stated reference uncertainties, raw display digits, offsets, graph of indication against reference, assumptions and unrounded calculations alongside the rounded report.
Instructor review: An educator reviews prerequisites, source interpretation, reasoning and accessibility before assessment. A paper response does not certify unobserved practical technique; approved hands-on work requires a separate record.
SM-U4: Randomize the assignment; mask the observation
Question: Does the supplied controlled design distinguish a treatment comparison from baseline, selection and observation biases?
Prerequisites: Subtract decimal lengths, average differences, and distinguish observational location from an assigned treatment; review Unit 1 sampling first.
Sources: OpenStax Introductory Statistics 2e, 1.4: Experimental Design and Ethics. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: allocation-draw; coded-growth; growth-transfer.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use the supplied allocation-draw, coded-growth, growth-transfer records, assigned source sections, calculator and an accessible graph or diagram. No physical apparatus is required.
Variables: Light duration is assigned; height change is measured. Starting height defines a block, while station, watering and reading rules are potential confounders.
Controls: Use comparable starting conditions, common period, water, soil and reading endpoints; in a real proposal the educator must verify independently assigned stations.
Sampling / replication: Four separately assigned pots per condition are the stated experimental units. Three leaves or height rereadings per pot are not new treatment replicates.
Analysis: Reconstruct the allocation, compute growth and within-block contrasts, rehearse a blinded-reading design and compare the fresh study without discarding disagreement.
Uncertainty: Four pots per condition provide a small comparison, not a magic sample size guaranteeing a real effect. If one shared station served every pot in a condition, treatment would be confounded with station. Multiple leaves or repeated height readings are subsamples, not additional assigned pots. Knowing the key ends blinding; a future observer needs an educator-held code key and a fixed endpoint rule.
Record: Retain the supplied random draw, block IDs, raw heights, growth formula, code key and release timing, control checklist, stated sample unit, uncertainty and proposed procedure with educator approval status.
Instructor review: An educator reviews prerequisites, source interpretation, reasoning and accessibility before assessment. A paper response does not certify unobserved practical technique; approved hands-on work requires a separate record.
SM-U5: A curve that fits can still fail its next test
Question: Which graph and model describe the record, and what happens when the model meets observations not used to choose it?
Prerequisites: Plot ordered pairs, subtract signed positions and divide by elapsed time for average velocity; core uses squares and honors compares predictive tests.
Sources: NIST/SEMATECH e-Handbook, 1.3.3.26: Scatter Plot; UC Museum of Paleontology, Understanding Science: Testing scientific ideas. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: model-track; model-transfer.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use the supplied model-track, model-transfer records, assigned source sections, calculator and an accessible graph or diagram. No physical apparatus is required.
Variables: Time is the ordered explanatory coordinate and position the response. Partition into training and held-out observations is fixed before model comparison.
Controls: Keep the same coordinate origin, units, plot scales and candidate equations. Never hide held-out points by changing the graph scale or observation labels.
Sampling / replication: These are multiple times along one synthetic trajectory, not independent repeated trajectories. A follow-up requires new independent trials or checks, not recopying points.
Analysis: Choose a representation, calculate signed average velocity, compute model predictions and residuals, compare fit in the chosen interval and revise the claim after counterevidence.
Uncertainty: One trajectory provides repeated times, not seven independent trials of the motion. An exact training fit cannot establish a mechanism or eliminate reading uncertainty. Residuals of -11 and -28 cm on new points are much larger than a 0.5 cm display step, but the record alone does not identify friction, a stop signal or a sensor fault. Retain counterevidence and check both model conditions and measurements.
Record: Retain source/date, input table, axes and scales, average velocity with units, candidate rules, pre-check predictions, signed residuals, revised claim and fresh transfer prediction labeled as unobserved.
Instructor review: An educator reviews prerequisites, source interpretation, reasoning and accessibility before assessment. A paper response does not certify unobserved practical technique; approved hands-on work requires a separate record.
SM-U6: Nine readings from three sheets are not nine sheets
Question: How much independent evidence do nested readings contain, and what can honestly be said about uncertainty?
Prerequisites: Compute group means and ranges; core distinguishes a sample unit from a measurement; honors uses squares, square roots and n - 1.
Sources: Lazic (2010), The problem of pseudoreplication in neuroscientific studies; NIST/SEMATECH e-Handbook, 1.3.5.6: Measures of Scale. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: nested-sheets; sheet-transfer.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use the supplied nested-sheets, sheet-transfer records, assigned source sections, calculator and an accessible graph or diagram. No physical apparatus is required.
Variables: Track sheet identity, coupon identity and mass gain. The outcome is coupon mass gain summarized per independent sheet, not a treatment comparison.
Controls: The paper scenario assumes equal coupon area, common timing, common method and one batch. A real study must verify these conditions and calibration separately.
Sampling / replication: Independently sampled sheets are replicates; coupons within a sheet are subsamples. New observations of the same coupon would be repeat readings, another distinct level.
Analysis: Group before calculating uncertainty, compare raw and sheet-mean ranges, document exclusion sensitivity and recompute after one new independent sheet.
Uncertainty: There are three independent sheets and nine coupon readings, not nine independent sheets. Adjacent coupons may resemble one another. Even correctly grouped data from one batch do not describe all brands or batches. For honors, s = sqrt(sum((sheet mean - overall mean)^2)/(n - 1)) and SE = s/sqrt(n), assuming independent comparable sheets. SE is not a 95% confidence interval and omits possible systematic error.
Record: Retain every row and ID, grouping decision, independent n, averaging weights, SD/SE formulas if used, bias limitations, sensitivity label, source/date and the fourth-sheet revision.
Instructor review: An educator reviews prerequisites, source interpretation, reasoning and accessibility before assessment. A paper response does not certify unobserved practical technique; approved hands-on work requires a separate record.
SM-U7: Approve the conditions, not just the answer
Question: Which conditions justify proceeding, modifying or declining a proposed activity, and what does a numerical technique comparison actually establish?
Prerequisites: Know how to contact the responsible educator and read the local safety plan; distinguish an unknown substance from a known dry object. Review Unit 3 before percent-error work.
Sources: NSTA: Safety and School Science Instruction; Columbia University / ORI, Data Acquisition and Management: Foundation Text; JCGM International Vocabulary of Metrology (VIM), 2.13: Measurement accuracy. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: decision-cards; technique-readings; technique-transfer.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use only the fictional decision cards, supplied ruler readings, source sections and an accessible response sheet. No biological material, liquid, electrical apparatus or personal record is required. Any separate dry-card/ruler practical needs educator approval first.
Variables: Decision variables are the known hazard, missing information, authorized actor and stopping condition. The separate numerical outcome is indicated length under two viewing positions.
Controls: No student contact with unknown contents or spills; no real personal or health data. Keep ruler origin and reference card the same in the supplied comparison and do not generalize its offset.
Sampling / replication: Three readings per viewing position concern one reference card, not three independent demonstrations of competence. New scenario reasoning and actual observed technique are distinct evidence.
Analysis: Explain the scenario-specific decision in words, then compare reading means and reference agreement. Do not aggregate ethical judgments into an arbitrary safety score.
Uncertainty: Good agreement with a supplied reference does not prove handling skill. The difference between oblique and eye-level means illustrates possible parallax in this scenario, not a universal correction for all angles. The ethical decisions have no numerical risk score; missing identity, consent, training or equipment information can require stopping rather than estimating a reassuring number.
Record: Record each scenario, missing approval, proposed alternative and educator review; keep numerical units and reference assumptions separately. An actual observed practical record identifies the approved task, conditions, accommodations and actions witnessed, without private health details.
Instructor review: The educator reviews each decision and approves or declines any actual practice before materials are used. No public answer, synthetic dataset or correct calculation substitutes for observed PPE, handling, disposal or approved emergency rehearsal.
SM-U8: Write the revision the new evidence requires
Question: How should a scientific claim change when a new batch reverses the original comparison?
Prerequisites: Compute count/denominator percentages, distinguish percentage points from relative change and compare two labeled groups; review the preserved rate activity before proceeding.
Sources: UC Museum of Paleontology, Understanding Science: Testing scientific ideas; OpenStax Introductory Statistics 2e, 1.2: Data, Sampling, and Variation in Data and Sampling. Assigned Semmelweis historical explanation; see the lesson for exact section focus.
Supplied inputs: claim-batches; claim-transfer.
Teaching, selected-level tasks and checked answers; fresh transfer question and solution; criterion-specific evidence and practical limits.
Materials: Use the supplied claim-batches, claim-transfer records, assigned source sections, calculator and an accessible graph or diagram. No physical apparatus is required.
Variables: Pattern and batch identify groups; number inspected is the denominator and out-of-tolerance cards the numerator. A cause has not been independently isolated.
Controls: Hold the stated tolerance definition and inspection rule fixed when computing rates; flag undocumented allocation or supplier differences rather than assume comparability.
Sampling / replication: Cards are distinct inspected items in each batch. Separate batches test stability in a different context; repeated inspection of one card would not increase the denominator of distinct cards.
Analysis: Compute within-batch and pooled rates with denominators, display reversal, revise the written claim and propose a design that could test the remaining uncertainty.
Uncertainty: The pilot is small and later batches may differ. Pooling requires a reason to treat studies as comparable, and these unequal totals weight them differently. A difference of pooled percentages is descriptive, not a significance test or proof of equivalence. No data here identify the mechanism producing failures. A challenge to the original claim should trigger review of the record, not invented explanations.
Record: Retain source/date, synthetic label, numerator/denominator pairs, graph choice, pooled and separated analyses, old and revised memo, critique response, fresh transfer and a separate live-defense review record.
Instructor review: An educator reviews prerequisites, source interpretation, reasoning and accessibility before assessment. A paper response does not certify unobserved practical technique; approved hands-on work requires a separate record.