Weighing an Empire: Metrology and Debasement
Statistics / data literacy / math elective · grades 9–12 · Two 45-minute periods (or one block)
Standards: Common Core HSS-ID.A.1–4 · HSS-IC.B.6 · NGSS practice 4
Students use recorded specimen weights to compute descriptive statistics for a coin type, plot the trend across a century, and argue about what the spread means when nobody designed the sample.
Learning objectives
By the end of the period, students can:
- Compute mean, median, range, and standard deviation from real measurements.
- Represent a time series and describe its trend in plain language.
- Distinguish measurement error, wear, and deliberate policy in a data spread.
- State the limits of a conclusion drawn from a non-random sample.
Procedure
| Stage | Time | What happens |
|---|---|---|
| Setup | 10 min | Explain what a specimen is and why two coins of the same type weigh differently: wear, clipping, and official standard. |
| Data collection | 15 min | Students pull the recorded weights for their type from the coin card, or from the public API for a whole reign. |
| Computation | 20 min | Mean, median, range, standard deviation. Plot weight against date for the reign. |
| Interpretation | 20 min | Where does the line fall, and is that debasement, wear, or too few coins? Write the honest version. |
| Homework | — | One paragraph: what extra data would settle the question? |
What the numbers mean (student handout)
- Weight
- Grams, as recorded by the holding museum. Worn coins weigh less than issued.
- Diameter
- Millimetres; varies with flan preparation more than with policy.
- Standard
- The intended weight set by the issuing authority — never directly observed.
- Sample
- The coins that survived, were found, were kept, and were measured.
- Bias
- Every filter above removes coins non-randomly. Say so in your conclusion.
Rubric (25 points)
| Criterion | Points | What earns full credit |
|---|---|---|
| Correct statistics | 10 | Calculations are right and clearly labelled with units. |
| Representation | 5 | The plot has labelled axes and a readable scale. |
| Interpretation | 5 | The trend is described accurately, without overclaiming. |
| Uncertainty | 5 | Sampling bias is named specifically, not as a generic caveat. |
Coins used in the examples
-
Trajan, aureus — the gold standard against which silver is judged
—
IMP CAES NERVA TRAIAN AVG GERM
Images stay on canoanumis.org with museum attribution; the printable packet carries catalog numbers and links instead, so nothing needs licensing.
Differentiation and assessment
- Support: supply a prepared spreadsheet of weights; the task is interpretation only.
- Extension: compare two reigns and test whether the difference is meaningful.
- Cross-curricular: pair with the history track's unit on the third-century crisis.
The graded version
In a pilot, every student gets a different coin from the filter you choose, auto-gradable parts are checked against the catalog record, and scores flow into your LMS gradebook over LTI 1.3. Setup takes about fifteen minutes, once, for an LMS administrator.
Request a pilot More in the Data & Patterns: Hoard and Metrology Analysis track