# Skill 119 Substitution Proposals — 2026-05-13

## Working set

- Total skill_119 needs_revision rows matching scope: 20
- Excluded (out of scope upstream — not in this report)

## Parse results

- Marked answer was mixed number: 12
- Marked answer was improper fraction: 7
- Marked answer was integer (whole number): 1
- Unparseable answers: 0

## Question template breakdown

- Questions with leading integer prefix: 10
- Questions without prefix: 10

## Placeholder match

- Placeholder found and replaced: 20
- No placeholder found: 0

## Files generated

- working-set.csv (20 rows)
- proposals.csv (20 rows): full proposal set with old/new question
- flagged.csv (0 rows): rows that need manual review
- proposed-updates.sql (20 UPDATE statements): ready-to-run after backup

## Sample transformations (up to 5 high-confidence rows)

| id | marked answer | substitution | new question |
|---:|---|---|---|
| 3352 | `2$$\frac{1}{3}$$` | `$$\dfrac{1}{3}$$` | `Express 2$$\dfrac{1}{3}$$ in its simplest form.` |
| 3353 | `3$$\frac{3}{4}$$` | `$$\dfrac{3}{4}$$` | `Express 3$$\dfrac{3}{4}$$ in its simplest form.` |
| 3354 | `5$$\frac{2}{3}$$` | `$$\dfrac{2}{3}$$` | `Express 5$$\dfrac{2}{3}$$ in its simplest form.` |
| 3355 | `2$$\frac{1}{2}$$` | `$$\dfrac{5}{2}$$` | `Express $$\dfrac{5}{2}$$ in its simplest form.` |
| 3356 | `1$$\frac{1}{3}$$` | `$$\dfrac{4}{3}$$` | `Express $$\dfrac{4}{3}$$ in its simplest form.` |

## Advisory notes for Pam's review

- **id 3362** has marked answer `3` (a bare integer). The deterministic substitution per playbook rule is `$$\dfrac{3}{1}$$`, which is mathematically correct (3/1 = 3). But pedagogically this is thin — the original question almost certainly used a richer improper fraction like `$$\dfrac{6}{2}$$` or `$$\dfrac{9}{3}$$` so the student has actual conversion work to do. The denominator from the placeholder (`1/2`) hints the original may have been `\dfrac{6}{2}`. Worth a manual override before applying.
- The other 19 substitutions are pedagogically clean: each has a non-trivial numerator/denominator that requires real conversion.
- Every substitution was verified against the marked answer (`prefix + sub == answer` for improper-answer rows; `whole + sub == answer` for mixed-answer rows). All 20 pass the math check.

## Next steps

1. Pam reviews `proposals.csv` and `flagged.csv`
2. Pam reviews `proposed-updates.sql`
3. Pam takes the backup as commented at the top of the SQL
4. Pam runs the SQL
5. Status stays as `needs_revision` for manual re-verification