## SAT Math -- Curriculum Overlay

This addendum applies only to Digital SAT Math questions. Use it for course-wide
SAT Math rules that are narrower than the base and type guidance.

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## SAT Math Item Format

Determine the item format **semantically**, from what the student is asked to do — not from JSON field names or shapes (see the SCHEMA / FORMAT AGNOSTICISM block in the base prompt). Schema differences (which JSON key carries the choices, whether labels are A/B/C/D, populated/empty option arrays, renderer character limits) are never on their own grounds for failure. The rules below are item-writing **content** specifications published by SAT — they constrain what the question itself says to the student, not how the JSON is shaped.

**MCQ** (the student picks from a presented set of answer choices)
- The SAT item-writing specification requires **exactly 4 distinct answer choices**. An MCQ with 2, 3, 5, or any number of choices other than 4 fails `specification_compliance` (item-writing content rule, not a schema rule — labels A/B/C/D vs other labels are not the concern, the count of presented options is).
- "All of the above" and "None of the above" are explicitly prohibited by the SAT item-writing specification and fail `specification_compliance` (not `distractor_quality`).

**SPR / grid-in** (the student types a numeric answer; no selectable choices presented)
- The expected answer must be numerically resolvable (integer, decimal, fraction, or an acceptable numeric range). If the keyed answer is not numerically resolvable for an SPR-style item, that is a `factual_accuracy` or `clarity_precision` problem with the content — not a schema problem.
- Do not fail `specification_compliance` for renderer/UI shape rules (character limits, tolerance fields, value-object structure, etc.). Those are platform concerns, not content quality.
- With no distractors present, set `distractor_quality = 1.0` unless another rule creates a distractor issue.

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## Stimulus Requirements

Many SAT Math items are self-contained and need no stimulus. When the item text
references a stimulus (e.g., "use the table," "based on the scatterplot," "the
figure above/below," or similar directives) and no matching stimulus exists, fail
`stimulus_quality`.

When a data display or geometry figure is present, it must be internally consistent and
match the question text. Contradictory labels, axes, values, angle/side labels, or a figure
that reveals the asked-for unknown fail `stimulus_quality`.

---

## SAT Math Metric Rules

### factual_accuracy

Verify the keyed answer by solving the problem. A mathematically wrong key fails
`factual_accuracy`.

No two answer choices may be algebraically equivalent. Equivalent choices create an
ambiguous key and fail `factual_accuracy`.

Notation must be consistent enough to preserve meaning. Pure style mismatch belongs under
`clarity_precision`; a variable/quantity contradiction between stem and options fails
`factual_accuracy`.

### distractor_quality

For MCQ items, each distractor must map to a plausible mathematical error, not just a
nearby number. A distractor with no traceable error pathway fails `distractor_quality`.
Common math error paths include sign errors, order-of-operations errors, misapplied
formulas, solving for the wrong quantity, unit confusion, inverse/reciprocal errors, and
confusion between related algebraic forms.

Choices should have comparable notation style and simplification. A choice that telegraphs
or hides the key by being uniquely simplified, formatted, or precise fails
`distractor_quality`.

### curriculum_alignment

The item must exercise the stated SAT Math substandard, not merely describe a concept or
ask for formula recall. It must stay inside the assessment boundary defined for that
substandard.

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## Difficulty Calibration

When the substandard supplies its own difficulty definitions, use them. Otherwise apply
the general definitions below.

**Easy**
- A single-step procedure, direct formula application, or simple substitution with all
  required values explicit in the item.

**Medium**
- Multi-step procedures requiring selection or sequencing, contextual interpretation of a
  coefficient/constant, equation creation from a word problem, or basic conceptual
  reasoning.

**Hard**
- Multi-step reasoning under constraints, parameter analysis, special-case reasoning
  (no/one/infinite solutions, conditions on coefficients), connecting algebraic and
  graphical representations, or transfer of the targeted skill to a novel-but-supported
  context.
- Length alone is not difficulty.
