# Open Prep AI Pack Kit: Generated Templates

Kit revision: **2026-08-29**

This focused component is included inside the complete generated-template bundle. For advanced modular use, pair it with `math-drill-ai-pack-authoring-start.md`, the named schema, and both complete examples below. It covers only `kind: "generated_template"` packages.

## Canonical contract

- Format: `math-drill-question-pack`
- Schema version: `2`
- Kind: `generated_template`
- Required collection: `templates` (1 to 500)
- Canonical schema: `question-pack-v2.schema.json`
- Copy-ready standard example: `question-pack-template-example.mathdrill.json`
- Copy-ready Interview Math example: `question-pack-interview-math-example.mathdrill.json`

Use the standard example for ordinary generated math. Use the Interview Math example only when learners should select a setup, calculate, and interpret the result.

## Practical template pattern

A template needs `id`, category, 1 to 10 tags, 1 to 4 difficulty values, prompt template, variables, formula, and explanation template:

```json
{
  "id": "units-times-price",
  "category": "business_math",
  "tags": ["revenue", "multiplication"],
  "difficulty": ["beginner", "intermediate"],
  "promptTemplate": "A fictional shop sells {units} items at ${price} each. What is revenue?",
  "variables": {
    "units": { "type": "integer", "values": [100, 150, 200] },
    "price": { "type": "currency", "min": 8, "max": 12, "step": 2 }
  },
  "formula": { "expression": "units * price", "outputVariable": "revenue" },
  "answerUnit": "currency",
  "explanationTemplate": {
    "steps": ["Revenue equals units times price.", "{units} x ${price} = ${revenue}."]
  }
}
```

Place that object in the `templates` array of the shared version 2 envelope. The two canonical examples are complete importable packages.

## Variable and formula rules

Each template defines 1 to 20 case-sensitive variables. Variable names must be identifiers, and `answer`, `__proto__`, `constructor`, and `prototype` are reserved. Define each variable from exactly one source:

- `values`: 1 to 100 unique values; or
- a range with `min`, `max`, and optional positive `step`.

Variable types are `integer`, `decimal`, `percentage`, and `currency`. Integer values and range fields are whole numbers. A range has at most 10,001 reachable values. The default step is 1 for integer and 0.1 otherwise, but an explicit step is clearer.

Percentage variables are display numbers: use `25` when the prompt shows 25%, then use `rate / 100` in the formula. Variable `unit` is metadata and does not rescale the number.

Formula expressions allow only numeric literals, declared variables, parentheses, unary signs, and `+ - * / ^`. They do not allow functions, assignments, comparisons, commas, JavaScript, or a `%` operator. Every identifier must resolve. Every reachable combination must produce a finite number without division by zero.

Import checks up to 256 deterministic representative combinations, including boundaries and values near zero. This is bounded validation, not an exhaustive proof of a large Cartesian product. Test all risky denominators and sign boundaries yourself. The runtime surfaces an actionable package error if an unprobed combination fails.

Variables always combine as an independent Cartesian product. For example, `volume: [100, 200]` and `price: [10, 20]` create four combinations, not the two same-position pairs. If volume 100 must use price 10 and volume 200 must use price 20, create two templates (or otherwise encode one independent driver) instead of parallel arrays. Never rely on array position to pair dependent values.

## Placeholders and answers

Placeholders are exact, case-sensitive `{identifier}` tokens. Prompts, explanations, and Interview Math labels may reference declared variables. Explanations may also reference `{answer}` or `formula.outputVariable`. Do not put either answer token in a prompt.

Placeholders render raw stored values without commas, currency conversion, percent conversion, or scale formatting. Put visible signs or scale words around the token. The formula result becomes the answer directly. A percentage answer must return a fraction such as `0.25`; percentage points return a point count such as `5`. For `answerUnit: "k"`, `"m"`, or `"b"`, return the number in that displayed scale: an answer of 12 million is value `12` with unit `m`. The learner may type `12`, select M, or type `12M`; a contradictory suffix is rejected.

Generated answers default to a tolerance that accepts a correctly calculated value rounded to two displayed decimal places: absolute `0.005` for ordinary display values and `0.00005` for canonical percentage fractions (half of `0.01` percentage point). A template can override this with `tolerance` using the same `absolute`, relative `percentage`, or inclusive `range` shapes as fixed numeric answers. Absolute tolerance must be between `0` and `1000000000`; relative percentage tolerance must be between `0` and `1`; range endpoints must be finite and ordered. Optional `roundingRule` is learner-facing guidance and does not alter grading by itself. Omit both fields for the safe two-decimal default, set `tolerance` explicitly for a different comparison policy, and use `fixed_numeric` when each authored question needs a different answer rule.

## Optional Interview Math

Either omit `caseStyle` from every template or include it on every template. An Interview Math pack requires `category: "case_math"` throughout.

`caseStyle` requires:

- `calculationStepCount`: 2 through 6;
- one supported industry;
- `interviewMath.expectedUnit` equal to `answerUnit`, or `none` when no answer unit is set;
- 2 to 10 unique equation choices, exactly one with `setupCorrect: true`, which must also have `formulaCorrect: true`;
- 2 to 10 unique interpretation choices, exactly one with `isCorrect: true`.

Other equation choices may recognize the formula while applying an incorrect setup. Choice labels can use valid variable placeholders and are shuffled locally.

## Authoring quality check

- There are enough distinct combinations for the largest likely drill, and duplicate variants are not the intended content.
- All prompt and explanation placeholders resolve exactly.
- Boundary, zero, negative, and exponent cases are safe and finite.
- Every Cartesian-product combination is semantically valid; dependent value pairs were split into separate templates.
- The output unit matches the raw formula result.
- Interview Math is consistently enabled or absent across the entire pack.
- A human has independently checked every formula, answer unit, setup flag, interpretation flag, and source fact.
- The final response follows the Start Here binding output contract and is ready for app validation.