{
  "version": 3,
  "sources": [
    {
      "id": "frp2025",
      "title": "ФРП Математика 5–9, базовый уровень, 2025",
      "url": "https://edsoo.ru/wp-content/uploads/2025/07/2025_ooo_frp_matematika-5-9_baza.pdf",
      "checked": "2026-10-18"
    }
  ],
  "notes": [
    "Каталог навыков по содержанию и тематическому планированию ФРП, а не копия оглавления.",
    "Повторение ранее изученных навыков отмечено в названии там, где нужно. Статус ready относится только к указанным типам заданий.",
    "Квадратные уравнения впервые изучаются в 8 классе; в 9 оставлены для совместимости и повторения."
  ],
  "subjects": {
    "math": "Математика",
    "algebra": "Алгебра",
    "geometry": "Геометрия",
    "statistics": "Вероятность и статистика"
  },
  "topics": [
    {
      "id": "5-math-read",
      "title": "Чтение и запись многозначных чисел",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-compare",
      "title": "Сравнение натуральных чисел",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-round",
      "title": "Округление натуральных чисел",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-line",
      "title": "Числа на координатной прямой",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-roman",
      "title": "Римская запись чисел",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-add",
      "title": "Сложение и вычитание натуральных чисел",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-mul",
      "title": "Умножение и деление натуральных чисел",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-remainder",
      "title": "Деление с остатком",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-powers",
      "title": "Степень с натуральным показателем",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-order",
      "title": "Порядок действий и скобки",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
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      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
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    },
    {
      "id": "5-math-laws",
      "title": "Свойства действий для удобного счёта",
      "grade": 5,
      "subject": "math",
      "section": "Натуральные числа",
      "status": "planned",
      "types": [],
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      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-letters",
      "title": "Значение буквенного выражения",
      "grade": 5,
      "subject": "math",
      "section": "Выражения, уравнения, делимость",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-unknown",
      "title": "Неизвестный компонент действия",
      "grade": 5,
      "subject": "math",
      "section": "Выражения, уравнения, делимость",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-divisors",
      "title": "Делители и кратные",
      "grade": 5,
      "subject": "math",
      "section": "Выражения, уравнения, делимость",
      "status": "planned",
      "types": [],
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      "source": "frp2025",
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      "intendedTypes": [
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    },
    {
      "id": "5-math-prime",
      "title": "Простые и составные числа",
      "grade": 5,
      "subject": "math",
      "section": "Выражения, уравнения, делимость",
      "status": "planned",
      "types": [],
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      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-divrules",
      "title": "Признаки делимости на 2, 3, 5, 9, 10",
      "grade": 5,
      "subject": "math",
      "section": "Выражения, уравнения, делимость",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-factor",
      "title": "Разложение на множители",
      "grade": 5,
      "subject": "math",
      "section": "Выражения, уравнения, делимость",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-meaning",
      "title": "Дробь как часть целого",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-mixed",
      "title": "Смешанное число и неправильная дробь",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-reduce",
      "title": "Сокращение и основное свойство дроби",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-denominator",
      "title": "Приведение к общему знаменателю",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-fraccompare",
      "title": "Сравнение обыкновенных дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-fracadd",
      "title": "Сложение дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
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      ]
    },
    {
      "id": "5-math-fracsub",
      "title": "Вычитание дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
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      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
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    },
    {
      "id": "5-math-fracmul",
      "title": "Умножение дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
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      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
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      ]
    },
    {
      "id": "5-math-fracdiv",
      "title": "Деление дробей и обратные числа",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-part",
      "title": "Часть от целого и целое по части",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
        "example"
      ]
    },
    {
      "id": "5-math-decimal",
      "title": "Десятичная и обыкновенная запись",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
      "generatorId": null,
      "source": "frp2025",
      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
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    },
    {
      "id": "5-math-deccompare",
      "title": "Сравнение десятичных дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
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      "pages": "14–15",
      "category": "core",
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    },
    {
      "id": "5-math-decadd",
      "title": "Сложение и вычитание десятичных дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
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      "category": "core",
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    },
    {
      "id": "5-math-decmul",
      "title": "Умножение и деление десятичных дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
      "types": [],
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      "pages": "14–15",
      "category": "core",
      "intendedTypes": [
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    },
    {
      "id": "5-math-decround",
      "title": "Округление десятичных дробей",
      "grade": 5,
      "subject": "math",
      "section": "Дроби",
      "status": "planned",
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      "id": "5-math-parts",
      "title": "Задачи на части",
      "grade": 5,
      "subject": "math",
      "section": "Практические задачи",
      "status": "planned",
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      "category": "core",
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    },
    {
      "id": "5-math-motion",
      "title": "Путь, скорость, время",
      "grade": 5,
      "subject": "math",
      "section": "Практические задачи",
      "status": "planned",
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      "category": "core",
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    },
    {
      "id": "5-math-cost",
      "title": "Цена, количество, стоимость",
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      "subject": "math",
      "section": "Практические задачи",
      "status": "planned",
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      "category": "core",
      "intendedTypes": [
        "example"
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    },
    {
      "id": "5-math-units",
      "title": "Перевод единиц длины, массы, времени",
      "grade": 5,
      "subject": "math",
      "section": "Практические задачи",
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      "category": "core",
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    },
    {
      "id": "5-math-logic",
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      "subject": "math",
      "section": "Практические задачи",
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      "category": "core",
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        "example"
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    },
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      "id": "5-math-tables",
      "title": "Чтение таблиц и столбчатых диаграмм",
      "grade": 5,
      "subject": "math",
      "section": "Практические задачи",
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      "category": "core",
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        "example"
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    },
    {
      "id": "5-math-segments",
      "title": "Отрезки, прямые и ломаные",
      "grade": 5,
      "subject": "math",
      "section": "Наглядная геометрия",
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      "category": "core",
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        "geometry"
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    },
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      "id": "5-math-angles",
      "title": "Виды и измерение углов",
      "grade": 5,
      "subject": "math",
      "section": "Наглядная геометрия",
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      "category": "core",
      "intendedTypes": [
        "geometry"
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    },
    {
      "id": "5-math-triangle",
      "title": "Треугольники и многоугольники",
      "grade": 5,
      "subject": "math",
      "section": "Наглядная геометрия",
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      "category": "core",
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        "geometry"
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    },
    {
      "id": "5-math-perimeter",
      "title": "Периметр многоугольника",
      "grade": 5,
      "subject": "math",
      "section": "Наглядная геометрия",
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      "category": "core",
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        "geometry"
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    },
    {
      "id": "5-math-rectangle",
      "title": "Площадь прямоугольника и квадрата",
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        "geometry"
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    },
    {
      "id": "5-math-composite",
      "title": "Площадь составной фигуры",
      "grade": 5,
      "subject": "math",
      "section": "Наглядная геометрия",
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      "category": "core",
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      "id": "5-math-areaunits",
      "title": "Единицы площади",
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      "subject": "math",
      "section": "Наглядная геометрия",
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      "id": "5-math-solids",
      "title": "Куб и параллелепипед, развёртки",
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      "subject": "math",
      "section": "Наглядная геометрия",
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      "id": "5-math-volume",
      "title": "Объём куба и параллелепипеда",
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      "subject": "math",
      "section": "Наглядная геометрия",
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      "id": "5-math-volumeunits",
      "title": "Единицы объёма",
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      "subject": "math",
      "section": "Наглядная геометрия",
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      "grade": 6,
      "subject": "math",
      "section": "Натуральные числа и делимость",
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        "example"
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      "category": "core"
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      "section": "Натуральные числа и делимость",
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        "example"
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      "category": "core"
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      "title": "Делители и кратные",
      "grade": 6,
      "subject": "math",
      "section": "Натуральные числа и делимость",
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      "types": [
        "example"
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      "category": "core"
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