{
  "id": "math.fractions.improper-impossible",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.improper-impossible",
  "uuid": "5211ad46-cba5-4c3d-92ff-9fa79d9ed753",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "A fraction cannot be more than one whole",
  "statement": "A fraction is always part of one whole, so the numerator can never be bigger than the denominator and a fraction can never be greater than 1.",
  "kind": "undergeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "4.NF.B.3",
      "uri": "http://corestandards.org/Math/Content/4/NF/B/3/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "add two proper fractions whose sum exceeds one",
      "signature": "adjusts the result so it stays below or equal to one",
      "example": {
        "item": "3/4 + 3/4 = ?",
        "expected": "6/4 (= 1 1/2)",
        "response": "6/8 (or 1)"
      }
    },
    {
      "item_shape": "place an improper fraction on a number line",
      "signature": "places it below 1 or says it cannot be placed",
      "example": {
        "item": "Mark 5/4 on a number line from 0 to 2",
        "expected": "one quarter past 1",
        "response": "just below 1 (or 'not a real fraction')"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Ask directly whether 7/4 is a number. A slip is an arithmetic error; the belief is the stated rule 'the top can't be bigger than the bottom'.",
    "vs": {
      "math.fractions.mixed-to-improper-add-all": "That bug accepts improper fractions but converts to them wrongly; this belief rejects them."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/B/3/",
        "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/B/3/",
        "label": "CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b"
      },
      {
        "external": "http://corestandards.org/Math/Content/3/NF/A/2/",
        "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"
      }
    ],
    "confusable_with": [
      "math.fractions.mixed-to-improper-add-all"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "4.NF.B.3",
      "uri": "http://corestandards.org/Math/Content/4/NF/B/3/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "paper",
        "citation": "Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518.",
        "doi": "10.1016/j.learninstruc.2004.06.015",
        "note": "A developmental stage in which fractions are understood as always smaller than the unit."
      },
      {
        "type": "book",
        "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."
      },
      {
        "type": "book",
        "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)"
      }
    ],
    "origin": "llm-drafted",
    "notes": "Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review."
  },
  "history": {
    "changelog": [
      {
        "version": "0.1.1",
        "date": "2026-09-05",
        "change": "Schema 0.2 migration: about/alignments carry a free-string scheme (corestandards.org URLs relabelled CCSS where present); trust computed from reviews[] (none yet, so low); no change to the statement or evidence."
      }
    ]
  },
  "license": "CC-BY-4.0"
}