{
  "id": "math.fractions.of-quantity-swap-roles",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.of-quantity-swap-roles",
  "uuid": "721c3f30-4b4e-4ffb-ac77-3433d1a18164",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Swapping numerator and denominator when finding a fraction of a quantity",
  "statement": "To find a/b of a quantity you divide the quantity by a and multiply by b.",
  "kind": "procedural-bug",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "4.NF.B.4",
      "uri": "http://corestandards.org/Math/Content/4/NF/B/4/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "find a non-unit fraction of a whole-number quantity",
      "signature": "divides by the numerator and multiplies by the denominator",
      "example": {
        "item": "Find 3/4 of 20",
        "expected": "15",
        "response": "26 2/3 (20 / 3 x 4)"
      }
    },
    {
      "item_shape": "find a unit fraction of a quantity",
      "signature": "divides by 1 and multiplies by the denominator",
      "example": {
        "item": "Find 1/5 of 30",
        "expected": "6",
        "response": "150"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "The answer is larger than the original quantity for a proper fraction and the learner does not object. A slip is a wrong division or multiplication within the right method."
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/B/4/",
        "label": "CCSS 4.NF.B.4: multiply a fraction by a whole number"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/B/4/",
        "label": "CCSS 4.NF.B.4: multiply a fraction by a whole number"
      },
      {
        "external": "http://corestandards.org/Math/Content/3/NF/A/1/",
        "label": "CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts"
      }
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "4.NF.B.4",
      "uri": "http://corestandards.org/Math/Content/4/NF/B/4/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "book",
        "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)",
        "note": "CSMS fractions: errors on 'fraction of a quantity' items."
      },
      {
        "type": "book",
        "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."
      }
    ],
    "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"
}