{
  "id": "math.fractions.divide-larger-by-smaller",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.divide-larger-by-smaller",
  "uuid": "78a649f3-688d-49a2-a85c-7be491860757",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "You can only divide a larger number by a smaller one",
  "statement": "In a division the bigger number must be divided by the smaller number, so if the divisor is bigger the two numbers should be swapped.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "6.NS.A.1",
      "uri": "http://corestandards.org/Math/Content/6/NS/A/1/"
    }
  ],
  "level_band": [
    "primary",
    "middle",
    "adult"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "divide a fraction by a larger whole number",
      "signature": "swaps dividend and divisor so that the larger number is divided by the smaller",
      "example": {
        "item": "1/2 / 3 = ?",
        "expected": "1/6",
        "response": "6"
      }
    },
    {
      "item_shape": "write the division for a word problem where the dividend is smaller than the divisor",
      "signature": "writes the numbers in the order that makes the dividend larger",
      "example": {
        "item": "3/4 of a litre is shared equally between 3 people. Write the division.",
        "expected": "3/4 / 3",
        "response": "3 / 3/4"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "A slip is one reversed pair. The belief is a stated rule ('you can't divide a small number by a big one') and is applied to whole numbers too (3 / 12 rewritten as 12 / 3).",
    "vs": {
      "math.fractions.divide-makes-smaller": "Divide-makes-smaller keeps the order and gets a smaller wrong result; this belief changes the order."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/6/NS/A/1/",
        "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/6/NS/A/1/",
        "label": "CCSS 6.NS.A.1: interpret and compute quotients of fractions"
      },
      {
        "external": "http://corestandards.org/Math/Content/5/NF/B/7/",
        "label": "CCSS 5.NF.B.7: divide unit fractions by whole numbers and whole numbers by unit fractions"
      }
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "6.NS.A.1",
      "uri": "http://corestandards.org/Math/Content/6/NS/A/1/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "paper",
        "citation": "Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.",
        "doi": "10.5951/jresematheduc.16.1.0003"
      },
      {
        "type": "paper",
        "citation": "Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102.",
        "doi": "10.5951/jresematheduc.20.1.0095",
        "note": "Preservice teachers reversing dividend and divisor so the divisor is smaller."
      },
      {
        "type": "paper",
        "citation": "Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25.",
        "doi": "10.2307/749817"
      }
    ],
    "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"
}