{
  "id": "math.fractions.unequal-parts",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.unequal-parts",
  "uuid": "e7a0875c-e339-4404-9f39-1f73cfe9206f",
  "version": "0.1.2",
  "status": "draft",
  "trust": "low",
  "title": "Any part of a shape cut into b pieces is 1/b",
  "statement": "If a shape is cut into b pieces, each piece is one b-th of the shape, whether or not the pieces are the same size.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "3.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/3/NF/A/1/"
    }
  ],
  "level_band": [
    "early-primary",
    "primary"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "name the fraction shaded in a shape divided into unequal parts",
      "signature": "counts pieces and writes shaded/total, ignoring the sizes of the pieces",
      "example": {
        "item": "A rectangle is cut into 4 pieces of different sizes; the largest is shaded. What fraction is shaded?",
        "expected": "Cannot tell from the count; it is more than 1/4",
        "response": "1/4"
      }
    },
    {
      "item_shape": "judge whether a shape shows a given fraction",
      "signature": "accepts an unequal partition as showing the fraction",
      "example": {
        "item": "Does this circle, cut into 3 pieces of different sizes with 1 shaded, show 1/3?",
        "expected": "No, the parts are not equal",
        "response": "Yes"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Ask directly whether the pieces need to be the same size. A slip is a miscount with equal parts assumed; the belief is a stated 'it doesn't matter, there are four pieces'.",
    "vs": {
      "math.fractions.part-to-part": "Use a shape with equal parts. Part-to-part writers give 3/2 for 3 shaded of 5; this belief gives 3/5 correctly and only fails on unequal partitions."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "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"
      }
    ],
    "resolved_by": [
      {
        "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"
      }
    ],
    "confusable_with": [
      "math.fractions.part-to-part"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "3.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/3/NF/A/1/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "book",
        "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."
      },
      {
        "type": "book",
        "citation": "Steffe, L. P., & Olive, J. (2010). Children's Fractional Knowledge. Springer.",
        "doi": "10.1007/978-1-4419-0591-8",
        "note": "Equipartitioning as a prerequisite scheme for fractional knowledge."
      },
      {
        "type": "book",
        "citation": "Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge."
      }
    ],
    "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."
      },
      {
        "version": "0.1.2",
        "date": "2026-09-07",
        "change": "Re-kinded from the withdrawn `missing-prerequisite` to `overgeneralization`: the belief is the b-pieces-means-b-ths rule applied past the equal-parts condition it depends on, which is a belief the learner holds rather than an absence."
      }
    ]
  },
  "license": "CC-BY-4.0"
}