{
  "id": "math.fractions.mixed-to-improper-add-all",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.mixed-to-improper-add-all",
  "uuid": "be94771a-f7b8-4af6-acb3-a3fe723a0d20",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Converting a mixed number by adding all its numbers",
  "statement": "To write a mixed number as an improper fraction you add the whole number to the numerator and keep the denominator.",
  "kind": "procedural-bug",
  "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": "convert a mixed number to an improper fraction",
      "signature": "numerator = whole + numerator; denominator unchanged",
      "example": {
        "item": "Write 2 1/3 as an improper fraction",
        "expected": "7/3",
        "response": "3/3"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Consistent across items. A slip is a wrong product within the multiply-then-add method.",
    "vs": {
      "math.fractions.add-whole-to-numerator": "Same surface result on 2 + 1/3, but this bug is triggered by mixed-number notation, not by a plus sign.",
      "math.fractions.improper-impossible": "Improper-impossible believers refuse to write 7/3 at all."
    }
  },
  "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"
      }
    ],
    "confusable_with": [
      "math.fractions.add-whole-to-numerator",
      "math.fractions.improper-impossible"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "4.NF.B.3",
      "uri": "http://corestandards.org/Math/Content/4/NF/B/3/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "book",
        "citation": "Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon."
      },
      {
        "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"
}