{
  "id": "math.fractions.equivalence-additive",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.equivalence-additive",
  "uuid": "5aadfc6d-33f3-4336-908b-02c278e40508",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "Equivalent fractions by adding the same number",
  "statement": "You get an equivalent fraction by adding the same number to the numerator and the denominator, or by subtracting the same number from both.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "4.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/4/NF/A/1/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "complete an equivalent fraction with a given denominator",
      "signature": "adds the difference in denominators to the numerator",
      "example": {
        "item": "2/3 = ?/6",
        "expected": "4/6",
        "response": "5/6"
      }
    },
    {
      "item_shape": "simplify a fraction",
      "signature": "subtracts the same number from numerator and denominator",
      "example": {
        "item": "Simplify 6/8",
        "expected": "3/4",
        "response": "5/7 (or 4/6)"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Consistent across items; the learner defends it as 'you have to do the same to both'. A slip is a single wrong numerator with multiplicative reasoning elsewhere.",
    "vs": {
      "math.fractions.cancel-matching-digits": "Digit cancellers only act when a digit repeats (16/64); additive reasoners act on any fraction."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/A/1/",
        "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/4/NF/A/1/",
        "label": "CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b)"
      }
    ],
    "confusable_with": [
      "math.fractions.cancel-matching-digits"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "4.NF.A.1",
      "uri": "http://corestandards.org/Math/Content/4/NF/A/1/",
      "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: additive strategies on equivalence items."
      },
      {
        "type": "book",
        "citation": "Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson."
      },
      {
        "type": "paper",
        "citation": "Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341.",
        "doi": "10.5951/jresematheduc.15.5.0323"
      },
      {
        "type": "book",
        "citation": "Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge.",
        "note": "Additive versus multiplicative reasoning."
      }
    ],
    "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"
}