{
  "id": "math.fractions.number-line-whole-is-line",
  "uri": "https://open-misconceptions.github.io/miscon-data/m/math.fractions.number-line-whole-is-line",
  "uuid": "fb647fd2-a6ef-40a4-a0ac-abd0d497e750",
  "version": "0.1.1",
  "status": "draft",
  "trust": "low",
  "title": "The whole line is the whole",
  "statement": "On a number line the fraction refers to the whole line drawn, so 1/2 is at the middle of the line wherever the line ends.",
  "kind": "overgeneralization",
  "domain": "math.fractions",
  "about": [
    {
      "scheme": "CCSS",
      "code": "3.NF.A.2",
      "uri": "http://corestandards.org/Math/Content/3/NF/A/2/"
    }
  ],
  "level_band": [
    "primary",
    "middle"
  ],
  "locale": "en",
  "evidence_patterns": [
    {
      "item_shape": "place a fraction on a number line longer than one unit",
      "signature": "places the fraction at that fraction of the whole drawn segment rather than of the unit interval",
      "example": {
        "item": "Mark 1/2 on a number line from 0 to 3",
        "expected": "halfway between 0 and 1",
        "response": "at 1 1/2, the middle of the line"
      },
      "notes": "On a 0-to-2 line the two placements for 1/2 differ (1/2 vs 1); on 0-to-1 they coincide, so 0-to-1 lines cannot detect this belief."
    },
    {
      "item_shape": "read the fraction shown by a point on a number line longer than one unit",
      "signature": "reports the point's position as a fraction of the drawn line",
      "example": {
        "item": "A point is at 1 1/2 on a line from 0 to 3. What number is it?",
        "expected": "1 1/2",
        "response": "1/2"
      }
    }
  ],
  "discriminators": {
    "vs_slip": "Correct on 0-to-1 lines and wrong on longer lines, consistently. A slip has no such dependence on line length.",
    "vs": {
      "math.fractions.two-whole-numbers": "Learners who see a fraction as two whole numbers fail 0-to-1 lines too, placing 3/4 at 3 or 4."
    }
  },
  "relations": {
    "conflicts_with": [
      {
        "external": "http://corestandards.org/Math/Content/3/NF/A/2/",
        "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"
      }
    ],
    "resolved_by": [
      {
        "external": "http://corestandards.org/Math/Content/3/NF/A/2/",
        "label": "CCSS 3.NF.A.2: understand a fraction as a number on the number line"
      },
      {
        "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.two-whole-numbers"
    ]
  },
  "alignments": [
    {
      "scheme": "CCSS",
      "code": "3.NF.A.2",
      "uri": "http://corestandards.org/Math/Content/3/NF/A/2/",
      "relation": "about"
    }
  ],
  "provenance": {
    "sources": [
      {
        "type": "paper",
        "citation": "Bright, G. W., Behr, M. J., Post, T. R., & Wachsmuth, I. (1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19(3), 215-232.",
        "doi": "10.5951/jresematheduc.19.3.0215",
        "note": "Number-line tasks: students using the whole line rather than the unit interval."
      },
      {
        "type": "book",
        "citation": "Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)"
      }
    ],
    "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"
}