miscon:math.fractions.improper-impossible · draft · trust low · v0.1.1 · kind undergeneralization

A fraction cannot be more than one whole

A fraction is always part of one whole, so the numerator can never be bigger than the denominator and a fraction can never be greater than 1.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.improper-impossible
UUID
5211ad46-cba5-4c3d-92ff-9fa79d9ed753
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 4.NF.B.3 http://corestandards.org/Math/Content/4/NF/B/3/

Evidence patterns

Pattern 0: add two proper fractions whose sum exceeds one

adjusts the result so it stays below or equal to one

Item3/4 + 3/4 = ?
Expected6/4 (= 1 1/2)
Response6/8 (or 1)

Pattern 1: place an improper fraction on a number line

places it below 1 or says it cannot be placed

ItemMark 5/4 on a number line from 0 to 2
Expectedone quarter past 1
Responsejust below 1 (or 'not a real fraction')

Discriminators

vs a slip. Ask directly whether 7/4 is a number. A slip is an arithmetic error; the belief is the stated rule 'the top can't be bigger than the bottom'.

vs math.fractions.mixed-to-improper-add-all. That bug accepts improper fractions but converts to them wrongly; this belief rejects them.

Relations

conflicts_with
CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b http://corestandards.org/Math/Content/4/NF/B/3/
resolved_by
CCSS 4.NF.B.3: understand a fraction a/b with a > 1 as a sum of fractions 1/b http://corestandards.org/Math/Content/4/NF/B/3/
CCSS 3.NF.A.2: understand a fraction as a number on the number line http://corestandards.org/Math/Content/3/NF/A/2/
confusable_with
math.fractions.mixed-to-improper-add-all

Alignments

Provenance

Origin: llm-drafted

  1. Stafylidou, S., & Vosniadou, S. (2004). The development of students' understanding of the numerical value of fractions. Learning and Instruction, 14(5), 503-518. doi:10.1016/j.learninstruc.2004.06.015
    A developmental stage in which fractions are understood as always smaller than the unit.
  2. Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson.
  3. Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)

Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review.

Review status

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Formats

Cite

miscon:math.fractions.improper-impossible
https://open-misconceptions.github.io/miscon-data/m/math.fractions.improper-impossible