miscon:math.fractions.mixed-to-improper-add-all · draft · trust low · v0.1.1 · kind procedural-bug

Converting a mixed number by adding all its numbers

To write a mixed number as an improper fraction you add the whole number to the numerator and keep the denominator.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.mixed-to-improper-add-all
UUID
be94771a-f7b8-4af6-acb3-a3fe723a0d20
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: convert a mixed number to an improper fraction

numerator = whole + numerator; denominator unchanged

ItemWrite 2 1/3 as an improper fraction
Expected7/3
Response3/3

Discriminators

vs a 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.

vs math.fractions.improper-impossible. Improper-impossible believers refuse to write 7/3 at all.

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/
confusable_with
math.fractions.add-whole-to-numerator
math.fractions.improper-impossible

Alignments

Provenance

Origin: llm-drafted

  1. Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.
  2. Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson.

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

Review status

Status draft, trust low (computed from the reviews below against the reviewer registry).

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Formats

Cite

miscon:math.fractions.mixed-to-improper-add-all
https://open-misconceptions.github.io/miscon-data/m/math.fractions.mixed-to-improper-add-all