miscon:math.fractions.add-whole-to-numerator · draft · trust low · v0.1.1 · kind procedural-bug

Adding a whole number to the numerator

To add a whole number and a fraction you add the whole number to the numerator.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-whole-to-numerator
UUID
692fc169-3842-429b-bf5a-36be6eb6e910
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 a whole number and a proper fraction

adds the whole number to the numerator and keeps the denominator

Item2 + 1/3 = ?
Expected2 1/3 (= 7/3)
Response3/3 (= 1)

Discriminators

vs a slip. The result is smaller than the whole-number addend and the learner accepts it, consistently. A slip is not repeated across items.

vs math.fractions.mixed-to-improper-add-all. That bug adds all three numbers when converting a mixed number; this one appears when a whole number and fraction are added with a plus sign.

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.mixed-to-improper-add-all

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.
  3. Braithwaite, D. W., Pyke, A. A., & Siegler, R. S. (2017). A computational model of fraction arithmetic. Psychological Review, 124(5), 603-625. doi:10.1037/rev0000072

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.add-whole-to-numerator
https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-whole-to-numerator