miscon:math.fractions.subtract-across · draft · trust low · v0.1.1 · kind overgeneralization

Subtracting fractions across numerators and denominators

Fractions are subtracted by subtracting the numerators and subtracting the denominators.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.subtract-across
UUID
f9b8d0fd-1f46-47ac-8fc7-d4923e7ef2c8
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 5.NF.A.1 http://corestandards.org/Math/Content/5/NF/A/1/

Evidence patterns

Pattern 0: subtract two fractions with unlike denominators

difference numerator = a - c and difference denominator = b - d for a/b - c/d

Item3/4 - 1/2 = ?
Expected1/4
Response2/2 (= 1)

Pattern 1: subtract two fractions with like denominators

subtracts denominators to get zero and cannot finish, or writes the numerator difference over 0

Item3/5 - 1/5 = ?
Expected2/5
Response2/0 (or 'impossible')

Discriminators

vs a slip. Like-denominator items are diagnostic: the bug produces a zero denominator and the learner stalls. A slip does not.

vs math.fractions.add-across. Same mechanism for the other operation. Most learners with one have the other; test both.

Relations

conflicts_with
CCSS 5.NF.A.1: add and subtract fractions with unlike denominators http://corestandards.org/Math/Content/5/NF/A/1/
resolved_by
CCSS 5.NF.A.1: add and subtract fractions with unlike denominators http://corestandards.org/Math/Content/5/NF/A/1/

Alignments

Provenance

Origin: llm-drafted

  1. Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296. doi:10.1016/j.cogpsych.2011.03.001
  2. 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
  3. Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.

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.subtract-across
https://open-misconceptions.github.io/miscon-data/m/math.fractions.subtract-across