miscon:math.fractions.invert-both · draft · trust low · v0.1.1 · kind procedural-bug

Inverting both fractions when dividing

To divide fractions you flip both fractions and then multiply.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.invert-both
UUID
aa675277-3fb6-44fe-aad9-20dacc62d775
Domain
math.fractions
Level band
middle, secondary, adult
Locale
en
About
CCSS 6.NS.A.1 http://corestandards.org/Math/Content/6/NS/A/1/

Evidence patterns

Pattern 0: divide two proper fractions

inverts both dividend and divisor and multiplies

Item1/2 / 3/4 = ?
Expected2/3
Response8/3

Discriminators

vs a slip. Consistent across items. A slip produces one inverted-both answer; the bug produces it every time and the learner can recite 'flip them and multiply'.

vs math.fractions.invert-dividend. Invert-dividend gives 6/4 on 1/2 / 3/4; invert-both gives 8/3.

Relations

conflicts_with
CCSS 6.NS.A.1: interpret and compute quotients of fractions http://corestandards.org/Math/Content/6/NS/A/1/
resolved_by
CCSS 6.NS.A.1: interpret and compute quotients of fractions http://corestandards.org/Math/Content/6/NS/A/1/
confusable_with
math.fractions.invert-dividend

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. Newton, K. J. (2008). An extensive analysis of preservice elementary teachers' knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. doi:10.3102/0002831208320851
  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.invert-both
https://open-misconceptions.github.io/miscon-data/m/math.fractions.invert-both