miscon:math.fractions.of-quantity-swap-roles · draft · trust low · v0.1.1 · kind procedural-bug

Swapping numerator and denominator when finding a fraction of a quantity

To find a/b of a quantity you divide the quantity by a and multiply by b.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.of-quantity-swap-roles
UUID
721c3f30-4b4e-4ffb-ac77-3433d1a18164
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 4.NF.B.4 http://corestandards.org/Math/Content/4/NF/B/4/

Evidence patterns

Pattern 0: find a non-unit fraction of a whole-number quantity

divides by the numerator and multiplies by the denominator

ItemFind 3/4 of 20
Expected15
Response26 2/3 (20 / 3 x 4)

Pattern 1: find a unit fraction of a quantity

divides by 1 and multiplies by the denominator

ItemFind 1/5 of 30
Expected6
Response150

Discriminators

vs a slip. The answer is larger than the original quantity for a proper fraction and the learner does not object. A slip is a wrong division or multiplication within the right method.

Relations

conflicts_with
CCSS 4.NF.B.4: multiply a fraction by a whole number http://corestandards.org/Math/Content/4/NF/B/4/
resolved_by
CCSS 4.NF.B.4: multiply a fraction by a whole number http://corestandards.org/Math/Content/4/NF/B/4/
CCSS 3.NF.A.1: understand a fraction 1/b as one part of a whole partitioned into b equal parts http://corestandards.org/Math/Content/3/NF/A/1/

Alignments

Provenance

Origin: llm-drafted

  1. Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)
    CSMS fractions: errors on 'fraction of a quantity' items.
  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

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Formats

Cite

miscon:math.fractions.of-quantity-swap-roles
https://open-misconceptions.github.io/miscon-data/m/math.fractions.of-quantity-swap-roles