miscon:math.fractions.add-numerators-keep-denominator · draft · trust low · v0.1.1 · kind overgeneralization

Adding numerators and keeping one denominator

To add fractions you add the numerators and keep the denominator, whichever denominator is written, because the denominator is just a label that does not take part in the sum.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-numerators-keep-denominator
UUID
434a29b0-8c52-4db3-a2d6-81c86e5e5d6c
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: add two fractions with unlike denominators

response numerator = a + c; response denominator is one of the given denominators (usually the first or the larger), with no conversion of the addends

Item1/2 + 1/3
Expected5/6
Response2/3

Like-denominator items are answered correctly, which is the discriminator against math.fractions.add-across.

Discriminators

vs a slip. Consistent across unlike-denominator items; the learner can state the rule ("the bottom stays") when asked.

vs math.fractions.add-across. Give a like-denominator item. This belief answers 1/4 + 2/4 = 3/4 correctly; add-across gives 3/8.

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/
confusable_with
math.fractions.add-across

Alignments

Provenance

Origin: literature

  1. Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.
  2. Ni, Y., & Zhou, Y.-D. (2005). Teaching and learning fraction and rational numbers: The origins and implications of whole number bias. Educational Psychologist, 40(1), 27-52. doi:10.1207/s15326985ep4001_3

Stub created so that math.fractions.add-across's discriminator resolves. Needs a second evidence pattern and review.

Review status

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Formats

Cite

miscon:math.fractions.add-numerators-keep-denominator
https://open-misconceptions.github.io/miscon-data/m/math.fractions.add-numerators-keep-denominator