miscon:math.fractions.equivalence-additive · draft · trust low · v0.1.1 · kind overgeneralization

Equivalent fractions by adding the same number

You get an equivalent fraction by adding the same number to the numerator and the denominator, or by subtracting the same number from both.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.equivalence-additive
UUID
5aadfc6d-33f3-4336-908b-02c278e40508
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 4.NF.A.1 http://corestandards.org/Math/Content/4/NF/A/1/

Evidence patterns

Pattern 0: complete an equivalent fraction with a given denominator

adds the difference in denominators to the numerator

Item2/3 = ?/6
Expected4/6
Response5/6

Pattern 1: simplify a fraction

subtracts the same number from numerator and denominator

ItemSimplify 6/8
Expected3/4
Response5/7 (or 4/6)

Discriminators

vs a slip. Consistent across items; the learner defends it as 'you have to do the same to both'. A slip is a single wrong numerator with multiplicative reasoning elsewhere.

vs math.fractions.cancel-matching-digits. Digit cancellers only act when a digit repeats (16/64); additive reasoners act on any fraction.

Relations

conflicts_with
CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b) http://corestandards.org/Math/Content/4/NF/A/1/
resolved_by
CCSS 4.NF.A.1: explain why a fraction a/b is equivalent to (n x a)/(n x b) http://corestandards.org/Math/Content/4/NF/A/1/
confusable_with
math.fractions.cancel-matching-digits

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: additive strategies on equivalence items.
  2. Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson.
  3. Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341. doi:10.5951/jresematheduc.15.5.0323
  4. Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge.
    Additive versus multiplicative reasoning.

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.equivalence-additive
https://open-misconceptions.github.io/miscon-data/m/math.fractions.equivalence-additive