miscon:math.fractions.part-to-part · draft · trust low · v0.1.1 · kind notation-confusion

Writing the shaded part over the unshaded part

A fraction compares the shaded part with the unshaded part, so the number of shaded pieces goes on top and the number of unshaded pieces goes underneath.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.part-to-part
UUID
15a57c88-bbde-47b3-bd0d-6771a62e6cec
Domain
math.fractions
Level band
early-primary, primary
Locale
en
About
CCSS 3.NF.A.1 http://corestandards.org/Math/Content/3/NF/A/1/

Evidence patterns

Pattern 0: name the fraction shaded in a shape divided into equal parts

writes shaded/unshaded instead of shaded/total

ItemA bar is cut into 5 equal parts and 3 are shaded. What fraction is shaded?
Expected3/5
Response3/2

Discriminators

vs a slip. Consistent across items, and the learner produces 'fractions' larger than one for a majority-shaded shape without noticing. A slip is one miswritten denominator.

vs math.fractions.unequal-parts. Unequal-parts believers write the correct denominator (the total count) on equal-parts shapes; part-to-part writers do not.

Relations

conflicts_with
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/
resolved_by
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/
confusable_with
math.fractions.unequal-parts

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 items: part-part responses on shaded-region tasks.
  2. Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson.
  3. Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge.
    Distinguishes part-whole from ratio (part-part) interpretations.

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.part-to-part
https://open-misconceptions.github.io/miscon-data/m/math.fractions.part-to-part