miscon:math.fractions.unequal-parts · draft · trust low · v0.1.2 · kind overgeneralization

Any part of a shape cut into b pieces is 1/b

If a shape is cut into b pieces, each piece is one b-th of the shape, whether or not the pieces are the same size.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.unequal-parts
UUID
e7a0875c-e339-4404-9f39-1f73cfe9206f
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 unequal parts

counts pieces and writes shaded/total, ignoring the sizes of the pieces

ItemA rectangle is cut into 4 pieces of different sizes; the largest is shaded. What fraction is shaded?
ExpectedCannot tell from the count; it is more than 1/4
Response1/4

Pattern 1: judge whether a shape shows a given fraction

accepts an unequal partition as showing the fraction

ItemDoes this circle, cut into 3 pieces of different sizes with 1 shaded, show 1/3?
ExpectedNo, the parts are not equal
ResponseYes

Discriminators

vs a slip. Ask directly whether the pieces need to be the same size. A slip is a miscount with equal parts assumed; the belief is a stated 'it doesn't matter, there are four pieces'.

vs math.fractions.part-to-part. Use a shape with equal parts. Part-to-part writers give 3/2 for 3 shaded of 5; this belief gives 3/5 correctly and only fails on unequal partitions.

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.part-to-part

Alignments

Provenance

Origin: llm-drafted

  1. Kerslake, D. (1986). Fractions: Children's Strategies and Errors. NFER-Nelson.
  2. Steffe, L. P., & Olive, J. (2010). Children's Fractional Knowledge. Springer. doi:10.1007/978-1-4419-0591-8
    Equipartitioning as a prerequisite scheme for fractional knowledge.
  3. Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3rd ed.). Routledge.

Drafted from the cited literature for the Open Misconceptions seed pack; statement, examples and discriminators are original text. Awaiting maintainer review.

Review status

Status draft, trust low (computed from the reviews below against the reviewer registry).

No reviews yet.

Formats

Cite

miscon:math.fractions.unequal-parts
https://open-misconceptions.github.io/miscon-data/m/math.fractions.unequal-parts