miscon:math.fractions.no-number-between · draft · trust low · v0.1.1 · kind overgeneralization

No number between neighbouring fractions

Fractions come one after another like whole numbers, so between two fractions that are 'next to each other' there is no other number.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.no-number-between
UUID
a18f0879-fc85-4c07-8da5-d1e68e72c460
Domain
math.fractions
Level band
middle, secondary
Locale
en
About
CCSS 6.NS.C.6 http://corestandards.org/Math/Content/6/NS/C/6/

Evidence patterns

Pattern 0: ask how many numbers lie between two fractions

answers none, or a small finite count found by listing

ItemHow many numbers are there between 1/5 and 2/5?
ExpectedInfinitely many
ResponseNone

Pattern 1: ask for a fraction between two given fractions with consecutive numerators

says there is none, or gives one only by changing to a bigger denominator and then says that is the only one

ItemName a fraction between 3/7 and 4/7
Expectedany of 7/14 ... e.g. 1/2
ResponseThere isn't one

Discriminators

vs a slip. A slip is failing to find one on a single item. The belief is a stated rule ('there's nothing between them') that survives being shown an example, or is repaired to 'there are a few, but not infinitely many'.

Relations

conflicts_with
CCSS 6.NS.C.6: understand a rational number as a point on the number line http://corestandards.org/Math/Content/6/NS/C/6/
resolved_by
CCSS 6.NS.C.6: understand a rational number as a point on the number line http://corestandards.org/Math/Content/6/NS/C/6/
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/
specializes
math.fractions.two-whole-numbers

Alignments

Provenance

Origin: llm-drafted

  1. Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: A conceptual change approach. Learning and Instruction, 14(5), 453-467. doi:10.1016/j.learninstruc.2004.06.013
    Discreteness of the rational number set as a synthetic model carried over from natural numbers.
  2. Vamvakoussi, X., & Vosniadou, S. (2010). How many decimals are there between two fractions? Aspects of secondary school students' understanding of rational numbers and their notation. Cognition and Instruction, 28(2), 181-209. doi:10.1080/07370001003676603
  3. Van Hoof, J., Verschaffel, L., & Van Dooren, W. (2015). Inappropriately applying natural number properties in rational number tasks: Characterizing the development of the natural number bias through primary and secondary education. Educational Studies in Mathematics, 90(1), 39-56. doi:10.1007/s10649-015-9613-3

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.no-number-between
https://open-misconceptions.github.io/miscon-data/m/math.fractions.no-number-between