miscon:math.fractions.number-line-whole-is-line · draft · trust low · v0.1.1 · kind overgeneralization

The whole line is the whole

On a number line the fraction refers to the whole line drawn, so 1/2 is at the middle of the line wherever the line ends.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.number-line-whole-is-line
UUID
fb647fd2-a6ef-40a4-a0ac-abd0d497e750
Domain
math.fractions
Level band
primary, middle
Locale
en
About
CCSS 3.NF.A.2 http://corestandards.org/Math/Content/3/NF/A/2/

Evidence patterns

Pattern 0: place a fraction on a number line longer than one unit

places the fraction at that fraction of the whole drawn segment rather than of the unit interval

ItemMark 1/2 on a number line from 0 to 3
Expectedhalfway between 0 and 1
Responseat 1 1/2, the middle of the line

On a 0-to-2 line the two placements for 1/2 differ (1/2 vs 1); on 0-to-1 they coincide, so 0-to-1 lines cannot detect this belief.

Pattern 1: read the fraction shown by a point on a number line longer than one unit

reports the point's position as a fraction of the drawn line

ItemA point is at 1 1/2 on a line from 0 to 3. What number is it?
Expected1 1/2
Response1/2

Discriminators

vs a slip. Correct on 0-to-1 lines and wrong on longer lines, consistently. A slip has no such dependence on line length.

vs math.fractions.two-whole-numbers. Learners who see a fraction as two whole numbers fail 0-to-1 lines too, placing 3/4 at 3 or 4.

Relations

conflicts_with
CCSS 3.NF.A.2: understand a fraction as a number on the number line http://corestandards.org/Math/Content/3/NF/A/2/
resolved_by
CCSS 3.NF.A.2: understand a fraction as a number on the number line http://corestandards.org/Math/Content/3/NF/A/2/
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.two-whole-numbers

Alignments

Provenance

Origin: llm-drafted

  1. Bright, G. W., Behr, M. J., Post, T. R., & Wachsmuth, I. (1988). Identifying fractions on number lines. Journal for Research in Mathematics Education, 19(3), 215-232. doi:10.5951/jresematheduc.19.3.0215
    Number-line tasks: students using the whole line rather than the unit interval.
  2. Hart, K. M. (Ed.). (1981). Children's Understanding of Mathematics: 11-16. John Murray. (Concepts in Secondary Mathematics and Science project.)

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.number-line-whole-is-line
https://open-misconceptions.github.io/miscon-data/m/math.fractions.number-line-whole-is-line