miscon:math.fractions.divide-larger-by-smaller · draft · trust low · v0.1.1 · kind overgeneralization

You can only divide a larger number by a smaller one

In a division the bigger number must be divided by the smaller number, so if the divisor is bigger the two numbers should be swapped.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.divide-larger-by-smaller
UUID
78a649f3-688d-49a2-a85c-7be491860757
Domain
math.fractions
Level band
primary, middle, adult
Locale
en
About
CCSS 6.NS.A.1 http://corestandards.org/Math/Content/6/NS/A/1/

Evidence patterns

Pattern 0: divide a fraction by a larger whole number

swaps dividend and divisor so that the larger number is divided by the smaller

Item1/2 / 3 = ?
Expected1/6
Response6

Pattern 1: write the division for a word problem where the dividend is smaller than the divisor

writes the numbers in the order that makes the dividend larger

Item3/4 of a litre is shared equally between 3 people. Write the division.
Expected3/4 / 3
Response3 / 3/4

Discriminators

vs a slip. A slip is one reversed pair. The belief is a stated rule ('you can't divide a small number by a big one') and is applied to whole numbers too (3 / 12 rewritten as 12 / 3).

vs math.fractions.divide-makes-smaller. Divide-makes-smaller keeps the order and gets a smaller wrong result; this belief changes the order.

Relations

conflicts_with
CCSS 6.NS.A.1: interpret and compute quotients of fractions http://corestandards.org/Math/Content/6/NS/A/1/
resolved_by
CCSS 6.NS.A.1: interpret and compute quotients of fractions http://corestandards.org/Math/Content/6/NS/A/1/
CCSS 5.NF.B.7: divide unit fractions by whole numbers and whole numbers by unit fractions http://corestandards.org/Math/Content/5/NF/B/7/

Alignments

Provenance

Origin: llm-drafted

  1. Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17. doi:10.5951/jresematheduc.16.1.0003
  2. Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102. doi:10.5951/jresematheduc.20.1.0095
    Preservice teachers reversing dividend and divisor so the divisor is smaller.
  3. Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25. doi:10.2307/749817

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

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Cite

miscon:math.fractions.divide-larger-by-smaller
https://open-misconceptions.github.io/miscon-data/m/math.fractions.divide-larger-by-smaller