miscon:math.fractions.multiply-makes-bigger · draft · trust low · v0.1.1 · kind overgeneralization

Multiplication always makes bigger

Multiplying always gives a result larger than the number you started with, so multiplying by a fraction cannot make a number smaller.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-makes-bigger
UUID
04246969-9c77-41b0-a67b-b48be9b2f5a3
Domain
math.fractions
Level band
primary, middle, secondary, adult
Locale
en
About
CCSS 5.NF.B.5 http://corestandards.org/Math/Content/5/NF/B/5/

Evidence patterns

Pattern 0: predict whether a product will be larger or smaller than a factor, without calculating

predicts the product of a number and a proper fraction is larger than the number

ItemWithout calculating, is 8 x 3/4 more or less than 8?
ExpectedLess
ResponseMore

Pattern 1: choose the operation for a word problem with a fractional multiplier

rejects multiplication because the answer must be smaller, and divides instead

ItemA recipe uses 2/3 of a 6-cup bag of flour. How much flour is used? Which operation?
Expected6 x 2/3 = 4
Response6 / 2/3 (or 6 / 2 = 3)

Discriminators

vs a slip. A slip is one wrong prediction. The belief is stated as a rule and generalises to decimals (0.5 x 8 'must be more than 8'); it often coexists with math.fractions.divide-makes-smaller.

vs math.fractions.divide-makes-smaller. Mirror belief; test each separately with prediction items for multiplication and division by a proper fraction.

Relations

conflicts_with
CCSS 5.NF.B.5: interpret multiplication as scaling http://corestandards.org/Math/Content/5/NF/B/5/
resolved_by
CCSS 5.NF.B.5: interpret multiplication as scaling http://corestandards.org/Math/Content/5/NF/B/5/
CCSS 5.NF.B.4: multiply a fraction or whole number by a fraction http://corestandards.org/Math/Content/5/NF/B/4/

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
    Implicit repeated-addition model of multiplication: the product must exceed the multiplicand.
  2. Bell, A., Swan, M., & Taylor, G. (1981). Choice of operation in verbal problems with decimal numbers. Educational Studies in Mathematics, 12(4), 399-420. doi:10.1007/BF00308139
  3. 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
  4. Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction arithmetic. Journal of Educational Psychology, 107(3), 909-918. doi:10.1037/edu0000025
    Direction-of-effect items show adults and children expecting multiplication to increase.

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.multiply-makes-bigger
https://open-misconceptions.github.io/miscon-data/m/math.fractions.multiply-makes-bigger