miscon:math.fractions.cancel-matching-digits · draft · trust low · v0.1.1 · kind notation-confusion

Cancelling matching digits

A fraction is simplified by crossing out a digit that appears in both the numerator and the denominator.

Stable URI
https://open-misconceptions.github.io/miscon-data/m/math.fractions.cancel-matching-digits
UUID
9b81e6e0-ad37-42aa-9494-bc6892e7140b
Domain
math.fractions
Level band
middle, secondary
Locale
en
About
CCSS 4.NF.A.1 http://corestandards.org/Math/Content/4/NF/A/1/

Evidence patterns

Pattern 0: simplify a fraction whose numerator and denominator share a digit

deletes the shared digit from both numbers

ItemSimplify 12/24
Expected1/2
Response1/4 (cancelling the 2s)

16/64 = 1/4 and 19/95 = 1/5 happen to be true, which reinforces the rule.

Discriminators

vs a slip. Ask the learner to simplify 16/64 and then 12/24 and explain. The belief is 'the sixes cancel'; a slip has no digit-based rule.

vs math.fractions.equivalence-additive. Additive reasoners subtract from both parts; digit cancellers delete a digit and leave the rest.

Relations

conflicts_with
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/
resolved_by
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/
confusable_with
math.fractions.equivalence-additive

Alignments

Provenance

Origin: llm-drafted

  1. Ashlock, R. B. (2010). Error Patterns in Computation: Using Error Patterns to Help Each Student Learn (10th ed.). Allyn & Bacon.
  2. Brown, J. S., & VanLehn, K. (1980). Repair theory: A generative theory of bugs in procedural skills. Cognitive Science, 4(4), 379-426. doi:10.1207/s15516709cog0404_3
    Repair theory: bugs formed by over-literal reading of a procedure's surface form.

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.cancel-matching-digits
https://open-misconceptions.github.io/miscon-data/m/math.fractions.cancel-matching-digits