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Misconceptions of Multiplication and Division
Transcript of Misconceptions of Multiplication and Division
Carry out short division of numbers involving decimals.
Ignore decimal point when calculating, then simply ‘slot back in’. Comes from over generalization of adding decimals.
Find remainders after division
Lack of understanding of WHAT the remainder actually represents, need to see calculation in concrete way, i.e. cubes left over after division.
Know and use halving as the inverse of doubling
Children confuse the words ‘halving’ and ‘doubling’.
Lack of understanding that two operations are linked, often taught separately.
Standard Algorithm ( carried digit )
The small carried digit is often the most difficult, it gets added in before the second multiplication or is forgotten.
Standard Algorithm ( bring down / long division)
The place value of a middle zero is left out, it gets misplaced with another digit or is forgotten
Chapman Kate, Mathematics Organization: National Centre for Excellence in the Teaching of
Mathematics (2006). https://www.ncetm.org.uk/
Karp,Karen S., and Jennifer M. Bay-Williams. “Chapter 13: Developing Strategies for Multiplication &
“Elementary and Middle School Mathematics.” By John A. Van De Walle, 8th ed. N.p.: Pearson, 2013
236-57. “The National Strategies”.
Multiply decimals mentally by 10 or 100, and explain the effect.
Misunderstand the concept of making a number 10/100/1000 times bigger.
Know by heart all multiplication facts up to 10x10.
Children not understand the meaning of ‘lots of’ or ‘groups of’. Children see it as a test of their memory, not linking tables facts.
Understand the operation of multiplication as repeated addition or as describing an array.
Children are sometime display arrays of cubes/objects in an unclear pattern and have a hard time figuring out the solution.
Preventing misconceptions/ errors for Multiplication
Area Model: It supports students understanding and reasoning of multiplication
Partial Product: Students record the products and add using column sheets.
Preventing misconceptions/ errors for Division
Division Algorithm: It introduces one digit divisors. Its useful for students who struggle with the basics
The Explicit Trade method and the use of place value columns help with leaving out a middle zero.
Division Algorithm Example:
Explicit trade method example:
Area Model Example:
Partial Product Example:
75 - 5 = 70
12 - 2 = 10