Fractions: Concepts and Computation

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FractionsConcepts and Computation
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• Mathematics Methods
• Dr. Dawn Parker

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Pattern Block Fraction Puzzles

• Puzzle 1
• Build a triangle that is one-third green and
  two-thirds red.
• Puzzle 2
• Build a triangle that is two-thirds red,
  one-ninth green, and two-ninths blue.
• Puzzle 3
• Build a parallelogram that is three-fourths blue
  and one-fourth green.

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Models for Fractions

• Region or Area Models
• Pie pieces
• Geoboards
• Pattern Blocks
• Drawings on Grid Paper
• Length or Measurement Models
• Number Lines
• Cuisenaire Rods
• Folded Paper Strips
• Set Models
• Drawings using Xs and Os
• Two Color Counters
• Objects of various shapes or colors

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Fractional-Parts Counting
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• Counting fractional parts to see how multiple
  parts compare to the whole creates a foundation
  for the two parts of a fraction.
• As students count each collection of parts,
  discuss the relationship to one whole. Take this
  opportunity to lay verbal groundwork for
  understanding fractions and mixed fractions.

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Top and Bottom Numbers

• The way we write fractions with a top and bottom
  number and a bar between them is a convention
  that is taught to students.
• Convention should be made clear by the use of
  demonstrations with students explaining what the
  top number and bottom number stand for
• Top numberThis is the counting number. It tells
  how many shares or parts we have. It tells how
  many have been counted.
• Bottom numberThis tells what is being counted.
  It tells what fractional part is being counted.
  If it is a 4, it means we are counting fourths.
• (Top NumberCounts)
• (Bottom NumberWhat is being counted)

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Numerator and Denominator

• To count a set is to enumerate it. Enumeration
  is the process of counting. The common name for
  the top number of a fraction is the numerator.
• Denomination is used to differentiate among
  branches of religions. It names a class or type
  of thing. The common name for the bottom of a
  fraction is the denominator.

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Fraction Number Sense

• Number sense with fractions requires that
  students have some intuitive feel for fractions.
  Students should know about how big a particular
  fraction is and be able to tell easily which of
  two fractions is larger.
• Benchmarks of Zero, One-Half, and One
• Bigger, Smaller, Equal (Equivalent)
• Use terms like lowest terms, or simplest
  termsrather than reduce (writing fractions in
  lowest terms is a separate issue than performing
  computations)