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Nuts & Bolts: Fractions and Decimals Continuum

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Fractions and Decimals Continuum

Fractions (Fair Shares)

  • Realizes that fractional parts must be equal (e.g. one third is not just one of three parts but one of three equal parts).
  • Develops familiarity with conventional fraction words and notation (though students can write their solution in any way that communicates accurately; e.g. a student might write 1/2 + 1/4 as "half plus another piece that is half of the half).
  • Becomes familiar with grouping unit fractions, those that have a numerator of one (for example: 1/6 + 1/6 + 1/6 = 3/6
  • Develops familiarity with common equivalents, especially relationships among halves, thirds, and sixths (for example, students exchange 2/6 for 1/3; they may also begin to make exchanges based on 1/6 + 1/3 = 1/2
  • Understands that the relationships that occur between 0 and 1 also occur between any consecutive whole numbers ( 1/2 + 1/6 = 2/3 so 2 1/2 + 1/6 = 2 2/3)
  • Understands the relationship between fractions and division (e.g. by solving problems in which the whole is a number of things rather than a single thing, and the fractional part is a group of things as well, as in 1/3 of 6 is 2).
  • Relates notation for common fractions (1/2, 1/4, 3/4, 1/5, 1/10) with notation for decimals on the calculator (0.5, 0.25, 0.75, 0.2, 0.1)
  • Uses different notations for the same problem ( e.g. 6 2 and 1/2 of 6)
  • Uses logical reasoning and number sense to identify a number (Ten Minute Math).
  • Develops flexibility in solving problems by finding several ways to reach a solution (Ten Minute Math).

 

Fractions and Area (Different Shapes, Equal Pieces)

  • Understands that equal fractions of a whole have the same area but are not necessarily congruent.
  • Experiences that cutting and pasting shapes conserves their area.
  • Becomes familiar with the relationships among halves, fourths, and eighths, and then among thirds, sixths, and twelfths.
  • Knows that equal fractions of different-sized wholes will be different in area.
  • Uses different combinations to make a whole.
  • Works with fractions that have numerators larger than one.
  • Compares any fraction to the landmarks 0, 1/2, 1, and 2.
  • Uses both numerical reasoning and areas to order fractions (e.g. 4/9 is smaller than 1/2 because 2 x 4/9 = 8/9 which is less than 1).
  • Uses the size of the numerator to compare fractions that have the same denominator and uses the size of the denominator to compare fractions with the same numerator.
  • Understand the fractions "missing one piece" are ordered inversely to the size of the missing piece (e.g. 2/3 is smaller that 3/4 because the 1/3 missing is larger than the 1/4 missing.
  • Identifies equivalent fractions.
  • Uses logical reasoning and relationships among numbers to guess a number (Ten Minute Math).

 

Fractions, percents, and decimals (Name That Portion)

  • Interprets everyday situations that involve fractions, decimals, and percents
  • Uses fractions and percents to name portions of groups.
  • Breaks fraction, decimals, and percents into familiar parts
  • Approximates data as familiar fractions and percent, and in circle graphs
  • Represents, compares, and orders fractions (common; mixed number; with numerators larger than 1; with different denominators), decimals, and percents using landmark numbers and visual models.
  • Chooses models and notations to compute with fractions, percents, and decimals.
  • Identifies and labels fractions between 0 and 1 on a number line to make an array of fractions
  • Finds patterns in an array of fraction number lines and in a decimal table.
  • Solves word problems and expresses answers to fit the context.
  • Finds decimals that are smaller than, larger than, or in between other decimals.
  • Plans and conducts surveys, and compiles, organizes, and communicates, results.
  • Finds ways to describe number relationships, including fraction notation, factor pairs, and equations(Ten Minute Math).
  • Interprets, poses questions about, and uses fractions to describe data (Ten Minute Math).

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