
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 differentsized 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).
