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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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