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Grade 5 Math
Grade Level
Content Expectations
At the end of Grade 5 students should be
proficient in the following areas:
Understand division of whole numbers
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N.MR.05.01 |
Understand the meaning of division
of whole numbers with and without remainders;
relate division to fractions and to repeated subtraction. |
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N.MR.05.02 |
Relate division of whole numbers with remainders to the form
a = bq + r, e.g., 34 ÷ 5 = 6 r 4, so 5 · 6 + 4 = 34; note remainder (4) is less
than divisor (5). |
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N.MR.05.03 |
Write mathematical statements involving division for given
situations. |
Multiply and
divide whole numbers
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N.FL.05.04 |
Multiply a multi-digit number by a two-digit number; recognize
and be able to
explain common computational errors such as not accounting for place value. |
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N.FL.05.05 |
Solve applied problems involving multiplication and
division of whole numbers.* |
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N.FL.05.06 |
Divide fluently up to a four-digit number by a two-digit
number. |
Find prime factorizations of whole numbers
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N.MR.05.07 |
Find the prime factorization of
numbers from 2 through 50, express in exponential
notation, e.g., 24 = 23 x 31, and understand that every whole
number greater than 1 is
either prime or can be expressed as a product of primes.* |
Understand meaning of decimal fractions and percentages
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N.ME.05.08 |
Understand the relative magnitude of ones, tenths, and
hundredths and the
relationship of each place value to the place to its right, e.g., one is 10
tenths, one
tenth is 10
hundredths. |
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N.ME.05.09 |
Understand percentages as parts out of 100, use % notation,
and express a part
of a whole as a percentage. |
Understand fractions as division statements: find equivalent
fractions
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N.ME.05.10 |
Understand a fraction as a statement of division, e.g., 2 ÷ 3
= , using simple
fractions and pictures to represent. |
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N.ME.05.11 |
Given two fractions, e.g., and , express them as
fractions with a common
denominator, but not necessarily a least common denominator, e.g., =
and = ; use
denominators less than 12 or factors of 100.* |
Multiply and divide fractions
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N.ME.05.12 |
Find the product of two unit fractions with small
denominators using an area model.* |
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N.MR.05.13 |
Divide a fraction by a whole number and a whole
number by a fraction, using simple
unit fractions.* |
Add and
subtract
fractions using common denominators
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N.FL.05.14 |
Add and subtract fractions with unlike denominators through
12 and/or 100, using
the common denominator that is the product of the denominators of the 2
fractions,
e.g.,
+ : use 80 as the common denominator.* |
Multiply and divide by powers of ten
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N.MR.05.15 |
Multiply a whole number by powers of 10: 0.01, 0.1, 1, 10,
100, 1,000; and
identify patterns. |
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N.FL.05.16 |
Divide numbers by 10's, 100's, 1,000's using mental
strategies. |
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N.MR.05.17 |
Multiply one-digit and two-digit whole numbers by decimals up
to two decimal places. |
Solve applied problems with fractions
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N.FL.05.18 |
Use mathematical statements to represent an applied
situation involving addition and
subtraction of fractions.* |
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N.MR.05.19 |
Solve contextual problems that involve finding sums and
differences of fractions with
unlike denominators using knowledge of equivalent fractions.* |
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N.FL.05.20 |
Solve applied problems involving fractions and decimals;
include rounding of answers
and checking reasonableness.* |
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N.MR.05.21 |
Solve for the unknown in equations such as 14 +
x = 712 .* |
Express, interpret, and use ratios; find equivalences
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N.MR.05.22 |
Express fractions and decimals as percentages and vice versa. |
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N.ME.05.23 |
Express ratios in several ways given applied situations, e.g.,
3 cups to 5 people,
3 : 5, 3 ; recognize and find equivalent ratios. |
Know, and convert among, measurement units within a given system
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M.UN.05.01 |
Recognize the equivalence of 1 liter, 1,000 ml and 1,000 cm3
and include
conversions among liters, milliliters, and cubic centimeters. |
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M.UN.05.02 |
Know the units of measure of volume: cubic centimeter, cubic
meter, cubic inches,
cubic feet, cubic yards, and use their abbreviations (cm3, m3, in3, ft3, yd3). |
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M.UN.05.03 |
Compare the relative sizes of one cubic inch to one cubic
foot, and one
cubic
centimeter to one cubic meter. |
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M.UN.05.04 |
Convert measurements of length, weight, area, volume, and time
within a given
system using easily manipulated numbers. |
Find areas
of geometric shapes using formulas
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M.PS.05.05 |
Represent relationships between areas of rectangles,
triangles, and parallelograms
using models. |
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M.TE.05.06 |
Understand and know how to use the area formula of a triangle:A = bh (where b is
length of the base and h is the height), and represent using
models and
manipulatives. |
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M.TE.05.07 |
Understand and know how to use the area formula for a
parallelogram:
A = bh, and represent using models and manipulatives. |
Understand the concept of volume
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M.TE.05.08 |
Build solids with unit cubes and state their volumes. |
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M.TE.05.09 |
Use filling (unit cubes or liquid), and counting or measuring
to find the volume of a
cube and rectangular prism. |
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M.PS.05.10 |
Solve applied problems about the volumes of rectangular prisms
using
multiplication and division and using the appropriate units. |
Know the meaning of angles, and solve problems
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G.TR.05.01 |
Associate an angle with a certain amount of turning; know that
angles are
measured
in degrees; understand that 90°, 180°, 270°, and 360° are associated
respectively,
with 14 , 12 , and 34 , and full turns |
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G.GS.05.02 |
Measure angles with a protractor and classify them as acute,
right, obtuse,
or straight. |
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G.GS.05.03 |
Identify and name angles on a straight line and vertical
angles. |
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G.GS.05.04 |
Find unknown angles in problems involving angles on a straight
line, angles
surrounding a point, and vertical angles. |
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G.GS.05.05 |
Know that angles on a straight line add up to 180° and angles
surrounding a
point add up to 360°; justify informally by "surrounding" a point with angles. |
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G.GS.05.06 |
Understand why the sum of the interior angles of a triangle is
180° and the sum
of the interior angles of a quadrilateral is 360°, and use these properties to
solve problems. |
Solve problems about geometric shapes
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G.GS.05.07 |
Find unknown angles and sides using the properties of:
triangles, including right,
isosceles, and equilateral triangles; parallelograms, including rectangles and
rhombuses;
and trapezoids. |
Construct and interpret line graphs
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D.RE.05.01 |
Read and interpret line graphs, and solve problems based on
line graphs, e.g.,
distance-time graphs, and problems with two or three line graphs on same axes,
comparing different data. |
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D.RE.05.02 |
Construct line graphs from tables of data; include axis labels
and scale. |
Find and interpret mean and mode for a given set of data
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D.AN.05.03 |
Given a set of data, find and interpret the mean (using the
concept of fair share)
and mode. |
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D.AN.05.04 |
Solve multi-step problems involving means. |
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