Grade 5
Standards
Continue to address the grades PreK-4
standards as needed.
Number
Sense and Operations
Students engage in problem solving,
communicating, reasoning, connecting, and representing as
they:
5.N.1 Demonstrate an understanding of (positive
integer) powers of ten, e.g., 102,
105.
5.N.2 Demonstrate an understanding of place
value through millions and thousandths.
5.N.3 Represent and compare large (millions)
and small (thousandths) positive numbers in various forms, such as expanded
notation without exponents, e.g., 9724 = 9 x 1000 + 7 x 100 + 2 x 10 +
4.
5.N.4 Demonstrate an understanding of fractions
as a ratio of whole numbers, as parts of unit wholes, as parts of a collection,
and as locations on the number line.
This standard is intentionally the same as
standard 6.N.4.
5.N.5 Identify and determine common equivalent
fractions (with denominators 2, 4, 5, 10) and mixed numbers (with denominators
2, 4, 5, 10), decimals, and percents (through one hundred percent), e.g.,
3/4 = 0.75 = 75%.
5.N.6 Find and position whole numbers, positive
fractions, positive mixed numbers, and positive decimals on a number
line.
5.N.7 Compare and order whole numbers, positive
fractions, positive mixed numbers, positive decimals, and
percents.
5.N.8 Apply the number theory concepts of
common factor, common multiple, and divisibility rules for 2, 3, 5, and 10 to
the solution of problems. Demonstrate an understanding of the concepts of prime
and composite numbers.
5.N.9 Solve problems involving multiplication
and division of whole numbers, and multiplication of positive fractions with
whole numbers.
5.N.10
Demonstrate an understanding of how parentheses affect expressions
involving addition, subtraction, and multiplication, and use that understanding
to solve problems, e.g., 3 x (4 + 2) = 3 x 6.
5.N.11
Demonstrate an understanding of the inverse relationship of addition and
subtraction, and use that understanding to simplify computation and solve
problems.
This standard is
intentionally the same as standard 6.N.12.
5.N.12
Accurately and efficiently add and subtract whole numbers and positive
decimals. Multiply and divide (using double-digit divisors) whole numbers.
Multiply positive decimals with whole numbers.
5.N.13
Accurately and efficiently add and subtract positive fractions and mixed
numbers with like denominators and with unlike denominators (2, 4, 5, 10 only);
multiply positive fractions with whole numbers. Simplify fractions in cases when
both the numerator and the denominator have 2, 3, 4, 5, or 10 as a common
factor.
5.N.14
Estimate sums and differences of whole numbers, positive fractions, and
positive decimals. Estimate products of whole numbers and products of positive
decimals with whole numbers. Use a variety of strategies and judge the
reasonableness of the answer.
Patterns,
Relations, and Algebra
Students engage in problem solving,
communicating, reasoning, connecting, and representing as
they:
5.P.1 Analyze and determine the rules for
extending symbolic, arithmetic, and geometric patterns and progressions, e.g.,
ABBCCC; 1, 5, 9, 13…; 3, 9, 27...
This
standard is intentionally the same as standard 6.P.1.
5.P.2 Replace variables with given values and
evaluate/simplify, e.g., 2(m) + 3 when m = 4.
This standard is intentionally the same as
standard 6.P.2.
5.P.3 Use the properties of equality to solve
problems with whole numbers, e.g., if o + 7 = 13, then o = 13 – 7, therefore o = 6 ; if 3 x o = 15, then o = 15 ÷ 3, therefore o = 5.
5.P.4 Represent real situations and
mathematical relationships with concrete models, tables, graphs, and rules in
words and with symbols, e.g., input-output tables.
This standard is intentionally the same as
standard 6.P.4.
5.P.5 Solve problems involving proportional
relationships using concrete models, tables, graphs, and paper-pencil
methods.
5.P.6 Interpret graphs that represent the
relationship between two variables in everyday situations.
Geometry
Students engage in problem solving,
communicating, reasoning, connecting, and representing as
they:
5.G.1 Identify, describe, and compare special
types of triangles (isosceles, equilateral, right) and quadrilaterals (square,
rectangle, parallelogram, rhombus, trapezoid), e.g., recognize that all
equilateral triangles are isosceles, but not all isosceles triangles are
equilateral.
5.G.2 Identify, describe, and compare special
types of three-dimensional shapes (cubes, prisms, spheres, pyramids) based on
their properties, such as edges and faces.
5.G.3 Identify relationships among points and
lines, e.g., intersecting, parallel, perpendicular.
5.G.4 Using ordered pairs of whole numbers
(including zero), graph, locate, and identify points, and describe paths on the
Cartesian coordinate plane.
5.G.5 Describe and perform transformations on
two-dimensional shapes, e.g., translations, rotations, and
reflections.
5.G.6 Identify and describe line symmetry in
two-dimensional shapes, including shapes that have multiple lines of
symmetry.
5.G.7 Determine if two triangles or two
quadrilaterals are congruent by measuring sides or a combination of sides and
angles, as necessary; or by motions
or series of motions, e.g., translations, rotations, and
reflections.
Measurement
Students engage in problem solving,
communicating, reasoning, connecting, and representing as
they:
5.M.1 Apply the concepts of perimeter and area
to the solution of problems involving triangles and rectangles. Apply formulas
where appropriate.
5.M.2 Identify, measure, describe, classify,
and draw various angles. Draw triangles given two sides and the angle between
them, or given two angles and the side between them, e.g., draw a triangle with
one right angle and two sides congruent.
5.M.3 Solve problems involving simple unit
conversions within a system of measurement.
5.M.4 Find volumes and surface areas of
rectangular prisms.
This standard is
intentionally the same as standard 6.M.6.
5.M.5 Find the sum of the measures of the
interior angles in triangles by measuring the angles, and without measuring the
angles.
Data
Analysis, Statistics, and Probability
Students engage in problem solving,
communicating, reasoning, connecting, and representing as
they:
5.D.1 Given a set of data, find the median,
mean, mode, maximum, minimum, and range, and apply to solutions of
problems.
5.D.2 Construct and interpret line plots, line
graphs, and bar graphs. Interpret and label circle graphs.
5.D.3 Predict the probability of outcomes of
simple experiments (e.g., tossing a coin, rolling a number cube) and test the
predictions.