Fifth Grade Math
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Standard 1: The student uses numerical and computational concepts and procedures in a variety of situations. |
Benchmark 1: NUMBER SENSE - The student
demonstrates number sense for rational numbers, pi, and simple algebraic
expressions in one variable in a variety of situations.
Fifth Grade Knowledge Base Indicators
The student:
1. uses a variety of computational methods including mental
arithmetic (doubles and neighbors), paper and pencil, concrete materials,
or technological tools such as calculators and computers.
2. explains and performs whole number division and expresses
remainders as a whole number or a fractional part; addition, subtraction
and multiplication of decimals; addition and subtraction of fractions and
mixed numbers without regrouping and expresses answers in simplest form.
3. finds factors and multiples of whole numbers.
Fifth
Grade Application Indicators
The
student:
1.
uses arithmetic operations and inverse
relationships to formulate and solve real-world problems involving
selected rational numbers.
|
Standard
2: The student uses
algebraic concepts and procedures in a variety of situations. |
Benchmark
1: PATTERNS - The student recognizes,
describes, extends, develops, and explains the general rule of patterns
from a variety of situations.
Fifth
Grade Knowledge Base Indicators
The student:
1. identifies, states, and continues patterns presented in a
variety of formats: numeric,
visual, oral, written, kinesthetic, pictorial, tabular, graphical, or
listing.
2. recognizes patterns involving two changes.
3. creates a pattern.
Special Note: Working with
various types of patterns is an important precursor to working with
functions and sequences in middle school and high school.
Fifth
Grade Application Indicators
The student:
1. generalizes a pattern using a written description.
2. recognizes the same general pattern presented in different
representations.
Benchmark
2: VARIABLES, EQUATIONS, AND
INEQUALITIES - The student uses variables, symbols, rational numbers, and
simple algebraic expressions in one variable to solve linear equations and
inequalities in a variety of situations.
Fifth Grade Knowledge Base Indicators
The student:
1. explains and uses symbols to represent unknown quantities and
variable relationships.
2. explains and uses the following symbols:
=, <, >, ≠, <,
>.
3. solves one-step linear equations involving one unknown.
4. solves one-step linear inequalities involving one unknown.
Fifth
Grade Application Indicators
The student:
1. uses symbols, variables, inequalities, and equations to
represent problems involving variable situations and unknown quantities.
2. formulates and solves problems involving linear relationships
and unknown quantities.
Benchmark
3: FUNCTIONS - The student
recognizes, describes, and examines constant and linear relationships in a
variety situations.
Fifth Grade Knowledge Base Indicators
The student:
1. uses letters and symbols to describe whole number relationships.
Fifth
Grade Application Indicators
The student:
1. converts between verbal, numerical, and graphical models or
concrete materials used to describe mathematical relationships.
Benchmark
4: MODELS - The student develops and
uses models to represent and justify mathematical relationships found in a
variety of situations.
Fifth
Grade Knowledge Base Indicators
The student:
1. uses mathematical models to represent and explain mathematical
concepts and procedures.
2. creates mathematical models to show the relationship between two
or more things.
The
student knows, explains, and uses mathematical models such as:
the number line to model the relationship between rational numbers and
rational number operations;
pictorial representation of addition, subtraction of rational
number with regrouping;
equations and inequalities to model numerical relationships;
manipulatives or pictures to model computational procedures;
three-dimensional geometric models;
graphs, tables, and charts to describe,
interpret or analyze data;
diagrams or pictures to model problem situations; and
Venn diagrams to show the relationships between characteristics of two
or more sets.
Fifth Grade Application Indicators
The student:
1. recognizes that the same situation can be represented in more
than one way.
2. explains why some
models are more useful than others in certain situations.
|
Standard
3: The student uses
geometric concepts and procedures in a variety of situations. |
Benchmark
1: GEOMETRIC FIGURES AND THEIR
PROPERTIES - The student recognizes, applies, and compares properties of
geometric figures in a variety of situations.
Fifth
Grade Knowledge Base Indicators
The
student:
1. uses appropriate technology, manipulatives, or drawings to
recognize and investigate properties of simple geometric figures.
2. recognizes and describes regular polygons having up to ten
sides.
3. recognizes an ellipse.
4. recognizes, draws or describes points, lines, line segments,
rays, and angles as right, obtuse or acute.
5. identifies and explains circumference, radius, and diameter.
6. identifies faces, edges, and bases on three dimensional objects.
7. recognizes perpendicular lines.
Fifth
Grade Application Indicators
The
student:
1.
formulates and solves real-world problems by applying properties of
geometric figures.
Benchmark
2: MEASUREMENT AND ESTIMATION - The
student estimates, measures, and uses measurement formulas in a variety of
situations.
Fifth Grade Knowledge Base Indicators
The student:
1. knows and uses area and perimeter formulas for rectangles and
squares.
2. uses standard units of measurement to the nearest eighth and
fourth inch, metric measurement to the nearest whole centimeter, meter,
and kilometer, or nonstandard unit of measure to the nearest whole unit.
3. selects, explains the selection of, or uses measurement tools,
units of measure and degrees of accuracy appropriate to the given
situation.
4. performs conversions within the standard and metric measurement
systems such as millimeters to centimeters.
Fifth
Grade Application Indicators
The student:
1. formulates and solves real-world problems by applying
measurements and measurement formulas.
2. uses estimation to check reasonableness of measurements and
calculations.
3. adjusts original measurements based on additional information
(estimation from a frame of reference).
4. uses map scales to measure distance between locations and makes
simple scale drawings using grid paper.
Benchmark
3: TRANSFORMATIONAL GEOMETRY - The
student recognizes and performs transformations of two-dimensional figures
in a variety situations.
Fifth Grade Knowledge Base Indicators
The student:
1. recognizes, explains and performs up to two transformations on
two-dimensional figures.
2. recognizes how pyramids, triangular prisms,
rectangular prisms, cylinders, cones, and spheres would appear from
a variety of visual perspectives (top, bottom, side, and corners).
Fifth
Grade Application Indicators
The student:
1. describes and draws two-dimensional shapes as they would appear
after undergoing two
specified transformations without actually performing the
transformations with concrete objects.
Benchmark
4: GEOMETRY FROM AN ALGEBRAIC
PERSPECTIVE - The student will
analyze two-dimensional geometry using a coordinate system in a variety of
situations.
Fifth Grade Knowledge Base Indicators
The student:
1. explains the relationships among fractions, whole numbers, and
where they appear on a number line.
2. maps paths between locations and compares lengths of different
paths on a coordinate grid.
Fifth
Grade Application Indicators
The student:
1. uses coordinate grids to formulate and solve real-world problems
involving distance and location.
|
Standard
4: The student uses
concepts and procedures of data analysis in a variety of situations.
|
Benchmark
1:
PROBABILITY - The student uses probability to generate convincing
arguments, draw conclusions, and make decisions in a variety of
situations.
Fifth Grade Knowledge Base Indicators
The student:
1. lists all possible outcomes of a single event in a clear and
organized manner.
2. recognizes simple experiments where the probabilities of all
outcomes are equal.
Fifth Grade Application Indicators
The student:
1. conducts experiments and/or simulations, records the results in
charts, tables or graphs, and uses the results to draw conclusions and
make predictions.
2. compares what should happen (theoretical/expected results) with
what did happen (experimental/empirical results) in a simple experiment.
Benchmark
2: STATISTICS -
The student generates, organizes, and interprets rational number and other
data in a variety of situations. The
student applies measures of central tendency when drawing conclusions from
the data.
Fifth
Grade Knowledge Base Indicators
The student:
1. organizes, reads, and displays numerical (quantitative) and
non-numerical (qualitative) data in a clear, organized, and accurate
manner including correct titles, labels, and intervals or categories.
Specific formats for the display of numerical and categorical data
include: frequency distributions; stem-and-leaf plots; bar, line and
circle graphs; Venn diagrams or other pictorial displays; and charts and
tables.
2. conducts, and explains sampling techniques (observations,
surveys, random sampling) for gathering data.
3. ranks the values of a numerical data set containing simple
fractions and decimals, identifies maximum and minimum data values, and
calculates the range for a data set.
4. calculates and explains the mean (average) for a whole number
data set.
5. calculates and explains the median for a whole number data set
containing an even number of data points.
6. determines and explains the mode(s).
Fifth
Grade Application Indicators
The student:
1. uses data analysis to make accurate inferences,
decisions/predictions, and to develop convincing arguments from data
displayed in a variety of formats. (see
listing of graphical displays)
2. recognizes or explains the affects of scale and/or interval
changes on graphs of whole number data sets.
3. recognizes that the same data set can be displayed in a variety
of formats and discusses why a particular format may be more appropriate
than another.