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Middle School (6-8) ->
Mathematics
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GRADE SIX
Grade Level Expectations for
Mathematics
These are the
core grade level expectations based on the McRel standards and
benchmarks that should be taught during sixth grade and represent what
a student will learn. They are written from the student point of view.
Local sites may add additional grade level expectations to correspond
with their curriculum. These grade level expectations are aligned with
McRel standards. The number listed is in reference to McRel 3rd
edition. The grade level
expectations that are aligned with and developed by ITBS/ITED are noted
in italics. Not all standards are addressed at every grade level
which is appropriate considering a student’s development.
MATH
1. Problem solving - Uses a variety of strategies in the
problem-solving process
(1.1) Solves single-step and
multiple-step math problems
(1.1.1) Brainstorms possible
approaches before starting a problem
(1.1.2)
Breaks complex problems into simpler parts
(1.2) Identifies extraneous or
insufficient information in problems
(1.3) Chooses a method for solving a
problem - some methods more helpful than others
(1.4)
Checks reasonableness of results of each part of problem solving process
(1.5) Constructs a physical
representation for complex problems
2.
Concept of Numbers - Understands and applies basic and advanced
properties of the concept of numbers
(2.1) Checks reasonableness of
results through estimation - estimates
measurements with appropriate precision
(2.1.1) Uses standard rounding
to estimate
(2.1.2) Uses order of magnitude
to estimate
(2.1.3) Uses number sense to
estimate
(2.2) Represents, compares, and
orders numbers; fractions and decimals
(2.3) Describes and applies
properties of numbers
(2.4) Classifies numbers by
divisibility
(2.5) Demonstrates ways of
performing operations
(2.6) Uses place value; writes
numbers in standard, expanded, and exponential form
(2.7) Uses and interprets
operational and relationship symbols
(2.8) Solves equations and
inequalities
(2.9) Uses variable expressions
to model situations
(2.10) Explores numerical
patterns
(2.11)
Understands the basic relationship of fractions to decimals and
fractions to whole numbers and percents to decimals
(2.12)
Uses number lines to model a variety of numbers
(2.13)
Identifies prime and composite numbers
(2.14)
Communicates mathematical concepts through writing and speaking
3.
Computation - Uses basic and advanced procedures while performing the
process of computation
(3.1) Rounds decimals and
fractions
(3.2)
Uses order of operations effectively
(3.3)
Multiplies three-digit numbers
(3.4)
Divides using two-digit numbers
(3.5)
Interprets remainders
4.
Measurement - Understands and applies basic and advanced properties of
the concept of measurement
(4.1) Measures length/distance,
time, temperature, weight, mass, and volume
(4.2) Identifies and uses
appropriate units of measurement
(4.2.1) Selects and uses
appropriate units of measurement according to type and size of unit
(standard and metric)
(4.2.2)
Converts units within a system, e.g. feet to inches, quarts to pints,
hours to minutes
(4.3)
Estimates, calculates, and compares perimeter, area, and volume
(4.4)
Applies given measurement formulas for perimeter, area, circumference,
volume, and surface area in problem situations
5.
Geometry - Understands and applies basic and advanced properties of the
concepts of geometry
(5.1) Recognizes and classifies
angles, points, lines, rays and segments and understands the
characteristics of slope
(5.2)
Compares shapes in terms of such concepts as parallel, perpendicular,
congruence, and symmetry (turns, flips, sides to investigate concepts
of symmetry, similarity, and congruence)
(5.3) Identifies, classifies,
and compares geometric figures
(5.4) Describes geometric
properties, patterns, and relationships
(5.5) Applies the concepts of perimeter,
area, and volume
(5.6) Solves real-world problem involving area of geometric figures
6.
Data analysis - Understands and applies basic and advanced concepts of
statistics and data analysis
(6.1)
Gathers and records data to make generalizations
(6.2) Understands that data comes in many different forms and that
collecting, organizing and displaying data can be done in many ways
(6.3) Finds mean, median, mode, and range
(6.4) Reads amounts on
scales of bar and line graphs
(6.5) Locates amounts in
specific cells of a table
(6.6) Compares quantities
to determine ranks, sums, or differences and to find ratios
(6.7) Uses tables and
graphs to determine rates or identify trends, understand underlying or
functional relationships, and generalize or draw conclusions
7.
Probability - Understands and applies basic concepts of probability
(7.1) Applies probability concepts and
counting rules
(7.2) Understands and
applies measures of central tendency and variability
(7.3) Identifies common errors in the presentation of statistics
(7.4) Understands probabilities and the ways they can be expressed
(7.5) Understands procedures for selecting an unbiased sample
8.
Functions and Algebra - Understands and applies basic concepts of
functions and algebra
(8.1) Constructs a pattern and articulates why the pattern works
(8.2) Solves real-world problems involving formulas with one variable
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GRADE SEVEN
Grade Level Expectations for
Mathematics
These are the
core grade
level expectations based on the McRel standards and benchmarks that
should be taught during seventh grade and represent what a student will
learn. They are written from the student point of view. Local sites may
add additional grade level expectations to correspond with their
curriculum. These grade level expectations are aligned with McRel
standards. The number listed is in reference to McRel 3rd edition. The grade level expectations that are
aligned with and developed by ITBS/ITED are noted in italics.
Not all standards are addressed at every grade level which is
appropriate considering a student’s development.
MATH
1. Problem solving - Uses a variety of strategies in
the problem-solving process
(1.1) Solves single-step and
multiple-step math problems
(1.1.1) Brainstorms possible
approaches before starting a problem
(1.1.2)
Breaks complex problems into simpler parts
(1.2)
Identifies extraneous or insufficient information in problems
(1.3)
Chooses a method for solving a problem - some methods more helpful than
others
(1.4)
Checks reasonableness of results of each part of problem solving process
(1.5)
Constructs a physical representation for complex problems
(1.6)
Understands there is more than one way to solve mathematical problems
(1.7)
Can determines information required to solve a problem, choosing
methods and setting limits for acceptable solution
2.
Concept of Numbers - Understands and applies basic and advanced
properties of the concept of numbers
(2.1) Checks reasonableness of
results through estimation - estimates
measurements with appropriate
precision
(2.1.1) Uses standard rounding
to estimate
(2.1.2)
Uses order of magnitude to estimate
(2.1.3)
Uses number sense to estimate
(2.2)
Represents, compares, and orders numbers; fractions and decimals
(2.3)
Describes and applies properties of numbers
(2.4)
Classifies numbers by divisibility
(2.5)
Demonstrates ways of performing operations
(2.6)
Uses place value; writes numbers in standard, expanded, and exponential
form
(2.7)
Uses and interprets operational and relationship symbols
(2.8)
Solves equations and inequalities
(2.9)
Uses variable expressions to model situations
(2.10)
Explores numerical patterns
(2.11)
Understands the basic relationship of fractions to decimals and
fractions to whole numbers and percents to decimals
(2.12)
Identifies prime and composite numbers
(2.13)
Communicates mathematical concepts through writing and speaking
(2.14)
Understands the concepts of ratio, proportion, and percent and the
relationships among them
(2.15)
Understands the characteristic and uses of exponents and scientific
notation
(2.16)
Uses number theory concepts, e.g. divisibility and remainders, factors,
multiples, prime, relatively prime to solve problems
3. Computation - Uses basic and advanced procedures while performing
the process of computation
(3.1) Adds, subtracts,
multiplies, and divides whole number, fractions, decimals, integers and
rational numbers
(3.2)
Rounds decimals and fractions
(3.3)
Uses order of operations effectively
(3.4)
Selects and uses appropriate computational methods for a given situation
4.
Measurement - Understands and applies basic and advanced properties of
the concept of measurement
(4.1) Measures length/distance,
time, temperature, weight, mass, and volume
(4.2)
Identifies and uses appropriate units of measurement
(4.2.1) Selects and uses
appropriate units and tools, depending on degree of accuracy required
to find measurements for real-world problems
(4.2.2)
Converts units within a system, e.g. feet to inches, quarts to pints,
hours to minutes
(4.3)
Estimates, calculates, and compares perimeter, area, and volume
(4.4)
Applies given measurement formulas for perimeter, area, circumference,
volume, and surface area in problem situations
(4.5)
Understands procedures for basic indirect measurements, e.g., using
grids to estimate area of irregular figures
5.
Geometry - Understands and applies basic and advanced properties of the
concepts of geometry
(5.1) Understands the
relationships between two-and three-dimensional representations of a
figure, e.g., scale drawings, blueprints, planar cross sections
(5.2)
Understands the mathematical concepts of similarity and congruency
(5.3)
Understands the basic concept of the Pythagorean theorem (introduction)
(5.4)
Compares shapes in terms of such concepts as parallel, perpendicular,
congruence, and symmetry (turns, flips, sides to investigate concepts
of symmetry, similarity, and congruence)
(5.5)
Identifies, classifies, and compares geometric figures
(5.6)
Describes geometric properties, patterns, and relationships
(5.7)
Applies the concepts of perimeter, area, and volume
(5.8)
Solves real-world problem involving area of geometric figures
6.
Data analysis - Understands and applies basic and advanced concepts of
statistics and data analysis
(6.1) Gathers and records data
to make generalizations
(6.2)
Understands that data comes in many different forms and that
collecting, organizing and displaying data can be done in many ways
(6.3)
Finds mean, median, mode, and range
(6.4)
Reads, interprets, organizes, and displays data in charts, tables,
plots, and graphs
(6.5)
Reads amounts on scales of bar and line graphs
(6.6)
Locates amounts in specific cells of a table
(6.7)
Compares quantities to determine ranks, sums or differences, and to
find ratios
(6.8)
Uses tables and graphs to determine rates or identify trends,
understand underlying or functional relationships, and generalize or
draw conclusions
(6.9) Understands basic concepts
about how samples are chosen
7.
Probability - Understands and applies basic concepts of probability
(7.1) Applies probability
concepts and counting rules
(7.2)
Understands and applies measures of central tendency and variability
(7.3)
Identifies common errors in the presentation of statistics
(7.4)
Understands probabilities and the ways they can be expressed
(7.5)
Understands how predictions are based on data and probabilities
(7.6)
Determines probability using simulations or experiments
8.
Functions and Algebra - Understands and applies basic concepts of
functions and algebra
(8.1) Constructs a pattern and
articulates why the pattern works
(8.2)
Understands that a variable can be used in many ways
(8.3)
Understands basic operations of algebraic expressions, e.g., combining
like terms, expanding, substituting for unknowns
(8.4)
Understands various representations of patterns and functions and the
relationships among them
(8.5)
Solves real-world problems involving formulas with one variable
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GRADE EIGHT
Grade Level Expectations for
Mathematics
These are the
core grade
level expectations based on the McRel standards and benchmarks that
should be taught during eighth grade and represent what a student will
learn. They are written from the student point of view. Local sites may
add additional grade level expectations to correspond with their
curriculum. These grade level expectations are aligned with McRel
standards. The number listed is in reference to McRel 3rd edition. The grade level expectations that are
aligned with and developed by ITBS/ITED are noted in italics.
Not all standards are addressed at every grade level which is
appropriate considering a student’s development.
MATH
1. Problem solving - Uses a variety of strategies in
the problem-solving process
(1.1) Solves single-step and
multiple-step math problems
(1.1.1) Brainstorms possible
approaches before starting a problem
(1.1.2)
Breaks complex problems into simpler parts
(1.2)
Identifies extraneous or insufficient information in problems
(1.3)
Chooses a method for solving a problem - some methods more helpful than
others
(1.4)
Checks reasonableness of results of each part of problem solving process
(1.5)
Constructs a physical representation for complex problems
(1.6)
Understands there is more than one way to solve mathematical problems
(1.7)
Can determine information required to solve a problem, choosing
methods, and setting limits for acceptable solution
(1.8)
Understands the role of written symbols in representing mathematical
ideas and the use of precise language in conjunction with the special
symbols of mathematics
2. Concept of Numbers - Understands and applies basic and advanced
properties of the concepts of numbers
(2.1) Checks reasonableness of
results through estimation - estimates
measurements with appropriate
precision
(2.1.1) Uses standard rounding
to estimate
(2.1.2)
Uses order of magnitude to estimate
(2.1.3)
Uses number sense to estimate
(2.2)
Represents, compares, and orders numbers; fractions and decimals
(2.3)
Describes and applies properties of numbers
(2.4)
Classifies numbers by divisibility
(2.5)
Demonstrates ways of performing operations
(2.6)
Uses place value; writes numbers in standard, expanded, and exponential
form
(2.7)
Uses and interprets operational and relationship symbols
(2.8)
Solves equations and inequalities
(2.9)
Uses variable expressions to model situations
(2.10)
Explores numerical patterns
(2.11)
Communicates mathematical concepts through writing and speaking
(2.12)
Understands the characteristics and uses of exponents and scientific
notation
(2.13)
Uses number theory concepts, e.g. divisibility and remainders, factors,
multiples, prime, relatively prime to solve problems
(2.14)
Understands the role of positive and negative integers in the number
system
3. Computation - Uses basic and advanced procedures while performing
the processes of computation
(3.1) Uses order of operations
effectively
(3.2)
Interprets remainders
(3.3)
Understands exponentiation of rational numbers and root-extraction,
e.g., squares and square roots, cubes and cube roots
(3.4)
Understands the properties of operations with rational numbers, e.g.,
distributive property, commutative property, and associative properties
of addition and multiplication, inverse properties, and identity
properties
(3.5)
Selects and uses appropriate computational methods for a given situation
4. Measurement - Understands and applies basic and advanced properties
of the concepts of measurement
(4.1) Measures length/distance,
time, temperature, weight, mass, and volume
(4.2)
Identifies and uses appropriate units of measurement
(4.2.1) Selects and uses
appropriate units and tools, depending on degree of accuracy required
to find measurements for real-world problems
(4.2.2)
Converts units within a system, e.g. feet to inches, quarts to pints,
hours to minutes
(4.3)
Estimates, calculates, and compares perimeter, area, and volume
(4.4)
Applies given measurement formulas for perimeter, area, circumference,
volume, and surface area in problem situations
(4.5)
Understands procedures for basic indirect measurements, e.g., using
grids to estimate area of irregular figures
(4.6)
Understands the basic concept of rate as a measure, e.g., miles per hour
5. Geometry - Understands and applies basic and advanced properties of
the concepts of geometry
(5.1) Understands the
relationships between two-and three-dimensional representations of a
figure, e.g., scale drawings, blueprints
(5.2)
Uses geometric methods (i.e., using an unmarked straight edge and a
compass using an algorithm) to complete basic geometric constructions,
e.g., perpendicular bisector of a line segment, angle bisector
(5.3)
Understands the mathematical concepts of similarity and congruency
(5.4)
Understands the basic concept of the Pythagorean theorem (introduction)
(5.5)
Uses the intersection of two-dimensional figures (e.g., lines,
triangles, squares) to derive geometric definitions such as parallel,
perpendicular, Pythagorean theorem, and mid point
(5.6)
Identifies, classifies, and compares geometric figures
(5.7)
Describes geometric properties, patterns, and relationships
(5.8)
Applies the concepts of perimeter, area, and volume
(5.9)
Solves real-world problems involving area of geometric figures
6. Data analysis - Understands and applies basic and advanced concepts
of statistics and data analysis
(6.1) Gathers and records data
to make generalizations
(6.2)
Finds mean, median, mode, and range
(6.3)
Reads, interprets, organizes, and displays data in charts, tables,
plots and graphs
(6.4)
Reads amounts on scales of bar and line graphs
(6.5)
Locates amounts in specific cells of a table
(6.6)
Compares quantities to determine ranks, sums or differences and to find
ratios
(6.7)
Uses tables and graphs to determine rates or identify trends,
understand underlying or functional relationships, and generalize or
draw conclusions
(6.8)
Understands the basic concept of outliers
(6.9)
Understands faulty arguments, common errors, and misleading
presentations of data
7. Probability - Understands and applies basic and advanced concepts of
probability
(7.1) Applies probability
concepts and counting rules
(7.2)
Understands and applies measures of central tendency and variability
(7.3)
Identifies common errors in the presentation of statistics
(7.4)
Understands the relationship between the numerical expression of a
probability (e.g., fraction, percentage, odds) and the events that
produce these numbers
(7.5)
Understands how predictions are based on data and probabilities
(7.6)
Determines probability using simulations or experiments
(7.7)
Understands procedures for selecting an unbiased sample
8. Functions and Algebra - Understands and applies basic and advanced
properties of functions and algebra
(8.1) Constructs a pattern and
articulates why the pattern works
(8.2)
Understands that a variable can be used in many ways
(8.3)
Understands basic operations of algebraic expressions, e.g., combining
like terms, expanding, substituting for unknowns
(8.4)
Understands various representations of patterns and functions and the
relationships among them
(8.5)
Understands the basic concept of a function, i.e., functions describe
how changes in one quantity or variable result in changes in another
(8.6)
Uses substitution within given formulas and expressions with real world
problems
(8.7)
Solves simple systems of equations graphically
(8.8)
Uses the rectangular coordinate system to model and solve problems
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