
Middle School  Mathematics

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 problemsolving process
(1.1) Solves singlestep and multiplestep 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 threedigit numbers
(3.4) Divides using twodigit 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 realworld 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 realworld problems involving formulas with one variable

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 problemsolving process
(1.1) Solves singlestep and multiplestep 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 realworld 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 twoand threedimensional 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 realworld 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 realworld problems involving formulas with one variable

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 problemsolving process
(1.1) Solves singlestep and multiplestep 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 rootextraction, 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 realworld 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 twoand threedimensional 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 twodimensional 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 realworld 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

Teacher
Miss Connie Kordick






