Mathematics Cumulative Progress Indicators (CPIs) for the end of the designated grade span

Place a "+" for an expectation that represents a strength & a "-" for a weakness

+ or -

STANDARD 4.3     (PATTERNS AND ALGEBRA)     ALL STUDENTS WILL REPRESENT AND ANALYZE RELATIONSHIPS AMONG VARIABLE QUANTITIES  AND SOLVE PROBLEMS INVOLVING PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS AND PROCESSES.

D.    Procedures

By the end of Grade 2, students will:

 1.   Understand and apply (but don’t name) the following properties of addition:

·        Commutative (e.g., 5 + 3 = 3 + 5)

·        Zero as the identity element (e.g., 7 + 0 = 7)

·        Associative (e.g., 7 + 3 + 2 can be found by first adding either 7 + 3 or 3 + 2)

Building upon knowledge and skills gained in preceding grades, by the end of Grade 3, students will:

 1.         Understand and apply the properties of operations and numbers.

·        Commutative (e.g., 3 x 7 = 7 x 3)

·        Identity element for multiplication is 1 (e.g., 1 x 8 = 8)

·        Any number multiplied by zero is zero

 2.         Understand and use the concepts of equals, less than, and greater than to describe relations between numbers.

·        Symbols ( = , < , > )

Building upon knowledge and skills gained in preceding grades, by the end of Grade 4, students will:

 1.         Understand, name, and apply the properties of operations and numbers.

·        Commutative (e.g., 3 x 7 = 7 x 3)

·        Identity element for multiplication is 1 (e.g., 1 x 8 = 8)

·        Associative (e.g., 2 x 4 x 25 can be found by first multiplying either 2 x 4 or 4 x 25)

·        Division by zero is undefined 

·        Any number multiplied by zero is zero.

 2.         Understand and use the concepts of equals, less than, and greater than in simple number sentences.

·        Symbols ( = , < , > )

Building upon knowledge and skills gained in preceding grades, by the end of Grade 5, students will:

 1.         Solve simple linear equations with manipulatives and informally

·        Whole-number coefficients only, answers also whole numbers

·        Variables on one side of equation

Building upon knowledge and skills gained in preceding grades, by the end of Grade 6, students will:

 1.       Solve simple linear equations with manipulatives and informally.

·        Whole-number coefficients only, answers also whole numbers

·        Variables on one or both sides of equation

 2.       Understand and apply the properties of operations and numbers.

·        Distributive property

·        The product of a number and its reciprocal is 1

 3.       Evaluate numerical expressions.

 4.       Extend understanding and use of inequality.

·        Symbols ( ³ , ¹ , £ )

Building upon knowledge and skills gained in preceding grades, by the end of Grade 7, students will:

 1.       Use graphing techniques on a number line.

·        Absolute value

·        Arithmetic operations represented by vectors (arrows) (e.g., “-3 + 6” is “left 3, right 6”)

 2.       Solve simple linear equations informally and graphically.

·        Multi-step, integer coefficients only (although answers may not be integers)

·        Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology

 3.       Create, evaluate, and simplify algebraic expressions involving variables.

·        Order of operations, including appropriate use of parentheses

·        Substitution of a number for a variable

 4.       Understand and apply the properties of operations, numbers, equations, and inequalities.

·        Additive inverse

·        Multiplicative inverse

Building upon knowledge and skills gained in preceding grades, by the end of Grade 8, students will:

 1.         Use graphing techniques on a number line.

·        Absolute value

·        Arithmetic operations represented by vectors (arrows) (e.g., “-3 + 6” is “left 3, right 6”)

 2.       Solve simple linear equations informally, graphically, and using formal algebraic methods.

·        Multi-step, integer coefficients only (although answers may not be integers)

·        Using paper-and-pencil, calculators, graphing calculators, spreadsheets, and other technology

 3.       Solve simple linear inequalities.

 4.       Create, evaluate, and simplify algebraic expressions involving variables.

·        Order of operations, including appropriate use of parentheses

·        Distributive property

·        Substitution of a number for a variable

·        Translation of a verbal phrase or sentence into an algebraic expression, equation, or inequality, and vice versa

 5.       Understand and apply the properties of operations, numbers, equations, and inequalities.

·        Additive inverse

·        Multiplicative inverse

·        Addition and multiplication properties of equality

·        Addition and multiplication properties of inequalities

Building upon knowledge and skills gained in preceding grades, by the end of Grade 12, students will:

 1.       Evaluate and simplify expressions.

·        Add and subtract polynomials

·        Multiply a polynomial by a monomial or binomial

·        Divide a polynomial by a monomial

 2.       Select and use appropriate methods to solve equations and inequalities.

·        Linear equations – algebraically

·        Quadratic equations – factoring (when the coefficient of x² is 1) and using the quadratic formula

·        All types of equations using graphing, computer, and graphing calculator techniques

 3.       Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.