Northwest Evaluation Association Learning Continuum Release 1.0

Algebraic Concepts - includes patterns, functions, solving equations, order of operations, properties, simplifying expressions and continues up through more difficult skills in Algebra specific content.

Skills and Concepts

RIT scores between 151 and 160

Patterns, Sequences, Functions
· Find and extend patterns
· Recognize and extend a pattern: shape, color and size
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Determine what operation is needed to solve a word problem (addition and subtraction)
New Vocabulary in this range: none
New Signs and Symbols: € for answer to equation

RIT scores between 161 and 170

Solving Equations, Simplifying Expressions, Order of Operations
· Solve for missing numbers in an addition or subtraction sentence
· Determine what operation is needed to solve a word problem (any operation)
New Vocabulary in this Range: none
New Signs and Symbols: ( ) used in equations

RIT score between 171 and 180

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Solve for missing factors in a multiplication or division sentence
· Evaluate a numerical equation involving more than one operation
Properties
· Demonstrate the associative, commutative, and zero property of addition
New Vocabulary in this Range: none
New Signs and Symbols: <, > symbols

RIT score between 181 and 190

Patterns, Sequences, Functions
· Find and extend patterns, both increasing and decreasing
· Complete a table according to a rule
· Choose and apply an appropriate problem solving strategy: Find a pattern
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Use inverse operations to find missing equation
· Write number sentences using addition
· Identify missing elements in number sentences
Properties
· Identify the associative, commutative, identity and zero property of multiplication
Ordered Pairs
· Graph ordered pairs in the first quadrant
New Vocabulary in this Range: sign
New Signs and Symbols: - used as negative

RIT score between 191 and 200

Patterns, Sequences, Functions
· Count and write by 4's
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Use symbols of inequality, < and > to write and complete number sentences
· Solve simple addition problems with "n" as an addend or sum
· Solve simple multiplication problems with "n" as a multiple or product
· Solve simple division problems with "n" as a quotient or divisor
· Identify the base and the exponent of a given numerical expression and calculate its value
· Evaluate numerical expressions using the order of operations
· Solve whole number equations with any operation
New Vocabulary in this Range: if-then, product, sum
New Signs and Symbols: variables, exponents

RIT scores between 201 and 210

Patterns, Sequences, Functions
· Use of a function "machine" to determine input and output
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Evaluate an expression involving more than one operation (order of operations)
· Use the basic properties of multiplication to write an algebraic expression that is equivalent to a given algebraic expression
· Solve equations involving more than one operation
· Multiply and divide polynomials
· Solve equations involving rational numbers (addition and subtraction)
Properties
· Use strategies to develop computational fluency with multiplication: zero property, property of one, arrays, doubles, nine patterns
· Use the basic properties of addition to write an algebraic expression equivalent to a given algebraic expression
· Understand the properties of integers: commutative, associative, identity, zero property of multiplication, distributive property of multiplication over addition, and inverse property of addition
New Vocabulary in this Range: input, output, table, associative, equation
New Signs and Symbols: £, ³

RIT scores between 211 and 220

Patterns, Sequences, Functions
· Use logic to solve a problem involving a function table
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Solve decimal equations (one step, addition and subtraction)
· Solve integer equations (one step, multiplication and division)
· Evaluate expressions using the order of operations (may include parentheses or exponents)
· Solve quadratic equations
New Vocabulary in this Range: commutative, solve, square numbers, input, output, number sequence
New Signs and Symbols: none

RIT scores between 221 and 230

Patterns, Sequences, Functions
· Complete a function table according to a rule
· Recognize and continue a number pattern and/or geometric representation (e.g. Fibonacci sequence, triangular numbers)
· State a rule to explain a number pattern, including arithmetic progression
· Investigate geometric patterns and relationships and describe them algebraically
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Use boxes or other symbols to stand for any number in expressions or equations
· Solve whole number equations with one variable (multiplication and division)
· Solve integer equations (one step, all four operations)
· Solve equations involving more than one operation
· Definition and application of absolute value
· Solve one-step linear equations in one variable using addition, subtraction, multiplication, and division with integer solutions
· Simplify numeric expressions by applying properties of rational numbers (e.g. identity, inverse, distributive, associative, commutative)
New Vocabulary in this Range: absolute value, evaluate, quotient
New Signs and Symbols: square root symbol, %, absolute value symbol

RIT scores between 231 and 240

Patterns, Sequences, Functions
· Using whole numbers, complete a function table based on a given rule
· Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change (change in x-value) is constant
· Identify linear equation for a straight line
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Write an algebraic expression to model a situation
· Evaluate an algebraic expression for given values
· Explore equivalent ratios involving missing variables
· Use the correct order of operations to evaluate numeric and algebraic expressions
· Simplify and evaluate expressions that include positive and negative integral components
· Simplify polynomials by combining like terms
· Use the rules of exponents to multiply and divide monomials
· Solve simple linear equations and inequalities over the rational numbers
New Vocabulary in this Range: inequality, if-then statement, term in sequence, square numbers, negative coefficient
New Signs and Symbols: I = p x r x t

RIT scores between 241 and 250

Patterns, Sequences, Functions
· Students analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically
· Determine whether a relation is defined by a graph, a set of ordered pairs, or a symbolic expression is a function and justify the conclusion
· Use a function table to determine inverse variation
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Students solve equations and inequalities involving absolute values
· Understand the concepts of parallel lines and perpendicular lines and how those slopes are related
· Solve a system of two linear equations in two variables algebraically and interpret the answer graphically
· Graph a linear function in two variables using the slope-intercept method and identify intercepts
· Solve a system of two linear inequalities in two variables and identify the solution set
· Understand and use the rules of exponents, including negative exponents
· Add, subtract, multiply, and divide monomials and polynomials
· Apply basic factoring techniques to second- and simple third-degree polynomials, including finding a common factor for all terms in a polynomial, recognizing the difference of two squares, and recognizing perfect squares of binomials
· Add, subtract, multiply, and divide rational expressions and functions
· Simplify an expression containing imaginary roots
· Find the difference of two squares
New Vocabulary in this Range: regression equation, varies inversely as the square, slope of parallel lines, solution to system, factor (used with equations)
New Signs and Symbols: none

RIT scores between 251 and 260

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Simplify embedded expressions before solving linear equations and inequalities in one variable
· Identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers
· Solve problems that use variables in expressions describing geometric quantities by solving for one variable
· Solve equations with variables as exponents
· Use the rules of exponents to multiply polynomials by monomials
· Derive linear equations by using the point-slope function
· Find the slope given two points on the line of a given graph
· Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line
· Simplify monomials containing integer powers and roots
· Identify the equation of a parabola
· Simplify expressions containing cube roots
· Solve expressions containing factorials
· Find the number of possible solutions for a system of equations
· Cube a binomial
Quadratic Formula and Equations
· Solve a quadratic equation by factoring or completing the square
· Know the quadratic formula and demonstrates its proof by completing the square
· Identify discriminant and roots
· Use the quadratic formula to find the roots of a second-degree polynomial and solve quadratic equations
· Graph quadratic functions and know that their roots are the x-intercepts
Trigonometry
· Find sin and cosine of a given angle
· Solve logarithmic functions
New Vocabulary in this Range: parabola, intercepts, number of solutions, simultaneous equations, counterexample, solution set, sin A, cosine, tangent, discriminant, imaginary solutions, difference of two squares, read solution set from graph, factor completely
New Signs and Symbols: none

RIT scores between 261 and 270

Patterns, Sequences, Functions
· Determine the domain of independent variables and the range of dependent variables in a relation that is defined by a graph, a set of ordered pairs, or a symbolic expression
· Analyze properties and relationships of functions (e.g. linear, polynomial, rational)
Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Find the slope of a line parallel to a given line
· Find the x-intercept of a given equation
· Solve equations with fractions as exponents
· Analyze a graph to identify the appropriate system of equations
· Determine the vertex of a parabola
· Determine which of several equations can be factored
· Determine commonalities between three given equations of lines
Trigonometry
· Use graph to identify trigonometric functions of angles
· Find cosine, sine, and tangent of any given angle
· Use law of cosines
New Vocabulary in this Range: none
New Signs and Symbols: none

RIT scores between 271 and 280

Solving Equations and Inequalities, Simplifying Expressions, Order of Operations
· Identify the region defined by a linear inequality
New Vocabulary in this Range: none
New Signs and Symbols: none