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Algebra 1 Skills

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  • Algebra Foundations
    • Real Number System
      • Comparing Real Numbers
        • Order positive decimals
        • Order positive fractions
        • Condensed: Order positive decimals & fractions
        • Order decimals & fractions
        • Order rational numbers, no radicals, no exponents
        • Order real numbers, no exponents
        • Order real numbers, exponents are positive
        • Order real numbers
        • Comparing expressions on given interval
      • Application of Comparing Real Numbers
        • Order real numbers, positive exponents, percents are whole, including real-world context
        • Order real numbers, positive exponents, percents are whole, including real-world context
        • Given table, order rational numbers, real-world context
        • Given set or list, order rational numbers, real-world context
      • Classifying Real Numbers
        • Determine relationships between subsets of rational numbers
        • Determine relationships between subsets of real numbers
        • Determine result of adding & multiplying rational & irrational numbers
    • Algebraic Properties
      • Identify properties used in numerical expressions
      • Identify properties used to solve linear equations
      • Identify properties used in numerical & algebraic expressions
      • Identify steps to solve linear equations
      • Evaluate & identify equivalent numerical expressions, including real-world context
      • Identify equivalent algebraic expressions, including real-world context
    • Numerical Absolute Value
      • Determine absolute value of integers
      • Determine absolute value of integers, including real-world context
      • Determine absolute value of numeric expression
      • Determine absolute value of rational numbers
    • Order of Operations
      • Order of Operations, Only Postives
        • Evaluate numerical expressions, # + #(#)
        • Evaluate numerical expressions, #/# + #
        • Evaluate numerical expressions, #/# + #, decimals
        • Evaluate numerical expressions, # ± #(#), decimals
        • Evaluate numerical expressions, #(# + #), decimals
        • Evaluate numerical expressions, # + #(#)^#
        • Evaluate numerical expressions, #(#)^# + #/#
        • Evaluate numerical expressions, # + #(# + #)^#
        • Evaluate numerical expressions, up to four operations
        • Evaluate numerical expressions, including rationals & up to two sets of grouping symbols
        • Identify first steps in evaluating numerical expressions using grouping symbols
        • Evaluate numerical expressions, up to two sets of grouping symbols, real-world context
      • Order of Operations, Three or Four Integers
        • Evaluate sum or difference of three integers, at least one difference
        • Evaluate sum or difference of four integers, at least one difference
        • Evaluate sum or difference of four integers, two grouped in parentheses, at least one difference
        • Evaluate sum or difference of four integers, two grouped in absolute value, at least one difference
        • Evaluate numerical expressions, three or four integers, including multiplication & division
        • Evaluate numerical expressions, three or four integers, including multiplication & division as fraction
        • Evaluate numerical expressions, three or four integers, one exponent, including multiplication
        • Evaluate numerical expressions, four integers, including multiplication & exponents
        • Evaluate numerical expressions, real-world context
      • Order of Operations, Five or More Integers
        • Evaluate sum or difference of six integers, two grouped in parentheses, two grouped in absolute value, at least one difference
        • Evaluate numerical expressions, five integers, two grouped in parentheses, including multiplication & division
        • Evaluate numerical expressions, five integers, two grouped in absolute value, including multiplication & division
        • Evaluate numerical expressions, five integers, one exponent, two grouped in parentheses, including multiplication & division
        • Evaluate numerical expression quotients, five to seven integers, including multiplication, division, & absolute value
        • Evaluate numerical expression quotients, five to seven integers, one exponent, including multiplication, division, & absolute value
        • Condensed: Evaluate numerical expressions
      • Order of Operations, Rational Numbers
        • Identify equivalent expressions using order of operations
        • Evaluate numerical expressions, fractions, no exponents
        • Evaluate numerical expressions, decimals, no exponents
        • Evaluate numerical expressions, decimals & fractions, no exponents
        • Evaluate numerical expressions, fractions
        • Evaluate numerical expressions, decimals
        • Evaluate numerical expressions, decimals & fractions
    • Scientific Notation
      • Basic Scientific Notation
        • Identify correct conversion of number from scientific notation with positive exponent to standard form
        • Identify correct conversion of number from scientific notation with negative exponent to standard form
        • Convert number from scientific notation with positive exponent to standard form
        • Convert number from scientific notation with negative exponent to standard form
        • Identify correct conversion of number from standard form to scientific notation with positive exponent
        • Identify correct conversion of number from standard form to scientific notation with negative exponent
        • Convert number from standard form to scientific notation with positive exponent
        • Convert number from standard form to scientific notation with negative exponent
        • Condensed: Identify correct conversion of number between scientific notation & standard form
        • Condensed: Convert number between scientific notation & standard form
        • Convert number from word form to scientific notation
        • Compare two numbers in scientific notation
      • Scientific Notation, Round First
        • Round & convert number from standard form to scientific notation with positive exponent
        • Round & convert number from standard form to scientific notation with negative exponent
        • Condensed: Round & convert number from standard form to scientific notation
      • Basic Operations with Scientific Notation
        • Add numbers in scientific notation
        • Subtract numbers in scientific notation 
        • Multiply numbers in scientific notation 
        • Divide numbers in scientific notation 
        • Condensed: Add, subtract, multiply, & divide numbers in scientific notation
      • Application of Scientific Notation
        • Convert number from standard form to scientific notation, real-world context
        • Convert numbers between standard form & scientific notation, real-world context
        • Add numbers in scientific notation, real-world context
        • Subtract numbers in scientific notation, real-world context
        • Multiply numbers in scientific notation, real-world context
        • Divide numbers in scientific notation, real-world context
        • Compare magnitude of numbers in scientific notation, real-world context
    • Coordinate Plane
      • Basic Coordinate Plane
        • Plot integer points
        • Plot integer points on coordinate plane, point on axis
        • Given integer point on graph, determine coordinates
        • Given integer point on graph, determine coordinates, point on axis
        • Given lattice point, determine coordinates
        • Plot points on coordinate plane, student selects scales
        • Condensed: Plot integer points or determine coordinates
        • Given rational point, determine location on coordinate plane
        • Plot rational points on coordinate plane
        • Plot or identify rational points on coordinate plane
        • Plot rational points on coordinate plane, graph scale at most one-half
        • Condensed: Plot or identify points on coordinate plane
      • Application of Coordinate Plane
        • Identify first quadrant points or parts of coordinate plane
        • Identify locations or parts of coordinate plane using first quadrant points
        • Identify description of process to plot first quadrant points
        • Determine or identify first quadrant points, real-world context
        • Determine or identify first quadrant points, including cardinal directions, real-world context
        • Condensed: Plot or determine coordinates of first quadrant rational points
    • Inferential Reasoning Word Problems
      • Identify appropriate steps to solve problem, real-world context
      • Determine reasonable estimates, linear relationships, real-world context
      • Determine reasonable estimates, multi-step, real-world context
  • Expressions
    • Evaluating Expressions
      • Evaluating Expressions, Only Positives
        • Evaluate addition expressions for specified value, one variable, whole numbers
        • Evaluate addition expressions for specified value, one variable, at least one fraction
        • Evaluate addition expressions for specified value, one variable, at least one decimal
        • Evaluate subtraction expressions for specified value, one variable, whole numbers
        • Evaluate subtraction expressions for specified value, one variable, at least one fraction
        • Evaluate subtraction expressions for specified value, one variable, at least one decimal
        • Evaluate expressions for specified value, one variable, including multiple operations, at least one decimal
        • Evaluate expressions for specified values, two variables, multiple operations, including powers & real-world context
      • Evaluating Expressions, Including Negatives
        • Evaluate expressions for specified value, one variable, two terms, only sums & differences
        • Evaluate expressions for specified value, one variable, one term, two factors
        • Evaluate linear expressions for specific values
        • Evaluate expressions for specified value, one variable, one term, three factors
        • Evaluate expressions for specified value, one variable, two terms
        • Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers
        • Evaluate expressions for specified value, one variable, two terms, multiple operations, including powers of absolute values
        • Evaluate expressions for specified values, two variables, two terms
        • Evaluate expressions for specified values, two variables, two terms, one term with three factors
        • Evaluate expressions for specified values, two variables, multiple operations, including absolute value & powers
        • Evaluate expressions for specified values, two variables, quotient of expressions
        • Evaluate algebraic expressions, including variable exponents
    • Simplifying Expressions
      • Combining Like Terms
        • Simplify algebraic expressions, combine two terms, positives
        • Simplify algebraic expressions, combine two terms
        • Simplify algebraic expressions, one variable, positive integer coefficients
        • Simplify algebraic expressions, one variable, integer coefficients
        • Simplify algebraic expressions, one variable, rational coefficients
        • Simplify algebraic expressions, two variables, positive integer coefficients
        • Simplify algebraic expressions, two variables, integer coefficients
      • Distributive Property
        • Simplify algebraic expressions, one variable, distribute once, integer multiplier
        • Simplify algebraic expressions, one variable, distribute once, fraction multiplier
        • Simplify algebraic expressions, one variable, distribute once, decimal multiplier
        • Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
        • Identify equivalent numerical & algebraic expressions, including distribution, including real-world context
        • Simplify algebraic expressions, one variable, distribute once, variable multiplier
        • Simplify algebraic expressions, one variable, distribute once, variable with coefficient multiplier
        • Simplify algebraic expressions, one variable, distribute once, including rationals
        • Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers
      • Distributive Property & Combining Like Terms
        • Identify equivalent expressions involving distribution
        • Simplify algebraic expressions, one variable, distribute once & combine like terms
        • Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
        • Simplify algebraic expressions, one variable, distribute once & product of two factors
        • Condensed: Simplify algebraic expressions, one variable, distribute once, including combine like terms & product of two factors
        • Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
        • Simplify algebraic expressions, one variable, distribute twice
        • Simplify algebraic expressions, two variables, distribute twice
      • Writing Rational Expression as Two Terms
        • Convert linear binomials divided by constants to sum or difference of two terms
  • Ratios, Rates, & Proportions
    • Rates
      • Determine unit rates, whole numbers, real-world context
      • Determine unit rates, fractions, real-world context
      • Determine unit rates, mixed numbers, real-world context
      • Given unit rate, determine specified value in proportional relationship, real-world context
      • Condensed: Determine or apply unit rates, real-world context
      • Given rate, convert time unit to determine quantity over time interval, real-world context
      • Given rate of travel, determine distance or time
      • Given rate & comparison, determine unit rates, real-world context
      • Determine & compare unit rates, real-world context
      • Given proportional relationship, determine specified quantity, real-world context
      • Given proportional relationship, determine specified quantity, including decimals, real-world context
    • Ratios
      • Basic Ratios
        • Determine part to whole ratio, decimal grids
        • Determine part to part ratio, decimal grids
        • Identify percents, area models
        • Given ratio, identify table
        • Given table of proportional relationship, determine value or equivalent ratio
        • Compare rates
      • Application of Ratios
        • Determine part to whole ratio, strip diagrams, real-world context
        • Determine part to part ratio, strip diagrams, real-world context
        • Determine part to whole ratio, double number lines, real-world context
        • Determine part to part ratio, including double number lines, including real-world context
        • Determine specified values in ratios, strip diagrams, real-world context
        • Determine specified values in proportional relationships, real-world context
        • Determine ratios or specified quantities from table or identify table from given ratio, real-world context
        • Compare rates or determine specified values in proportional relationships, real-world context
    • Proportions
      • Basic Proportions
        • Solve proportions, whole numbers
        • Solve proportions
        • Solve proportions, mixed number components, whole number cross products
        • Solve proportions, mixed number components
        • Solve proportions, one binomial expression
        • Solve proportions, two binomial expressions
        • Condensed: Solve proportions, binomial expressions
      • Application of Proportions
        • Solve proportions, exact answers, real-world context
        • Solve proportions, rounded answers, real-world context
        • Solve proportions involving time, real-world context
        • Condensed: Solve proportions, including real-world context
  • Equations
    • One-Step Equations
      • Condensed: Solve one-step linear equations, addition or subtraction
      • Condensed: Solve one-step linear equations, multiplication or division
      • Solve one-step linear equations, fractional answers
      • Solve one-step linear equations, fractional coefficients
      • Solve one-step linear equations, fractional coefficients & constants
      • Condensed: Solve one-step linear equations, including fractional coefficients & fractional answers
      • Determine one-step linear equations, real-world context
      • Determine one-step equations, including decimals, real-world context
      • Given one-step linear equation, identify real-world situation represented by equation
      • Given one-step equation, identify real-world situation represented by equation
    • Two-Step Equations
      • Solve two-step linear equations, algebra tiles
      • Determine if given value is solution to two-step linear equations
      • Solve ax ± b = c
      • Condensed: Solve x/a ± b = c
      • Solve two-step linear equations, fractional answers
      • Solve two-step linear equations, fractional coefficients
      • Solve two-step linear equations, decimal coefficients
      • Condensed: Solve two-step linear equations
      • Condensed: Solve one- or two-step linear equations, fractional coefficients
      • Condensed: Solve one- or two-step linear equations, including fractional answers
      • Determine two-step linear equations, real-world context
      • Given two-step linear equation, identify real-world situation represented by equation
    • Multi-Step Equations
      • Multi-Step Equations, no Distribution
        • Solve linear equations, sum or difference on one side
        • Solve linear equations, product on one side
        • Solve linear equations, like terms on both sides
        • Solve (ax ± b)/c = d
      • Multi-Step Equations, with Distribution
        • Solve linear equations, distributive property on one side
        • Solve linear equations, distributive property on one side, up to two terms on other side
        • Solve three-step linear equations involving distribution of decimal multiplier
        • Solve three-step linear equations involving distribution, fractional multiplier cancels if distributed
        • Solve three-step linear equations involving distribution, fractional multiplier doesn't cancel if distributed
        • Condensed: Solve three-step linear equations involving distribution, including fractional & decimal answers
        • Solve linear equations, term minus distributive property on one side
        • Solve linear equations, distributive property & additional term on one side
        • Condensed: Solve linear equations involving distributive property on one side
    • Equations with Variables on Both Sides
      • Equations with Variables on Both Sides
        • Solve linear equations, variables on both sides
        • Solve linear equations, binomials on both sides, decimals
        • Solve linear equations, variables as numerators on both sides
        • Solve linear equations, binomials on both sides, fractions
        • Condensed: Solve linear equations, variables on both sides or like terms
        • Condensed: Solve linear equations, variables on both sides, rationals
        • Solve multi-step linear equations
        • Solve linear equations, distributive property on both sides, integers
        • Solve linear equations, distributive property on both sides, rationals
        • Solve linear equations, distributive property on both sides, additional term on one side
        • Solve linear equations, distributive property & additional term on one side & binomial on other side
      • Application of Equations with Variables on Both Sides
        • Determine equations with variables on both sides, real-world context
        • Determine & solve linear equations with variables on both sides, real-world context
        • Given equation with variables on both sides, identify real-world situation represented by equation
    • Solving for Specified Variable
      • Given linear equation of form ay = bx, solve for y
      • Given linear equation of form ay = bx + c, solve for y
      • Given linear equation of form a + by = cx, solve for y
      • Given linear equation with two terms on each side, solve for specified variable
      • Given linear equation with three terms on one side, solve for specified variable
      • Condensed: Given linear equation in various forms, solve for specified variable
      • Solve for specific variable in mathematical formula
      • Solve for specific variable in scientific formula
    • Absolute Value Equations
      • Solve linear absolute value equations
      • Solve linear absolute value equations, extra constant or coefficient
      • Condensed: Solve linear absolute value equations, including extra constant or coefficient
      • Solve linear absolute value equations, variable on both sides
    • Identifying Number of Solutions
      • Determine number of solutions in linear equations, distribute at most one time
      • Determine number of solutions in linear equations, distribute up to two times
      • Condensed: Determine number of solutions in linear equations
      • Solve linear equations, including no solution & infinitely many solutions
  • Inequalities
    • One-Variable Inequalities
      • Basic One-Variable Inequalities
        • Graph inequalities on number line
        • Determine graph from inequality or inequality from graph
        • Given graph, determine inequality
        • Solve & graph one-step inequalities, whole number coefficients
        • Solve & graph one-step inequalities, integer coefficients
        • Solve & graph one-step inequalities, including fractional coefficients
        • Solve & graph one-step inequalities, including negative & fractional coefficients
      • Two-Step or Multi-Step One-Variable Inequalities
        • Solve & graph two-step inequalities
        • Condensed: Solve & graph inequalities
        • Determine equivalence of inequalities & solution set
        • Solve multi-step inequalities, including variables on both sides
        • Solve multi-step inequalities using distributive property
        • Solve & graph inequalities, variables on both sides, including distributive property
      • Application of One-Variable Inequalities
        • Determine one-step inequalities, including real-world context
        • Identify one-step inequalities that model real-world problems or interpret inequality components
        • Given one-step inequality, identify real-world problem modeled by inequality
        • Given one-step inequality, identify real-world problem modeled by inequality, rational numbers
        • Determine one-step inequalities, rational numbers, including real-world context
        • Given two-step inequality, identify real-world problem modeled by inequality
        • Determine & solve two-step inequalities, greater than, real-world context
        • Determine & solve two-step inequalities, less than, real-world context
        • Determine two-step inequalities, rational numbers, including real-world context
        • Determine inequalities with variables on both sides, real-world context
        • Given inequality with variable on both sides, identify real-world problem modeled by inequality
    • Linear Inequalities
      • Linear Inequalities Solutions & Non-Solutions
        • Given linear inequality & x-value, determine y-value
        • Given linear inequality, determine solutions & non-solutions, slope-intercept form
        • Given linear inequality graph, determine solutions & non-solutions
        • Condensed: Given linear inequalities & graphs, determine solutions & non-solutions
      • Basic Linear Inequalities
        • Graph linear inequalities, slope-intercept form, only oblique lines
        • Graph linear inequalities, slope-intercept form, including vertical & horizontal lines
        • Given linear inequality, identify correct graph, slope-intercept form
        • Given linear inequality, determine graph, slope-intercept form
        • Given graph, identify linear inequality, slope-intercept form
        • Condensed: Determine equivalent linear inequalities & graphical solutions
        • Graph linear inequalities, vertical & horizontal lines
        • Graph linear inequalities, various forms
        • Given graph, determine linear inequality
      • Application of Linear Inequalities
        • Given description, determine inequality, graph, & possible solutions
        • Given graph, determine inequalities in standard form, real-world context
        • Given description, determine linear inequalities in standard form, including tables, real-world context
        • Given description & table, graph linear inequality, real-world context
        • Given description, determine linear inequalities in standard form & specific solutions, real-world context
        • Given description, determine linear inequality in standard form, graph, & determine specific solutions, real-world context
        • Given description, determine linear inequality in various forms, graph, & determine specific solutions, real-world context
        • Solve linear programming problems, real-world context
    • Compound Inequalities
      • Solve compound inequalities, "and" solutions, multiple choice
      • Solve & graph compound inequalities, "and" solutions
      • Solve & graph compound inequalities, "and" solutions, including real-world context
      • Solve & graph compound inequalities, "or" solutions
      • Condensed: Solve & graph compound inequalities
      • Given description, determine graph of inequality
      • Given description, determine compound inequality, graph, & possible solutions
      • Interpret meaning of inequality, real-world context
    • Absolute Value Inequalities
      • Absolute Value Inequalities with Setup
        • Given linear absolute value inequality, determine compound inequality
        • Solve & graph linear absolute value inequalities, "and" solutions, including setup
        • Solve & graph linear absolute value inequalities, "or" solutions, including setup
        • Solve & graph linear absolute value inequalities, including setup
        • Condensed: Solve & graph linear absolute value inequalities, including setup
        • Solve & graph linear absolute value inequality, extra coefficient or constant, including setup
        • Condensed: Solve & graph linear absolute value inequalities, including extra constant or coefficient & setup
      • Absolute Value Inequalities without Setup
        • Solve & graph linear absolute value inequalities, "and" solutions
        • Solve & graph linear absolute value inequalities, "or" solutions
        • Condensed: Solve & graph linear absolute value inequalities
        • Solve & graph linear absolute value inequalities, including extra constant or coefficient
        • Solve & graph linear absolute value inequalities, extra constant or coefficient, multiple choice
        • Create linear absolute value inequalities, real-world context
        • Create linear absolute value equations, real-world context
  • Functions
    • Identifying Functions
      • Determine function definition, fill in the blank
      • Determine & justify functions, table representations, no domain & range language
      • Determine functions, set & table representations
      • Identify & determine functions, set & table representations
      • Determine functions, mapping representations, no domain & range language
      • Determine functions, mapping representations
      • Given relation & additional point, determine functions, multiple representations
      • Determine functions, graphical representations
      • Given step graphs, identify functions
      • Determine functions, multiple representations, including justification, no domain & range language
      • Identify functions, description representations
    • Identifying & Justifying Functions
      • Determine & justify functions, mapping representations, no domain & range language
      • Determine & justify functions, mapping representations
      • Determine & justify functions, set representations, no domain & range language
      • Determine & justify functions, set representations
      • Identify functions using equivalent mapping diagrams & sets of ordered pairs
      • Determine & justify functions, table representations
      • Determine & justify functions, graphical representations
      • Identify & justify functions & non-functions, graphical representations
      • Identify functions, multiple representations, including justification
      • Condensed: Identify, justify, & determine functions
    • Domain & Range of Functions
      • Determine if value is in domain or range, set & table representations
      • Determine if value is in domain or range, graphical representations
      • Given graph, determine domain & range
      • Determine restricted domain & range of linear functions
      • Determine discrete domain & range, real-world context
      • Determine continuous domain & range, real-world context
      • Condensed: Determine domain & range, including real-world context
    • Function Notation
      • Given set or table, determine function value
      • Given linear function, determine function value
      • Condensed: Given graph or linear function, determine function value
      • Given quadratic function, determine function value
      • Condensed: Given linear or quadratic function, determine function value
      • Given graph, determine function value
      • Interpret & solve problems involving function notation, real-world context
    • Determine Parent Functions & Points of Intersection
      • Determine whether given table represents linear or exponential function
      • Determine points of intersection of various functions, not absolute value or polynomial
      • Condensed: Determine points of intersection of functions
      • Determine whether given table represents linear, exponential, or quadratic function
      • Determine whether given graph represents linear, exponential, or quadratic function
      • Condensed: Determine what function given table or graph represents
    • Graph Functions
      • Given various functions, identify graph
      • Given graph, identify various functions
    • Inverse Functions
      • Determine inverse of linear function
      • Determine inverse of quadratic & square root functions
      • Determine inverse of cubic & cube root functions
      • Condensed: Determine inverse of linear, quadratic, square root, cubic, & cube root functions
      • Determine inverse of various functions
  • Linear Concepts
    • Determining Solution of Linear Equation
      • Given linear equation in slope-intercept form, determine if point is on line
      • Given linear equation in slope-intercept form, identify point on line
      • Given linear equation in standard form, determine if point is on line
      • Given linear equation in standard form, identify point on line
      • Given horizontal or vertical linear equation, determine if point is on line
      • Given horizontal or vertical linear equation, identify point on line
      • Given linear equation in slope-intercept form & value of one variable, determine value of other variable
      • Given linear equation in slope-intercept form & y-value, determine x-value, fractional coefficients or constants
      • Condensed: Given linear equation in slope-intercept form & graph, identify point on line
      • Given graph of linear equation, identify point on line
    • Slope of Line
      • Finding & Using Slope
        • Given equation in slope-intercept form, determine next value in table, Δx = 1
        • Given equation in slope-intercept form, determine next value in table
        • Given equation in slope-intercept form, determine values in table
        • Given table of linear equation, determine rate of change & specific value
        • Given table, determine rate of change & specific value, function notation, integer rate of change
        • Given table, determine rate of change & specific value, function notation
        • Given table of linear function, determine slope & y-intercept
        • Given linear graph, determine slope & y-intercept, integer slope
      • Comparing Slopes
        • Identify linear table with most extreme rate of change
        • Identify linear graph with most extreme rate of change
        • Given description, compare rates of change, real-world context
        • Compare rates of changes represented differently
        • Condensed: Compare rates of change
      • Identifying Slope Category
        • Given graph of horizontal or vertical line, determine rate of change
        • Given linear graph, identify type of slope
        • Identify linear graph with specific type of slope
        • Given linear equation, identify type of slope
        • Given table of linear equation, identify type of slope
        • Condensed: Identify type of slope
      • Finding Slope
        • Finding Slope Given Points
          • Given two points with integer coordinates, determine rate of change
          • Given two points, determine rate of change, integer solution, including undefined
          • Given two points, determine rate of change, one coordinate is fraction
          • Given two points, determine rate of change, two coordinates are fractions
          • Given table of linear equation, determine rate of change
        • Finding Slope Given Equation or Graph
          • Given equation in point-slope form, identify slope
          • Given equation in slope-intercept form, determine rate of change, integer solution
          • Given equation in slope-intercept form, determine rate of change
          • Given equation of horizontal or vertical line, determine rate of change
          • Given linear equation in standard form, determine rate of change
          • Given linear graph, determine rate of change, integer solution
          • Given linear graph, determine rate of change
          • Given linear graph, determine rate of change, various scales
          • Given linear graph, determine slope & y-intercept
          • Given graph of piece-wise function, determine rate of change over specific interval
      • Application of Slope
        • Given graph or table of linear function, determine slope or y-intercept, real-world context
        • Given right triangle, use legs to determine slope, real-world context
        • Given graph of similar right triangles, identify equivalent slopes
    • Writing Equation of Line
      • Writing Equation Given Point & Slope
        • Given slope & y-intercept, determine equation
        • Given point & integer slope, determine linear equation in point-slope form, including slope-intercept form conversion
        • Given point & integer slope or rate of change, determine linear equation in slope-intercept form
        • Given point & integer slope, determine linear equation in slope-intercept form
        • Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
        • Given point & fractional slope, determine linear equation in slope-intercept form, integer y-intercept
        • Given point & fractional slope, determine linear equation in slope-intercept form, fractional y-intercept
      • Writing Equation Given Two Points
        • Given two points, determine linear equation in slope-intercept form, integer slope
        • Given two points, determine linear equation in point-slope form, integer slope, including slope-intercept form conversion
        • Given two points, determine linear equation in standard form, integer slope, including slope-intercept form conversion
        • Given two points, determine linear equation in slope-intercept form, fractional slope
        • Given two points, determine linear equation in point-slope form, fractional slope, including slope-intercept form conversion
        • Given two points, determine linear equation in standard form, fractional slope, including slope-intercept form conversion
        • Given two points, determine linear equation, undefined slope
        • Given two points, determine linear equation, zero slope
        • Given linear table, determine slope, y-intercept, & equation
        • Given intercepts, determine linear equation in slope-intercept form
      • Writing Equation Given Various Components
        • Given linear equation, write equation in requested form
        • Given points or slope & point, determine linear equation in standard form
        • Given points or slope & point, determine linear equation in point-slope or standard form
        • Given points or slope & point, determine linear equation in various forms
        • Condensed: Given two points, determine linear equation in slope-intercept form, including horizontal & vertical lines
      • Writing Equation Given Graph
        • Writing Equation Given Graph Through Origin
          • Given linear graph through origin, determine equation in slope-intercept form, integer slope, 1 ≤ |m| ≤ 3
          • Given linear graph through origin, determine equation in slope-intercept form, integer slope
          • Given linear graph through origin with points shown on line, determine equation in slope-intercept form, integer slopes
        • Writing Equation Given Graph, Slope-Intercept Form
          • Given linear graph, determine equation in slope-intercept form, m = 1
          • Given linear graph, determine equation in slope-intercept form, m = 1, various scales
          • Given linear graph, determine equation in slope-intercept form, m = ±1, various scales
          • Given linear graph, determine equation in slope-intercept form, integer slopes
          • Given linear graph, identify equation in slope-intercept form, integer slopes, various scales
          • Given linear graph, determine equation in slope-intercept form, integer slopes, various scales
          • Given linear graph, determine equation in slope-intercept form, fractional slopes
          • Given linear graph, determine slope, y-intercept, & equation
          • Given linear graph, identify equation, slope-intercept form
          • Condensed: Given linear graph, determine equation in slope-intercept form & specific value, various scales, including real-world context
          • Given equation in slope-intercept form, identify graph, integer slopes, various scales
        • Writing Equation Given Graph, Various Forms
          • Given linear graph, determine equation in point-slope form
          • Given linear graph, determine equation in standard form
          • Given linear graph, identify equation, various forms
        • Identify Equivalent Graphs & Equations
          • Identify equivalent linear graphs & equations in slope-intercept form
          • Identify equivalent linear graphs & equations in slope-intercept form, various scales
          • Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
    • Intercepts
      • Intercepts, Given Graph
        • Given linear graph, plot y-intercept
        • Given linear graph, plot x-intercept
        • Given linear graph, determine coordinates of y-intercept
        • Given linear graph, determine coordinates of x-intercept
        • Given linear graph, locate intercept or determine coordinates, various scales
        • Given linear graph, identify equation, various forms
      • Intercepts, Given Equation
        • Given linear equation in slope-intercept form, plot y-intercept
        • Given equation of horizontal or vertical line, plot y-intercept
        • Given linear equation in slope-intercept form, determine coordinates of y-intercept
        • Given linear equation in slope-intercept form, determine coordinates of x-intercept
        • Given linear equation in standard form, determine coordinates of y-intercept
        • Given equation of horizontal or vertical line, determine coordinates of y-intercept
        • Given equation of horizontal or vertical line, determine coordinates of x-intercept
        • Given linear equation, determine intercepts
        • Condensed: Given linear equation, determine x- or y-intercepts
    • Equations, Tables, & Graphs
      • Equation to Table
        • Fill Missing Value in Table
          • Given linear equation, fill missing value in table, m = 1
          • Given linear equation, fill missing value in table, m = 1, Δx ≥ 5
          • Given linear equation, fill missing value in table, integer slope, Δx ≥ 5
          • Given linear equation, fill missing value in table, integer slope, b = 0
          • Given linear equation, fill missing value in table, integer slope, b = 0, Δx ≥ 5
          • Given linear equation, fill missing value in table, integer slope
          • Given linear equation & one x-value, determine y-value in table
        • Fill Table
          • Given linear equation & table, determine another point, m = 1
          • Given linear equation & table, determine another point, integer slope, b = 0
          • Given linear equation, determine table values
          • Given linear equation & two x-values, determine y-values in table
          • Given linear equation, fill table, m = 1
          • Given linear equation, fill table, integer slope, b = 0
          • Given linear equation, fill table, integer slope
          • Given horizontal or vertical linear equation, fill table
          • Given description & linear equation, fill table & determine solution, real-world context
      • Equation to Graph
        • Standard Form to Graph
          • Given linear equation in standard form, graph
          • Given linear equation in standard form, graph, scrambled variable terms
          • Determine linear equation in standard form & graph, real-world context
          • Condensed: Determine linear equation in standard form & graph, including real-world context
        • Slope-Intercept Form to Graph
          • Slope-Interecept Form to Graph Scale of One
            • Graph linear equations, m = 1
            • Graph linear equations, integer slope not including one & negative one, b = 0
            • Graph linear equations, integer slope not including one & negative one
            • Graph proportional linear equation
            • Graph linear equations, fractional slope
            • Condensed: Given linear equation or description, determine graph, fractional slope, including real-world context
            • Given description of linear equation, identify graph, fractional slope, real-world context
            • Condensed: Identify equivalent equations, graphs, & tables
          • Slope-Intercept Form to Graph Various Scales
            • Graph linear equations, m = 1, various scales
            • Given equation in slope-intercept form, graph line, m = ±1, various scales
            • Graph linear equations, integer slope, various scales
            • Graph linear equations, fractional slope, various scales
            • Graph linear equations, including horizontal & vertical, integer slope, various scales
            • Condensed: Graph linear equations, including horizontal & vertical, various scales
      • Basic Graphing
        • Given table, graph proportional linear equation
        • Given point & integer slope, graph line
        • Given point & slope, graph line
      • Graph to Table
        • Given linear graph, determine table value, m = 1, table point off graph
        • Given linear graph, determine table value, table point off graph
        • Given linear graph with points shown on line, determine table value
        • Given linear graph through origin with points shown on line, determine table values, one table point off graph
        • Given linear graph through origin with points shown on line, determine table value, table point off graph
        • Given linear graph through origin, determine table value
        • Given linear graph through origin, determine table value, table point off graph
        • Given linear graph through origin, determine table values, one table point off graph
      • Table to Equation
        • Given table, determine linear equation, m = 1
        • Given table, determine linear equation, integer slope, b = 0
        • Given table, determine linear equation, integer slope
        • Given table representing horizontal linear equation, determine equation
        • Given table representing vertical linear equation, determine equation
        • Given table, identify linear equation in slope-intercept form, rational constants & coefficients
        • Given description, determine linear equation, fill table, & determine solution, real-world context
    • Identifying Key Features of Linear Function
      • Given table of linear equation, determine slope & intercepts
      • Given graph of linear equation, determine slope & intercepts
      • Given linear equation in standard form, determine slope
      • Given linear equation in standard form, solve for y
      • Given equation in slope-intercept form, identify slope & y-intercept
      • Given linear equation, determine slope & intercepts
      • Condensed: Given linear equation in standard form, solve for y or determine slope
      • Condensed: Given linear equation in various forms, determine slope or convert to slope-intercept form
      • Given positive point & whole number slope, determine y-intercept, equation, & specific value
      • Given point & integer slope, determine y-intercept, equation, & specific value
      • Given linear graph, determine equation in slope-intercept form & specific value, various scales
    • Vertical & Horizontal Lines
      • Given vertical linear equation, determine graph
      • Given horizontal linear equation, determine graph
      • Given graph of vertical line, determine equation
      • Given graph of horizontal line, determine equation
      • Condensed: Given graph of horizontal or vertical line, determine equation
    • Perpendicular, Parallel, or Neither
      • Identifying Parallel or Perpendicular Lines
        • Given equation in slope-intercept form, determine slope of parallel line
        • Given equation in slope-intercept form, determine slope of perpendicular line
        • Given two slope-intercept form equations, identify as parallel or perpendicular
        • Condensed: Given equation in slope-intercept form, determine slope of parallel or perpendicular line
        • Given equation in various forms, determine slope of parallel line
        • Given equation in various forms, determine slope of perpendicular line
        • Condensed: Given equation in various forms, determine slope of parallel or perpendicular line
        • Given two equations in standard form, identify as parallel or perpendicular
        • Given two pairs of points, determine if lines containing points are parallel or perpendicular
        • Identify equation that is parallel or perpendicular to line through two given points
      • Writing Equations of Parallel or Perpendicular Lines
        • Given equation in slope-intercept form, determine equation of parallel line through specified point
        • Given equation in slope-intercept form, determine equation of perpendicular line through specified point
        • Given equation in slope-intercept form, determine equation of parallel or perpendicular line through specified point
        • Determine equation of line through specified point parallel or perpendicular to x-axis
        • Determine equation of line through specified point parallel or perpendicular to y-axis
        • Condensed: Determine equation of line through specified point parallel or perpendicular to x- or y-axis
        • Given equation in various forms, determine equation of parallel line through specified point
        • Given equation in various forms, determine equation of perpendicular line through specified point
        • Given equation in various forms, determine equation of parallel or perpendicular line through specified point
    • Line of Best Fit & Scatter Plots
      • Identify positive & negative correlations in scatter plots
      • Identify linear & nonlinear associations in scatter plots
      • Condensed: Interpret scatter plots
      • Sketch line of best fit
      • Sketch line of best fit & determine equation, graph scales of one
      • Sketch line of best fit & determine equation, various graph scales
      • Condensed: Sketch line of best fit & determine equation
      • Sketch line of best fit & determine predicted value
      • Sketch line of best fit & determine equation, real-world context
      • Determine residuals
    • Linear Word Problems
      • Identifying Key Features Given Verbal Description
        • Form 1 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope, only input to output questions
        • Form 2 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope
        • Given slope & intercept, interpret linear relationship & determine slope-intercept equation, including negative slope
        • Form 3 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
        • Form 4 – Given point & slope, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
        • Form 5 – Given two points, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
        • Form 6 – Given linear graph, interpret linear relationship & determine slope-intercept equation
        • Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slope-intercept equation, & graph
        • Given description of linear relationship, determine slope, y-intercept, & equation, real-world context
        • Determine linear equation in standard form & graph, real-world context
        • Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
      • Choosing Correct Model Given Verbal Description
        • Given description of linear equation, identify graph, integer slope, real-world context
        • Given description or table, determine linear graph, real-world context
        • Given description, determine equation & specific value, real-world context
        • Given description of linear relationship, identify graph, table, or equation, real-world context
        • Identify equivalent representations of linear relationship, including real-world context
        • Given linear word problem, identify graph
        • Given linear equation, interpret slope & y-intercept, real-world context
    • Absolute Value Functions
      • Determine x- & y-intercepts of absolute value functions
      • Determine minimum & maximum of absolute value functions
      • Identify & graph reflections of absolute value functions
      • Identify & graph vertical & horizontal shifts of absolute value functions
      • Identify & graph vertical & horizontal stretches & compressions of absolute value functions
      • Given absolute value equation, identify description of transformation
      • Condensed: Determine graphical attributes of absolute value functions
      • Graph absolute value functions using all transformations
      • Condensed: Graph absolute value functions using any transformation
      • Graph absolute value functions using vertex & intercepts
      • Determine points of intersection of absolute value functions
      • Compare absolute value functions represented differently
  • Systems
    • Systems of Equations
      • Determining Solution to System of Equations
        • Given tables, determine system of linear equations
        • Given table representing system of linear equations, determine solution, real-world context
        • Given graph of system of linear equations, identify specific domain value, real-world context
        • Graph systems of linear equations & determine solutions, including real-world context
        • Given system of linear equations, identify x- or y-value of solution
        • Given system of linear equations, identify solution
        • Given system of linear equations, identify solution or x- or y-value of solution
        • Given system of linear equations & description, identify solution, real-world context
        • Condensed: Given system of linear equations, identify solution, including real-world context
        • Determine systems of linear equations & solutions, real-world context
        • Determine & justify solutions to systems of linear equations, real-world context
        • Condensed: Determine systems of linear equations & solutions, including real-world context
      • Solving Systems of Equations, Graphing
        • Given graph of system of linear equations, determine solution, rays on graph to establish pattern
        • Given graph of system of linear equations, determine equations in slope-intercept form
        • Determine & verify graphical solutions to systems of linear equations, slope-intercept form
        • Given system of linear equations, graph system, including tables
        • Given system of linear equations, determine point of intersection, slope-intercept form
        • Given system of linear equations, graph & determine point of intersection, slope-intercept form
        • Given description of system of linear equations, graph & determine equations or tables
        • Condensed: Given system of linear equations or description, graph system, including real-world context
      • Solving Systems of Equations, Substitution
        • Given system of linear equations with same isolated variable, determine point of intersection, integer coordinates
        • Given system of linear equations, determine point of intersection, integer coordinates, one horizontal or vertical & one slope-intercept form
        • Given system of linear equations, determine point of intersection, integer coordinates, one equation in standard form
        • Condensed: Given system of linear equations, determine solution, substitution bias
        • Solve, interpret, or determine systems of linear equations, slope-intercept form, real-word context
        • Solve, interpret, or determine systems of linear equations, standard form, real-word context
        • Determine systems of linear equations & solutions, substitution bias, real-world context
        • Determine solutions of linear equations, substitution bias, including given system, real-world context
        • Solve systems of linear equations, infinite possibilities or no solution
        • Condensed: Solve or determine system of equations, likely to have same variable isolated
      • Solving Systems of Equations, Elimination
        • Given system of linear equations in standard form, determine point of intersection, integer coordinates
        • Determine systems of linear equations & solutions, elimination bias, real-world context
        • Solve systems of linear equations, multiply at most one equation
        • Solve systems of linear equations, multiply one or both equations
        • Condensed: Solve or determine system of equations, both equations in standard form
      • Solving Systems of Equations, Mixed Methods
        • Given system of linear equations, determine point of intersection, at least one equation with variables on both sides
        • Condensed: Determine systems of linear equations & solutions
    • Systems of Inequalties
      • Basic Systems of Inequalities
        • Given graph, determine solution of systems of linear inequalities
        • Determine equivalent systems of linear inequalities & graphical solutions
        • Graph systems of two linear inequalities, slope-intercept form
        • Graph systems of three linear inequalities, slope-intercept form
        • Solve systems of linear inequalities
      • Application of Systems of Inequalities
        • Given linear system of inequalities graph, identify true statements
        • Given description, determine system of linear inequalities in standard form & solution point, real-world context
        • Given description, determine system of linear inequalities in standard form & identify solution point, including three inequalities, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form & determine solution points, real-world context
        • Given description & graph, determine system of linear inequalities in standard form & shaded region, real-world context
        • Given description & graph, determine system of linear inequalities in standard form & shaded region, including three inequalities, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form, shaded region, & true statements, real-world context
        • Given description of system of linear inequalities, identify graph of system
        • Given description, determine system of linear inequalities in standard form & identify graph, real-world context
        • Given description, determine system of linear inequalities in standard form & graph, real-world context
        • Condensed: Given description, determine system of linear inequalities in standard form & shaded region & determine solution points, real-world context
        • Condensed: Graph system of linear inequalities & determine system of linear inequalities, including real-world context
  • Exponents
    • Power Rule of Exponents
      • Apply power rule, one variable, positive exponents
      • Apply power rule, including multiple variables, positive exponents
      • Apply power & product rules of exponents, one variable, positive exponents
      • Apply product & power rules of exponents, one variable, coefficient of negative one
      • Apply power & product rules of exponents, multiple variables, positive exponents
      • Apply power & product rules of exponents, fraction with numerator of one, positive exponents
    • Product Rule of Exponents
      • Product of Powers, Only Variables
        • Express repeated variables as powers, single variable
        • Express repeated variables as powers, multiple variables
        • Express powers as repeated variables
        • Simplify single variable powers, negative base or coefficient
        • Apply product rule of exponents, one variable, positive exponents
        • Apply product rule of exponents, one variable, positive exponents, displayed with parentheses
        • Apply product rule of exponents, two variables, three to four factors, positive exponents
        • Apply product rule of exponents, two variables, four to six factors, positive exponents
      • Product of Powers, Including Coefficients
        • Express repeated variables as powers or powers as repeated variables
        • Express repeated variables as powers, coefficients other than one
        • Apply product rule of exponents, positive exponents
        • Apply product rule of exponents, one variable, positive exponents, coefficients other than one
    • Quotient Rule of Exponents
      • Apply quotient rule of exponents, one variable, positive exponents, greater exponent in numerator
      • Apply quotient rule of exponents, one variable, positive exponents, greater exponent in denominator
      • Apply quotient rule of exponents, positive exponents
      • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents
      • Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, positive exponents
      • Apply product & quotient rules of exponents, one or two variables, positive exponents
    • Negative Exponents
      • Basic Negative Exponents
        • Express negative power using positive exponent
      • Power Rule with Negative Exponents
        • Apply power rule, one variable, at least one negative exponent
        • Apply power rule, one variable, including non-positive exponents
        • Apply power rule, one variable, coefficient of negative one, at least one negative exponent
        • Apply power rule, including multiple variables & negative exponents
        • Apply power rule, coefficient of negative one, multiple variables, including negative exponents
        • Apply power rule, negative base or coefficient, multiple variables, including negative exponents
        • Apply power rule, including multiple variables & negative exponents
        • Apply power rule, coefficient of negative one in power, including multiple variables & negative exponents
        • Apply power rule of exponents, negative exponents
        • Apply power & product rules of exponents, fraction with numerator of one, including negative exponents
        • Apply power & product rules of exponents, fraction with numerator of one, coefficient of negative one in power, including negative exponents
        • Apply product, quotient, & power rules of exponents, multiple variables, coefficient of negative one
      • Product Rule with Negative Exponents
        • Apply power rule, multiple variables, coefficients other than one, including negative exponents
        • Apply product rule of exponents, one variable, no coefficients, at least one negative exponent
        • Apply product rule of exponents, negative exponents
        • Apply product rule of exponents, two variables, three to four factors, at least one negative exponent
        • Apply product rule of exponents, two variables, three to four factors, one variable cancels
        • Apply product rule of exponents, two variables, four to six factors, at least one negative exponent
        • Apply product rule of exponents, two variables, four to six factors, at least one variable cancels
        • Apply product rule, multiple variables, coefficients other than one, including negative exponents
      • Quotient Rule with Negative Exponents
        • Apply quotient rule of exponents, one variable, at least one negative exponent
        • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, at least one negative exponent
        • Apply quotient rule of exponents, two or three variables, two or three factors in numerator & denominator, at least one negative exponent
        • Apply quotient rule of exponents, negative exponents
        • Apply product & quotient rules of exponents, one or two variables, at least one negative exponent
    • Mixed Properties of Exponents
      • Simplifying Exponential Expressions
        • Express negative power using positive exponent, coefficient other than one
        • Apply power rule of exponents, positive exponents
        • Simplify powers, fractional algebraic base, including negative exponents
        • Apply product rule of exponents, coefficients other than one
        • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, positive exponents, coefficients other than one
        • Apply quotient rule of exponents, one or two variables, one or two factors in numerator & denominator, including negative exponents, coefficients other than one
        • Apply product, quotient, & power rules of exponents, one variable
        • Apply product & quotient rules of exponents, multiply two fractions, one or two variables, at least one non-positive exponent
        • Apply power, product, & quotient rules of exponents, positive exponents
        • Apply power, product, & quotient rules of exponents, including negative exponents
        • Apply power, product, & quotient rules of exponents, including negative exponents & coefficient of negative one in power
      • Multiplying Exponential Expressions
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one negative exponent
        • Apply product & quotient rules of exponents, divide fractions, one or two variables, coefficients other than one, including negative exponents
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, positive exponents
        • Apply product & quotient rules of exponents, multiply two fractions, multiple variables, at least one non-positive exponent
        • Apply power, product, & quotient rules of exponents, multiply fractions, positive exponents
        • Apply power, product, & quotient rules of exponents, multiply fractions, including negative exponents
      • Dividing Exponential Expressions
        • Apply product & quotient rules of exponents, divide two fractions, one or two variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, multiply fractions, one or two variables, coefficients other than one, including negative exponents
        • Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
        • Apply product & quotient rules of exponents, divide two fractions, multiple variables, at least one non-positive exponent
        • Apply power, product, & quotient rules of exponents, divide fractions, positive exponents
        • Apply power, product, & quotient rules of exponents, divide fractions, including negative exponents
      • Mixed Operations of Exponential Expressions
        • Apply product & quotient rules of exponents, negative exponents
        • Apply product & quotient rules of exponents, negative exponents, coefficients other than one
        • Apply product, quotient, & power rules of exponents, multiple variables
    • Application of Exponents
      • Determine algebraic expressions for perimeter & area of rectangles
      • Given algebraic expressions for area & side of rectangles, determine expression for missing side
    • Numerical Exponential Expressions
      • Evaluate powers, whole number base, non-positive exponent
      • Evaluate powers, integer base, non-positive exponent, including negative coefficients
      • Evaluate powers, positive fractional base, including non-positive exponents
      • Evaluate powers, fractional base, positive exponent
      • Evaluate powers, fractional base, negative exponent
      • Evaluate powers, fractional bases
      • Condensed: Evaluate powers with negative exponents
    • Rational Exponents
      • Evaluate numerical expressions with rational exponents
      • Simplify numerical expressions with rational exponents
  • Radicals & Roots
    • Simplifying Radicals
      • Determine square roots of perfect squares
      • Determine principal square root of perfect squares
      • Simplify square roots
      • Simplify square roots, coefficient greater than one
      • Identify steps to simplify square roots
      • Given square root expression, evaluate for specific value
      • Condensed: Simplify square roots, including algebraic expressions
      • Evaluate perfect cube roots
      • Simplify radical expressions, perfect powers
      • Multiply radical expressions, numbers & variables
      • Add & subtract radical expressions, one or two variables, simplified radicals
      • Add & subtract radical expressions, one or two variables, radicals to simplify
      • Condensed: Add & subtract radical expressions
    • Solving Radicals
      • Solve perfect square root equations
      • Condensed: Determine square roots of perfect squares
      • Solve perfect cube root equations
      • Condensed: Determine cube roots of perfect cubes
      • Condensed: Evaluate & compare perfect square & cube roots
      • Solve square root equations, square root = #
      • Solve square root equations, square root = square root
      • Solve square root equations, add & subtract from root
  • Quadratic Functions
    • Identifying Key Features of Quadratic Functions
      • Determine Intercepts
        • Determine x-intercept(s) of quadratic functions
        • Determine y-intercept of quadratic functions
        • Determine x-intercepts/zeros & y-intercepts of quadratic functions, vertex form
        • Determine zero(s)/x-intercept(s) of quadratic functions, b = 0
        • Determine zero(s) of quadratic functions
        • Given graph or table of quadratic function, determine x- & y- intercepts
      • Determine Maximum & Minimum Values
        • Given graph of quadratic function, determine minimum or maximum value
        • Given quadratic equation, determine minimum or maximum value
        • Determine minimum & maximum of quadratic functions
      • Determine Vertex, Symmetry, Increase & Decrease, & End Behavior
        • Determine vertex of quadratic functions
        • Determine symmetry of quadratic functions
        • Determine intervals of increase & decrease of quadratic functions
        • Determine intervals where quadratic function is positive or negative
        • Determine end behavior of quadratic functions
      • Determine Attributes & Graph
        • Determine axis of symmetry, vertex, & minimum & maximum of quadratic functions, vertex form
        • Given graph of quadratic function, determine attributes
        • Condensed: Determine graphical attributes of quadratic functions
        • Condensed: Given graph, equation, or table, determine attributes of quadratic function
        • Given quadratic equation, determine attributes & graph, a ≠ ±1
        • Given quadratic equation, determine attributes & graph, a = 1
        • Given quadratic equation, determine attributes & graph, a = -1
        • Condensed: Given quadratic equation, determine attributes & graph
    • Graphing Quadratic Functions
      • Given quadratic equation, determine graph, b = 0
      • Given quadratic equation, determine graph, b = 0, including fractional leading coefficient
      • Graph quadratic equations
      • Given quadratic equation in vertex form, determine graph
      • Given quadratic equation in standard form, determine graph
      • Graph quadratic functions using all transformations
      • Given equation, graph quadratic function
      • Given quadratic equation, vertex, & point, graph function & determine attributes
      • Condensed: Graph quadratic functions using any transformation
    • Writing Equations of Quadratic Functions
      • Given graph of quadratic function, determine equation
      • Given graph of quadratic function, determine equation
      • Given vertex & point, determine quadratic equation, vertex form
      • Given quadratic equation in standard form, determine vertex form of equation
      • Given vertex & point, determine quadratic equation, standard form
      • Given graphical attributes, determine equation of parabola
      • Given quadratic equation in vertex form, determine standard form of equation
    • Solving Quadratic Functions
      • Solving Quadratics, Zero Product
        • Apply zero product property to solve factored quadratic equations
        • Identify zeros of factored quadratics
        • Determine relationship between zeros & linear factors of quadratic functions
      • Solving Quadratics, Factoring GCF
        • Solve quadratic binomial equation by factoring out GCF
        • Solve quadratic binomial equation by factoring out GCF, one term on each side
        • Solve quadratic binomial equation by factoring out GCF, combining like terms necessary
      • Solving Quadratics, Factoring Trinomials & Difference of Squares
        • Solve quadratic equations using factoring, a = 1, b > 0, 0 < c ≤ 40, zero on one side
        • Solve quadratic equations using factoring, a = 1, b ≠ 0, |c| ≤ 40, zero on one side
        • Solve quadratic equations using factoring, a = 1, b ≠ 0, c ≤ 40, terms on both sides
        • Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, terms on both sides
        • Solve quadratic equations using factoring, 0 < a ≤ 10, b > 0, 0 < c ≤ 40, zero on one side
        • Solve quadratic equations using factoring, |a| ≤ 10, b ≠ 0, |c| ≤ 40, zero on one side
        • Solve quadratic equations using factoring, |a| ≤ 10, |c| ≤ 40, terms on both sides
        • Solve quadratic equations using factoring, 1 ≤ a ≤ 10, b > 0, 1 ≤ c ≤ 10, zero on one side
        • Solve quadratic equations using factoring, difference of squares
        • Factor perfect square trinomials, degree two, one variable
        • Factor perfect square trinomials, degree two, two variables
      • Solving Quadratics, Square Root Method
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer solutions
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, rounded solutions
        • Determine solutions to quadratic equations, a ≠ ±1, b = 0, integer or rounded solutions
        • Determine fractional solution to quadratic equations, a ≠ ±1, b = 0
        • Determine exact solution to quadratic equations, a = ±1, b = 0
        • Condensed: Determine solutions to quadratic equations, a ≠ ±1, b = 0
      • Solving Quadratics, Quadratic Formula
        • Given quadratic equation in standard form, determine discriminant
        • Given quadratic equation in standard form, determine number of solutions
        • Given quadratic equation in standard form, determine solutions rounded to nearest hundredth
        • Given quadratic equation, determine solutions rounded to nearest hundredth, constant on one side
        • Given quadratic equation, determine solutions rounded to nearest hundredth, combine like terms first
        • Given quadratic equation in standard form, determine attributes & solutions rounded to nearest hundredth
        • Given quadratic equation in standard form, determine exact solutions
        • Given quadratic equation in standard form, determine exact solutions, combine like terms first
      • Solving Quadratics, Completing the Square
        • Determine constant required to complete the square, a ≥ 1, including fractions
        • Solve quadratic equations, complete the square, integers, a = 1, real solutions
        • Solve quadratic equations, complete the square, integers, a > 1, real solutions
        • Solve quadratic equations, complete the square, a > 1, real solutions
        • Condensed: Solve quadratic equations, complete the square, integers, real solutions
    • Transformations of Quadratic Functions
      • Identify & graph vertical & horizontal shifts of quadratic functions
      • Identify & graph vertical & horizontal stretches & compressions of quadratic functions
      • Given quadratic equation, identify description of transformation
      • Identify descriptions of graphs of quadratic parent functions & transformed functions
      • Given description of transformation, determine quadratic function
      • Describe parameter changes to quadratic parent functions
      • Determine effects of parameter changes in quadratic relationships, real-world context
    • Vertical Motion Problems
      • Given initial height & velocity of object in vertical motion, determine function, table, & graph of position
      • Given initial height & velocity of object in vertical motion, determine position function & maximum height
      • Given initial height & velocity of object in vertical motion, determine position function & time to maximum height
      • Given initial height & velocity of object in vertical motion, determine position function & time to ground
      • Given initial height & velocity of object in vertical motion, determine position function & specific time
      • Given initial height at ground & positive velocity of object in vertical motion, determine position function & time to ground
      • Given initial height & negative velocity of object in vertical motion, determine position function & specific time
      • Given initial height & velocity of object in vertical motion, determine position function, specific time, & specific height
      • Given height of dropped object, determine position function & specific time
      • Condensed: Given initial height & velocity of object in vertical motion, determine position function, maximum height, or time to maximum height
      • Condensed: Given initial height & velocity of object in vertical motion, determine position function & specific times
      • Condensed: Given initial height & velocity of object in vertical motion, determine position graph, position function, & specific times
    • Domain & Range of Quadratic Functions
      • Given description of domain & range of quadratic function, choose graph
      • Given graph of quadratic function, determine domain & range
      • Given equation of quadratic function, determine domain & range
      • Condensed: Determine domain & range of quadratic function
      • Determine restricted domain & range of quadratic functions
  • Absolute Value Functions
    • Given graph, determine absolute value equation
    • Given description of transformation, determine absolute value equation
    • Condensed: Graph absolute value functions using any transformation
  • Exponential Functions
    • Evaluating Exponential Functions
      • Given exponential function, determine function value, non-negative input
      • Given exponential function, determine function value, negative input
      • Given exponential function, determine function value, rational base
      • Given exponential function, determine function value, rational coefficient
      • Given exponential function, determine function value, rational base & coefficient
    • Graphing Exponential Functions
      • Given exponential growth function, determine graph
      • Given exponential growth function, determine graph, includes fractional coefficients
      • Given exponential growth or decay function, determine graph, includes fractional coefficients
      • Given graph, identify solution to exponential equation
      • Given graph, determine equation of exponential function
      • Given equation, graph exponential function
      • Given equation, graph exponential function, including base e
    • Writing Exponential Functions
      • Given table, determine exponential growth function
      • Given table, determine exponential decay function
      • Given table, determine linear or exponential growth function
      • Given graph, determine equation of exponential function
    • Application of Exponential Functions
      • Calculate investment value, annual compounding
      • Calculate investment value, various compounding
      • Calculate depreciating asset value, annual compounding
      • Condensed: Calculate investment & depreciating asset values, annual compounding
      • Determine exponential function, real-world context
      • Given table, determine attributes of exponential function
      • Interpret values in exponential functions, real-world context
    • Given absolute value equation, identify description of transformation
  • Polynomials
    • Standard Form of Polynomials
      • Identify leading coefficient of polynomials
      • Identify leading coefficient of polynomials, including two variables
      • Identify terms of expressions
      • Determine degree, leading coefficient, & type of polynomial
      • Condensed: Determine degree, lead coefficient, standard form, & type of polynomial, including two variables
      • Determine standard form of polynomial, no like terms
      • Determine standard form of polynomial, like terms
      • Determine standard form of polynomial, no like terms, including two variables
      • Determine standard form of polynomial, like terms, including two variables
    • Classifying Polynomials
      • Determine degree of polynomials
      • Determine degree of polynomials, including two variables
      • Identify polynomial as monomial, binomial, or trinomial
      • Identify polynomial as monomial, binomial, or trinomial, including two variables
      • Classify polynomials by degree
      • Classify polynomials by degree & number of terms
      • Condensed: Classify polynomials & identify components of polynomials
    • Operations of Polynomials
      • Addition & Subtraction of Polynomials
        • Add binomials & trinomials, degrees zero to two
        • Subtract binomials & trinomials, degrees zero to two
        • Add binomials & trinomials, degrees zero to three
        • Subtract binomials & trinomials, degrees zero to three
        • Condensed: Add or subtract binomials & trinomials
      • Multiplication & Division of Polynomials
        • Multiply monomial times binomial or trinomial, degrees zero to two
        • Multiply monomial times binomial or trinomial, mixed degrees
        • Multiply binomial times binomial, both degree one
        • Square linear binomial
        • Condensed: Multiply binomial times binomial
        • Multiply binomial times binomial, mixed degrees
        • Multiply linear binomial times quadratic trinomial
        • Multiply binomial times trinomial, mixed degrees
        • Divide polynomials, degree one or two by degree one or two
        • Divide polynomials, degree three or four by degree one
        • Divide polynomials, divisor supports synthetic division
      • Mixed Operations of Polynomials
        • Condensed: Add or subtract binomials & trinomials or multiply monomial times binomial or trinomial
    • Factoring Polynomials
      • GCF or LCM of Polynomials
        • Determine GCF in polynomials, one variable
        • Determine GCF of two monomials, two variables
        • Determine LCM of two monomials, two variables
        • Condensed: Determine GCF or LCM of two monomials, two variables
        • Factor GCF in polynomials, degree one or two, one variable
        • Factor GCF in polynomials, one variable
        • Factor GCF in polynomials, including two variables
        • Determine missing component of GCF
        • Given GCF & one monomial, identify second monomial
      • Factoring Trinomials, a=1
        • Factor quadratic trinomials, a = 1, b > 0, c > 0
        • Factor quadratic trinomials, a = 1
        • Factor quadratic trinomials, a = 1, terms scrambled
        • Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10
        • Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < |c| ≤ 10
        • Condensed: Factor quadratic trinomials, 1 ≤ a ≤ 10, 0 < c ≤ 10 or 0 < |c| ≤ 10
      • Factoring Trinomials, a>1
        • Factor quadratic trinomials, 1 < a ≤ 10, no GCF
        • Factor quadratic trinomials, 1 < |a| ≤ 10, 0 < |c| ≤ 30
        • Factor quadratic trinomials, 1 < a ≤ 10, 0 < c ≤ 30
        • Factor quadratic trinomials, 1 < |a| ≤ 30, 0 < |c| ≤ 40
        • Factor quadratic trinomials, 1 < a ≤ 30, 0 < c ≤ 40
      • Factoring Using Difference of Squares
        • Factor difference of two squares, degree two, one variable, coefficient one
        • Factor difference of two squares, degree two, one variable, terms scrambled
        • Factor difference of two squares, degree two, one variable
        • Factor difference of two squares, two variables
        • Factor difference of two squares, one or two variables
        • Condensed: Factor difference of two squares, degree two
      • Mixed Factoring
        • Factor GCF & remaining quadratic expression, a = 1, one variable
        • Factor GCF & remaining quadratic expression, a ≥ 1, one variable
        • Factor common binomial
        • Factor binomial & its opposite
        • Factor cubic polynomial by grouping, one variable
        • Factor cubic polynomial by grouping & difference of two squares, one variable
        • Identify factors of polynomials
    • Application of Polynomials
      • Determine sums of polynomials or missing polynomial addends
      • Determine differences of polynomials or missing polynomial subtrahends
      • Condensed: Determine sums or differences of polynomials or missing polynomial operands
      • Given polynomial & sum of polynomials, determine missing polynomial
      • Given polynomial & difference of polynomials, determine missing polynomial
      • Add & subtract polynomials to determine expressions for perimeter of various shapes
      • Given monomial & binomial or trinomial, multiply or identify missing value
      • Determine missing value to make polynomial statement true, multiplication
      • Multiply polynomials to determine expressions for areas of rectangles & triangles
      • Divide quadratic trinomial by linear binomial, word problem context
      • Add & multiply polynomials to determine expressions for area & perimeter of rectangles & triangles
  • Rational Expressions & Functions
    • Operations of Rational Expressions
      • Multiply rational expressions
      • Divide rational expressions
    • Simplifying Rational Expressions
      • Simplify rational expressions by factoring GCF, one monomial & one binomial
      • Simplify rational expressions by factoring GCF, two binomials
      • Simplify rational expressions by factoring GCF, two binomials, remaining binomials cancel
      • Simplify rational expressions by factoring GCF, one trinomial or difference of squares
      • Simplify rational expressions by factoring GCF, trinomials & differences of squares
      • Simplify rational expressions by factoring GCF, remaining leading coefficient one
      • Condensed: Simplify rational expressions
      • Condensed: Simplify rational expressions, including trinomials
    • Rational Functions
      • Identify value that makes rational expression undefined
      • Determine values that make rational expressions undefined
      • Given rational function, determine function value
      • Graph rational functions
  • Sequences
    • Arithmetic Sequences
      • Determine terms in arithmetic sequences
      • Given arithmetic sequence, determine common difference & next term
      • Given formula, determine specific term of arithmetic sequence
      • Determine common difference, first term, & formula of arithmetic sequences
      • Condensed: Determine formula & specific terms of arithmetic sequences
    • Geometric Sequences
      • Given formula, determine specific term of geometric sequence
      • Determine formula & specific term of geometric sequences
      • Determine function & specific term for geometric sequences, real-world context
      • Condensed: Determine formula or specific term of geometric sequences
    • Arithmetic & Geometric Sequences
      • Identify arithmetic & geometric sequences & determine common difference or common ratio
      • Given table, determine difference in terms in arithmetic sequence, real-world context
      • Given formula, determine terms in arithmetic & geometric sequences
      • Determine function & specific term for arithmetic & geometric sequences, real-world context
      • Condensed: Identify arithmetic & geometric sequences & determine components of sequences
  • Data Analysis & Probability
    • Counting Methods
      • Fundamental Counting Principle
        • Determine number of combinations using fundamental counting principle, real-world context
        • Determine number of combinations using fundamental counting principle, including repeated letters & digits, real-world context
      • Permutations
        • Given visual model, determine permutations, specified items predetermined
        • Determine permutations using all items, real-world context
        • Determine permutations, real-world context
        • Determine permutation of letters in word, nondistinct letters
        • Determine permutation of letters in word, distinct letters
        • Determine permutations, one nondistinct item, real-world context
        • Determine permutations, multiple nondistinct items, real-world context
        • Condensed: Determine permutation of letters in word, including nondistinct letters
      • Combinations
        • Given lists, determine combinations, choose from one list, real-world context
        • Given lists, determine combinations, choose from two lists, real-world context
        • Determine combinations, real-world context
      • Permutations & Combinations
        • Determine combinations & permutations, two questions, real-world context
        • Determine combinations & permutations, four questions, real-world context
    • Probabiltiy
      • Basic Probability
        • Determine sample spaces
        • Classify probabilities by levels of likelihood
        • Determine odds
        • Determine probabilities & odds, including visual models
        • Determine equivalent probabilities & odds
        • Determine theoretical probabilities
        • Determine theoretical probabilities, fraction answers
        • Determine probabilities of single events
        • Determine probabilities & complementary probabilities of single events, including visual models
        • Determine probabilities & complementary probabilities of single events as fractions, decimals, or percents, including visual models
        • Determine probabilities of flipping coins specified number of times
      • Compound Probability
        • Determine AND Probabilities
          • Given visual model, determine "and" probability as fraction, decimal, or percent, dependent events
          • Determine "and" probabilities, independent events, visuals provided
          • Determine "and" probabilities, independent events, same sample space
          • Determine "and" probabilities, independent events, two distinct sample spaces
          • Determine probabilities of flipping coins & rolling die
          • Determine "and" probabilities, dependent events, multiple choice
          • Determine "and" probabilities, dependent events
          • Determine "and" probabilities, independent & dependent events
          • Determine "and" probabilities, independent & dependent events, including complementary events
        • Determine OR Probabilities
          • Given visual model, determine "or" probability
          • Given visual model, determine "or" probability as fraction, decimal, or percent
          • Determine "or" probabilities as fractions 
          • Determine "or" probabilities as fractions, decimals, or percents
          • Determine "or" probabilities
        • Given visual model, determine "or" probability
        • Given visual model, determine "or" probability as fraction, decimal, or percent
        • Determine "and" probabilities, independent events, visuals provided
        • Determine "and" probabilities, independent events, same sample space
        • Determine "and" probabilities, independent events, two distinct sample spaces
        • Determine "and" probabilities, dependent events, multiple choice
        • Determine "and" probabilities, dependent events
        • Given visual model, determine "and" probability as fraction, decimal, or percent, dependent events
        • Determine probabilities of flipping coins & rolling die
        • Determine "or" probabilities as fractions 
        • Determine "or" probabilities as fractions, decimals, or percents
        • Determine "and" probabilities, independent & dependent events
        • Determine "and" probabilities, independent & dependent events, including complementary events
        • Determine "or" probabilities
      • Experimental Probability & Sampling
        • Identify samples & populations
        • Identify biased samples & questions
        • Identify variables of interest
        • Identify simulations used to acquire simple random samples
        • Identify simulations to model probability events
        • Identify statistical inferences
        • Condensed: Identify samples, populations, variables of interest, & statistical inferences
        • Determine size of sample spaces, compound events
        • Determine sample spaces, compound events
        • Determine experimental probabilities
        • Determine experimental probabilities, fraction answers
        • Compare data from two samples, various representations
      • Predictions from Probabilities
        • Determine inferences from samples
        • Determine predicted values or compare likelihood of events
        • Determine predicted values, theoretical probability
        • Determine predicted values, experimental probability
        • Determine predicted values, experimental or theoretical probability
        • Determine predicted values, theoretical probability, compound events
        • Determine predicted values, experimental probability, compound events
      • Mixed Probability
        • Determine "or" probabilities
        • Determine "or" probabilities, including "and" situations
        • Condensed: Determine probabilities
        • Condensed: Determine experimental & theoretical probabilities
      • Conditional Probaility
        • Determine conditional probabilities from two-way frequency tables
        • Determine conditional probabilities, including two-way frequency tables
    • Data Analysis
      • Measures of Center & Spread
        • Calculating Measures of Center & Spread
          • Identify definition of mean, median, mode, or range
          • Determine mean, median, mode, & range
          • Determine mean, median, mode, or range
          • Determine mean, median, mode, or range from various graphs
          • Given various representations of data, identify mean, median, mode, & range
          • Given mean, median, or range, determine missing or additional value in data set
          • Given mean, median, mode, or range, determine missing value in data set
          • Given additional value in data set, determine change in mean, median, mode, or range
          • Condensed: Determine mean, median, mode, or range, including graphs
          • Determine interquartile range of data
        • Interpreting Measures of Center & Spread
          • Identify & interpret measures of center
          • Identify & interpret measures of variability
          • Identify measures of center based on data distribution
          • Identify measures of variability based on data distribution
          • Determine or interpret shapes & features of graphs
          • Determine or interpret measures of center & spread from graphs
          • Given various representations of data, identify outlier
          • Identify outliers in scatter plots
          • Identify scatterplots with clustered data
      • Stem-&-Leaf Plots
        • Determine mean, median, mode, & range from stem-&-leaf plots
        • Determine mean, median, mode, or range from stem-&-leaf plots
      • Box Plots
        • Determine five-number summary
        • Given boxplot, determine values from five-number summary
        • Determine characteristics of boxplots
        • Solve problems involving interpretation of box plots
        • Solve problems involving five-number summary
        • Solve problems involving interpretation of stacked box plots, real-world context
        • Condensed: Determine five-number summary, including box plots