8th Grade Skills

Real Numbers

Classifying Real Numbers
 Classify numbers as rational or irrational
 Determine relationships between subsets of rational numbers
 Determine relationships between subsets of real numbers
 Determine result of adding & multiplying rational & irrational numbers

Approximating Values of Real Numbers
 Identify location of rational or irrational numbers on number lines
 Identify location of irrational numbers on number lines
 Estimate irrational values
 Estimate irrational numbers, integer radicands, including number line representations
 Estimate irrational numbers, decimal radicands, including number line representations
 Estimate irrational numbers, fraction radicands, including number line representations
 Condensed: Estimate irrational numbers, including number line representations
 Estimate irrational values, multiple terms or factors
 Estimate irrational values, including cube roots & number line representations

Comparing & Ordering Real Numbers

Basic Comparing & Ordering Real Numbers
 Compare rational numbers, positive
 Order positive fractions
 Order positive decimals
 Condensed: Order positive decimals & fractions
 Order decimals & fractions
 Order positive rational numbers, no radicals, no exponents
 Order rational numbers, no radicals, no exponents
 Order real numbers, no exponents
 Order real numbers, exponents are positive
 Order real numbers

Application of Comparing & Ordering Real Numbers
 Given table, order rational numbers, realworld context
 Given set or list, order rational numbers, realworld context
 Order real numbers, positive exponents, percents are whole, including realworld context
 Order real numbers, positive exponents, percents are whole, including realworld context


Identifying Real Numbers on a Number Line

Identifying Integers on a Number Line
 Identify integers on number lines, negative
 Identify integers on number lines, negative, vertical number lines

Identifying Rational Numbers on a Number Line, Only Positives

Identifying Decimals on a Number Line, Only Positives
 Given decimals, identify locations on number line
 Identify decimals on number lines, positive
 Identify decimals on number lines, vertical number lines, positive
 Identify decimals on number lines, positive, vertical number lines
 Plot decimals on number lines, increment 0.1 or 0.01
 Identify or plot decimals on number lines, increment 0.1
 Identify or plot decimals on number lines, increment 0.2
 Identify or plot decimals on number lines, increment 0.5
 Identify or plot decimals or determine lengths on number line, increment 0.01
 Condensed: Identify or plot decimals on number lines
 Compare decimals on number line
 Identify & compare rational numbers on number lines, positive

Identifying Fractions on a Number Line, Only Positives
 Identify or plot fractions or determine lengths on number line


Identifying Rational Numbers on a Number Line, Including Negatives
 Identify or determine rational values on number line, vertical number lines
 Identify rational numbers on number lines, negative
 Identify rational numbers on number lines, negative, vertical number lines
 Identify location of rational numbers on number lines
 Identify rational numbers on number lines, vertical number lines
 Condensed: Identify rational numbers on number lines, including vertical number lines
 Plot rational numbers on number lines, negative
 Condensed: Identify or plot decimals or fractions on number lines
 Condensed: Identify or plot rational numbers on number lines
 Identify & compare rational numbers on number lines



Scientific Notation

Basic Scientific Notation

Basic Scientific Notation, Positive Exponents
 Identify correct conversion of number from scientific notation with positive exponent to standard form
 Identify correct conversion of number from standard form to scientific notation with positive exponent
 Convert number from scientific notation with positive exponent to standard form
 Convert number from standard form to scientific notation with positive exponent
 Round & convert number from standard form to scientific notation with positive exponent
 Compare two numbers in scientific notation

Basic Scientific Notation, Negative Exponents
 Identify correct conversion of number from scientific notation with negative exponent to standard form
 Identify correct conversion of number from standard form to scientific notation with negative exponent
 Convert number from scientific notation with negative exponent to standard form
 Convert number from standard form to scientific notation with negative exponent
 Round & convert number from standard form to scientific notation with negative exponent

Basic Scientific Notation, All Exponents
 Condensed: Identify correct conversion of number between scientific notation & standard form
 Condensed: Convert number between scientific notation & standard form
 Condensed: Round & convert number from standard form to scientific notation


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, realworld context
 Convert numbers between standard form & scientific notation, realworld context
 Add numbers in scientific notation, realworld context
 Subtract numbers in scientific notation, realworld context
 Multiply numbers in scientific notation, realworld context
 Divide numbers in scientific notation, realworld context
 Compare magnitude of numbers in scientific notation, realworld context


Exponents & Radicals

Numerical Exponential Expressions

Numerical Exponential Expressions, Whole Number Bases
 Evaluate whole number raised to power, base up to 10, exponent up to six
 Evaluate powers, whole number base, nonpositive exponent
 Rewrite negative powers as positive powers
 Apply product rule for exponents, whole number bases & powers
 Apply quotient rule for exponents, whole number bases & powers
 Apply power rule for exponents, whole number bases & powers
 Condensed: Apply product, quotient, or power rules for exponents, whole number bases & powers
 Apply combination of product, quotient, & power rules for exponents, whole number bases & powers
 Apply combination of product, quotient, & power rules for exponents, whole number bases, integer powers

Numerical Exponential Expressions, Integer Bases
 Determine opposites of squares or cubes of positive integers
 Determine squares or cubes of positive or negative integers
 Evaluate powers, integer base, nonpositive exponent, including negative coefficients

Numerical Exponential Expressions, Fractional Bases
 Evaluate powers, fractional base, positive exponent
 Evaluate powers, fractional base, negative exponent
 Evaluate powers, fractional bases


Variable Exponential Expressions

Variable Exponential Expressions, Product Rule
 Express repeated variables as powers, single variable
 Express repeated variables as powers, multiple variables
 Express repeated variables as powers, coefficients other than one
 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

Variable Exponential Expressions, Quotient Rule
 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, one or two variables, one or two factors in numerator & denominator, positive exponents

Variable Exponential Expressions, Power Rule
 Apply power rule, one variable, positive exponents
 Apply power rule, including multiple variables, positive exponents

Variable Exponential Expressions, Mixed Rules
 Apply power & product rules of exponents, one variable, positive exponents
 Apply power & product rules of exponents, multiple variables, positive exponents
 Apply product, quotient, & power rules of exponents, one variable


Simplifying Roots
 Determine square roots of perfect squares
 Determine principal square root of perfect squares
 Evaluate perfect cube roots
 Compare perfect square & cube roots
 Simplify square roots
 Simplify square roots, coefficient greater than one
 Condensed: Simplify square roots, including algebraic expressions

Solving Radicals
 Determine square roots of perfect squares, radicand up to 100
 Determine square roots of perfect squares, radicand up to 400
 Solve perfect square root equations
 Solve perfect cube root equations
 Condensed: Determine square roots of perfect squares
 Condensed: Determine cube roots of perfect cubes
 Condensed: Evaluate & compare perfect square & cube roots

Operations with Radicals
 Add & subtract radical expressions, one or two variables, simplified radicals
 Add & subtract radical expressions, one or two variables, radicals to simplify
 Multiply radical expressions, numbers & variables
 Condensed: Add & subtract radical expressions


Expressions

Translating Expressions
 Identify words or phrases that indicate specified operation or comparison
 Interpret numerical expressions
 Determine algebraic expressions that represent realworld situations
 Given phrase, determine onestep algebraic expression
 Identify equivalent multistep algebraic expressions & phrases
 Determine algebraic expressions that represent realworld situations, including twovariable expressions
 Given phrase, determine multistep algebraic expression
 Given phrase, determine & evaluate multistep algebraic expression

Evaluating Expressions

Evaluating Expressions, Only Positives

Evaluating Addition 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 expressions for specified value, one variable, only sums, at least one decimal

Evaluating Subtraction Expressions, Only Positives
 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 subtraction expressions for specified value, one variable, at least one decimal

Evaluating Multiplication Expressions, Only Positives
 Evaluate multiplication expressions for specified value, one variable
 Evaluate multiplication expressions for specified value, one variable, at least one fraction
 Evaluate multiplication expressions for specified value, one variable, at least one decimal

Evaluating Division Expressions, Only Positives
 Evaluate division expressions for specified value, one variable
 Evaluate division expressions for specified value, one variable, at least one fraction
 Evaluate division expressions for specified value, one variable, at least one decimal


Evaluating Expressions, Including Negatives
 Evaluate expressions for specified value, one variable, one term, two factors
 Evaluate expressions for specified value, one variable, one term, three factors
 Evaluate expressions for specified value, one variable, two terms, only sums & differences
 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 value, one variable, two terms
 Condensed: Evaluate expressions for specified value, one variable
 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, variable multiplier
 Simplify algebraic expressions, one variable, distribute once, variable with coefficient multiplier
 Condensed: Simplify algebraic expressions, one variable, distribute once, including variable multipliers
 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

Distributive Property & Combining Like Terms
 Identify equivalent expressions involving distribution, two or more terms
 Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
 Simplify algebraic expressions, one variable, distribute once & subtract from constant or variable term
 Simplify algebraic expressions, one variable, distribute once & combine like terms
 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 twice
 Simplify algebraic expressions, two variables, distribute twice



Equations

Solving OneStep Equations

Addition OneStep Equations
 Solve x + a = b, a > 0, b > 0, x > 0
 Solve x + a = b, a > 0, b > 0, x < 0
 Solve x + a = b, a > 0, b < 0, x < 0
 Solve x + a = b, a < 0, b > 0, x > 0
 Solve x + a = b, a < 0, b < 0, x > 0
 Solve x + a = b, a < 0, b < 0, x < 0
 Solve a + x = b

Subtraction OneStep Equations
 Solve x – a = b, a < 0, b > 0, x > 0
 Solve x – a = b, a < 0, b > 0, x < 0
 Solve x – a = b, a < 0, b < 0, x < 0
 Solve x – a = b, a > 0, b > 0, x > 0
 Solve x – a = b, a > 0, b < 0, x > 0
 Solve x – a = b, a > 0, b > 0, x < 0

Multiplication OneStep Equations
 Solve ax = b, a > 0, b > 0
 Solve ax = b, a > 0, b < 0
 Solve ax = b, a < 0, b < 0
 Solve ax = b, a < 0, b > 0
 Solve x = b
 Solve onestep linear equations, fractional coefficients & constants
 Solve onestep linear equations, fractional coefficients
 Solve onestep linear equations, fractional answers
 Condensed: Solve onestep linear equations, including fractional coefficients & fractional answers

Division OneStep Equations
 Solve x/a = b, a > 0, b > 0
 Solve x/a = b, a > 0, b < 0
 Solve x/a = b, a < 0, b > 0
 Solve x/a = b, a < 0, b < 0

Mixed Operations OneStep Equations
 Condensed: Solve onestep linear equations, addition or subtraction
 Condensed: Solve onestep linear equations, multiplication or division

Application of OneStep Equations
 Given rate & time, determine distance
 Given distance & rate or time, determine missing quantity
 Determine onestep linear equations, realworld context
 Determine onestep equations, including decimals, realworld context
 Given onestep linear equation, identify realworld situation represented by equation
 Given onestep equation, identify realworld situation represented by equation
 Determine & solve onestep linear equations, realworld context


Solving TwoStep Equations

Multiplication TwoStep Equations

Multiplication TwoStep Equations with Addition
 Solve ax + b = c, a > 0, b > 0, c > 0, x > 0
 Solve ax + b = c, b > 0, c > 0, x < 0
 Solve ax + b = c, a > 0, b > 0, c < 0, x < 0
 Solve ax + b = c, a > 0, b < 0, c > 0, x > 0
 Solve ax + b = c, a > 0, b < 0, c < 0, x > 0
 Solve ax + b = c, b < 0, c < 0, x < 0
 Solve ax + b = c, a < 0, b > 0, c > 0, x > 0
 Solve ax + b = c, a < 0, b < 0, c > 0, x < 0
 Solve ax + b = c, a < 0, b < 0, c < 0, x < 0

Multiplication TwoStep Equations with Subtraction
 Solve ax – b = c, a > 0, b < 0, c > 0, x > 0
 Solve ax – b = c, b < 0, c > 0, x < 0
 Solve ax – b = c, a > 0, b < 0, c < 0, x < 0
 Solve ax – b = c, a > 0, b > 0, c > 0, x > 0
 Solve ax – b = c, a > 0, b > 0, c < 0, x > 0
 Solve ax – b = c, b > 0, c < 0, x < 0
 Solve ax – b = c, a < 0, b < 0, c > 0, x > 0
 Solve ax – b = c, a < 0, b > 0, c > 0, x < 0
 Solve ax – b = c, a < 0, b > 0, c < 0, x < 0


Division TwoStep Equations

Division TwoStep Equations with Addition
 Solve x/a + b = c, a > 0, b > 0, c > 0, x > 0
 Solve x/a + b = c, b > 0, c > 0, x < 0
 Solve x/a + b = c, a > 0, b > 0, c < 0, x < 0
 Solve x/a + b = c, a > 0, b < 0, c > 0, x > 0
 Solve x/a + b = c, a > 0, b < 0, c < 0, x > 0
 Solve x/a + b = c, b < 0, c < 0, x < 0
 Solve x/a + b = c, a < 0, b > 0, c > 0, x > 0
 Solve x/a + b = c, a < 0, b < 0, c > 0, x < 0
 Solve x/a + b = c, a < 0, b < 0, c < 0, x < 0

Division TwoStep Equations with Subtraction
 Solve x/a – b = c, a > 0, b < 0, c > 0, x > 0
 Solve x/a – b = c, b < 0, c > 0, x < 0
 Solve x/a – b = c, a > 0, b < 0, c < 0, x < 0
 Solve x/a – b = c, a > 0, b > 0, c > 0, x > 0
 Solve x/a – b = c, a > 0, b > 0, c < 0, x > 0
 Solve x/a – b = c, b > 0, c < 0, x < 0
 Solve x/a – b = c, a < 0, b < 0, c > 0, x > 0
 Solve x/a – b = c, a < 0, b > 0, c > 0, x < 0
 Solve x/a – b = c, a < 0, b > 0, c < 0, x < 0


Mixed Operations TwoStep Equations
 Condensed: Solve x/a ± b = c
 Condensed: Solve twostep linear equations
 Solve twostep linear equations, fractional answers
 Solve twostep linear equations, decimal coefficients
 Solve twostep linear equations, fractional coefficients
 Solve linear equations, sum or difference on one side
 Solve linear equations, product on one side

Application & Modeling of TwoStep Equations
 Solve twostep linear equations, algebra tiles, positive coefficients
 Determine twostep linear equations, realworld context
 Solve problems that can be represented by onestep equations, including algebra tiles, realworld context
 Solve problems that can be represented by twostep equations, realworld context
 Determine equations or identify realworld situations represented by onestep or twostep equations
 Given equation with variables on both sides, identify realworld situation represented by equation
 Determine solutions to problems using common formulas, including simple interest, area & perimeter, & d = rt, realworld context


Solving One or TwoStep Equations
 Condensed: Solve one or twostep linear equations, including fractional answers
 Condensed: Solve one or twostep linear equations, fractional coefficients
 Solve ax ± b = c

Solving MultiStep Equations
 Solve linear equations, like terms on both sides
 Solve linear equations, distributive property on one side
 Solve threestep linear equations involving distribution, fractional multiplier cancels if distributed
 Solve threestep linear equations involving distribution, fractional multiplier doesn’t cancel if distributed
 Solve linear equations, distributive property on one side, up to two terms on other side
 Solve linear equations, distributive property & additional term on one side
 Solve threestep linear equations involving distribution of decimal multiplier
 Solve linear equations, term minus distributive property on one side
 Solve (ax ± b)/c = d
 Condensed: Solve threestep linear equations involving distribution, including fractional & decimal answers

Solving Equations with Variables on Both Sides

Basic Equations with Variables on Both Sides
 Solve linear equations, variables on both sides
 Solve linear equations, binomials on both sides, decimals
 Solve linear equations, binomials on both sides, fractions
 Solve linear equations, variables as numerators on both sides
 Condensed: Solve linear equations, variables on both sides, rationals
 Solve multistep linear equations
 Condensed: Solve linear equations, variables on both sides or like terms
 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
 Solve linear equations, including no solution & infinitely many solutions

Application & Modeling of Equations with Variables on Both Sides
 Given algebra tiles, determine & solve onevariable equations with variables on both sides
 Solve problems that can be represented by onestep equations, including algebra tiles, realworld context
 Determine & solve linear equations with variables on both sides, realworld context


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


Inequalities

Identifying & Graphing Inequalities
 Graph inequalities on number line
 Given graph, determine inequality
 Determine graph from inequality or inequality from graph

Solving OneStep Inequalities

Basic OneStep Inequalities
 Solve onestep inequalities, x + #
 Solve onestep inequalities, x – #
 Condensed: Solve onestep inequalities, x ± #
 Solve onestep inequalities, a * x, a > 0
 Solve onestep inequalities, a * x, a < 0
 Condensed: Solve onestep inequalities, a * x
 Solve onestep inequalities, x/a, a > 0
 Solve onestep inequalities, x/a, a < 0
 Condensed: Solve onestep inequalities, x/a

Basic Solving & Graphing OneStep Inequalities

Addition & Subtraction
 Solve & graph onestep inequalities, x + #
 Solve & graph onestep inequalities, x – #
 Condensed: Solve & graph onestep inequalities, x ± #

Multiplication & Division
 Solve & graph onestep inequalities, a * x, a > 0
 Solve & graph onestep inequalities, whole number coefficients
 Solve & graph onestep inequalities, a * x, a < 0
 Solve & graph onestep inequalities, integer coefficients
 Condensed: Solve & graph onestep inequalities, a * x
 Solve & graph onestep inequalities, x/a, a > 0
 Solve & graph onestep inequalities, x/a, a < 0
 Condensed: Solve & graph onestep inequalities, x/a

Mixed Operations
 Solve & graph onestep inequalities, including fractional coefficients
 Solve & graph onestep inequalities, including negative & fractional coefficients


Application of OneStep Inequalities
 Given inequality, identify phrase or realworld problem that represents inequality
 Represent realworld problems as inequalities
 Determine onestep inequalities, including realworld context
 Identify onestep inequalities that model realworld problems or interpret inequality components
 Given onestep inequality, identify realworld problem modeled by inequality
 Determine onestep inequalities, rational numbers, including realworld context
 Given onestep inequality, identify realworld problem modeled by inequality, rational numbers
 Determine, solve, & graph onestep inequalities, including realworld context


Solving TwoStep Inequalities

Basic Solving TwoStep Inequalities
 Determine if given value is solution to twostep inequality
 Solve twostep inequalities modeled with algebra tiles
 Solve twostep inequalities, integers
 Solve twostep inequalities, fractions
 Solve twostep inequalities, decimals
 Condensed: Solve twostep inequalities
 Solve & graph twostep inequalities, integers
 Solve & graph twostep inequalities, decimals
 Solve & graph twostep inequalities, fractions
 Condensed: Solve & graph twostep inequalities
 Solve & graph twostep inequalities

Application & Modeling of TwoStep Inequalities
 Determine if given value is solution to twostep inequality
 Solve twostep inequalities modeled with algebra tiles
 Determine & solve twostep inequalities, greater than, realworld context
 Determine & solve twostep inequalities, less than, realworld context
 Determine twostep inequalities, rational numbers, including realworld context
 Given twostep inequality, identify realworld problem modeled by inequality


Solving MultiStep Inequalities
 Solve multistep inequalities using distributive property
 Solve & graph inequalities, variables on both sides, including distributive property
 Determine inequalities with variables on both sides, realworld context
 Given inequality with variable on both sides, identify realworld problem modeled by inequality

Solving Mixed Inequalities
 Determine equivalence of inequalities & solution set
 Condensed: Solve & graph inequalities
 Solve multistep inequalities, including variables on both sides


Linear Concepts

Proportional Relationships

Graphing Proportional Relationships
 Given unit rate, determine graph of proportional relationship, realworld context
 Given table, graph proportional linear equation
 Graph proportional linear equation
 Determine graph of proportional relationship, realworld context

Identifying Independent & Dependent Variables
 Given description, identify dependent or independent variable
 Given equation, identify dependent or independent variable
 Given table, identify dependent or independent variable
 Given table or graph, identify dependent or independent variable

Writing Equations, Completing Tables or Graphs
 Given multiplicative relationship in table, determine equation, realworld context
 Given constant of proportionality, determine table, graph, or equation
 Given equation, determine constant of proportionality, graph, or table
 Given table, determine constant of proportionality, graph, or equation
 Given graph, determine constant of proportionality, table, or equation
 Condensed: Determine equivalent representations of proportional relationships
 Determine or identify equivalent representations of proportional relationships

Finding Constant of Proportionality
 Given equation, determine constant of proportionality
 Given equation, determine constant of proportionality, realworld context
 Given table, determine constant of proportionality
 Given graph, determine constant of proportionality, including realworld context
 Determine constants of proportionality, realworld context
 Condensed: Determine constants of proportionality
 Identify linear table with most extreme rate of change
 Identify linear graph with most extreme rate of change
 Compare rates of changes represented differently


Proportional & NonProportional

Additive & Multiplicative Relationships
 Given table, determine additive or multiplicative equation
 Identify components of additive & multiplicative equations
 Identify graphs of additive & multiplicative relationships
 Identify situations modeled by additive & multiplicative relationships
 Identify equivalent representations of additive & multiplicative relationships, including decimals & fractions
 Condensed: Given additive or multiplicative relationship in table, determine equation

Writing Equations, Completing Tables or Graphs

Determine Graphs
 Given linear equation, determine yvalues in table & identify graph, first quadrant
 Given linear equation & table, identify graph
 Given linear equation & table, determine graph

Determine Tables
 Identify tables that represent realworld situations, y = mx or y = x + b
 Given linear equation, determine yvalues in table, realworld context

Determine Equations
 Given additive relationship in table, determine equation
 Given multiplicative relationship in table, determine equation
 Determine equations that represent realworld situations, including twostep equations
 Given linear graph & table, determine equation
 Determine equations that represent realworld situations, y = mx or y = x + b

Mixed Representations
 Given slopeintercept equation, determine table & identify graph
 Condensed: Determine tables or equations of additive & multiplicative relationships
 Condensed: Determine equations & graphs of additive & multiplicative relationships
 Identify equivalent representations of additive & multiplicative relationships
 Determine equations or identify graphs that represent realworld situations, y = mx or y = x + b
 Identify representation of proportional relationship, various representations, realworld context


Identifying Proportional vs. NonProportional
 Identify graphs showing proportional relationship
 Identify equations showing proportional relationship
 Identify tables showing proportional relationship
 Identify tables, graphs, or equations showing proportional relationship
 Identify proportional & nonproportional relationships, realworld context


Determining Solution to a Linear Equation
 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 slopeintercept form, determine if point is on line
 Given linear equation in standard form, determine if point is on line
 Given linear equation in slopeintercept form, identify point on line
 Given linear equation in standard form, identify point on line
 Given graph of linear equation, identify point on line
 Condensed: Given linear equation in slopeintercept form & graph, identify point on line
 Given linear equation in slopeintercept form & value of one variable, determine value of other variable
 Given linear equation in slopeintercept form & yvalue, determine xvalue, fractional coefficients or constants
 Identify linear & nonlinear relationships, various representations

Slope of a Line

Identifying Slope Category
 Given linear graph, identify type of slope
 Given linear equation, identify type of slope
 Identify linear graph with specific type of slope
 Given table of linear equation, identify type of slope
 Given graph of horizontal or vertical line, determine rate of change
 Condensed: Identify type of slope

Finding Slope

Finding Slope from an Equation
 Given equation of horizontal or vertical line, determine rate of change
 Given equation in slopeintercept form, determine rate of change, integer solution
 Given equation in slopeintercept form, determine rate of change
 Given linear equation in standard form, determine rate of change
 Given equation in pointslope form, identify slope

Finding Slope from a Graph
 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 graph of piecewise function, determine rate of change over specific interval

Finding Slope from Two Points
 Given two points, determine rate of change, integer solution, including undefined
 Given two points with integer coordinates, determine rate of change
 Given two points, determine rate of change, one coordinate is fraction
 Given two points, determine rate of change, two coordinates are fractions

Finding Slope from a Table
 Given table of linear equation, determine rate of change


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, realworld context

Application of Slope
 Given right triangle, use legs to determine slope, realworld context
 Given graph of similar right triangles, identify equivalent slopes
 Given description, determine equation & specific value, realworld context

Finding & Using Slope
 Given equation in slopeintercept form, determine next value in table, Δx = 1
 Given equation in slopeintercept form, determine next value in table
 Given equation in slopeintercept form, determine values in table
 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 equation, determine rate of change & specific value


Intercepts

XIntercept
 Given linear graph, plot xintercept
 Given linear graph, determine coordinates of xintercept
 Given equation of horizontal or vertical line, determine coordinates of xintercept
 Given linear equation in slopeintercept form, determine coordinates of xintercept

YIntercept
 Given linear graph, plot yintercept
 Given linear graph, determine coordinates of yintercept
 Given equation of horizontal or vertical line, determine coordinates of yintercept
 Given linear equation in slopeintercept form, determine coordinates of yintercept
 Given equation of horizontal or vertical line, plot yintercept
 Given linear equation in slopeintercept form, plot yintercept
 Given linear equation in standard form, determine coordinates of yintercept

Both Intercepts
 Given linear graph, locate intercept or determine coordinates, various scales
 Given linear equation, determine intercepts
 Condensed: Given linear equation, determine x or yintercepts


Writing Equation of a Line

Writing Equation Given Point & Slope
 Given slope & yintercept, determine equation
 Given point & integer slope, determine linear equation in slopeintercept form
 Given point & integer slope or rate of change, determine linear equation in slopeintercept form
 Given point & fractional slope, determine linear equation in slopeintercept form, integer yintercept
 Given point & fractional slope, determine linear equation in slopeintercept form, fractional yintercept
 Given point & fractional slope, determine linear equation in pointslope form, including slopeintercept form conversion
 Given point & integer slope, determine linear equation in pointslope form, including slopeintercept form conversion
 Given positive point & whole number slope, determine yintercept, equation, & specific value
 Given point & integer slope, determine yintercept, equation, & specific value

Writing Equation Given Two Points
 Given two points, determine linear equation, zero slope
 Given two points, determine linear equation, undefined slope
 Given two points, determine linear equation in slopeintercept form, integer slope
 Given two points, determine linear equation in slopeintercept form, fractional slope
 Given two points, determine linear equation in standard form, integer slope, including slopeintercept form conversion
 Given two points, determine linear equation in pointslope form, integer slope, including slopeintercept form conversion
 Given two points, determine linear equation in standard form, fractional slope, including slopeintercept form conversion
 Given two points, determine linear equation in pointslope form, fractional slope, including slopeintercept form conversion

Writing Equation Given Various Components
 Identify equivalent linear graphs & equations in slopeintercept form
 Identify equivalent linear graphs & equations in slopeintercept form, various scales
 Condensed: Identify equivalent linear graphs & equations in slopeintercept form, integers slopes, various scales
 Given points or slope & point, determine linear equation in standard form
 Given points or slope & point, determine linear equation in various forms
 Given points or slope & point, determine linear equation in pointslope or standard form
 Given intercepts, determine linear equation in slopeintercept form
 Condensed: Given linear graph, determine equation in slopeintercept form & specific value, various scales, including realworld context
 Condensed: Given two points, determine linear equation in slopeintercept form, including horizontal & vertical lines

Writing Equation Given Graph

Given Graph with YIntercept of Zero, Write Equation
 Given linear graph through origin with points shown on line, determine equation in slopeintercept form, integer slopes
 Given linear graph through origin, determine equation in slopeintercept form, integer slope
 Given linear graph through origin, determine equation in slopeintercept form, integer slope, 1 ≤ m ≤ 3

Given Graphs with Varying YIntercepts, Write Equation

SlopeIntercept Form
 Given linear graph, determine equation in slopeintercept form, m = 1
 Given linear graph, determine equation in slopeintercept form, m = 1, various scales
 Given linear graph, determine equation in slopeintercept form, m = ±1, various scales
 Given linear graph, determine equation in slopeintercept form, integer slopes
 Given linear graph, identify equation in slopeintercept form, integer slopes, various scales
 Given linear graph, determine equation in slopeintercept form, integer slopes, various scales
 Given equation in slopeintercept form, identify graph, integer slopes, various scales
 Condensed: Identify equivalent linear graphs & equations in slopeintercept form, integers slopes, various scales
 Given linear graph, determine equation in slopeintercept form, fractional slopes
 Given linear graph, identify equation, slopeintercept form
 Given linear graph, determine slope, yintercept, & equation
 Given linear graph, determine equation in slopeintercept form & specific value, various scales

Standard Form
 Given linear graph, determine equation in standard form

PointSlope Form
 Given linear graph, determine equation in pointslope form

Various Forms
 Given linear graph, identify equation, various forms




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

Identifying Key Features of a Linear Function
 Given linear graph, determine slope & yintercept, integer slope
 Given linear graph, determine slope & yintercept
 Given graph of linear equation, determine slope & intercepts
 Given table of linear equation, determine slope & intercepts
 Given linear equation, determine slope & intercepts
 Given linear equation in standard form, solve for y
 Given linear equation in standard form, determine slope
 Condensed: Given linear equation in standard form, solve for y or determine slope

Equations, Graphs, & Tables

Basic Graphing
 Given point & integer slope, graph line
 Given point & slope, graph line

Equation to Table

m = 1
 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 & table, determine another point, m = 1
 Given linear equation, fill table, m = 1

Various Slopes
 Given linear equation & one xvalue, determine yvalue in table
 Given linear equation & two xvalues, determine yvalues in table
 Given linear equation, fill missing value in table, integer slope
 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, Δx ≥ 5
 Given linear equation & table, determine another point, integer slope, b = 0
 Given description & linear equation, fill table & determine solution, realworld context
 Given horizontal or vertical linear equation, fill table
 Given linear equation, fill table, integer slope, b = 0
 Given linear equation, determine table values
 Given linear equation, fill table, integer slope


Equation to Graph

Standard Form to Graph
 Given linear equation in standard form, graph
 Given linear equation in standard form, graph, scrambled variable terms
 Condensed: Determine linear equation in standard form & graph, including realworld context

SlopeIntercept Form to Graph
 Graph linear equations, including horizontal & vertical, integer slope, various scales
 Graph linear equations, fractional slope
 Given slopeintercept equation, determine table & graph
 Condensed: Graph linear equations, including horizontal & vertical, various scales
 Graph linear equations, m = 1
 Graph linear equations, m = 1, various scales
 Graph linear equations, integer slope not including one & negative one, b = 0
 Given equation in slopeintercept form, graph line, m = ±1, various scales
 Graph linear equations, integer slope not including one & negative one
 Graph linear equations, integer slope, various scales
 Graph linear equations, fractional slope, various scales
 Condensed: Given linear equation or description, determine graph, fractional slope, including realworld context


Graph to Table
 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, determine yvalues in table
 Given linear graph through origin, determine table values, one table point off graph
 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 through origin, determine table value, table point off graph

Table to Equation
 Given table representing horizontal linear equation, determine equation
 Given table representing vertical linear equation, determine 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, identify linear equation in slopeintercept form, rational constants & coefficients
 Given description, determine linear equation, fill table, & determine solution, realworld context


Perpendicular, Parallel, or Neither

Identifying Parallel or Perpendicular Lines
 Given equation in slopeintercept form, determine slope of parallel line
 Given equation in slopeintercept form, determine slope of perpendicular line
 Condensed: Given equation in slopeintercept 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 slopeintercept form equations, identify as parallel or perpendicular
 Given two equations in standard form, identify as parallel or perpendicular
 Identify equation that is parallel or perpendicular to line through two given points
 Given two pairs of points, determine if lines containing points are parallel or perpendicular

Writing Equations of Parallel or Perpendicular Lines
 Given equation in slopeintercept form, determine equation of parallel line through specified point
 Given equation in slopeintercept form, determine equation of perpendicular line through specified point
 Given equation in slopeintercept form, determine equation of parallel or perpendicular line through specified point
 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
 Determine equation of line through specified point parallel or perpendicular to xaxis
 Determine equation of line through specified point parallel or perpendicular to yaxis
 Condensed: Determine equation of line through specified point parallel or perpendicular to x or yaxis


Line of Best Fit & Scatter Plots

Interpret Scatter Plots
 Identify positive & negative correlations in scatter plots
 Identify outliers in scatter plots
 Identify linear & nonlinear associations in scatter plots
 Identify scatterplots with clustered data
 Given data, determine scatter plot
 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
 Sketch line of best fit & determine equation, realworld context
 Sketch line of best fit
 Sketch line of best fit & determine predicted value
 Condensed: Sketch line of best fit & determine equation
 Determine residuals


Linear Word Problems

Identifying Key Features Given Verbal Description
 Given graph or table of linear function, determine slope or yintercept, realworld context
 Given description of linear relationship, determine slope, yintercept, & equation, realworld context
 Form 1 – Given slope & intercept, interpret linear relationship, determine slopeintercept equation, & graph, positive slope, only input to output questions
 Form 2 – Given slope & intercept, interpret linear relationship, determine slopeintercept equation, & graph, positive slope
 Form 3 – Given slope & intercept, interpret linear relationship, determine slopeintercept equation, & graph, including negative slope
 Form 4 – Given point & slope, interpret linear relationship, determine slopeintercept equation, & graph, including negative slope
 Form 5 – Given two points, interpret linear relationship, determine slopeintercept equation, & graph, including negative slope
 Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slopeintercept equation, & graph
 Form 6 – Given linear graph, interpret linear relationship & determine slopeintercept equation
 Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
 Determine linear equation in standard form & graph, realworld context
 Given slope & intercept, interpret linear relationship & determine slopeintercept equation, including negative slope

Choosing Correct Model Given Verbal Description
 Given description or table, determine linear graph, realworld context
 Given description of linear equation, identify graph, integer slope, realworld context
 Given linear word problem, identify graph
 Given description of linear relationship, identify graph, table, or equation, realworld context
 Given linear equation, interpret slope & yintercept, realworld context
 Identify equivalent representations of linear relationship, including realworld context
 Given description of linear equation, identify graph, fractional slope, realworld context



Functions

Identifying Functions
 Determine functions, set & table representations
 Determine functions, mapping representations, no domain & range language
 Determine functions, mapping representations
 Determine functions, graphical representations
 Identify & determine functions, set & table representations
 Given step graphs, identify functions
 Given relation & additional point, determine functions, multiple representations
 Identify functions, description representations

Identifying & Justifying Functions
 Identify functions using equivalent mapping diagrams & sets of ordered pairs
 Determine & justify functions, table representations, no domain & range language
 Determine & justify functions, mapping representations, no domain & range language
 Determine & justify functions, set representations, no domain & range language
 Determine functions, multiple representations, including justification, no domain & range language
 Determine & justify functions, table representations
 Determine & justify functions, mapping representations
 Determine & justify functions, set representations
 Determine & justify functions, graphical representations
 Identify functions, multiple representations, including justification
 Identify & justify functions & nonfunctions, graphical representations
 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
 Condensed: Determine domain & range, including realworld context


Systems of Equations

Determining Solution to Systems of Equations
 Given system of linear equations, identify x or yvalue of solution
 Given system of linear equations, identify solution
 Given system of linear equations, identify solution or x or yvalue of solution
 Given system of linear equations & description, identify solution, realworld context
 Condensed: Given system of linear equations, identify solution, including realworld context
 Determine systems of linear equations & solutions, realworld context
 Condensed: Determine systems of linear equations & solutions, including realworld context

Solving Systems of Equations, Graphing
 Determine & verify graphical solutions to systems of linear equations, slopeintercept form
 Given system of linear equations, determine point of intersection, slopeintercept form
 Given system of linear equations, graph system, including tables
 Given description of system of linear equations, graph & determine equations or tables
 Condensed: Given system of linear equations or description, graph system, including realworld context
 Given system of linear equations, graph & determine point of intersection, slopeintercept form
 Given graph of system of linear equations, determine equations in slopeintercept form

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 slopeintercept 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
 Determine solutions of linear equations, substitution bias, including given system, realworld context
 Solve systems of linear equations, infinite possibilities or no solution
 Determine systems of linear equations & solutions, substitution bias, realworld context
 Solve, interpret, or determine systems of linear equations, slopeintercept form, realword context
 Solve, interpret, or determine systems of linear equations, standard form, realword context
 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
 Given system of linear equations, determine point of intersection, at least one equation with variables on both sides
 Determine systems of linear equations & solutions, elimination bias, realworld context
 Condensed: Solve or determine system of equations, both equations in standard form

Solving Systems of Equations, Mixed Methods
 Graph systems of linear equations & determine solutions, including realworld context
 Determine & justify solutions to systems of linear equations, realworld context
 Condensed: Determine systems of linear equations & solutions


Ratios, Rates, Proportions, & Percents

Ratios

Use Ratios & Rates
 Identify unit rates
 Rewrite ratios
 Given ratio, determine reduced form
 Identify equivalent ratios or determine missing component of proportion
 Determine ratios, various forms, realworld context
 Condensed: Simplify ratios, identify equivalent ratios, & determine missing components of proportions
 Compare rates
 Determine specified values in proportional relationships, realworld context
 Determine part to part ratio, strip diagrams, realworld context
 Determine part to whole ratio, various models
 Determine & identify equivalent rates of changes, various representations
 Determine & compare unit rates, realworld context

Determine Ratios & Percents
 Condensed: Determine ratios & percents, decimal grids
 Condensed: Determine ratios & percents, double number lines, including realworld context
 Condensed: Determine ratios & percents, strip diagrams, realworld context


Rates

Determine Unit Rates
 Determine unit rates, whole numbers, realworld context
 Determine unit rates, fractions, realworld context
 Given rate & comparison, determine unit rates, realworld context
 Determine unit rates, mixed numbers, realworld context

Use Rates to Solve Problems
 Given unit rate, determine specified value in proportional relationship, realworld context
 Given unit conversion rate, convert measurement units
 Given proportional relationship, determine specified quantity, realworld context
 Given rate, convert time unit to determine quantity over time interval, realworld context
 Given rate of travel, determine distance or time
 Determine & apply unit rates to determine specified quantities, realworld context
 Condensed: Determine or apply unit rates, realworld context
 Condensed: Determine ratios, relationship between ratio terms, & specified quantities, realworld context
 Determine ratios, realworld context
 Given ratio, determine relationship between ratio terms, realworld context
 Condensed: Given extended ratio, determine ratio or specified quantity, realworld 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, realworld context
 Solve proportions, rounded answers, realworld context
 Solve proportions involving time, realworld context


Percents

Percent Conversions

Convert Fractions
 Convert fractions to decimals, denominator power of 10
 Convert fractions to decimals, denominator factor of power of 10
 Convert fractions to rounded decimals
 Convert fractions to decimals, including improper fractions, including repeating decimals
 Convert mixed numbers to decimals, including repeating decimals
 Condensed: Convert fractions to decimals & percents
 Condensed: Convert proper & improper fractions to rounded percents

Convert Decimals
 Convert decimals to fractions
 Convert decimals to mixed numbers
 Convert decimals to fractions or mixed numbers, including repeating decimals
 Convert repeating decimals to fractions
 Condensed: Convert decimals to fractions & percents

Convert Percents
 Condensed: Convert percents to decimals & fractions


Application of Percents
 Determine simple interest
 Determine simple interest & total amount
 Given simple interest earned, determine principal, rate, or time
 Determine annually compounded interest
 Determine compound interest
 Condensed: Determine compound interest on savings & loans
 Determine & compare simple & compound interest



Data Analysis & Probability

Measures of Center & Spread

Calculating Measures of Center & Spread
 Identify definition of mean, median, mode, or range
 Determine mean, median, mode, or range
 Determine mean, median, mode, & range
 Determine mean, median, mode, or range from stem&leaf plots
 Determine mean, median, mode, or range from various graphs
 Given various representations of data, identify mean, median, mode, & range
 Condensed: Determine mean, median, mode, or range, including graphs
 Given additional value in data set, determine change in mean, median, mode, or range
 Given mean, median, mode, or range, determine missing value in data set
 Given mean, median, or range, determine missing or additional value in data set
 Determine interquartile range of data

Interpreting Measures of Center & Spread
 Identify measures of center based on data distribution
 Identify measures of variability based on data distribution
 Determine or interpret measures of center & spread from graphs
 Identify & interpret measures of center
 Identify & interpret measures of variability


Frequency Tables
 Determine twoway frequency tables
 Given data, identify frequency table or determine missing element of table
 Given twoway frequency tables, identify associations
 Determine specified probabilities in twoway frequency tables
 Determine conditional probabilities from twoway frequency tables
 Determine conditional probabilities, including twoway frequency tables
 Interpret twoway frequency tables, joint distribution
 Interpret twoway frequency tables, conditional distribution
 Interpret twoway frequency tables, marginal distribution
 Condensed: Interpret twoway frequency tables
 Solve onestep problems from frequency & relative frequency tables, realworld context
 Solve problems from frequency tables, realworld context

Pie Graphs
 Solve problems involving interpretation of pie charts
 Solve problems involving interpretation of pie charts displayed using fractions, decimals, or percents
 Determine percent of category in pie charts

Dot Plots
 Given data represented in various ways, identify dot plot
 Solve onestep problems from dot plots, realworld context
 Solve multistep problems from dot plots, realworld context
 Determine mean from dot plots
 Determine median from dot plots
 Determine & compare means from two dot plots
 Determine & compare medians from two dot plots
 Determine mean absolute deviation from dot plots
 Compare mean absolute deviations from two dot plots
 Compare characteristics of sidebyside dot plots

Stem&Leaf Plots
 Given data, identify stemandleaf plot
 Solve onestep problems from stemandleaf plots, realworld context
 Solve multistep problems from stemandleaf plots, realworld context

Box Plots
 Solve problems involving interpretation of box plots
 Given boxplot, determine values from fivenumber summary
 Determine fivenumber summary
 Solve problems involving fivenumber summary
 Solve problems involving interpretation of stacked box plots, realworld context
 Condensed: Determine fivenumber summary, including box plots

Basic Probability
 Determine sample spaces
 Classify probabilities by levels of likelihood
 Determine probabilities of single events
 Determine theoretical probabilities
 Determine probabilities of flipping coins specified number of times
 Determine probabilities of flipping coins & rolling die
 Determine probabilities & complementary probabilities of single events, including visual models
 Determine probabilities & odds, including visual models

Compound Probability
 Determine sample spaces
 Determine size of sample spaces, compound events
 Determine “or” probabilities
 Determine “or” probabilities
 Given visual model, determine “or” probability as fraction, decimal, or percent
 Determine “or” probabilities as fractions, decimals, or percents
 Determine “and” probabilities, independent events, same sample space
 Determine “and” probabilities, independent events, two distinct sample spaces
 Determine “and” probabilities, independent events, visuals provided
 Determine “and” probabilities, independent & dependent events
 Determine “and” probabilities, independent & dependent events, including complementary events
 Condensed: Determine probabilities

Predictions Using Probability
 Determine inferences from samples
 Determine predicted values, experimental probability
 Determine predicted values, theoretical probability
 Determine predicted values, experimental probability, compound events
 Determine predicted values, theoretical probability, compound events
 Determine predicted values or compare likelihood of events


Perimeter & Area

Rectangle Perimeter & Area

Basic Rectangle Perimeter & Area

Perimeter
 Determine perimeter of rectangles
 Given sides of rectangle, determine perimeter
 Determine perimeter of rectangles, including decimal dimensions
 Condensed: Determine perimeter of rectangles, including realworld context
 Given perimeter of rectangle & one side, determine dimension
 Given perimeter of rectangle & one side, determine dimension, including decimals

Area
 Given sides of rectangle, determine area
 Given length & width of rectangle, determine area
 Determine area of rectangles with fractional dimensions
 Given area & one dimension of rectangle, determine missing dimension
 Given area of rectangle & one dimension, determine other dimension


Application of Rectangle Perimeter & Area

Perimeter
 Given sides of rectangle, determine perimeter
 Determine perimeter of rectangles, realworld context
 Given model, identify formula & determine perimeter of rectangles
 Condensed: Identify formula & determine perimeter of rectangles & squares
 Given model, identify formula & determine perimeter of rectangles, including decimal dimensions
 Given perimeter & one dimension of rectangle, determine missing dimension
 Determine side length or perimeter of squares

Area
 Determine equations that represent area of rectangles, realworld context
 Given model, identify formula & determine area of rectangle
 Given sides of rectangle & cost per square unit, determine area & total cost, realworld context
 Determine area of shaded region between nested rectangles
 Determine area of rectangles with fractional dimensions using tiling method
 Condensed: Identify formula & determine perimeter or area of rectangles & squares
 Determine area of missing dimension of rectangles, realworld context



Parallelogram Area
 Determine area of parallelograms
 Determine equations that represent area of parallelograms, realworld context
 Given area & one dimension of parallelogram, determine missing dimension

Triangle Area
 Determine area of triangles, internal height
 Determine area of triangles, external height
 Determine area of triangles
 Determine area of triangles, internal height, mixed numbers
 Determine area of triangles, external height, mixed numbers
 Determine area of triangles, mixed numbers
 Determine equations that represent area of triangles, realworld context
 Given area & one dimension of triangle, determine missing dimension
 Given area & one dimension of triangle, determine missing dimension, mixed numbers

Trapezoid Area
 Determine area of trapezoids
 Determine equations that represent area of trapezoids, realworld context
 Given area & base lengths of trapezoid, determine height

Circle Area & Circumference
 Given radius or diameter, determine circumference
 Determine circumference of circle, exact answers, multiple choice, including realworld context
 Given radius or diameter, determine area
 Determine area of circle, exact answers, including realworld context
 Given radius or diameter, determine area or circumference
 Condensed: Determine area or circumference of circle
 Determine areas of semicircles & quarter circles

Mixed Figures Perimeter & Area

Perimeter
 Determine perimeter of polygons, including realworld context
 Given coordinates of vertices, determine side lengths & perimeter of polygons

Area
 Determine areas of rectangles & parallelograms
 Determine areas of triangles & trapezoids
 Determine algebraic expressions that represent area of rectangles & triangles
 Determine area of shaded region between nested shapes
 Determine area of polygons in coordinate plane
 Determine area of polygons in coordinate plane, realworld context
 Given coordinates of vertices, determine area of triangle or rectangle
 Given area, determine dimensions of rectangles & parallelograms
 Given area, determine dimensions of triangles
 Condensed: Determine areas & dimensions of rectangles & parallelograms
 Condensed: Determine areas & dimensions of triangles & trapezoids

Perimeter & Area
 Identify formulas for area & perimeter of basic shapes
 Determine dimension of rectangles, including realworld context


Compound Figure Area
 Determine area of composite figures on coordinate plane, no circular shapes
 Determine area of composite figures, no circular shapes
 Determine area of composite figures, rectangle with various figures attached, no circular parts
 Determine area of composite figures, rectangle with various figures attached
 Determine area of composite figures
 Determine area of composite figures, at least three subdivisions
 Determine area of composite figures, realworld context


Surface Area & Volume

Pyramid Surface Area & Volume
 Determine surface area of pyramids
 Determine surface area of pyramids
 Determine lateral surface area of pyramids
 Determine volume of pyramids
 Given surface area, determine dimension of pyramid
 Given volume, determine dimension of pyramid

Prism Surface Area & Volume

Rectangular Prism Surface Area & Volume

Basic Rectangular Prism Surface Area & Volume
 Determine surface area of rectangular prisms
 Determine volume of rectangular prisms using unit cubes
 Determine volume of rectangular prisms, various representations
 Determine volume of rectangular prisms, whole numbers or decimals
 Determine volumes of rectangular prisms, fractional dimensions
 Determine volume of rectangular prisms, whole numbers, decimals, or fractions
 Given base area & edge or all edges, determine volume of rectangular prism
 Given volume, determine edges of rectangular prisms
 Given volume, determine dimension of rectangular prism, fractional dimensions
 Determine volume or edge of rectangular prisms, whole numbers
 Condensed: Determine volume or dimension of rectangular prisms, fractional dimensions

Application of Rectangular Prism Surface Area & Volume
 Determine volume of rectangular prisms using repeated layers of base area, realworld context
 Determine volume of rectangular prisms, whole numbers, including realworld context
 Determine volume or edge of rectangular prisms, whole numbers or decimals, realworld context
 Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, realworld context
 Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including realworld context


Triangular Prism Surface Area & Volume
 Determine surface area of triangular prisms

Mixed Prism Surface Area & Volume
 Determine volume of rectangular prisms, whole numbers or decimals
 Determine volume of composite figures, rectangular & triangular prisms
 Determine surface area of composite figures, rectangular & triangular prisms
 Determine lateral surface area of prisms
 Determine lateral surface area of composite figures, rectangular & triangular prisms
 Condensed: Given net, determine surface area & lateral surface area of prisms & pyramids, including realworld context
 Condensed: Determine total surface area & lateral surface area of composite figures, rectangular & triangular prisms


Cylinder Surface Area & Volume
 Determine volume of cylinders
 Given base area & height, determine volume of cylinder
 Determine surface area of cylinders
 Determine lateral surface area of cylinders
 Given volume, determine dimension of cylinder
 Given surface area, determine dimension of cylinder
 Condensed: Given surface area or volume, determine dimension of cylinder

Cone Surface Area & Volume
 Determine volume of cones
 Determine surface area of cones
 Determine lateral surface area of cones
 Given volume, determine dimension of cone
 Given surface area, determine dimension of cone
 Condensed: Given surface area or volume, determine dimension of cone

Sphere Surface Area & Volume
 Determine volume of spheres
 Determine surface area of spheres
 Given volume, determine radius, diameter, or surface area of sphere
 Given surface area, determine radius, diameter, or volume of sphere
 Determine volume or radius of spheres
 Condensed: Given surface area or volume, determine dimension of sphere

Mixed Figures Surface Area & Volume

Mixed Figures Surface Area

Prisms, Pyramids, Cones, Cylinders, & Spheres
 Determine surface area of 3D figure, including calculator π approximation
 Determine surface area of prisms & pyramids
 Determine surface area of prisms, pyramids, cones, cylinders, & spheres
 Condensed: Determine surface area of 3D figures
 Determine lateral surface area of prisms & cylinders
 Condensed: Determine lateral surface area of 3D figures
 Determine lateral & total surface area of prisms & cylinders, including realworld context
 Given surface area, determine dimension of 3D figure, no visual provided

Composite Figures
 Determine surface area of composite figures, rectangular & triangular prisms, not requiring Pythagorean theorem
 Determine surface area of composite figures, prisms & pyramids
 Determine lateral surface area of composite figures, rectangular & triangular prisms, not requiring Pythagorean theorem
 Determine lateral surface area of composite figures, cylinders & cones
 Condensed: Determine total surface area & lateral surface area of composite figures, prisms & pyramids
 Condensed: Determine total surface area & lateral surface area of composite figures, cylinders & cones


Mixed Figures Volume
 Determine volumes of 3D figures
 Determine volume of cylinders, cones, & spheres
 Determine volume of cylinders, cones, & spheres, including realworld context
 Condensed: Determine volume of 3D figures
 Determine volume of composite figures, prisms & pyramids
 Condensed: Determine volume of composite 3D figures
 Identify & determine relationship between volumes of rectangular prisms & pyramids
 Identify & determine relationship between volumes of triangular prisms & pyramids
 Condensed: Identify & determine relationship between volumes of prisms & pyramids


Mixed Figures Surface Area Given Nets
 Identify equivalent representations of 3D figures & nets
 Given net, determine surface area of rectangular prism
 Given net, determine surface area of prisms
 Given net, determine surface area of pyramids
 Given net, determine surface area of prisms & pyramids
 Given net, determine surface area of rectangular & triangular prisms & pyramids
 Given net, determine lateral surface area of prisms
 Condensed: Given net, determine surface area & lateral surface area of prisms & pyramids, including realworld context


Similar Figures

Determine Dimensions
 Determine dimensions in similar figures, whole number dimensions
 Determine dimensions in similar figures
 Determine dimensions using similar figures & indirect measurements

Identify Proportion of Side Lengths
 Given similar figures, identify proportion of side lengths, triangles & quadrilaterals
 Given similar figures, identify proportion of side lengths, image orientations differ

Solve Problems Involving Scale Factor
 Determine scale factor or area of dilated figures
 Determine scale factor or perimeter of dilated figures
 Given scale factor, determine dimension
 Given scale factor, determine coordinates of image, preimage centered at origin
 Given scale factor, determine coordinates of image, preimage not centered at origin
 Condensed: Given scale factor, determine coordinates of image
 Identify scale factor of dilations, on coordinate plane
 Identify scale factor of dilations, not on coordinate plane
 Condensed: Identify scale factor of dilations


Transformations

Reflections
 Determine coordinates of reflected points
 Given figure on coordinate plane, determine reflected coordinates
 Identify rule or reflected point on coordinate plane
 Given coordinate vertices of figure, determine reflected image

Rotations
 Given figure on coordinate plane, determine rotated coordinates
 Identify rule or rotated point on coordinate plane
 Given coordinate vertices of figure, determine rotated image

Translations
 Given figure on coordinate plane, determine translated coordinates
 Identify rule or determine translated point on coordinate plane
 Given coordinate vertices of figure, determine translated image

Dilations
 Identify characteristics of dilations
 Identify rule or dilated point on coordinate plane, including variable scale factors
 Determine variable scale factor or variable measurement of dilated figures

Mixed Transformations

Identify Characteristics of Transformations, No Graph
 Identify characteristics of transformed line segments
 Identify characteristics of transformed lines
 Identify characteristics of transformed parallel lines
 Identify characteristics of transformed angles
 Identify characteristics of transformed lines, segments, & angles

Transformations, Given Graph
 Identify reflections & rotations on coordinate plane
 Identify rule for transformed shape on coordinate plane
 Identify rule or determine transformed point on coordinate plane
 Given similar figures, identify description of transformations
 Identify congruence transformations
 Given congruent figures, identify description of transformations
 Composition of transformations on coordinate plane
 Identify characteristics of transformations
 Condensed: Given figure on coordinate plane or coordinate vertices, determine transformed image or coordinates
 Condensed: Identify rule or determine transformed point on coordinate plane
 Condensed: Given similar or congruent figures, identify description of transformations



Pythagorean Theorem

Basic Pythagorean Theorem
 Given segment on coordinate plane, determine length
 Determine distance between points, including coordinate plane
 Determine Pythagorean triples
 Given three sides, classify triangles
 Given two sides, determine missing side of right triangle
 Apply converse of Pythagorean theorem

Application of Pythagorean Theorem
 Given two sides, determine missing side of right triangle, realworld context
 Solve problems using Pythagorean theorem, figure included, realworld context
 Given Pythagorean theorem model, determine specified component
 Determine side of right triangle or apply converse of Pythagorean theorem, including realworld context


Angle Relationships

Triangle Angle Sum Theorem
 Given two angle measures in triangle, determine & justify angle measure
 Determine similarity of triangles using AA similarity
 Determine sides of similar triangles using AA similarity
 Determine angles of similar triangles using AA similarity, algebraic expressions
 Apply triangle angle sum theorem to determine angles, algebraic expressions
 Apply triangle exterior angle theorem to determine angles, including algebraic expressions
 Apply triangle angle sum theorem to determine angles, multiple algebraic expressions
 Given description, apply triangle angle sum theorem to determine angles, algebraic expressions
 Condensed: Apply triangle angle sum theorem & exterior angle theorem to determine angles, including algebraic expressions

Vertical Angles
 Given parallel lines with transversal & angle, determine vertical angle
 Given parallel lines with transversal & angle, determine vertical angle, algebraic expressions

Alternate Interior & Alternate Exterior Angles
 Given parallel lines with transversal & angle, determine alternate interior angle
 Given parallel lines with transversal & angle, determine alternate exterior angle
 Given parallel lines with transversal & angle, determine alternate interior angle, algebraic expressions
 Given parallel lines with transversal & angle, determine alternate exterior angle, algebraic expressions

Corresponding & SameSide Interior Angles
 Given parallel lines with transversal & angle, determine corresponding angle
 Given parallel lines with transversal & angle, determine sameside interior angle
 Given parallel lines with transversal & angle, determine supplement to corresponding angle
 Given parallel lines with transversal & angle, determine corresponding angle, algebraic expressions
 Given parallel lines with transversal & angle, determine sameside interior angle, algebraic expressions
 Given parallel lines with transversal & angle, determine supplement to corresponding angle, algebraic expressions

Transversal Definitions
 Given parallel lines with transversal, identify specified angle pairs, only numbered angles, uses “sameside interior” terminology
 Given parallel lines with transversal & angles, identify specified angle pairs, uses “sameside interior” terminology
 Given parallel lines with transversal, identify specified angle pairs, only numbered angles, uses “consecutive” terminology
 Given parallel lines with transversal & angle, identify specified angle pairs, uses “consecutive” terminology
 Given parallel lines with transversal & angle, apply converse angle theorems, including algebraic expressions
 Given nonparallel lines & transversal, identify transversal & specified angle pairs

Mixed Angles Formed by Transversals
 Given parallel lines with transversal & angle, determine specified angle
 Given parallel lines with transversal & angle, determine & justify specified angle
 Given parallel lines with transversal & angle, determine specified angle, algebraic expressions


Financial Literacy
 Identify financially responsible decisions
 Identify benefits & costs of financial responsibility
 Identify or explain advantages & disadvantages of various payment methods
 Determine cost of repaying loan
 Determine how interest rates affect total cost of loans
 Determine how lengths of loans affect total cost of loans
 Determine savings in loan repayment based on various lengths of repayment
 Determine costs of one year of college education
 Estimate costs of twoyear college education
 Estimate costs of fouryear college education
 Condensed: Estimate or determine costs of college education
 Determine growth of money invested regularly over time