8th Grade Skills
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Real Numbers
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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
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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
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Comparing & Ordering Real Numbers
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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
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Application of Comparing & Ordering Real Numbers
- Given table, order rational numbers, real-world context
- Given set or list, order rational numbers, real-world context
- Order real numbers, positive exponents, percents are whole, including real-world context
- Order real numbers, positive exponents, percents are whole, including real-world context
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Identifying Real Numbers on a Number Line
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Identifying Integers on a Number Line
- Identify integers on number lines, negative
- Identify integers on number lines, negative, vertical number lines
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Identifying Rational Numbers on a Number Line, Only Positives
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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
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Identifying Fractions on a Number Line, Only Positives
- Identify or plot fractions or determine lengths on number line
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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
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Scientific Notation
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Basic Scientific Notation
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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
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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
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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
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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
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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
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Exponents & Radicals
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Numerical Exponential Expressions
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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, non-positive 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
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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, non-positive exponent, including negative coefficients
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Numerical Exponential Expressions, Fractional Bases
- Evaluate powers, fractional base, positive exponent
- Evaluate powers, fractional base, negative exponent
- Evaluate powers, fractional bases
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Variable Exponential Expressions
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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
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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
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Variable Exponential Expressions, Power Rule
- Apply power rule, one variable, positive exponents
- Apply power rule, including multiple variables, positive exponents
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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
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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
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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
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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
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Expressions
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Translating Expressions
- Identify words or phrases that indicate specified operation or comparison
- Interpret numerical expressions
- Determine algebraic expressions that represent real-world situations
- Given phrase, determine one-step algebraic expression
- Identify equivalent multi-step algebraic expressions & phrases
- Determine algebraic expressions that represent real-world situations, including two-variable expressions
- Given phrase, determine multi-step algebraic expression
- Given phrase, determine & evaluate multi-step algebraic expression
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Evaluating Expressions
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Evaluating Expressions, Only Positives
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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
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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
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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
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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
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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
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Simplifying Expressions
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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
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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
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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
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Equations
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Solving One-Step Equations
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Addition One-Step 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
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Subtraction One-Step 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
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Multiplication One-Step 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 one-step linear equations, fractional coefficients & constants
- Solve one-step linear equations, fractional coefficients
- Solve one-step linear equations, fractional answers
- Condensed: Solve one-step linear equations, including fractional coefficients & fractional answers
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Division One-Step 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
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Mixed Operations One-Step Equations
- Condensed: Solve one-step linear equations, addition or subtraction
- Condensed: Solve one-step linear equations, multiplication or division
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Application of One-Step Equations
- Given rate & time, determine distance
- Given distance & rate or time, determine missing quantity
- 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
- Determine & solve one-step linear equations, real-world context
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Solving Two-Step Equations
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Multiplication Two-Step Equations
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Multiplication Two-Step 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
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Multiplication Two-Step 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
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Division Two-Step Equations
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Division Two-Step 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
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Division Two-Step 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
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Mixed Operations Two-Step Equations
- Condensed: Solve x/a ± b = c
- Condensed: Solve two-step linear equations
- Solve two-step linear equations, fractional answers
- Solve two-step linear equations, decimal coefficients
- Solve two-step linear equations, fractional coefficients
- Solve linear equations, sum or difference on one side
- Solve linear equations, product on one side
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Application & Modeling of Two-Step Equations
- Solve two-step linear equations, algebra tiles, positive coefficients
- Determine two-step linear equations, real-world context
- Solve problems that can be represented by one-step equations, including algebra tiles, real-world context
- Solve problems that can be represented by two-step equations, real-world context
- Determine equations or identify real-world situations represented by one-step or two-step equations
- Given equation with variables on both sides, identify real-world situation represented by equation
- Determine solutions to problems using common formulas, including simple interest, area & perimeter, & d = rt, real-world context
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Solving One- or Two-Step Equations
- Condensed: Solve one- or two-step linear equations, including fractional answers
- Condensed: Solve one- or two-step linear equations, fractional coefficients
- Solve ax ± b = c
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Solving Multi-Step Equations
- Solve linear equations, like terms on both sides
- Solve linear equations, distributive property on one side
- 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
- 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 three-step linear equations involving distribution of decimal multiplier
- Solve linear equations, term minus distributive property on one side
- Solve (ax ± b)/c = d
- Condensed: Solve three-step linear equations involving distribution, including fractional & decimal answers
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Solving Equations with Variables on Both Sides
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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 multi-step 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
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Application & Modeling of Equations with Variables on Both Sides
- Given algebra tiles, determine & solve one-variable equations with variables on both sides
- Solve problems that can be represented by one-step equations, including algebra tiles, real-world context
- Determine & solve linear equations with variables on both sides, real-world context
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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
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Inequalities
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Identifying & Graphing Inequalities
- Graph inequalities on number line
- Given graph, determine inequality
- Determine graph from inequality or inequality from graph
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Solving One-Step Inequalities
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Basic One-Step Inequalities
- Solve one-step inequalities, x + #
- Solve one-step inequalities, x – #
- Condensed: Solve one-step inequalities, x ± #
- Solve one-step inequalities, a * x, a > 0
- Solve one-step inequalities, a * x, a < 0
- Condensed: Solve one-step inequalities, a * x
- Solve one-step inequalities, x/a, a > 0
- Solve one-step inequalities, x/a, a < 0
- Condensed: Solve one-step inequalities, x/a
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Basic Solving & Graphing One-Step Inequalities
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Addition & Subtraction
- Solve & graph one-step inequalities, x + #
- Solve & graph one-step inequalities, x – #
- Condensed: Solve & graph one-step inequalities, x ± #
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Multiplication & Division
- Solve & graph one-step inequalities, a * x, a > 0
- Solve & graph one-step inequalities, whole number coefficients
- Solve & graph one-step inequalities, a * x, a < 0
- Solve & graph one-step inequalities, integer coefficients
- Condensed: Solve & graph one-step inequalities, a * x
- Solve & graph one-step inequalities, x/a, a > 0
- Solve & graph one-step inequalities, x/a, a < 0
- Condensed: Solve & graph one-step inequalities, x/a
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Mixed Operations
- Solve & graph one-step inequalities, including fractional coefficients
- Solve & graph one-step inequalities, including negative & fractional coefficients
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Application of One-Step Inequalities
- Given inequality, identify phrase or real-world problem that represents inequality
- Represent real-world problems as 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
- Determine one-step inequalities, rational numbers, including real-world context
- Given one-step inequality, identify real-world problem modeled by inequality, rational numbers
- Determine, solve, & graph one-step inequalities, including real-world context
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Solving Two-Step Inequalities
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Basic Solving Two-Step Inequalities
- Determine if given value is solution to two-step inequality
- Solve two-step inequalities modeled with algebra tiles
- Solve two-step inequalities, integers
- Solve two-step inequalities, fractions
- Solve two-step inequalities, decimals
- Condensed: Solve two-step inequalities
- Solve & graph two-step inequalities, integers
- Solve & graph two-step inequalities, decimals
- Solve & graph two-step inequalities, fractions
- Condensed: Solve & graph two-step inequalities
- Solve & graph two-step inequalities
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Application & Modeling of Two-Step Inequalities
- Determine if given value is solution to two-step inequality
- Solve two-step inequalities modeled with algebra tiles
- 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
- Given two-step inequality, identify real-world problem modeled by inequality
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Solving Multi-Step Inequalities
- Solve multi-step inequalities using distributive property
- Solve & graph inequalities, variables on both sides, including distributive property
- Determine inequalities with variables on both sides, real-world context
- Given inequality with variable on both sides, identify real-world problem modeled by inequality
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Solving Mixed Inequalities
- Determine equivalence of inequalities & solution set
- Condensed: Solve & graph inequalities
- Solve multi-step inequalities, including variables on both sides
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Linear Concepts
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Proportional Relationships
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Graphing Proportional Relationships
- Given unit rate, determine graph of proportional relationship, real-world context
- Given table, graph proportional linear equation
- Graph proportional linear equation
- Determine graph of proportional relationship, real-world context
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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
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Writing Equations, Completing Tables or Graphs
- Given multiplicative relationship in table, determine equation, real-world 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
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Finding Constant of Proportionality
- Given equation, determine constant of proportionality
- Given equation, determine constant of proportionality, real-world context
- Given table, determine constant of proportionality
- Given graph, determine constant of proportionality, including real-world context
- Determine constants of proportionality, real-world 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
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Proportional & Non-Proportional
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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
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Writing Equations, Completing Tables or Graphs
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Determine Graphs
- Given linear equation, determine y-values in table & identify graph, first quadrant
- Given linear equation & table, identify graph
- Given linear equation & table, determine graph
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Determine Tables
- Identify tables that represent real-world situations, y = mx or y = x + b
- Given linear equation, determine y-values in table, real-world context
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Determine Equations
- Given additive relationship in table, determine equation
- Given multiplicative relationship in table, determine equation
- Determine equations that represent real-world situations, including two-step equations
- Given linear graph & table, determine equation
- Determine equations that represent real-world situations, y = mx or y = x + b
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Mixed Representations
- Given slope-intercept 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 real-world situations, y = mx or y = x + b
- Identify representation of proportional relationship, various representations, real-world context
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Identifying Proportional vs. Non-Proportional
- 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 & non-proportional relationships, real-world context
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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 slope-intercept form, determine if point is on line
- Given linear equation in standard form, determine if point is on line
- Given linear equation in slope-intercept 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 slope-intercept form & graph, 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
- Identify linear & non-linear relationships, various representations
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Slope of a Line
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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
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Finding Slope
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Finding Slope from an Equation
- Given equation of horizontal or vertical line, determine rate of change
- Given equation in slope-intercept form, determine rate of change, integer solution
- Given equation in slope-intercept form, determine rate of change
- Given linear equation in standard form, determine rate of change
- Given equation in point-slope form, identify slope
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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 piece-wise function, determine rate of change over specific interval
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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
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Finding Slope from a Table
- Given table of linear equation, determine rate of change
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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
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Application of Slope
- Given right triangle, use legs to determine slope, real-world context
- Given graph of similar right triangles, identify equivalent slopes
- Given description, determine equation & specific value, real-world context
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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, 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
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Intercepts
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X-Intercept
- Given linear graph, plot x-intercept
- Given linear graph, determine coordinates of x-intercept
- Given equation of horizontal or vertical line, determine coordinates of x-intercept
- Given linear equation in slope-intercept form, determine coordinates of x-intercept
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Y-Intercept
- Given linear graph, plot y-intercept
- Given linear graph, determine coordinates of y-intercept
- Given equation of horizontal or vertical line, determine coordinates of y-intercept
- Given linear equation in slope-intercept form, determine coordinates of y-intercept
- Given equation of horizontal or vertical line, plot y-intercept
- Given linear equation in slope-intercept form, plot y-intercept
- Given linear equation in standard form, determine coordinates of y-intercept
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Both Intercepts
- Given linear graph, locate intercept or determine coordinates, various scales
- Given linear equation, determine intercepts
- Condensed: Given linear equation, determine x- or y-intercepts
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Writing Equation of a Line
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Writing Equation Given Point & Slope
- Given slope & y-intercept, determine equation
- Given point & integer slope, determine linear equation in slope-intercept form
- Given point & integer slope or rate of change, determine linear equation in slope-intercept form
- 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
- Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
- Given point & integer slope, determine linear equation in point-slope form, including slope-intercept form conversion
- Given positive point & whole number slope, determine y-intercept, equation, & specific value
- Given point & integer slope, determine y-intercept, equation, & specific value
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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 slope-intercept form, integer slope
- Given two points, determine linear equation in slope-intercept form, fractional slope
- Given two points, determine linear equation in standard form, integer slope, including slope-intercept form conversion
- 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, fractional slope, including slope-intercept form conversion
- Given two points, determine linear equation in point-slope form, fractional slope, including slope-intercept form conversion
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Writing Equation Given Various Components
- 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
- 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 point-slope or standard form
- Given intercepts, determine linear equation in slope-intercept form
- Condensed: Given linear graph, determine equation in slope-intercept form & specific value, various scales, including real-world context
- Condensed: Given two points, determine linear equation in slope-intercept form, including horizontal & vertical lines
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Writing Equation Given Graph
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Given Graph with Y-Intercept of Zero, Write Equation
- Given linear graph through origin with points shown on line, determine equation in slope-intercept form, integer slopes
- Given linear graph through origin, determine equation in slope-intercept form, integer slope
- Given linear graph through origin, determine equation in slope-intercept form, integer slope, 1 ≤ |m| ≤ 3
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Given Graphs with Varying Y-Intercepts, Write Equation
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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 equation in slope-intercept form, identify graph, integer slopes, various scales
- Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
- Given linear graph, determine equation in slope-intercept form, fractional slopes
- Given linear graph, identify equation, slope-intercept form
- Given linear graph, determine slope, y-intercept, & equation
- Given linear graph, determine equation in slope-intercept form & specific value, various scales
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Standard Form
- Given linear graph, determine equation in standard form
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Point-Slope Form
- Given linear graph, determine equation in point-slope form
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Various Forms
- Given linear graph, identify equation, various forms
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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
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Identifying Key Features of a Linear Function
- Given linear graph, determine slope & y-intercept, integer slope
- Given linear graph, determine slope & y-intercept
- 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
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Equations, Graphs, & Tables
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Basic Graphing
- Given point & integer slope, graph line
- Given point & slope, graph line
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Equation to Table
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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
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Various Slopes
- Given linear equation & one x-value, determine y-value in table
- Given linear equation & two x-values, determine y-values 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, real-world 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
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Equation to Graph
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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 real-world context
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Slope-Intercept Form to Graph
- Graph linear equations, including horizontal & vertical, integer slope, various scales
- Graph linear equations, fractional slope
- Given slope-intercept 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 slope-intercept 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 real-world context
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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 y-values 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
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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 slope-intercept form, rational constants & coefficients
- Given description, determine linear equation, fill table, & determine solution, real-world context
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Perpendicular, Parallel, or Neither
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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
- 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 slope-intercept 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
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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
- 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 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
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Line of Best Fit & Scatter Plots
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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
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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, real-world context
- Sketch line of best fit
- Sketch line of best fit & determine predicted value
- Condensed: Sketch line of best fit & determine equation
- Determine residuals
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Linear Word Problems
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Identifying Key Features Given Verbal Description
- Given graph or table of linear function, determine slope or y-intercept, real-world context
- Given description of linear relationship, determine slope, y-intercept, & equation, real-world context
- 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
- 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
- Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slope-intercept equation, & graph
- Form 6 – Given linear graph, interpret linear relationship & determine slope-intercept equation
- Form 7 – Given linear word problem, graph & interpret relationship, four quadrants
- Determine linear equation in standard form & graph, real-world context
- Given slope & intercept, interpret linear relationship & determine slope-intercept equation, including negative slope
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Choosing Correct Model Given Verbal Description
- Given description or table, determine linear graph, real-world context
- Given description of linear equation, identify graph, integer slope, real-world context
- Given linear word problem, identify graph
- Given description of linear relationship, identify graph, table, or equation, real-world context
- Given linear equation, interpret slope & y-intercept, real-world context
- Identify equivalent representations of linear relationship, including real-world context
- Given description of linear equation, identify graph, fractional slope, real-world context
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Functions
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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
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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 & non-functions, 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 real-world context
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Systems of Equations
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Determining Solution to Systems of Equations
- 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
- Condensed: Determine systems of linear equations & solutions, including real-world context
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Solving Systems of Equations, Graphing
- Determine & verify graphical solutions to systems of linear equations, slope-intercept form
- Given system of linear equations, determine point of intersection, slope-intercept 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 real-world context
- Given system of linear equations, graph & determine point of intersection, slope-intercept form
- Given graph of system of linear equations, determine equations in slope-intercept form
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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
- Determine solutions of linear equations, substitution bias, including given system, real-world context
- Solve systems of linear equations, infinite possibilities or no solution
- Determine systems of linear equations & solutions, substitution bias, real-world context
- 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
- Condensed: Solve or determine system of equations, likely to have same variable isolated
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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, real-world 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 real-world context
- Determine & justify solutions to systems of linear equations, real-world context
- Condensed: Determine systems of linear equations & solutions
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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, real-world context
- Condensed: Simplify ratios, identify equivalent ratios, & determine missing components of proportions
- Compare rates
- Determine specified values in proportional relationships, real-world context
- Determine part to part ratio, strip diagrams, real-world context
- Determine part to whole ratio, various models
- Determine & identify equivalent rates of changes, various representations
- Determine & compare unit rates, real-world context
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Determine Ratios & Percents
- Condensed: Determine ratios & percents, decimal grids
- Condensed: Determine ratios & percents, double number lines, including real-world context
- Condensed: Determine ratios & percents, strip diagrams, real-world context
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Rates
-
Determine Unit Rates
- Determine unit rates, whole numbers, real-world context
- Determine unit rates, fractions, real-world context
- Given rate & comparison, determine unit rates, real-world context
- Determine unit rates, mixed numbers, real-world context
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Use Rates to Solve Problems
- Given unit rate, determine specified value in proportional relationship, real-world context
- Given unit conversion rate, convert measurement units
- Given proportional relationship, determine specified quantity, 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
- Determine & apply unit rates to determine specified quantities, real-world context
- Condensed: Determine or apply unit rates, real-world context
- Condensed: Determine ratios, relationship between ratio terms, & specified quantities, real-world context
- Determine ratios, real-world context
- Given ratio, determine relationship between ratio terms, real-world context
- Condensed: Given extended ratio, determine ratio or specified quantity, real-world context
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Proportions
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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
-
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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
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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
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Data Analysis & Probability
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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
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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
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Frequency Tables
- Determine two-way frequency tables
- Given data, identify frequency table or determine missing element of table
- Given two-way frequency tables, identify associations
- Determine specified probabilities in two-way frequency tables
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables
- Interpret two-way frequency tables, joint distribution
- Interpret two-way frequency tables, conditional distribution
- Interpret two-way frequency tables, marginal distribution
- Condensed: Interpret two-way frequency tables
- Solve one-step problems from frequency & relative frequency tables, real-world context
- Solve problems from frequency tables, real-world 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 one-step problems from dot plots, real-world context
- Solve multi-step problems from dot plots, real-world 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 side-by-side dot plots
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Stem-&-Leaf Plots
- Given data, identify stem-and-leaf plot
- Solve one-step problems from stem-and-leaf plots, real-world context
- Solve multi-step problems from stem-and-leaf plots, real-world context
-
Box Plots
- Solve problems involving interpretation of box plots
- Given boxplot, determine values from five-number summary
- Determine five-number summary
- 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
-
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
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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
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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
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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 real-world context
- Given perimeter of rectangle & one side, determine dimension
- Given perimeter of rectangle & one side, determine dimension, including decimals
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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
-
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Application of Rectangle Perimeter & Area
-
Perimeter
- Given sides of rectangle, determine perimeter
- Determine perimeter of rectangles, real-world 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
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Area
- Determine equations that represent area of rectangles, real-world context
- Given model, identify formula & determine area of rectangle
- Given sides of rectangle & cost per square unit, determine area & total cost, real-world 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, real-world context
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Parallelogram Area
- Determine area of parallelograms
- Determine equations that represent area of parallelograms, real-world context
- Given area & one dimension of parallelogram, determine missing dimension
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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, real-world context
- Given area & one dimension of triangle, determine missing dimension
- Given area & one dimension of triangle, determine missing dimension, mixed numbers
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Trapezoid Area
- Determine area of trapezoids
- Determine equations that represent area of trapezoids, real-world context
- Given area & base lengths of trapezoid, determine height
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Circle Area & Circumference
- Given radius or diameter, determine circumference
- Determine circumference of circle, exact answers, multiple choice, including real-world context
- Given radius or diameter, determine area
- Determine area of circle, exact answers, including real-world 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
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Perimeter
- Determine perimeter of polygons, including real-world 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, real-world 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 real-world context
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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, real-world context
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Surface Area & Volume
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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
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Rectangular Prism Surface Area & Volume
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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, real-world context
- Determine volume of rectangular prisms, whole numbers, including real-world context
- Determine volume or edge of rectangular prisms, whole numbers or decimals, real-world context
- Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, real-world context
- Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including real-world context
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Triangular Prism Surface Area & Volume
- Determine surface area of triangular prisms
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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 real-world context
- Condensed: Determine total surface area & lateral surface area of composite figures, rectangular & triangular prisms
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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
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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
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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
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Mixed Figures Surface Area & Volume
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Mixed Figures Surface Area
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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 real-world context
- Given surface area, determine dimension of 3D figure, no visual provided
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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
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Mixed Figures Volume
- Determine volumes of 3D figures
- Determine volume of cylinders, cones, & spheres
- Determine volume of cylinders, cones, & spheres, including real-world 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
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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 real-world context
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Similar Figures
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Determine Dimensions
- Determine dimensions in similar figures, whole number dimensions
- Determine dimensions in similar figures
- Determine dimensions using similar figures & indirect measurements
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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
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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, pre-image centered at origin
- Given scale factor, determine coordinates of image, pre-image 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
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Transformations
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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
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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
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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
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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
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Mixed Transformations
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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
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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
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Pythagorean Theorem
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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
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Application of Pythagorean Theorem
- Given two sides, determine missing side of right triangle, real-world context
- Solve problems using Pythagorean theorem, figure included, real-world context
- Given Pythagorean theorem model, determine specified component
- Determine side of right triangle or apply converse of Pythagorean theorem, including real-world context
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Angle Relationships
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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
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Vertical Angles
- Given parallel lines with transversal & angle, determine vertical angle
- Given parallel lines with transversal & angle, determine vertical angle, algebraic expressions
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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
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Corresponding & Same-Side Interior Angles
- Given parallel lines with transversal & angle, determine corresponding angle
- Given parallel lines with transversal & angle, determine same-side 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 same-side interior angle, algebraic expressions
- Given parallel lines with transversal & angle, determine supplement to corresponding angle, algebraic expressions
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Transversal Definitions
- Given parallel lines with transversal, identify specified angle pairs, only numbered angles, uses “same-side interior” terminology
- Given parallel lines with transversal & angles, identify specified angle pairs, uses “same-side 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 non-parallel lines & transversal, identify transversal & specified angle pairs
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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
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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 two-year college education
- Estimate costs of four-year college education
- Condensed: Estimate or determine costs of college education
- Determine growth of money invested regularly over time