7th Grade Skills

Integers

Integer Vocabulary & Scenarios
 Identify situations represented by positive & negative numbers, realworld context
 Determine representations of quantities using positive & negative numbers, realworld context

Opposites
 Determine opposites of numbers
 Identify opposite integers on number line
 Determine change, opposite integers, realworld context

Comparing Integers
 Compare two positive integers
 Compare two integers, one positive & one negative
 Compare two negative integers
 Interpret inequalities as statements about position

Addition of Integers

Modeling Addition of Integers
 Add integers using counters
 Classify sum of integers on number line
 Given number line model, determine or interpret integer sum expression, same signs
 Given number line model, determine or interpret integer sum expression, mixed signs

Basic Addition of Integers
 Add opposite integers
 Add opposite integers, up to two digits
 Add integers with same sign, start one digit & advance to two digits
 Add integers, one digit
 Add negative integers
 Add integers, positive sum
 Add integers, negative sum
 Add integers, start one digit & advance to two digits
 Add negative integers, up to two digits
 Add integers, up to two digits, positive sum
 Add integers, up to two digits, negative sum
 Condensed: Add positive & negative integers

Application of Addition of Integers
 Add integers with same sign, up to three digits, realworld context
 Add integers, up to three digits, realworld context
 Given model or table, add integers, realworld context
 Condensed: Add integers, realworld context


Subtraction of Integers

Modeling Subtraction of Integers
 Subtract integers using counters
 Given variables on number line, classify difference
 Subtract integers on number line, same signs
 Subtract integers on number line, mixed signs

Basic Subtraction of Integers, Positive Differences
 Subtract integers, positive difference
 Subtract negative integers, positive difference
 Subtract negative integers, up to two digits, positive difference
 Subtract integers, opposite signs, up to two digits, positive difference

Basic Subtraction of Integers, Negative Differences
 Subtract positive integers, negative difference
 Subtract negative integers, negative difference
 Subtract integers, negative difference
 Subtract positive integers, up to two digits, negative difference
 Subtract negative integers, up to two digits, negative difference
 Subtract integers, opposite signs, up to two digits, negative difference

Basic Subtraction of Integers, Mixed Differences
 Subtract positive integers, onedigit & onedigit
 Rewrite subtraction as addition & evaluate expression
 Subtract integers, various signs
 Condensed: Subtract integers, various signs, up to two digits

Application of Subtraction of Integers
 Determine differences between integers, same signs, realworld context
 Determine differences between integers, mixed signs, realworld context
 Determine differences between integers, various signs, realworld context


Multiplication of Integers

Modeling Multiplication of Integers
 Multiply integers using counters
 Multiply positive integers using number line models, includes negatives shown on number line
 Multiply positive integers times negative integers using number line models

Basic Multiplication of Integers
 Multiply integers, start one digit & advance to two digits
 Multiply integers, opposite signs
 Multiply negative integers
 Multiply integers, opposite signs, twodigit times twodigit
 Multiply negative integers, twodigit times twodigit
 Multiply integers, opposite signs, twodigit times two or threedigit
 Multiply negative integers, twodigit times two or threedigit
 Multiply three integers

Application of Multiplication of Integers
 Multiply positive integers, realworld context
 Multiply integers, mixed signs, realworld context


Division of Integers

Modeling Division of Integers
 Divide integers using counters
 Divide integers, both positive, up to twodigit dividend, number line model
 Divide integers, opposite signs, up to twodigit dividend, number line model

Basic Division of Integers
 Divide integers, opposite signs, up to threedigit dividend, up to twodigit divisor
 Divide integers, both negative, up to threedigit dividend, up to twodigit divisor
 Divide integers, opposite signs, up to fivedigit dividend, up to twodigit divisor
 Divide integers, both negative, up to fivedigit dividend, up to twodigit divisor
 Divide integers, one or both negative, start onedigit, advance up to threedigits
 Divide integers, one or both negative, start onedigit, advance up to threedigits, includes undefined

Application of Division of Integers
 Divide integers, same signs, realworld context
 Divide integers, opposite signs, realworld context


Mixed Operations of Integers
 Determine number of zero pairs or evaluate expressions using counters
 Condensed: Add or subtract integers using counters
 Estimate sums & differences of integers using frontend rounding
 Add or subtract three integers
 Add or subtract four integers
 Multiply & divide three integers
 Condensed: Multiply & divide integers
 Condensed: Add, subtract, multiply, & divide integers
 Evaluate numerical expressions, realworld context

Order of Operations of Integers, Sum & Difference Only
 Evaluate sum or difference of three integers, at least one difference
 Evaluate sum or difference of four integers, at least one difference
 Evaluate sum or difference of four integers, two grouped in parentheses, at least one difference
 Evaluate sum or difference of four integers, two grouped in absolute value, at least one difference
 Evaluate sum or difference of six integers, two grouped in parentheses, two grouped in absolute value, at least one difference

Order of Operations of Integers
 Evaluate numerical expressions, three or four integers, including multiplication & division
 Evaluate numerical expressions, three or four integers, including multiplication & division as fraction
 Evaluate numerical expressions, three or four integers, one exponent, including multiplication
 Evaluate numerical expressions, four integers, including multiplication & exponents
 Evaluate numerical expressions, five integers, two grouped in parentheses, including multiplication & division
 Evaluate numerical expressions, five integers, two grouped in absolute value, including multiplication & division
 Evaluate numerical expressions, five integers, one exponent, two grouped in parentheses, including multiplication & division
 Evaluate numerical expression quotients, five to seven integers, one exponent, including multiplication, division, & absolute value
 Evaluate numerical expression quotients, five to seven integers, including multiplication, division, & absolute value
 Condensed: Evaluate numerical expressions


Fractions

Converting Fractions

Converting Fractions to Decimals
 Identify & determine decimal equivalent of fractions, denominator less than 10
 Convert fractions to decimals, denominator power of 10
 Convert fractions to decimals, denominator factor of power of 10
 Convert fractions to decimals, denominator factor of 100
 Convert fractions to rounded decimals
 Convert fractions to decimals, including improper fractions, including repeating decimals
 Convert mixed numbers to decimals, including repeating decimals
 Convert fractions to decimals, up to two decimal places, realworld context

Converting Fractions to Percents or Decimals
 Convert fractions to percents, denominator factor of 100
 Convert fractions to percents, denominator factor of 100, rounding directions
 Convert fractions to rounded percents
 Convert improper fractions to rounded percents
 Condensed: Convert proper & improper fractions to rounded percents
 Convert fractions to mixed number percents
 Convert fractions to mixed number percents over 100
 Condensed: Convert fractions to decimals & percents


Addition of Fractions

Basic Addition of Fractions, Only Positives
 Add fractions, one denominator multiple of other, including improper sums
 Add fractions, one denominator multiple of other, including mixed number sums
 Add fractions, different denominators, including improper sums
 Add fractions, different denominators, including mixed number sums
 Add mixed numbers, different denominators
 Add mixed numbers, different denominators, fractional sum greater than one

Basic Addition of Fractions, Including Negatives
 Add fractions, common denominators, at least one negative
 Add fractions, common denominators, at least one negative, including improper differences
 Condensed: Add fractions, common denominators
 Condensed: Add fractions, common denominators, including improper sums
 Add fractions, different denominators, at least one negative
 Condensed: Add fractions, different denominators
 Condensed: Add fractions, no mixed numbers
 Add fractions, different denominators, at least one negative, including improper differences
 Condensed: Add fractions, including improper sums
 Condensed: Add fractions, different denominators, including improper sums
 Condensed: Add fractions, including mixed numbers
 Add mixed numbers, different denominators, at least one negative

Application of Addition of Fractions
 Add fractions, mixed signs, realworld context
 Add fractions, mixed signs, including improper sums, realworld context
 Add mixed numbers, mixed signs, realworld context


Subtraction of Fractions

Basic Subtraction of Fractions, Only Positives
 Subtract fractions, one denominator multiple of other, proper fraction difference
 Subtract fractions, one denominator multiple of other, including improper differences
 Subtract fractions, different denominators, positive proper differences
 Subtract fractions, different denominators, including mixed number differences
 Subtract mixed numbers, different denominators
 Subtract mixed numbers, different denominators, borrowing required

Basic Subtraction of Fractions, Common Denominators
 Subtract fractions, common denominators, at least one negative
 Subtract fractions, common denominators, including improper differences
 Subtract fractions, common denominators, at least one negative, including improper differences
 Condensed: Subtract fractions, common denominators
 Condensed: Subtract fractions, common denominators, including improper differences

Basic Subtraction of Fractions, Including Negatives
 Subtract fractions, different denominators, at least one negative
 Condensed: Subtract fractions, different denominators
 Condensed: Subtract fractions, no mixed numbers
 Subtract fractions, different denominators, at least one negative, including improper differences
 Subtract fractions, different denominators, negative proper differences
 Condensed: Subtract fractions, different denominators, including improper differences
 Condensed: Subtract fractions, including improper differences
 Subtract mixed numbers, different denominators, at least one negative
 Subtract mixed numbers, different denominators, borrowing required, negative difference
 Condensed: Subtract fractions, including mixed numbers
 Subtract fractions, different denominators, negative difference

Application of Subtraction of Fractions
 Subtract fractions, mixed signs, including improper differences, realworld context
 Subtract mixed numbers, mixed signs, realworld context


Multiplication of Fractions

Application & Modeling of Multiplication of Fractions
 Multiply whole numbers & fractions, area models
 Multiply whole numbers & fractions, realworld context
 Multiply fractions, positive, realworld context
 Multiply fractions & mixed numbers, mixed signs, realworld context

Basic Multiplication of Fractions, Only Positives
 Multiply whole numbers & unit fractions, whole number first
 Multiply whole numbers & unit fractions
 Multiply whole numbers & fractions, positive
 Multiply proper & improper fractions, positive
 Multiply fractions, positive
 Multiply fractions, positive, mixed number directions
 Multiply mixed numbers, positive

Basic Multiplication of Fractions, Including Negatives
 Multiply whole numbers & fractions, mixed signs
 Multiply fractions, mixed signs
 Multiply proper & improper fractions, mixed signs
 Condensed: Multiply fractions, including mixed signs
 Multiply fractions, mixed signs, mixed number directions
 Condensed: Multiply fractions, including mixed signs, mixed number directions
 Multiply mixed numbers, mixed signs
 Condensed: Multiply fraction & mixed numbers, including mixed signs, mixed number directions


Division of Fractions

Basic Division of Fractions, Only Positives
 Divide whole numbers by unit fractions
 Divide fractions, positive
 Divide fractions, positive, mixed number directions
 Divide mixed numbers, positive

Basic Division of Fractions, Including Negatives
 Divide fractions, mixed signs
 Condensed: Divide fractions, including mixed signs
 Divide fractions, mixed signs, mixed number directions
 Condensed: Divide fractions, including mixed signs, mixed number directions
 Divide mixed numbers, mixed signs
 Condensed: Divide fractions & mixed numbers, including mixed signs, mixed number directions

Application of Division of Fractions
 Determine or estimate quotients of whole numbers, fraction quotients
 Divide whole numbers & unit fractions, including unit fraction multiplication, realworld context
 Divide fractions & whole numbers, mixed signs, realworld context
 Divide fractions & mixed numbers, positive, realworld context
 Divide fractions, mixed numbers, & whole numbers, multistep, realworld context


Mixed Operations of Fractions

Basic Mixed Operations of Fractions
 Add or subtract fractions, different denominators, at least one negative, including improper results
 Add or subtract fractions, different denominators, at least one negative, including mixed number results
 Condensed: Add or subtract fractions
 Condensed: Add or subtract fractions, different denominators
 Add or subtract mixed numbers, different denominators, at least one negative, fractional sum greater than one
 Multiply & divide three fractions, mixed signs
 Add or subtract three fractions, positive & negative, different denominators
 Add or subtract four fractions, positive & negative, different denominators

Application of Mixed Operations of Fractions
 Add or subtract fractions, including estimation, realworld context
 Add & subtract fractions, realworld context



Decimals

Converting Decimals
 Convert decimals to percents
 Convert decimals to percents over 100
 Convert decimals to fractions
 Convert decimals to mixed numbers
 Convert decimals to fractions or mixed numbers
 Convert decimals to fractions or mixed numbers, including repeating decimals of thirds
 Convert decimals to fractions or mixed numbers, including repeating decimals
 Condensed: Convert decimals to fractions & percents

Addition of Decimals

Basic Addition of Decimals, Only Positives
 Add decimals, positive, up to two decimal places
 Add positive decimals, up to three decimal places
 Add decimals, positive, up to four decimal places

Basic Addition of Decimals, Including Negatives
 Add positive decimals, up to three decimal places
 Add negative decimals, up to three decimal places
 Add positive & negative decimals, up to three decimal places, positive sum
 Add positive & negative decimals, up to three decimal places, negative sum
 Condensed: Add decimals, up to three decimal places

Application of Addition of Decimals
 Add decimals, positive, up to two decimal places, realworld context
 Condensed: Add decimals, positive, up to two decimal places, including realworld context
 Add decimals, up to hundredths, same signs, realworld context
 Add decimals, up to two decimal places, mixed signs, realworld context
 Condensed: Add decimals, up to three decimal places, realworld context


Subtraction of Decimals

Basic Subtraction of Decimals, Only Positives
 Subtract decimals, up to two decimal places
 Subtract decimals, two decimal places
 Subtract decimals, up to three decimal places, positive difference

Basic Subtraction of Decimals, Including Negatives
 Subtract decimals, up to three decimal places, negative difference
 Subtract decimals, both negative, up to three decimal places, positive difference
 Subtract decimals, both negative, up to three decimal places, negative difference
 Subtract decimals, opposite signs, up to three decimal places, positive difference
 Subtract decimals, opposite signs, up to three decimal places, negative difference
 Condensed: Subtract decimals, up to three decimal places

Application of Subtraction of Decimals
 Subtract decimals, same signs, up to two decimal places, realworld context
 Subtract decimals, mixed signs, up to two decimal places, realworld context
 Subtract decimals, up to two decimal places, realworld context
 Condensed: Subtract decimals, up to two decimal places, including realworld context


Multiplication of Decimals

Basic Multiplication of Decimals, Only Positives
 Multiply decimals times onedigit whole numbers
 Multiply positive decimals, each factor up to two decimal places, factors up to 10 after decimal shift
 Multiply positive decimals, each factor up to two decimal places, factors up to 20
 Multiply positive decimals, each factor up to two decimal places
 Multiply decimals, products limited to two decimal places
 Multiply positive decimals, each factor up to three decimal places
 Multiply three positive decimals, products limited to three decimal places
 Condensed: Multiply decimals

Basic Multiplicaition of Decimals, Including Negatives
 Multiply decimals, both negative, each factor up to two decimal places with one nonzero digit
 Multiply decimals, opposite signs, each factor up to two decimal places with one nonzero digit
 Multiply decimals, both negative, each factor up to two decimal places, including integers up to 19
 Multiply decimals, opposite signs, each factor up to two decimal places, including integers up to 19
 Multiply decimals, both negative, each factor up to two decimal places
 Multiply decimals, opposite signs, each factor up to two decimal places, including integers up to 99
 Multiply decimals, both negative, each factor up to three decimal places
 Multiply decimals, opposite signs, each factor up to three decimal places
 Condensed: Multiply decimals, mixed signs

Application of Multiplication of Decimals
 Multiply decimals, products limited to two decimal places, realworld context
 Multiply decimals, mixed signs, realworld context
 Multiply decimals, realworld context


Division of Decimals

Basic Division of Decimals, Only Positives
 Divide whole numbers by decimals, up to two decimal places, integer quotients
 Divide decimals by whole numbers, up to two decimal places
 Divide decimals, up to two decimal places in quotients
 Divide decimals, up to three decimal places
 Divide decimals, up to three decimal places in dividend & divisor
 Condensed: Divide decimals or whole numbers

Basic Division of Decimals, Including Negatives
 Divide integers by decimals, twodigit dividend, divisor up to two decimal places, both negative
 Divide integers by decimals, twodigit dividend, divisor up to two decimal places, opposite signs
 Divide integers by decimals, twodigit dividend, divisor up to two decimal places, mixed signs
 Divide decimals, up to three decimal places, both negative
 Divide decimals, up to three decimal places, opposite signs
 Divide decimals, up to three decimal places
 Divide decimals, dividend up to four decimal places, divisor integer or up to two decimal places, both negative
 Divide decimals, dividend up to four decimal places, divisor integer or up to two decimal places, opposite signs
 Divide decimals, up to four decimal places
 Condensed: Divide decimals, mixed signs

Application of Division of Decimals
 Divide decimals, up to three decimal places, realworld context
 Divide fourdigit dividends by twodigit whole number divisors, including realworld context
 Divide decimals, same signs, realworld context
 Divide decimals, mixed signs, realworld context


Mixed Operations of Decimals
 Condensed: Add & subtract decimals, up to two decimal places
 Condensed: Add & subtract decimals, up to two decimal places, including realworld context
 Add & subtract decimals, up to two decimal places, realworld context
 Condensed: Add & subtract decimals, up to two decimal places, realworld context
 Add or subtract three decimals, positive & negative, hundredths
 Add or subtract four decimals, positive & negative, hundredths
 Multiply & divide three decimals, mixed signs
 Condensed: Add, subtract, multiply, & divide decimals, up to two decimal places


Rational Numbers

Classifying Rational Numbers
 Classify rational numbers by definitions
 Classify rational numbers using graphic organizers
 Classify rational numbers, including graphic organizers
 Determine relationships between subsets of real numbers
 Determine relationships between subsets of rational numbers

Absolute Value of Rational Numbers
 Determine absolute value of integers
 Determine absolute value of rational numbers
 Determine absolute value of integers, including realworld context
 Determine absolute value of numeric expression

Comparing & Ordering Rational Numbers
 Condensed: Order positive decimals & fractions
 Order decimals & fractions
 Order positive rational numbers, no radicals, no exponents
 Order rational numbers, no radicals, no exponents
 Given table, order rational numbers, realworld context
 Given set or list, order rational numbers, realworld context
 Order real numbers, exponents are positive
 Order real numbers, positive exponents, percents are whole, including realworld context
 Order real numbers, positive exponents, percents are whole, including realworld context

Estimating Rational Numbers

Basic Estimating of Rational Numbers
 Estimate sum of rational numbers, round both to nearest whole
 Estimate differences of rational numbers
 Estimate products of mixed numbers
 Estimate products of rational numbers, no decimals, round both factors to same place value
 Estimate products of rational numbers
 Estimate quotients of rational numbers, no decimals

Application of Estimating Rational Numbers
 Estimate sum of rational numbers, round both to nearest whole, realworld context
 Estimate differences of rational numbers, realworld context
 Estimate products of positive rational numbers, realworld contexts
 Estimate products of rational numbers, no decimals, round both factors to nearest whole number, realworld context
 Estimate quotients of rational numbers, no decimals, realworld context
 Estimate quotients of rational numbers, realworld context


Order of Operations of Rational Numbers
 Evaluate numerical expressions, # ± #(#), decimals
 Evaluate numerical expressions, #/# + #, decimals
 Evaluate numerical expressions, #(# + #), decimals
 Evaluate numerical expressions, decimals, no exponents
 Evaluate numerical expressions, fractions, no exponents
 Evaluate numerical expressions, decimals & fractions, no exponents
 Evaluate numerical expressions, decimals
 Evaluate numerical expressions, fractions
 Evaluate numerical expressions, decimals & fractions
 Evaluate numerical expressions, including rationals & up to two sets of grouping symbols

Mixed Operations of Rational Numbers
 Multiply decimals times fractions, at least one negative
 Multiply fractions times decimals, at least one negative
 Condensed: Multiply decimals & fractions
 Divide decimal by fraction, both less than one, both positive
 Divide fraction by decimal, both less than one, both positive
 Divide decimal by fraction, both less than one, mixed signs
 Divide fraction by decimal, both less than one, mixed signs
 Condensed: Divide decimals & fractions, both less than one
 Solve multistep problems with rational numbers, including percents, realworld context


Scientific Notation

Basic Scientific Notation
 Identify correct conversion of number from scientific notation with positive exponent to standard form
 Identify correct conversion of number from scientific notation with negative exponent to standard form
 Identify correct conversion of number from standard form to scientific notation with positive exponent
 Identify correct conversion of number from standard form to scientific notation with negative exponent
 Convert number from scientific notation with positive exponent to standard form
 Convert number from scientific notation with negative exponent to standard form
 Multiply decimal or whole number & 10 to negative exponent
 Convert number from standard form to scientific notation with positive exponent
 Convert number from standard form to scientific notation with negative exponent
 Condensed: Identify correct conversion of number between scientific notation & standard form
 Condensed: Convert number between scientific notation & standard form

Application of Scientific Notation
 Convert numbers between standard form & scientific notation, realworld context
 Convert number from standard form to scientific notation, realworld context

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

Powers of Ten
 Determine equivalent powers of 10 & fractions, decimals, or whole numbers
 Round & convert number from standard form to scientific notation with positive exponent
 Round & convert number from standard form to scientific notation with negative exponent
 Condensed: Round & convert number from standard form to scientific notation

Comparing & Ordering Scientific Notation
 Compare two numbers in scientific notation
 Compare magnitude of numbers in scientific notation, realworld context


Radicals & Roots
 Determine square roots of perfect squares
 Solve perfect square root equations
 Condensed: Determine square roots of perfect squares
 Evaluate perfect cube roots
 Solve perfect cube root equations
 Condensed: Determine cube roots of perfect cubes

Expressions

Translating Expressions
 Interpret numerical expressions
 Given phrase, determine onestep algebraic expression
 Determine algebraic expressions that represent realworld situations
 Identify equivalent multistep algebraic expressions & phrases
 Determine algebraic expressions that represent realworld situations, including twovariable expressions
 Identify algebraic expressions, involving distribution, realworld context
 Identify equivalent expressions involving distribution, two or more terms
 Given phrase, determine multistep algebraic expression
 Given phrase, determine & evaluate multistep algebraic expression

Equivalent Expressions
 Identify equivalent numerical expressions using counters
 Identify equivalent algebraic expressions using algebra tiles
 Identify equivalent expressions involving distribution
 Identify equivalent expressions or determine simplified expressions
 Identify equivalent numerical & algebraic expressions, including distribution, including realworld context

Evaluating Expressions

Basic Evaluating Expressions, Addition & Subtraction Only
 Evaluate addition expressions for specified value, one variable, whole numbers
 Evaluate addition expressions for specified value, one variable, at least one fraction
 Evaluate addition expressions for specified value, one variable, at least one decimal
 Evaluate subtraction expressions for specified value, one variable, whole numbers
 Evaluate subtraction expressions for specified value, one variable, at least one fraction
 Evaluate subtraction expressions for specified value, one variable, at least one decimal

Basic Evaluating Expressions
 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
 Evaluate expressions for specified values, two variables, two terms
 Evaluate expressions for specified value, one variable, two terms, only sums & differences
 Evaluate expressions for specified values, two variables, two terms, one term with three factors
 Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers

Application of Evaluating Expressions
 Evaluate or identify expressions that represent situations from descriptions, realworld context
 Evaluate expressions for specified values, two variables, multiple operations, including powers & realworld context
 Condensed: Evaluate expressions, including powers, fractions, whole numbers, & decimals, including realworld context


Distributing or Factoring Expressions
 Simplify algebraic expressions, one variable, distribute once, integer multiplier
 Simplify algebraic expressions, one variable, distribute once, decimal multiplier
 Simplify algebraic expressions, one variable, distribute once, fraction multiplier
 Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
 Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
 Factor GCF from linear binomial expressions, both terms positive
 Factor GCF from linear binomial expressions, both terms negative
 Factor GCF from linear binomial expressions, mixed signs
 Condensed: Factor GCF from linear binomial expressions
 Distribute or factor, linear binomial expressions

Simplifying Variable Expressions
 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, one variable, product of two factors
 Simplify algebraic expressions, one variable, product of two or three factors, one variable factor
 Simplify algebraic expressions, one variable, product of two or three factors
 Simplify algebraic expressions, product of two variable factors
 Simplify algebraic expressions, one variable, product of three factors, two variable factors
 Simplify algebraic expressions, two variables, positive integer coefficients


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 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
 Condensed: Solve onestep linear equations, multiplication or division
 Condensed: Solve onestep linear equations, including fractional coefficients & fractional answers
 Solve onestep linear equations, fractional coefficients & constants

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

Solving OneStep Equations
 Condensed: Solve onestep linear equations, addition or subtraction
 Condensed: Solve onestep linear equations, multiplication or division
 Solve onestep linear equations, fractional coefficients
 Solve onestep linear equations, fractional answers
 Solve onestep linear equations, fractional coefficients & constants
 Condensed: Solve onestep linear equations, including fractional coefficients & fractional answers

Application of OneStep Equations, Addition
 Determine addition equations, realworld context
 Solve addition equations, realworld context
 Determine & solve addition equations, including realworld context
 Determine & solve or apply addition equations, realworld context
 Determine, solve, & apply addition equations, realworld context

Appllication of OneStep Equations, Multiplication
 Determine multiplication equations, realworld context
 Determine & solve multiplication equations, realworld context
 Determine & solve multiplication equations, including realworld context
 Determine & solve multiplication equations, including required rounding, realworld context
 Determine, solve, & apply multiplication equations, realworld context
 Determine, solve, & apply multiplication equations, including required rounding, realworld context

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


Solving TwoStep Equations

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

Multiplication TwoStep Equations with Addition
 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, 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, 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

Multliplication TwoStep Equations with Subtraction
 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, 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, 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

Division TwoStep Equations with Addition
 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, 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, 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, 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, a < 0, b > 0, c > 0, x < 0
 Condensed: Solve x/a ± b = c
 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, b > 0, c < 0, x < 0
 Solve x/a – b = c, a < 0, b > 0, c < 0, x < 0

Rational Coefficient TwoStep Equations
 Determine if given value is solution to twostep linear equations
 Solve twostep linear equations, decimal coefficients
 Solve twostep linear equations, fractional coefficients
 Condensed: Solve one or twostep linear equations, fractional coefficients


Solving MultiStep Equations

Application & Modeling of MultiStep Equations
 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 linear equations & solve problems that can be represented by equations with distributive property on one side, realworld context
 Determine & solve linear equations with variables on both sides, realworld context

Basic MultiStep Equations
 Solve linear equations, distributive property on one side
 Solve threestep linear equations involving distribution of decimal multiplier
 Solve threestep linear equations involving distribution, fractional multiplier cancels if distributed
 Solve threestep linear equations involving distribution, fractional multiplier doesn’t cancel if distributed
 Condensed: Solve threestep linear equations involving distribution, including fractional & decimal answers
 Solve (ax ± b)/c = d
 Solve linear equations, variables as numerators on both sides
 Solve linear equations, binomials on both sides, decimals
 Solve linear equations, binomials on both sides, fractions
 Solve multistep linear equations



Inequalities

Identifying & Graphing Inequalities
 Graph inequalities on number line
 Given graph, determine inequality
 Determine graph from inequality or inequality from graph
 Identify solutions to inequalities, including realworld context

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

Basic Solving & Graphing OneStep Inequalities, Multiplication & Division
 Solve & graph onestep inequalities, a * x, a > 0
 Solve & graph onestep inequalities, a * x, a < 0
 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

Basic Solving & Graphing of OneStep Inequalities, Mixed Operations
 Solve & graph onestep inequalities, whole number coefficients
 Solve & graph onestep inequalities, integer coefficients
 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
 Determine onestep inequalities, rational numbers, including realworld context
 Identify onestep inequalities that model realworld problems or interpret inequality components
 Given onestep inequality, identify realworld problem modeled by inequality
 Given onestep inequality, identify realworld problem modeled by inequality, rational numbers
 Determine, solve, & graph onestep inequalities, including realworld context


Solving TwoStep Inequalities

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

Basic TwoStep Inequalities
 Solve twostep inequalities, integers
 Solve twostep inequalities, decimals
 Solve twostep inequalities, fractions
 Condensed: Solve twostep inequalities

Basic Solving & Graphing of TwoStep Inequalities
 Solve & graph twostep inequalities, integers
 Solve & graph twostep inequalities
 Solve & graph twostep inequalities, decimals
 Solve & graph twostep inequalities, fractions
 Condensed: Solve & graph twostep inequalities



Linear Concepts

Slope of a Line

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

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

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

Comparing Slopes
 Identify linear graph with most extreme rate of change
 Identify linear table with most extreme rate of change
 Given description, compare rates of change, 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, Given Graph
 Given linear graph, plot yintercept
 Given linear graph, plot xintercept
 Given linear graph, determine coordinates of yintercept
 Given linear graph, determine coordinates of xintercept
 Given linear graph, locate intercept or determine coordinates, various scales

Intercepts, Given Equation
 Given linear equation in slopeintercept form, determine coordinates of yintercept
 Given equation of horizontal or vertical line, determine coordinates of yintercept
 Given linear equation in slopeintercept form, determine coordinates of xintercept
 Given equation of horizontal or vertical line, determine coordinates of xintercept
 Given linear equation in slopeintercept form, plot yintercept
 Given equation of horizontal or vertical line, plot yintercept
 Given linear equation, determine intercepts
 Given linear equation in standard form, determine coordinates of yintercept

Writing Equation of a Line

Writing Equation Given Point & Slope
 Given point & integer slope, determine linear equation in pointslope form, including slopeintercept form conversion
 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 pointslope form, including slopeintercept form conversion
 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 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 in pointslope form, integer slope, including slopeintercept form conversion
 Given two points, determine linear equation in pointslope form, fractional slope, including slopeintercept form conversion
 Given two points, determine linear equation, undefined slope
 Given two points, determine linear equation, zero 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 standard 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 pointslope or standard form
 Given points or slope & point, determine linear equation in standard form
 Given points or slope & point, determine linear equation in various forms
 Given intercepts, determine linear equation in slopeintercept form
 Condensed: Given two points, determine linear equation in slopeintercept form, including horizontal & vertical lines
 Condensed: Given linear graph, determine equation in slopeintercept form & specific value, various scales, including realworld context

Writing Equation Given Graph

Given Graph of 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, 1 ≤ m ≤ 3
 Given linear graph through origin, determine equation in slopeintercept form, integer slope

Given Graph with Varying yIntercepts, Write Equation
 Given linear graph, determine equation in pointslope form
 Given linear graph, determine equation in slopeintercept form, m = 1
 Given linear graph, determine equation in slopeintercept form, integer slopes
 Given linear graph, determine equation in slopeintercept form, fractional slopes
 Given linear graph, determine slope, yintercept, & equation
 Given linear graph, determine equation in standard form
 Given linear graph, identify equation, slopeintercept form
 Given linear graph, identify equation, various forms

Given Graph with Varying yIntercepts & Scales, Write Equation
 Given linear graph, determine equation in slopeintercept form, m = 1, various scales
 Given linear graph, determine equation in slopeintercept form, integer slopes, various scales
 Given linear graph, determine equation in slopeintercept form, m = ±1, various scales
 Given linear graph, determine equation in slopeintercept form & specific value, various scales
 Given linear graph, identify 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



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

Determining Solution of Linear Equation
 Given horizontal or vertical linear equation, determine if point is 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 horizontal or vertical linear equation, identify point 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
 Identify linear & nonlinear relationships, various representations

Equations, Graphs, & Tables

Equation to Table, m=1
 Given linear equation, fill missing value in table, m = 1
 Given linear equation & table, determine another point, m = 1
 Given linear equation, fill missing value in table, m = 1, Δx ≥ 5
 Given linear equation, fill table, m = 1

Equation to Table
 Given horizontal or vertical linear equation, fill 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, Δx ≥ 5
 Given linear equation, fill missing value in table, integer slope, Δx ≥ 5
 Given linear equation, fill table, integer slope, b = 0
 Given linear equation, fill table, integer slope
 Given linear equation, determine table values
 Given linear equation & one xvalue, determine yvalue in table

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


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

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 table value, m = 1, table point off graph
 Given linear graph through origin, determine table values, one table point off graph
 Given linear graph through origin, determine table value, table point off graph
 Given linear graph, determine table value, table point off graph

Table to Equation
 Given table, identify linear equation in slopeintercept form, rational constants & coefficients
 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


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
 Given description of linear equation, identify graph, fractional slope, 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

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


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 table, identify dependent or independent variable
 Given equation, identify dependent or independent variable
 Given table or graph, identify dependent or independent variable
 Given description, identify dependent or independent variable

Writing Equations, Completing Tables, or Graphing
 Given constant of proportionality, determine table, graph, or equation
 Given table, determine constant of proportionality, graph, or equation
 Given graph, determine constant of proportionality, table, or equation
 Given equation, determine constant of proportionality, graph, or table
 Condensed: Determine equivalent representations of proportional relationships
 Determine or identify equivalent representations of proportional relationships
 Determine equations, tables, & graphs for proportional relationships, realworld context
 Given visual representation of proportional relationship, determine equation, table, & graph, realworld context

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 graph with most extreme rate of change
 Identify linear table with most extreme rate of change
 Compare rates of changes represented differently
 Given description, compare rates of change, realworld context


Proportional & NonProportional

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

Completing Tables or Graphing
 Given linear equation & table, identify graph
 Identify tables that represent realworld situations, y = mx or y = x + b
 Given linear equation, determine yvalues in table, realworld context
 Given linear equation, determine yvalues in table & identify graph, first quadrant
 Given slopeintercept equation, determine table & identify graph
 Given linear equation & table, determine graph

Writing Equations
 Given linear graph & table, determine equation
 Determine equations that represent realworld situations, y = mx or y = x + b
 Determine equations that represent realworld situations, including twostep equations
 Given additive relationship in table, determine equation
 Given multiplicative relationship in table, determine equation
 Identify equivalent representations of additive & multiplicative relationships
 Identify situations modeled by tables or equations, y = mx or y = x + b

Writing Equations, Completing Tables, or Graphing Mixed
 Condensed: Determine tables or equations of additive & multiplicative relationships
 Condensed: Determine equations & graphs of additive & multiplicative relationships
 Identify representation of proportional relationship, various representations, realworld context

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



Geometry

Perimeter & Area

Rectangle Perimeter
 Determine perimeter of rectangles
 Given sides of rectangle, determine perimeter
 Given sides of rectangle, determine perimeter
 Determine perimeter of rectangles, including decimal dimensions
 Determine perimeter of rectangles, realworld context
 Determine perimeter of rectangles, including decimal dimensions, realworld context
 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
 Given perimeter & relationship between sides, determine specific dimension
 Given perimeter & one dimension of rectangle, determine missing dimension

Rectangle Area
 Given sides of rectangle, determine area, model provided
 Given sides of rectangle, determine area
 Given area & one dimension of rectangle, determine missing dimension
 Determine area of missing dimension of rectangles, realworld context
 Given sides of rectangle & cost per square unit, determine area & total cost, realworld context

Parallelogram Perimeter & Area
 Determine area of parallelograms, model provided
 Determine area of parallelograms
 Determine area or perimeter of parallelograms
 Given area & one dimension of parallelogram, determine missing dimension

Trapezoid Area
 Determine area of trapezoids
 Given area & base lengths of trapezoid, determine height

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
 Given area & one dimension of triangle, determine missing dimension
 Given area & one dimension of triangle, determine missing dimension, mixed numbers

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

Compound Figure Area
 Determine area of shaded region between nested rectangles
 Determine area of shaded region between nested shapes
 Determine area of composite figures, rectangle with various figures attached, no circular parts
 Determine area of composite figures, no circular shapes
 Determine area of composite figures, rectangle with various figures attached
 Determine area of composite figures, at least three subdivisions
 Determine area of composite figures
 Determine area of composite figures, realworld context

Mixed Figures Perimeter & Area
 Identify formulas for area & perimeter of basic shapes
 Determine perimeter of polygons, including realworld context
 Determine areas of rectangles & parallelograms
 Determine areas of triangles & trapezoids
 Determine area of polygons in coordinate plane, realworld context
 Determine area of shaded region between nested shapes
 Given coordinates of vertices, determine side lengths & perimeter of polygons
 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


Surface Area & Volume

Net Surface Area
 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
 Given net, determine lateral surface area of pyramids
 Given net, determine lateral surface area of prisms & pyramids, realworld context
 Condensed: Given net, determine surface area & lateral surface area of prisms & pyramids, including realworld context

Rectangular Prism Surface Area & Volume
 Determine surface area of rectangular prisms
 Given base area & edge or all edges, determine volume of rectangular prism
 Determine volume of rectangular prisms, whole numbers or decimals
 Determine volume of rectangular prisms, whole numbers, decimals, or fractions
 Determine volumes of rectangular prisms, rational dimensions, realworld context
 Determine equations for volume of rectangular prisms, rational dimensions, realworld context
 Determine volume of rectangular prisms using various representations of cubic units, realworld context
 Determine volume of rectangular prisms & apply associative property to volume expressions
 Given volume, determine edges of rectangular prisms
 Determine volume or edge of rectangular prisms, whole numbers
 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

Cube Volume
 Determine volume of cubes, whole numbers or decimals
 Determine volume of rectangular prisms, whole numbers or decimals

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

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

Mixed Figures Surface Area & Volume
 Determine volumes of rectangular & triangular prisms, fractional dimensions
 Determine surface areas of 3D figures, no circles
 Determine surface area of 3D figures, realworld context
 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


Properties of Quadrilaterals & Triangles

Classifying Triangles
 Given three sides, classify triangles
 Classify triangles based on angles & sides

Triangle Angle Sum Theorem
 Given two angle measures in triangle, determine angle measure
 Apply triangle angle sum theorem to determine angles, multiple algebraic expressions

Triangle AngleSide Relationships
 Determine smallest & largest sides or angles in triangle
 Order angles in triangles
 Condensed: Determine angles & order side lengths & angles in triangles, including algebraic expressions

Triangle Inequality Theorem
 Apply triangle inequality theorem to determine side lengths
 Apply triangle inequality theorem to determine range of values for unknown side

Equilateral & Isosceles Triangles
 Solve problems involving perimeter of equilateral triangles
 Solve problems involving perimeter of isosceles triangles
 Condensed: Solve problems involving perimeter of equilateral & isosceles triangles
 Determine angle measure in isosceles triangle, at most one algebraic expression
 Given equilateral triangle & algebraic expression for angle, solve for variable
 Determine angle measure in isosceles triangle, up to two algebraic expressions
 Given equilateral triangle & algebraic expressions for sides, solve for variable or determine side length


Similar Figures

Similar Triangles
 Determine similar triangles using SAS similarity
 Determine similar triangles using SSS similarity
 Condensed: Determine similar triangles using SAS or SSS similarity
 Determine angles of similar triangles using AA similarity
 Determine sides of similar triangles using AA similarity
 Determine similarity of triangles using AA similarity
 Given similar triangles, determine perimeter
 Given similar triangles, determine area

Similar Polygons
 Identify corresponding parts of similar figures
 Given similar figures, identify proportion of side lengths, triangles & quadrilaterals
 Given similar figures, identify proportion of side lengths, image orientations differ
 Identify similar polygons
 Determine dimensions in similar figures, whole number dimensions
 Determine dimensions using similar figures & indirect measurements
 Determine dimensions in similar figures
 Determine parts using similar triangles, including realworld context
 Given similar rectangles, determine perimeter


Coordinate Plane

Basic Coordinates, First Quadrant
 Determine coordinates of first quadrant points
 Determine coordinates of first quadrant point, various scales
 Determine coordinates of first quadrant rational points
 Plot first quadrant points
 Plot first quadrant points, various scales
 Plot first quadrant rational points
 Plot or determine coordinates of first quadrant points
 Condensed: Plot or determine coordinates of first quadrant points
 Condensed: Plot or determine coordinates of first quadrant rational points, various scales

Application of Coordinates, First Quadrant
 Identify description of process to plot first quadrant points
 Identify locations or parts of coordinate plane using first quadrant points
 Identify first quadrant points or parts of coordinate plane
 Determine or identify first quadrant points, realworld context
 Determine or identify first quadrant points, including cardinal directions, realworld context
 Condensed: Plot or determine coordinates of first quadrant rational points

Integral Coordinates, All Quadrants
 Given integer point on graph, determine coordinates, point on axis
 Given integer point on graph, determine coordinates
 Given lattice point, determine coordinates
 Plot integer points on coordinate plane, point on axis
 Plot integer points
 Plot points on coordinate plane, student selects scales
 Condensed: Plot integer points or determine coordinates

Rational Coordinates, All Quadrants
 Given rational point, determine location on coordinate plane
 Plot rational points on coordinate plane
 Plot rational points on coordinate plane, graph scale at most onehalf
 Plot or identify rational points on coordinate plane
 Condensed: Plot or identify points on coordinate plane

Distance
 Determine distance between points on coordinate plane, horizontal or vertical
 Determine distance between points on coordinate plane, horizontal or vertical, realworld context

Transformations

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

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

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

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

Mixed Transformations
 Identify characteristics of transformed lines
 Identify characteristics of transformed parallel lines
 Identify characteristics of transformed line segments
 Identify characteristics of transformed angles
 Identify characteristics of transformed lines, segments, & angles
 Identify characteristics of transformations
 Identify rule or determine transformed point on coordinate plane
 Identify rule for transformed shape on coordinate plane
 Composition of transformations on coordinate plane
 Identify reflections & rotations on coordinate plane
 Condensed: Identify rule or determine transformed point on coordinate plane
 Condensed: Given figure on coordinate plane or coordinate vertices, determine transformed image or coordinates

Mixed Transformations, Congruence
 Given similar figures, identify description of transformations
 Identify congruence transformations
 Given congruent figures, identify description of transformations
 Condensed: Given similar or congruent figures, identify description of transformations



3D Figures
 Identify 3D figures & their bases
 Determine 2D orthographic representation of 3D blocks
 Identify equivalent representations of 3D figures & nets

Angles

Classifying Angles
 Identify angle names
 Identify angle pairs

Vertical Angles & Adjacent Angles
 Given vertical angles, determine angle measure
 Given parallel lines with transversal & angle, determine vertical angle
 Given figure, determine missing part of adjacent angle
 Given vertical angles, determine angle measure, one algebraic expression
 Given parallel lines with transversal & angle, determine vertical angle, algebraic expressions

Complementary Angles
 Given complementary angles, determine angle measure
 Given complementary angles, determine angle measure, one algebraic expression

Supplementary Angles
 Given supplementary angles, determine angle measure
 Given vertical angles, determine supplementary angle measure
 Given supplementary angles, determine angle measure, one algebraic expression

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 corresponding angle, algebraic expressions
 Given parallel lines with transversal & angle, determine sameside interior angle, algebraic expressions

Adjacent, Vertical, Supplementary, & Complementary Angles
 Determine angle measures, including figures or descriptions
 Determine complementary, supplementary, or equivalent angle measures
 Given vertical, complementary, or supplementary angles, determine angle measure, one algebraic expression
 Determine angle measures in figures, onestep algebraic expressions
 Given vertical angles, determine supplementary angle measure, algebraic expressions
 Determine complementary, supplementary, or equivalent angle measures, algebraic expressions
 Determine angle measures in figures, algebraic expressions
 Determine angle measures in figures, two algebraic expressions

Mixed Angles Formed by Transversals
 Given parallel lines with transversal & angle, identify specified angle pairs, uses “consecutive” terminology
 Given parallel lines with transversal, identify specified angle pairs, only numbered angles, uses “consecutive” terminology
 Given parallel lines with transversal & angle, determine supplement to corresponding angle
 Given parallel lines with transversal & angle, determine specified angle
 Determine angle measures involving parallel lines, onestep algebraic expressions
 Given parallel lines with transversal & angle, determine specified angle, algebraic expressions
 Determine angle measures involving parallel lines, algebraic expressions
 Determine angle measures involving parallel lines, algebraic expressions
 Given parallel lines with transversal & angle, determine supplement to corresponding angle, algebraic expressions


Scale
 Given scale, determine specified dimension in scaled figure, realworld context
 Given scale, determine area in scaled figure, realworld context
 Compare measurements drawn with different scale factors
 Compare measurements of scaled shapes, including 3D shapes


Ratios, Rates, & Proportions

Ratios

Simplifying Ratios
 Given ratio, identify table
 Condensed: Simplify ratios, identify equivalent ratios, & determine missing components of proportions
 Condensed: Determine ratios, relationship between ratio terms, & specified quantities, realworld context

Representing Ratios
 Determine part to whole ratio, strip diagrams, realworld context
 Determine part to part ratio, strip diagrams, realworld context
 Determine part to whole ratio, decimal grids
 Determine part to part ratio, decimal grids
 Determine part to whole ratio, double number lines, realworld context
 Determine part to part ratio, including double number lines, including realworld context
 Determine part to whole ratio, various models
 Determine part to part ratio, various models

Application of Ratios
 Given table, determine ratios, integers
 Compare rates or determine specified values in proportional relationships, realworld context
 Compare rates
 Determine specified values in proportional relationships, realworld context
 Given double number line model, determine percent or specified quantity, realworld context
 Condensed: Given extended ratio, determine ratio or specified quantity, realworld context


Rates

Basic Unit Rates
 Identify unit rates
 Given unit rate, determine specified value in proportional relationship, realworld context
 Determine unit rates, ratio tables, realworld context
 Determine unit rates, strip diagrams, realworld context
 Given double number line, determine unit rate, realworld context

Application of Rates
 Determine unit rates, whole numbers, realworld context
 Determine unit rates, fractions, realworld context
 Determine unit rates, mixed numbers, realworld context
 Given rate, convert time unit to determine quantity over time interval, realworld context
 Given rate of travel, determine distance or time
 Determine & compare unit rates, 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

Application of Proportions
 Solve proportions to convert measurement units
 Given proportional relationship, determine specified quantity, realworld context
 Solve proportions, exact answers, realworld context
 Solve proportions, rounded answers, realworld context
 Solve proportions involving time, realworld context



Percents

Converting Percents
 Convert percents to decimals
 Convert decimal percents to decimals
 Convert decimal percents less than one to decimals
 Convert percents to fractions
 Convert percents to fractions, realworld context
 Convert percents to mixed numbers
 Condensed: Convert percents to decimals & fractions
 Convert repeating decimals to fractions

Basic Finding Total, Part, or Percent of Number
 Given percent & whole, determine part, exact answers
 Given part & percent, determine whole, exact answers
 Given percent & whole, determine part, whole number answers
 Given part & percent, determine whole
 Given part & whole, determine percent

Application of Finding Total, Part, or Percent of Number
 Given percent & whole, determine part, realworld context
 Given part & percent, determine whole, realworld context
 Given part & whole, determine percent, realworld context
 Determine percent of change, whole numbers, including realworld context
 Determine percent of change, including realworld context
 Given percent, identify table that shows percent
 Determine specified values in tables involving percents
 Identify part of whole, realworld context

Finding Tip, Tax, Markup, Markdown, & Commission
 Determine tips
 Determine tax
 Determine markups
 Determine commissions
 Condensed: Determine tip, tax, discount, or markup
 Determine discount, tax, or total cost
 Determine increases involving tips, tax, & markups
 Determine decreases involving sales, discounts, & markdowns

Finding Percent of Change
 Determine percent of change, whole numbers, including realworld context
 Determine percent of change, including realworld context

Calculating Simple & Compound Interest
 Determine simple interest
 Determine simple interest & total amount
 Given simple interest earned, determine principal, rate, or time
 Determine income tax for earned wages
 Determine savings in loan repayment based on various lengths of repayment
 Determine compound interest
 Determine annually compounded interest
 Condensed: Determine compound interest on savings & loans
 Determine & compare simple & compound interest


Probability & Statistics

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

Interpreting Measures of Center & Spread
 Given various representations of data, identify outlier
 Identify measures of center based on data distribution
 Identify & interpret measures of center
 Identify & interpret measures of variability


Graphical Displays of Data

Dot Plots
 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

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

Pie Charts
 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

Frequency Tables
 Interpret twoway frequency tables, conditional distribution
 Interpret twoway frequency tables, marginal distribution
 Interpret twoway frequency tables, joint distribution
 Condensed: Interpret twoway frequency tables
 Determine twoway frequency tables
 Given twoway frequency tables, identify associations
 Determine specified probabilities in twoway frequency tables

Histograms
 Given various representations of data, determine histogram
 Solve problems involving interpretation of histograms

Mixed Graphical Displays
 Given data, determine statistical display
 Determine or interpret shapes & features of graphs
 Determine or interpret measures of center & spread from graphs
 Condensed: Solve problems involving interpretation of box plots & stem&leaf plots


Statistical Data
 Determine sample size, various representations
 Identify biased samples & questions
 Identify samples & populations
 Compare data from two samples, various representations
 Identify simulations used to acquire simple random samples
 Identify simulations to model probability events

Probability

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

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

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

Conditional Probability
 Determine conditional probabilities from twoway frequency tables
 Determine conditional probabilities, including twoway frequency tables



Conversions

Metric to Customary Conversions
 Convert metric to customary units of length
 Convert metric to customary units of weight & mass
 Convert metric to customary units of volume & capacity
 Convert metric to customary units of length, calculator expected
 Convert metric to customary units of weight & mass, calculator expected
 Convert metric to customary units of volume & capacity, calculator expected
 Convert metric to customary units of length, including multistep
 Convert metric to customary units of weight & mass, including multistep
 Convert metric to customary units of volume & capacity, including multistep

Customary to Metric Conversions
 Convert customary to metric units of length
 Convert customary to metric units of weight & mass
 Convert customary to metric units of length, calculator expected
 Convert customary to metric units of weight & mass, calculator expected
 Convert customary to metric units of volume & capacity, calculator expected
 Convert customary to metric units of length, including multistep
 Convert customary to metric units of weight & mass, including multistep

Customary & Metric Conversions
 Convert between customary & metric using dimensional analysis
 Convert between customary & metric using unit rates
 Convert between customary & metric using scale factors
 Convert between customary & metric, proportion bias
 Convert between customary & metric using conversion graphs
 Convert between customary & metric, realworld context
 Condensed: Convert between customary & metric
 Condensed: Convert between customary & metric using multiple representations of conversion factor
 Condensed: Convert between customary & metric, including multistep


Number Theory

Prime & Composite Numbers
 Identify prime & composite numbers
 Identify prime & composite numbers, realworld context

Factors & Multiples
 Identify multiples or nonmultiples of whole numbers
 Identify factors or nonfactors of whole numbers
 Identify factors or multiples of whole numbers
 Condensed: Identify factors, nonfactors, multiples, & nonmultiples of whole numbers

Prime Factorization
 Determine prime factorization of numbers up to 50
 Determine prime factorization of numbers up to 100
 Identify or complete prime factorization of numbers up to 144
 Identify equivalent expressions involving prime factorization

Greatest Common Factors
 Determine GCF of two numbers up to 100
 Determine GCF of two numbers up to 100 or multiples of 10
 Determine GCFs, realworld context
 Apply GCFs to determine number of items in groups, realworld context

Least Common Multiples
 Determine LCM of two numbers up to 100
 Determine LCM of two numbers up to 100 or multiples of 10
 Determine LCMs, realworld context
 Apply LCMs to determine number of items in groups, realworld context

Greatest Common Factors & Least Common Multiples
 Condensed: Determine GCF or LCM of two numbers up to 100 or multiples of 10
 Condensed: Determine GCFs & LCMs, realworld context
 Condensed: Apply GCFs & LCMs to determine number of items in groups, realworld context


Financial Literacy
 Classify assets & liabilities
 Determine net worth, assets, & liabilities
 Determine minimum income necessary to balance budget
 Determine minimum hourly wage necessary to balance budget
 Determine budget allocations
 Determine savings in loan repayment based on various lengths of repayment