6th Grade Skills

VIEW ALL SKILLS

Whole Numbers
- Addition of Whole Numbers
  - Basic Addition of Whole Numbers
    - Add three- & four-digit whole numbers
    - Condensed: Add four-digit & three- or four-digit whole numbers
    - Add four-digit whole numbers
  - Application of Addition of Whole Numbers
    - Add three- & four-digit whole numbers, real-world context
    - Add four-digit whole numbers, real-world context
    - Condensed: Add whole numbers, up to five digits, including real-world context
    - Condensed: Add whole numbers, up to five digits, real-world context
    - Add five-digit whole numbers, real-world context
    - Add five- or six-digit whole numbers, real-world context
- Subtraction of Whole Numbers
  - Basic Subtraction of Whole Numbers
    - Subtract whole numbers, four-digit & three-digit
    - Condensed: Subtract whole numbers, four-digit & three- or four-digit
    - Subtract whole numbers, five-digit & four- or five-digit
    - Condensed: Subtract whole numbers, four- to six-digit & two- to five-digit
    - Subtract whole numbers, six- or seven-digit & up to six digits
    - Subtract whole numbers, seven-digit & six- or seven-digit
  - Application of Subtraction of Whole Numbers
    - Subtract whole numbers, four-digit & three- or four-digit, real-world context
    - Subtract whole numbers, five-digit & four- or five-digit, real-world context
    - Subtract whole numbers, six-digit & five- or six-digit, real-world context
    - Subtract whole numbers, seven-digit & six- or seven-digit, real-world context
    - Condensed: Subtract whole numbers, four- to seven-digit & three- to six-digit, including real-world context
    - Condensed: Subtract whole numbers, four- to seven-digit & three- to six-digit, including real-world context
    - Condensed: Subtract whole numbers, four- to seven-digit & three- to six-digit, real-world context
- Multiplication of Whole Numbers
  - Application & Modeling of Multiplication of Whole Numbers
    - Condensed: Multiply whole numbers, one-digit & up to four-digit, real-world context
    - Condensed: Multiply whole numbers, one- or two-digit & up to four-digit, real-world context
    - Condensed: Multiply whole numbers using area models or decomposition, up to four-digit & one-digit
    - Condensed: Multiply whole numbers using area models or decomposition, two-digit & two-digit
    - Multiply whole numbers, three-digit & two-digit, including addition or subtraction step, real-world context
  - Basic Multiplication of Whole Numbers
    - Condensed: Multiply whole numbers, three- or four-digit & one-digit
    - Multiply whole numbers, two-digit & two-digit
    - Multiply whole numbers by decomposing factors, two-digit & two-digit
    - Multiply whole numbers, two-digit & two- or three-digit
    - Multiply whole numbers, three-digit & two-digit
    - Condensed: Multiply whole numbers, three- or four-digit & two-digit
    - Multiply whole numbers, four-digit & two-digit
    - Multiply whole numbers, both up to three digits
    - Condensed: Multiply whole numbers, up to four-digit & up to three-digit, no more than six total digits
  - Multiplicative Comparisons of Whole Numbers
    - Solve problems involving multiplicative comparisons
    - Solve problems involving multiplicative & additive comparisons of whole numbers
    - Solve problems involving multiplicative & additive comparisons
    - Condensed: Solve problems involving division of positive integers & multiplicative & additive comparisons, real-world context
- Division of Whole Numbers
  - Basic Division of Whole Numbers
    - Apply divisibility rules to two-digit dividends, divisor 2, 3, 4, 5, 6, 9, 10
    - Condensed: Determine quotient & remainder, two-digit dividend, up to two-digit divisor
    - Condensed: Determine quotient & remainder, three-digit dividend, up to two-digit divisor
    - Condensed: Determine quotient & remainder, four-digit dividend, up to two-digit divisor
    - Condensed: Determine quotient & remainder as fraction, two-digit dividend, up two two-digit divisor
    - Condensed: Determine quotient & remainder as fraction, three-digit dividend, up two two-digit divisor
    - Condensed: Determine quotient & remainder as fraction, four-digit dividend, up two two-digit divisor
    - Divide whole numbers with decimal quotient, up to three-digit dividend, up to three-digit divisor
  - Application of Division of Whole Numbers
    - Determine division equations, real-world context
    - Determine equivalence between area models & division equations
    - Determine equivalence between arrays & division equations
    - Condensed: Determine equivalence between models & division equations
    - Divide positive integers, up to four-digit dividend, one-digit divisor, real-world context
    - Divide positive integers, up to four-digit dividend, up to two-digit divisor, real-world context
    - Determine quotient, up to four-digit dividend, up to two-digit divisor, real-world context
    - Determine quotient or remainder, up to four-digit dividend, one-digit divisor, real-world context
    - Divide positive integers for decimal result, real-world context
- Mixed Operations of Whole Numbers
  - Diagrams of Mixed Operations of Whole Numbers
    - Solve multi-step problems involving models & whole number operations, initially add, real-world context
    - Solve multi-step problems involving models & whole number operations, initially subtract, real-world context
    - Solve multi-step problems involving models & whole number operations, initially multiply, real-world context
    - Solve multi-step problems involving models & whole number operations, initially divide, real-world context
    - Condensed: Solve multi-step problems involving models & whole number operations, real-world context
  - Equations of Mixed Operations of Whole Numbers
    - Solve two-step equation with isolated variable, real-world context
    - Identify multi-step equations, real-world context
    - Solve multi-step problems involving equations & whole number operations, initially add, real-world context
    - Solve multi-step problems involving equations & whole number operations, initially subtract, real-world context
    - Solve multi-step problems involving equations & whole number operations, initially multiply, real-world context
    - Solve multi-step problems involving equations & whole number operations, initially divide, real-world context
    - Condensed: Solve multi-step problems involving equations & whole number operations, real-world context
    - Determine & solve two-step equations with isolated variable, real-world context
  - Diagrams & Equations of Mixed Operations of Whole Numbers
    - Condensed: Solve multi-step problems involving equations, models, & whole number operations, real-world context
  - Application of Mixed Operations of Whole Numbers
    - Determine & evaluate addition or subtraction expressions, real-world context
    - Solve multi-step problems involving whole number operations, initially add, real-world context
    - Solve multi-step problems involving whole number operations, initially subtract, real-world context
    - Solve multi-step problems involving whole number operations, initially multiply, real-world context
    - Solve multi-step problems involving whole number operations, initially divide, real-world context
    - Solve multi-step problems involving division of positive integers, real-world context
    - Solve multi-step problems involving operations with whole numbers
    - Condensed: Solve multi-step problems involving whole number operations, real-world context
- Rounding & Estimating Whole Numbers
  - Basic Rounding & Estimating Whole Numbers
    - Round whole numbers to nearest ten
    - Round whole numbers to nearest hundred
    - Round whole numbers to nearest thousand
    - Condensed: Round whole numbers to nearest ten, hundred, & thousand
    - Round whole numbers using front-end rounding
    - Round whole numbers to specified place value, up to hundred-thousand
  - Application of Rounding Whole Numbers
    - Round whole numbers to nearest ten, real-world context
    - Round whole numbers to nearest hundred, real-world context
    - Round whole numbers to nearest thousand, real-world context
    - Condensed: Round whole numbers to nearest ten, hundred, & thousand, including real-world context
    - Condensed: Round whole numbers to nearest ten, hundred, & thousand, real-world context
  - Application of Estimating Whole Numbers
    - Estimate sums of whole numbers, up to six digits, including real-world context
    - Estimate differences of whole numbers, up to six digits, including real-world context
    - Estimate sums & differences of whole numbers by rounding to specified place values
    - Estimate products of whole numbers, two-digit factor times one-digit factor
    - Estimate quotients of whole numbers, up to six-digit dividend, up to three-digit divisor
    - Condensed: Estimate sums, differences, & products of whole numbers
    - Estimate sum of rational numbers, round both to nearest whole, real-world context
    - Determine division expression to estimate quotient using compatible numbers
    - Identify division expression to estimate quotient using compatible numbers, real-world context
- Comparing & Ordering Whole Numbers
  - Compare two positive integers
  - Compare three-digit whole numbers
  - Compare four-digit whole numbers
  - Compare five-digit whole numbers
  - Compare six-digit whole numbers
  - Order whole numbers up to 1,000,000,000, including real-world context
  - Condensed: Order whole numbers, up to 1,000,000,000, including real-world context
  - Order whole numbers up to 1,000,000,000, real-world context
Fractions
- Representing Fractions
  - Identify fractions or mixed numbers on decimal grid
  - Identify fractions on strip diagrams
  - Identify common fractions or mixed numbers on number line
- Equivalent Fractions
  - Determine how many fraction parts are in whole
  - Determine equivalent fractions, strip diagrams
  - Determine equivalent fractions, number lines
  - Determine equivalent fractions, area models
  - Determine equivalent fraction equations, area models
  - Determine equivalent fraction components
  - Identify or determine equivalent fraction components or fractions
- Simplifying Fractions
  - Reduce fractions, denominators less than 20
  - Reduce fractions, answer denominators less than 10
  - Reduce fractions, answer denominators less than 30
  - Reduce fraction part of mixed numbers
  - Simplify & reduce mixed numbers, improper fraction part
- Converting Fractions
  - Converting Fractions to Decimals
    - Given model, determine fraction & decimal equivalents, unreduced
    - Identify decimal equivalent of fractions, real-world context
    - 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 decimals, real-world context
    - Convert fractions to decimals, up to two decimal places, real-world context
    - Convert fractions to rounded decimals
    - Convert fractions to decimals, including improper fractions, including repeating decimals
    - Convert mixed numbers to decimals, including repeating decimals
  - Converting Improper Fractions & Mixed Numbers
    - Convert mixed numbers to improper fractions, denominators less than 10
    - Convert mixed numbers to improper fractions, includes denominators more than 10
    - Convert whole numbers to improper fractions
    - Convert improper fractions to mixed numbers, whole part up to 3
    - Convert improper fractions to mixed numbers, whole part up to 12
    - Condensed: Convert between improper fractions & mixed numbers
  - Converting Fractions to Percents
    - 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
    - Convert fractions to mixed number percents
    - Convert fractions to mixed number percents over 100
- Comparing & Ordering Fractions
  - Modeling Comparing Fractions
    - Determine equivalent fractions, strip diagrams
    - Compare two fractions, different denominators, number lines
    - Compare two fractions, different denominators, strip diagrams
    - Compare two fractions, different denominators, area models
    - Compare fractions, different denominators, visual model
    - Compare fractions, denominators less than 10
  - Basic Comparing & Ordering Fractions
    - Compare fractions, denominators less than 10
    - Compare fractions, denominators less than 30
    - Compare fractions between one-half & one
    - Compare fractions, same numerators, denominators differ by one, denominators less than 10,000
    - Compare fractions, different denominators
    - Order positive fractions
  - Determine equivalent fractions, strip diagrams
  - Compare two fractions, different denominators, area models
  - Compare two fractions, different denominators, number lines
  - Compare two fractions, different denominators, strip diagrams
  - Compare fractions, denominators less than 10
  - Compare fractions, denominators less than 30
  - Compare fractions between one-half & one
  - Compare fractions, same numerators, denominators differ by one, denominators less than 10,000
  - Compare fractions, different denominators
  - Compare fractions, different denominators, visual model
  - Order positive fractions
- Addition of Fractions
  - Condensed: Add fractions, common denominators, including real-world context
  - Add fractions, common denominators, real-world context
  - Add fractions, denominators of 10 & 100
  - 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
- Subtraction of Fractions
  - 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
- Mixed Addition & Subtraction of Fractions
  - Modeling & Application of Mixed Addition & Subtraction of Fractions
    - Identify expressions that represent addition or subtraction of unreduced fractions modeled by area models
    - Identify expressions that represent addition or subtraction of unreduced fractions modeled on number lines
    - Condensed: Given model, determine or interpret addition & subtraction of fractions
    - Add & subtract fractions, fraction strips
    - Add & subtract fractions, area models
    - Add & subtract fractions, number lines
    - Add & subtract fractions, various models
  - Basic Mixed Addition & Subtraction of Fractions
    - Condensed: Add or subtract fractions, common denominators, unreduced
    - Condensed: Add or subtract fractions, common denominators, real-world context
    - Condensed: Add or subtract fractions, different denominators
    - Add or subtract fractions, including estimation, real-world context
    - Add & subtract fractions, real-world context
    - Given subtraction expression of two fractions, identify expression using fourths that best estimates difference
- Multiplication of Fractions
  - Modeling Multiplication of Fractions
    - Identify model representation of multiplication of fraction & whole number
    - Condensed: Identify models or multiply whole numbers & fractions using area models
    - Multiply whole numbers & fractions, area models
    - Multiply whole numbers & fractions, including visual models
    - Multiply mixed numbers & proper fractions, visual models, real-world context
  - Basic Multiplication of Fractions
    - Multiply whole numbers & unit fractions, whole number first
    - Multiply whole numbers & unit fractions
    - Multiply whole numbers & fractions, positive
    - Multiply fractions, positive, mixed number directions
    - Multiply proper & improper fractions, positive
    - Multiply fractions, positive
    - Multiply mixed numbers, positive
    - Condensed: Multiply fraction & mixed numbers, including mixed signs, mixed number directions
  - Application of Multiplication of Fractions
    - Multiply whole numbers & fractions, real-world context
    - Multiply fractions, positive, real-world context
    - Multiply mixed numbers & proper fractions, real-world context
    - Determine part of whole using fraction multiplication, including visual models, including real-world context
    - Estimate products of rational numbers, no decimals, round both factors to nearest whole number, real-world context
  - Scaling Fractions
    - Determine whether quantities are increased or decreased when multiplied by fractions
    - Determine products & identify whether quantities are increased or decreased when multiplied by fraction
    - Compare products of fractions, mixed numbers, & whole numbers, including real-world context
    - Interpret fractional parts & fraction multiplication, real-world context
- Division of Fractions
  - Reciprocals
    - Determine reciprocals of whole numbers or fractions
    - Determine equivalent division & multiplication expressions using reciprocals
  - Modeling Division of Fractions
    - Divide whole numbers & unit fractions, area models
    - Divide whole numbers by unit fractions, number lines
    - Divide whole numbers & unit fractions, fraction strips
    - Divide whole numbers by unit fractions, models
    - Condensed: Divide whole numbers & fractions, various models
    - Identify division models & divide unit fractions by unit fractions
    - Determine visual representation & fraction quotient of division problems
  - Basic Division of Fractions
    - Determine representation of fraction as division expression
    - Divide whole numbers by unit fractions
    - Divide whole numbers & unit fractions
    - Divide fractions, positive, mixed number directions
    - Divide mixed numbers, positive
  - Application of Division of Fractions
    - Determine fraction & mixed number equivalence of division problems, real-world context
    - Determine or estimate quotients of whole numbers, fraction quotients
    - Estimate & determine quotients as fraction representation of division problem
    - Divide whole numbers & unit fractions, including unit fraction multiplication, real-world context
    - Divide fractions & mixed numbers, positive, real-world context
    - Divide fractions, mixed numbers, & whole numbers, multi-step, real-world context
Decimals
- Representing Decimals
  - Given tenths model, identify decimal
  - Given hundredths model, identify decimal
  - Given hundredths model, identify decimal as monetary amount
  - Determine value of decimal model, including money
- Comparing & Ordering Decimals
  - Basic Comparing & Ordering Decimals
    - Compare whole numbers up to 1,000,000,000
    - Given decimals, identify locations on number line
    - Compare decimals on number line
    - Compare decimals up to two decimal places, including real-world context
    - Compare decimals up to two decimal places & justify relationship, including real-world context
    - Compare decimals written in word form, up to three decimal places
    - Compare numbers, up to four-digit whole numbers or three-digit decimals
    - Identify & compare rational numbers on number lines, positive
    - Compare decimals written in word form, up to four decimal places
    - Order positive decimals
    - Order decimals up to 1,000,000,000
  - Application of Comparing & Ordering Decimals
    - Compare decimals up to two decimal places, including real-world context
    - Compare decimals up to three decimal places
    - Compare decimals up to three decimal places, real-world context
    - Order decimals up to two decimal places, including real-world context
    - Order decimals from table of place values, real-world context
    - Order decimals up to three decimal places, including real-world context
    - Condensed: Compare or order numbers up to 1,000,000,000
    - Compare & order decimals up to 1,000,000,000, real-world context
    - Compare or order positive & negative decimals, up to three decimal places
- Converting Decimals
  - Convert decimals to percents
  - Convert decimals to percents over 100
  - Given model, determine fraction & decimal equivalents, unreduced
  - Convert decimals to fractions
  - Convert decimals to fractions, real-world context
  - 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
    - Add decimals, positive, up to two decimal places
    - Add positive decimals, up to three decimal places
    - Add decimals, positive, up to four decimal places
  - Application of Addition of Decimals
    - Condensed: Add decimals, positive, up to two decimal places, including real-world context
    - Add decimals, positive, up to two decimal places, real-world context
- Subtraction of Decimals
  - Basic Subtraction of Decimals
    - Subtract decimals, up to two decimal places
    - Subtract decimals, two decimal places
    - Subtract decimals, up to three decimal places, positive difference
  - Application of Subtraction of Decimals
    - Condensed: Subtract decimals, up to two decimal places, including real-world context
    - Subtract decimals, up to two decimal places, real-world context
    - Make change
- Addition & Subtraction of Decimals
  - Basic Addition & Subtraction of Decimals
    - Condensed: Add & subtract decimals, up to two decimal places
  - Application of Addition & Subtraction of Decimals
    - Condensed: Add & subtract decimals, up to two decimal places, including real-world context
    - Add & subtract decimals, up to two decimal places, real-world context
    - Condensed: Add & subtract decimals, up to two decimal places, real-world context
    - Add & subtract decimals, up to three decimal places, real-world context
    - Add or subtract whole numbers or decimals, real-world context
    - Condensed: Add & subtract rational numbers, real-world context
- Multiplication of Decimals
  - Application & Modeling of Multiplication of Decimals
    - Determine equivalence between area models & multiplication equations
    - Determine equivalence between base-10 models & multiplication equations
    - Determine equivalence between number line models & multiplication equations
    - Condensed: Determine equivalence between models & multiplication equations
    - Multiply decimals, products limited to two decimal places, real-world context
  - Basic Multiplication of Decimals
    - Multiply decimals times one-digit whole numbers
    - Multiply decimals, products limited to two decimal places
    - 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 positive decimals, each factor up to three decimal places
    - Condensed: Multiply decimals
    - Multiply three positive decimals, products limited to three decimal places
- Division of Decimals
  - Application & Modeling of Division of Decimals
    - Identify expressions & equations representing multiplication & division of rational numbers
    - Identify base-10 model that represents quotient of decimal division
    - Determine equivalence of base-10 model & components of decimal division
    - Determine equivalence of base-10 model & components of decimal division, quotient limited to tenths
    - Given area model representing decimal division, interpret model & determine quotient, including real-world context
    - Given number line model representing decimal division, interpret model & determine quotient, including real-world context
    - Given model representing decimal division, interpret model & determine quotient, including money
    - Condensed: Given model representing decimal division, interpret model & determine quotient, including real-world context
    - Divide decimals, up to three decimal places, real-world context
    - Divide four-digit dividends by two-digit whole number divisors, including real-world context
  - Basic Division of Decimals
    - 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 in dividend & divisor
    - Divide decimals, up to three decimal places
    - Divide four-digit dividends by two-digit whole number divisors
    - Condensed: Divide decimals or whole numbers
- Mixed Operations with Decimals
  - Condensed: Solve problems with decimal & whole numbers, real-world context
  - Condensed: Add, subtract, multiply, & divide decimals, up to two decimal places
  - Solve multi-step problems with rational numbers, including percents, real-world context
- Rounding & Estimating Decimals
  - Basic Rounding & Estimating Decimals
    - Round decimal numbers to nearest whole, tenth, & hundredth
    - Round decimal numbers to nearest whole, tenth, hundredth, & thousandth
  - Application of Rounding & Estimating Decimals
    - Round numbers to nearest whole, ten, hundred, & thousand, real-world context
    - Round decimal numbers to nearest tenth & hundredth, including real-world context
    - Round decimal numbers to nearest tenth & hundredth, real-world context
    - Round decimal numbers to nearest tenth, hundredth, & thousandth, real-world context
    - Round decimal numbers to nearest whole, tenth, hundredth, & thousandth, including real-world context
    - Round decimal & whole numbers to specified place value
  - Rounding & Operations with Decimals
    - Round decimal numbers to nearest whole, tenth, & hundredth, real-world context
    - Condensed: Round decimal numbers to nearest whole, tenth, & hundredth, including real-world context
    - Estimate sum by rounding addends to nearest whole number, up to two decimal places
    - Estimate differences of decimals by rounding to nearest whole number
    - Condensed: Estimate sum or difference by rounding addends, minuend, & subtrahend, up to two decimal places
    - Estimate quotients of decimals & whole numbers using compatible numbers
    - Estimate solutions involving all operations, real-world context
    - Determine sums & differences of decimals then round solution, real-world context
Integers
- Classifying Numbers
  - Classify rational numbers by definitions
  - Classify rational numbers using graphic organizers
  - Classify rational numbers, including graphic organizers
- Absolute Value & Opposites
  - Determine opposites of numbers
  - Identify opposite integers on number line
  - Add opposite integers, up to two digits
  - Identify situations represented by positive & negative numbers, real-world context
  - Determine representations of quantities using positive & negative numbers, real-world context
  - Determine change, opposite integers, real-world context
  - Determine absolute value of integers
  - Determine absolute value of integers, including real-world context
  - Determine absolute value of rational numbers
  - Determine absolute value of numeric expression
- 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
    - Determine number represented by counters
    - 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 integers, positive sum
    - Add integers, negative sum
    - Add integers, start one digit & advance to two digits
    - Add negative integers
    - Add integers, up to two digits, positive sum
    - Add integers, up to two digits, negative sum
    - Add negative integers, up to two digits
    - Condensed: Add positive & negative integers
  - Application of Addition of Integers
    - Add integers with same sign, up to three digits, real-world context
    - Add integers, up to three digits, real-world context
    - Given model or table, add integers, real-world context
    - Condensed: Add integers, real-world 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 Difference
    - 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 Difference
    - Subtract integers, negative difference
    - Subtract positive integers, negative difference
    - Subtract negative 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
    - Rewrite subtraction as addition & evaluate expression
    - Subtract positive integers, one-digit & one-digit
    - Subtract integers, various signs
    - Condensed: Subtract integers, various signs, up to two digits
  - Application of Subtraction of Integers
    - Determine differences between integers, same signs, real-world context
    - Determine differences between integers, mixed signs, real-world context
    - Determine differences between integers, various signs, real-world 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 negative integers
    - Multiply integers, opposite signs
    - Multiply integers, start one digit & advance to two digits
    - Multiply negative integers, two-digit times two-digit
    - Multiply integers, opposite signs, two-digit times two-digit
    - Multiply negative integers, two-digit times two- or three-digit
    - Multiply integers, opposite signs, two-digit times two- or three-digit
    - Multiply three integers
  - Application of Multiplication of Integers
    - Multiply positive integers, real-world context
    - Multiply integers, mixed signs, real-world context
- Division of Integers
  - Modeling Division of Integers
    - Divide integers using counters
    - Divide integers, both positive, up to two-digit dividend, number line model
    - Divide integers, opposite signs, up to two-digit dividend, number line model
  - Basic Division of Integers
    - Divide integers, one or both negative, start one-digit, advance up to three-digits
    - Divide integers, one or both negative, start one-digit, advance up to three-digits, includes undefined
    - Divide integers, both negative, up to three-digit dividend, up to two-digit divisor
    - Divide integers, opposite signs, up to three-digit dividend, up to two-digit divisor
    - Divide integers, both negative, up to five-digit dividend, up to two-digit divisor
    - Divide integers, opposite signs, up to five-digit dividend, up to two-digit divisor
  - Application of Division of Integers
    - Divide integers, same signs, real-world context
    - Divide integers, opposite signs, real-world context
- Mixed Operations of Integers
  - Determine number of zero pairs or evaluate expressions using counters
  - Estimate sums & differences of integers using front-end rounding
  - Condensed: Add or subtract integers using counters
  - Condensed: Multiply & divide integers
  - Condensed: Add, subtract, multiply, & divide integers
Percents
- Representing Percents
  - Identify percents, decimal grids
  - Identify percents, strip diagrams, real-world context
  - Identify percents, area models
  - Determine percents & specified quantities, double number lines, real-world context
  - Condensed: Determine ratios & percents, decimal grids
  - Condensed: Determine ratios & percents, strip diagrams, real-world context
  - Condensed: Determine ratios & percents, various models
  - Condensed: Determine ratios & percents, double number lines, including real-world context
- 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, real-world context
  - Convert percents to mixed numbers
  - Condensed: Convert percents to decimals & fractions
- Finding Tip, Tax, Markup, Markdown, & Commission
  - Given percent, identify table that shows percent
  - Determine tips
  - Determine tax
  - Determine markups
  - Determine increases involving tips, tax, & markups
  - Determine commissions
  - Determine income tax for earned wages
  - Determine discount, tax, or total cost
  - Determine decreases involving sales, discounts, & markdowns
  - Condensed: Determine tip, tax, discount, or markup
  - Determine & compare savings from sales, rebates, & coupons
- Finding Total, Part, or Percent of a Number
  - Given model, determine & identify fractions, decimals, & percents
  - Given percent & whole, determine part, whole number answers
  - Given percent & whole, determine part, exact answers
  - Given percent & whole, determine rounded part
  - Given percent & whole, determine part, real-world context
  - Given part & percent, determine whole, exact answers
  - Given part & percent, determine whole
  - Given part & percent, determine whole, real-world context
  - Given part & whole, determine percent
  - Given part & whole, determine percent, real-world context
  - Determine specified values in tables involving percents
- Finding Percent of Change
  - Determine percent of change, whole numbers, including real-world context
  - Determine percent of change, including real-world context
- Calculating Simple Interest
  - Determine simple interest
  - Determine simple interest & total amount
  - Given simple interest earned, determine principal, rate, or time
Fractions, Decimals, & Percents Combined
- Comparing & Ordering Fractions & Decimals Combined
  - Condensed: Order positive decimals & fractions
  - Order positive rational numbers, no radicals, no exponents
  - Given set or list, order rational numbers, real-world context
  - Given table, order rational numbers, real-world context
- Fraction, Decimal, & Percent Conversions
  - Identify part of whole, real-world context
  - Given model, determine & identify fractions, decimals, & percents
  - Condensed: Convert proper & improper fractions to rounded percents
  - Condensed: Convert fractions to decimals & percents
- Basic Fractions & Decimals Combined
  - Multiply decimals times fractions, both positive
  - Multiply fractions times decimals, both positive
- Application of Fractions & Decimals Combined
  - Multiply decimals & fractions, real-world context
  - Add or subtract whole numbers, fractions, or decimals, real-world context
  - Condensed: Add & subtract rational numbers, real-world context
  - Solve multi-step problems with rational numbers, including percents, real-world context
Ratios, Rates, & Proportions
- Ratios
  - Basic Representing Ratios
    - Determine part to part ratio, decimal grids
    - Determine part to whole ratio, decimal grids
    - Condensed: Determine ratios & percents, decimal grids
    - Determine part to part ratio, various models
    - Determine part to whole ratio, various models
    - Condensed: Determine ratios & percents, various models
  - Representing Ratios Real-World
    - Given part & percent, identify model & determine whole, real-world context
    - Given double number line model, determine percent or specified quantity, real-world context
    - Determine part to part ratio, strip diagrams, real-world context
    - Determine part to whole ratio, strip diagrams, real-world context
    - Condensed: Determine ratios & percents, strip diagrams, real-world context
    - Determine part to part ratio, including double number lines, including real-world context
    - Determine part to whole ratio, double number lines, real-world context
    - Condensed: Determine ratios & percents, double number lines, including real-world context
  - Basic Ratios
    - Rewrite ratios
    - Given ratio, determine reduced form
    - Identify equivalent ratios or determine missing component of proportion
    - Given table, determine ratios, integers
    - Determine ratios, various forms, real-world context
    - Determine ratios, real-world context
  - Application of Ratios
    - Given ratio, determine relationship between ratio terms, real-world context
    - Interpret & apply ratios
    - Given proportional relationship as ratio, determine specified quantity, real-world context
    - Determine specified quantity in proportional relationship, including mixed numbers, real-world context
    - Condensed: Determine ratios, relationship between ratio terms, & specified quantities, real-world context
    - Given ratios a : b & b : c, determine a : c, real-world context
    - Given ratios a : b & b : c, determine specified quantity, real-world context
    - Condensed: Given extended ratio, determine ratio or specified quantity, real-world context
    - Given proportional relationship & extended ratio, determine specified quantity, real-world context
- Rates
  - Basic Unit Rates
    - Identify unit rates
    - Determine unit rates, ratio tables, real-world context
    - Determine unit rates, strip diagrams, real-world context
    - Given double number line, determine unit rate, real-world context
    - Identify measurement conversion unit rates
  - Application of Rates
    - Determine unit rates, whole numbers, real-world context
    - Determine unit rates, fractions, real-world context
    - Determine unit rates, mixed numbers, real-world context
    - Condensed: Determine or apply unit rates, real-world context
    - Determine & compare unit rates, real-world context
    - 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
    - Given unit conversion rate, convert measurement units
    - Identify measurement conversion rates
- Proportions
  - Solve proportions, whole numbers
  - Solve proportions
  - Solve proportions, mixed number components
  - Solve proportions to convert measurement units
  - Solve proportions, exact answers, real-world context
  - Solve proportions, rounded answers, real-world context
  - Compare rates or determine specified values in proportional relationships, real-world context
Number Lines
- Number Lines, Only Positives
  - Given range & increment, identify blank number line
  - Identify decimals on number lines, positive
  - Identify decimals on number lines, vertical number lines, positive
  - Identify or plot decimals on number lines, increment 0.5
  - Identify or plot decimals on number lines, increment 0.2
  - Condensed: Identify or plot decimals on number lines
  - Plot or locate percents on number line
  - Identify or plot fractions or determine lengths on number line
  - Determine location of rational numbers on number line
  - Determine location of rational numbers on number line, including negatives
  - Condensed: Identify or plot decimals or fractions on number lines
- Number Lines, Including Negatives
  - Identify integers on number lines, negative
  - Identify rational numbers on number lines, negative
  - Identify rational numbers on number lines, vertical number lines
  - Identify rational numbers on number lines, negative, vertical number lines
  - Condensed: Identify rational numbers on number lines, vertical
  - Condensed: Identify rational numbers on number lines, including vertical number lines
  - Identify or determine rational values on number line, vertical number lines
  - Plot rational numbers on number lines, negative
  - Identify or plot rational numbers on number lines & interpret, real-world context
  - Condensed: Identify or plot rational numbers on number lines
  - Identify & compare rational numbers on number lines
Number Theory
- Prime & Composite Numbers
  - Identify prime & composite numbers
  - Identify prime & composite numbers, real-world context
- Factors & Multiples
  - Identify factors or non-factors of whole numbers
  - Identify multiples or non-multiples of whole numbers
  - Identify factors or multiples of whole numbers
  - Condensed: Identify factors, non-factors, multiples, & non-multiples 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, real-world context
  - Apply GCFs to determine number of items in groups, real-world 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, real-world context
  - Apply LCMs to determine number of items in groups, real-world 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, real-world context
  - Condensed: Apply GCFs & LCMs to determine number of items in groups, real-world context
Expressions
- Expression Vocabulary
  - Determine definitions of coefficient, fill in the blank
  - Determine definitions of constant, fill in the blank
  - Determine definitions of variable, fill in the blank
  - Determine definitions of term, fill in the blank
  - Determine definitions of expression, fill in the blank
  - Determine definitions of evaluate, fill in the blank
  - Determine definitions of operation, fill in the blank
  - Determine definitions of arithmetic vocabulary, fill in the blank
  - Determine definitions of relationship vocabulary, fill in the blank
  - Identify parts of expressions
  - Identify multiple parts of expressions
- Whole Number Exponents
  - Convert expanded numerical expressions to exponential form
  - Convert exponential numerical expressions to expanded form
  - Convert descriptions of numerical exponential expressions to exponential form
  - Determine components & properties of whole-number exponents
  - Square positive integers up to 10
  - Simplify or evaluate numerical exponential expressions
- Translating Expressions
  - Identify words or phrases that indicate specified operation or comparison
  - Determine algebraic expressions that represent real-world situations
  - Given phrase, determine one-step algebraic expression
  - Interpret numerical expressions
  - Identify equivalent multi-step algebraic expressions & phrases
  - Given phrase, determine multi-step algebraic expression
  - Given phrase, determine & evaluate multi-step algebraic expression
  - Determine algebraic expressions that represent real-world situations, including two-variable expressions
- Equivalent Expressions
  - Identify equivalent numerical expressions using counters
  - Identify equivalent algebraic expressions using algebra tiles
  - Identify equivalent expressions or determine simplified expressions
  - Identify equivalent algebraic expressions, including real-world context
  - Evaluate & identify equivalent numerical expressions, including real-world context
- Evaluating Expressions
  - Basic Evaluating Expressions, Addition & Subtraction
    - Evaluate addition expressions for specified value, one variable, whole numbers
    - Evaluate subtraction 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, at least one fraction
    - Evaluate subtraction expressions for specified value, one variable, at least one decimal
    - Evaluate expressions for specified value, one variable, only sums, at least one decimal
    - Evaluate subtraction expressions for specified value, one variable, at least one decimal
  - Basic Evaluating Expressions, Multiplication & Division
    - Evaluate multiplication expressions for specified value, one variable
    - Evaluate division 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
    - Evaluate division expressions for specified value, one variable, at least one fraction
    - Evaluate division expressions for specified value, one variable, at least one decimal
  - Application of Evaluating Expressions
    - Condensed: Evaluate expressions for specified value, one variable
    - Evaluate expressions for specified values, two variables, multiple operations, including powers & real-world context
    - Condensed: Evaluate expressions, including powers, fractions, whole numbers, & decimals, including real-world context
    - Evaluate or identify expressions that represent situations from descriptions, real-world context
    - Evaluate expressions for specified value, one variable, including multiple operations, at least one decimal
- Distributing or Factoring Expressions
  - Identify equivalent expressions involving distribution
  - Identify equivalent expressions involving distribution, two or more terms
  - Identify algebraic expressions, involving distribution, real-world context
  - Apply distributive property to numerical expressions, real-world context
  - Factor GCF from linear binomial expressions, both terms positive
  - Distribute or factor, linear binomial expressions
- Simplifying Variable Expressions
  - Simplify algebraic expressions, combine two terms, positives
  - Simplify algebraic expressions, one variable, product of two factors, positives
  - Simplify algebraic expressions, one variable, product of three factors, positives
  - Simplify algebraic expressions, one variable, positive integer coefficients
  - Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
  - Simplify algebraic expressions, two variables, positive integer coefficients
Equations & Inequalities
- Equations
  - Equivalent Equations
    - Identify missing operations in numerical sentences
  - Solving Equations, Only Positives
    - Solve x + a = b, a > 0, b > 0, x > 0
    - Solve x – a = b, a > 0, b > 0, x > 0
    - Solve ax = b, a > 0, b > 0
    - Solve x/a = b, a > 0, b > 0
    - Solve one-step linear equations, rationals
  - Properties of Equations
    - Identify properties used in numerical expressions
    - Identify properties used in numerical & algebraic expressions
    - Identify properties used to solve linear equations
  - Solving Addition & Subtraction Equations, Including Negatives
    - 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
    - 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
    - Condensed: Solve one-step linear equations, addition or subtraction
  - Solving Multiplication & Division Equations, Including Negatives
    - 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
    - Condensed: Solve one-step linear equations, multiplication or division
  - Checking Solutions
    - Identify values that solve equations, variable & constant on left side
    - Identify values that solve equations, constant times variable
    - Identify values that solve equations, variable divided by constant
    - Identify values that solve equations, variable & constant on right side
    - Identify values that solve equations
    - Identify equations with given solution
  - Writing & Solving Equations, Addition
    - Determine addition equations, real-world context
    - Determine & solve addition equations, including real-world context
    - Determine, solve, & apply addition equations, real-world context
    - Solve addition equations, real-world context
    - Determine & solve or apply addition equations, real-world context
  - Writing & Solving Equations, Multiplication
    - Determine multiplication equations, real-world context
    - Determine & solve multiplication equations, real-world context
    - Determine & solve multiplication equations, including real-world context
    - Determine & solve multiplication equations, including required rounding, real-world context
    - Determine, solve, & apply multiplication equations, real-world context
    - Determine, solve, & apply multiplication equations, including required rounding, real-world context
  - Writing & Solving Equations, Mixed
    - Determine one-step equations, including decimals, real-world context
    - Given one-step linear equation, identify real-world situation represented by equation
    - Given rate & time, determine distance
    - Given distance & rate or time, determine missing quantity
    - Determine solutions to problems using common formulas, including simple interest, area & perimeter, & d = rt, real-world context
- Inequalities
  - Checking Solutions
    - Identify values that solve inequalities, variable & constant on left side
    - Identify values that solve inequalities, variable & constant on right side
    - Identify values that solve inequalities, constant minus variable on left side
    - Identify values that solve inequalities, constant minus variable on right side
    - Identify values that solve inequalities
  - Solving Inequalities, Only Positives
    - 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 & graph one-step inequalities, x + #
    - Solve & graph one-step inequalities, x – #
    - Condensed: Solve & graph one-step inequalities, x ± #
    - Solve & graph one-step inequalities, a * x, a > 0
  - Solving Inequalities, Including Negatives
    - Solve one-step inequalities, a * x, a < 0
    - Solve one-step inequalities, x/a, a > 0
    - Solve one-step inequalities, x/a, a < 0
    - Condensed: Solve one-step inequalities, x/a
  - Solving & Graphing Inequalities, Including Negatives
    - Condensed: Solve & graph one-step inequalities, x ± #
    - Solve & graph one-step inequalities, a * x, a < 0
    - 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
    - Solve & graph one-step inequalities, whole number coefficients
    - Solve & graph one-step inequalities, integer coefficients
    - Solve & graph one-step inequalities, including fractional coefficients
    - Solve & graph one-step inequalities, including negative & fractional coefficients
  - Basic Writing & Graphing Inequalities
    - Determine graph from inequality or inequality from graph
    - Graph inequalities on number line
    - Given graph, determine inequality
  - Application of Writing Inequalities
    - Represent real-world problems as inequalities
    - Determine one-step inequalities, including real-world context
    - Determine one-step inequalities, rational numbers, including real-world context
    - Given description, determine inequality, graph, & possible solutions
    - Given inequality, identify phrase or real-world problem that represents inequality
    - Given one-step inequality, identify real-world problem modeled by inequality
    - Given one-step inequality, identify real-world problem modeled by inequality, rational numbers
    - Identify one-step inequalities that model real-world problems or interpret inequality components
    - Determine, solve, & graph one-step inequalities, including real-world context
Linear Relationships
- Linear Relationships, Only Proportional
  - 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
  - Interpreting Points
    - Determine or interpret points on graphs showing proportional relationships
    - Given constant of proportionality, determine or interpret point, real-world context
  - Writing Equations, Completing Tables & Graphs
    - Given unit rate, determine graph of proportional relationship, real-world context
    - Determine graph of proportional relationship, real-world context
    - Given two points, determine linear graph & constant of proportionality
    - Given constant of proportionality, determine table, graph, or equation
    - Given table, determine constant of proportionality, graph, or equation
    - Given equation, determine constant of proportionality, graph, or table
    - Given graph, determine constant of proportionality, table, or equation
    - Condensed: Determine equivalent representations of proportional relationships
    - Determine or identify equivalent representations of proportional relationships
    - Determine equations, tables, & graphs for proportional relationships, real-world context
    - Given visual representation of proportional relationship, determine equation, table, & graph, real-world context
    - Identify representation of proportional relationship, various representations, real-world context
- Linear Relationships, Proportional & Non-Proportional
  - Additive & Multiplicative Relationships
    - Identify graphs of additive & multiplicative relationships
    - Given table, determine additive or multiplicative equation
    - Identify components of additive & multiplicative equations
    - Identify equivalent representations of additive & multiplicative relationships
    - Identify equivalent representations of additive & multiplicative relationships, including decimals & fractions
    - Identify situations modeled by additive & multiplicative relationships
    - Identify situations modeled by tables or equations, y = mx or y = x + b
    - Identify proportional & non-proportional relationships, real-world context
    - Identify tables that represent real-world situations, y = mx or y = x + b
    - Determine equations that represent real-world situations, y = mx or y = x + b
  - 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
    - Given table, determine graph & constant of proportionality
  - Identifying Proportional vs. Non-Proportional
    - Identify tables showing proportional relationship
    - Identify graphs showing proportional relationship
    - Identify equations showing proportional relationship
    - Identify tables, graphs, or equations showing proportional relationship
  - Writing Equations, Completing Tables & Graphs
    - Given linear equation & table, identify graph
    - Given linear equation & table, determine graph
    - Given linear graph, determine y-values in table
    - Given linear graph, determine y-values in table & equation
    - Given linear equation, determine y-values in table & graph, first quadrant
    - Determine equations that represent real-world situations, including two-step equations
    - Determine additive & multiplicative equations that represent real-world situations
    - Given graph of proportional relationship, determine table & equation, real-world context
Geometry
- 2D Figures
  - Classify angles from figure
  - Classify triangles by sides
  - Classify triangles by angles
  - Classify triangle based on given angle measures
  - Classify triangles based on angles & sides
  - Classify quadrilaterals shapes based on attributes
  - Classify polygons based on number of sides or relationship to other shapes
  - Classify polygons based on angles & parallel or perpendicular lines
  - Classify polygons using graphic organizers
  - Classify polygons using graphic organizers, including types of triangles
- 3D Figures
  - Identify 3D figures & their bases
  - Identify equivalent representations of 3D figures & nets
  - Determine 2D orthographic representation of 3D blocks
- Triangle Angle-Side Relationships
  - Given two angle measures in triangle, determine angle measure
  - Determine smallest & largest sides or angles in triangle
  - Order angles in triangles
  - Given congruent sides, identify congruent angles of isosceles triangle
  - Given congruent angles, identify congruent sides of isosceles triangle
  - Apply triangle inequality theorem to determine range of values for unknown side
  - Apply triangle inequality theorem to determine side lengths
  - Apply triangle angle sum theorem to determine appropriate equation & angles, algebraic expressions
- Perimeter
  - Modeling Perimeter
    - Given model, identify formula & determine perimeter of rectangles
    - Given model, identify formula & determine perimeter of rectangles, including decimal dimensions
    - Condensed: Identify formula & determine perimeter of rectangles & squares
  - Basic Perimeter
    - Determine perimeter of rectangles
    - Given sides of rectangle, determine perimeter
    - Determine perimeter of rectangles, including decimal dimensions
    - Determine side length or perimeter of squares
    - Given perimeter & one dimension of rectangle, determine missing dimension
    - Given perimeter of rectangle & one side, determine dimension
    - Given perimeter of rectangle & one side, determine dimension, including decimals
  - Application of Perimeter
    - Given sides of rectangle, determine perimeter
    - Condensed: Determine perimeter of rectangles, including real-world context
    - Determine perimeter of rectangles, real-world context
    - Determine perimeter of rectangles, including decimal dimensions, real-world context
    - Given perimeter & relationship between sides, determine specific dimension
    - Determine perimeter of polygons, including real-world context
    - Determine circumference of circle, exact answers, multiple choice, including real-world context
    - Given radius or diameter, determine circumference
    - Estimate diameter or circumference & identify equations using π
- Area
  - Trapezoid Area
    - Basic Trapezoid Area
      - Determine area of trapezoids
      - Given area & base lengths of trapezoid, determine height
    - Application & Modeling of Trapezoid Area
      - Determine area of triangles using models that decompose & rearrange parts
      - Given height & bases of trapezoid, determine area
      - Determine equations that represent area of trapezoids, real-world context
      - Given area & bases of trapezoid, determine height
  - Composite & Mixed Figure Area
    - Determine algebraic expressions that represent area of rectangles & triangles
    - Determine areas of triangles & trapezoids
    - Given area, determine dimensions of triangles
    - Condensed: Determine areas & dimensions of triangles & trapezoids
    - Condensed: Determine equations that represent area of triangles & quadrilaterals, real-world context
    - Determine perimeter of composite figures containing rectangles & squares, including real-world context
    - Determine area of composite figures on coordinate plane, no circular shapes
    - Determine area of polygons in coordinate plane
    - Determine area of polygons in coordinate plane, real-world context
    - Determine area of composite figures, rectangle with various figures attached, no circular parts
    - Determine area of composite figures, no circular shapes
    - Condensed: Determine area using models that decompose & rearrange parts
  - Triangle Area
    - Basic 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
    - Application & Modeling of Triangle Area
      - Given base & height of triangle, determine area
      - Determine area of triangles using models that decompose & rearrange parts
      - Determine equations that represent area of triangles, real-world context
      - Given area & one dimension of triangle, determine missing dimension
  - Circle Area
    - Determine area of circle, exact answers, including real-world context
    - Given radius or diameter, determine area
    - Given radius or diameter, determine area or circumference
    - Condensed: Determine area or circumference of circle
    - Identify approximate formulas for circumference & area of circles
  - Rectangle & Parallelogram Area
    - Modeling Area of Rectangles & Parallelograms
      - Given sides of rectangle, determine area, model provided
      - Given model, identify formula & determine area of square
      - Given model, identify formula & determine area of rectangle
      - Condensed: Given model, identify formula & determine area of square or rectangle
      - Determine area of rectangles with fractional dimensions using tiling method
      - Determine area of parallelograms, model provided
      - Determine area of parallelograms using models that decompose & rearrange parts
    - Basic Area of Rectangles & Parallelograms
      - Given length & width of rectangle, determine area
      - Given sides of rectangle, determine area
      - Determine area of rectangles with fractional dimensions
      - Determine area of parallelograms
      - Determine areas of rectangles & parallelograms
      - Given area & one dimension of rectangle, determine missing dimension
      - Given area of rectangle & one dimension, determine other dimension
      - Given area & one dimension of parallelogram, determine missing dimension
      - Given area, determine dimensions of rectangles & parallelograms
      - Condensed: Determine areas & dimensions of rectangles & parallelograms
    - Application of Area of Rectangles & Parallelograms
      - Determine equations that represent area of rectangles, real-world context
      - Condensed: Determine area of rectangles, including real-world context
      - Given sides of rectangle & cost per square unit, determine area & total cost, real-world context
      - Determine area of shaded region between nested rectangles
      - Given perimeter or side length, determine area of square, including real-world context
      - Determine equations that represent area of parallelograms, real-world context
      - Given base & height of rectangle or parallelogram, determine area
      - Determine area of missing dimension of rectangles, real-world context
      - Given area & one dimension of rectangle or parallelogram, determine missing dimension
- Area & Perimeter
  - Condensed: Identify formula & determine perimeter of rectangles & squares
  - Determine area or perimeter of parallelograms
  - Condensed: Determine equations that represent area of triangles & quadrilaterals, real-world context
  - Determine dimension of rectangles, including real-world context
- Surface Area
  - Calculating Surface Area with 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 lateral surface area of prisms
  - Surface Area of Rectangular & Triangular Prisms
    - Determine surface area of rectangular prisms
    - Determine surface area of triangular prisms
    - Determine surface areas of 3D figures, no circles
- Volume
  - Unit Cube Volume
    - Determine relationship between area, volume, & dimensions
    - Determine relationship between area, volume, square units, & cubic units
    - Determine volume of rectangular 3D figures using unit cubes
    - Determine volume of rectangular prisms using unit cubes
    - Determine volume of rectangular prisms using unit cubes
    - Determine volume of rectangular prisms, various representations
  - Basic Volume, Cubes
    - Determine volume of cubes, whole numbers or decimals
    - Determine volume of cubes, whole numbers, decimals, or fractions, no visual provided
    - Determine volume of cubes, whole numbers, decimals, or fractions
  - Basic Volume, Rectangular Prisms
    - Determine volume of rectangular prisms, whole numbers, volume less than 10,000
    - Determine volume of rectangular prisms, whole numbers or decimals
    - Determine volume of rectangular prisms, whole numbers, decimals, or fractions
    - Given base area & edge or all edges, determine volume of rectangular prism
    - Determine volumes of rectangular & triangular prisms, fractional dimensions
    - Given volume, determine edges of rectangular prisms
    - Determine volume or edge of rectangular prisms, whole numbers, volume less than 10,000
    - Determine volume or edge of rectangular prisms, whole numbers
    - Condensed: Determine volume or dimension of rectangular prisms, fractional dimensions
    - Determine volume of rectangular prisms, whole numbers or decimals
    - Determine volumes of rectangular prisms, fractional dimensions
    - Given volume, determine edge of rectangular prisms, up to four-digit dividend, up to two-digit divisor
  - Application of Volume, Cubes
    - Determine volume of cubes, whole numbers or decimals, real-world context
    - Determine volume of cubes, whole numbers, decimals, or fractions, real-world context
    - Condensed: Determine volume or side length of cubes, whole numbers, decimals, or fractions, including real-world context
  - Application of Volume, Rectangular Prisms
    - Determine volume of rectangular prisms using repeated layers of base area, real-world context
    - Determine volume of rectangular prisms using various representations of cubic units, real-world context
    - Determine volume of rectangular prisms, whole numbers, including real-world context
    - Determine volumes of rectangular prisms, rational dimensions, real-world context
    - Determine volumes of cubes & rectangular prisms
    - Determine volume of triangular prisms
    - Given volume & two dimensions of rectangular prism, determine missing dimension
    - Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, real-world context
    - Determine volume or edge of rectangular prisms, whole numbers or decimals, real-world context
    - Determine volume of composite rectangular prisms
    - Determine volume of rectangular prisms & apply associative property to volume expressions
    - Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including real-world context
- Coordinate Plane
  - Basic Coordinate Plane, Only First Quadarant
    - 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 Coordinate Plane, Only 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, real-world context
    - Determine or identify first quadrant points, including cardinal directions, real-world context
    - Condensed: Plot or determine coordinates of first quadrant rational points
  - Basic Coordinate Plane, All Quadrants
    - Given integer point on graph, determine coordinates, point on axis
    - Given integer point on graph, determine coordinates
    - Given lattice point, determine coordinates
    - Given rational point, determine location on coordinate plane
    - Plot integer points on coordinate plane, point on axis
    - Plot integer points
    - Plot points on coordinate plane, student selects scales
    - Plot rational points on coordinate plane
    - Plot rational points on coordinate plane, graph scale at most one-half
    - Condensed: Plot integer points or determine coordinates
    - Condensed: Plot or identify points on coordinate plane
    - Plot or identify rational points on coordinate plane
  - Reflections & Distance Between Points
    - Determine coordinates of reflected points
    - Determine distance between points on coordinate plane, horizontal or vertical
    - Determine distance between points on coordinate plane, horizontal or vertical, real-world context
Measurement & Data
- Conversions
  - Basic Customary Conversions
    - Convert between customary units of weight & mass
    - Convert between customary units of volume & capacity
    - Convert between customary units of length
    - Convert between customary units of length
    - Given unit conversion rate, convert measurement units
  - Application of Customary Conversions
    - Convert between customary units of volume & capacity
    - Convert between customary units of weight & mass
    - Condensed: Convert between customary units
    - Convert between customary units, including real-world context
    - Convert between customary units, real-world context
    - Convert between customary units to find sums or differences, including real-world context
  - Basic Metric Conversions
    - Convert between metric units of length
    - Convert between metric units
  - Application of Metric Conversions
    - Convert between metric units of weight & mass
    - Convert between metric units of volume & capacity
    - Convert between metric units of length, real-world context
    - Convert between metric units of weight & mass, real-world context
    - Convert between metric units of volume & capacity, real-world context
    - Convert between metric units, including real-world context
    - Given conversion chart, convert between metric units, real-world context
    - Condensed: Convert between metric units
    - Convert between metric units, real-world context
    - Condensed: Convert between customary or metric units
  - Basic Customary & Metric Conversions
    - Convert customary to metric units of length, calculator expected
    - Convert metric to customary units of length, calculator expected
    - Convert customary to metric units of volume & capacity, calculator expected
    - Convert metric to customary units of volume & capacity, calculator expected
    - Convert customary to metric units of weight & mass, calculator expected
    - Convert metric to customary units of weight & mass, calculator expected
    - Condensed: Convert between customary & metric, calculator expected
  - Application of Customary to Metric & Metric to Customary
    - Convert customary to metric units of length
    - Convert customary to metric units of weight & mass
    - Convert customary to metric units of volume & capacity
    - Convert metric to customary units of length
    - Convert metric to customary units of weight & mass
    - Convert metric to customary units of volume & capacity
  - Application of One-Step Customary & Metric Conversions
    - Condensed: Convert between customary & metric
    - Convert between customary & metric using conversion graphs
    - Convert between customary & metric using unit rates
    - Convert between customary & metric using dimensional analysis
    - Convert between customary & metric, proportion bias
    - Condensed: Convert between customary & metric using multiple representations of conversion factor
    - Convert between customary & metric, real-world context
    - Convert between customary & metric using scale factors
  - Application of Multi-Step Customary & Metric Conversions
    - Convert customary to metric units of length, including multi-step
    - Convert customary to metric units of weight & mass, including multi-step
    - Convert customary to metric units of volume & capacity, including multi-step
    - Convert metric to customary units of length, including multi-step
    - Convert metric to customary units of weight & mass, including multi-step
    - Convert metric to customary units of volume & capacity, including multi-step
    - Condensed: Convert between customary & metric, including multi-step
- Charts & Graphs
  - Frequency Tables
    - Given data, identify frequency table or determine missing element of table
    - Solve one-step problems from frequency tables, real-world context
    - Solve problems from frequency tables, real-world context
    - Solve one-step problems from frequency & relative frequency tables, real-world context
    - Solve multi-step problems from frequency tables, real-world context
    - Condensed: Interpret two-way frequency tables
  - Line Plots
    - Given data represented in various ways, identify dot plot
    - Determine equivalent fraction data sets & line plots
    - Solve one-step problems from dot plots, real-world context
    - Solve problems involving dot plots
    - Solve problems involving line plots & fractions
    - Add or subtract fractions from line plots, common denominator
    - Solve multi-step problems from dot plots, real-world context
  - Bar & Double Bar Graphs
    - Given table, determine equivalent bar graph
    - Given bar graph, determine equivalent table
    - Given table, determine equivalent bar graph, including double bar graphs
    - Condensed: Given bar graph, determine equivalent table or pictograph
    - Determine or interpret percentage bar graphs
    - Solve problems involving bar graphs
    - Solve one-step problems from bar graphs, real-world context
    - Solve one-step problems from double bar graphs, real-world context
    - Add, subtract, & multiply fractions in bar graphs, common denominator
    - Solve multi-step problems from bar graphs, real-world context
    - Solve multi-step problems from double bar graphs, real-world context
  - Stem-&-Leaf Plots
    - Given data, identify stem-and-leaf plot
    - 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
  - Scatter Plots
    - Given data, determine scatter plot
    - Identify equivalent representations of data in tables & scatter plots
    - Solve one-step problems from scatter plots, real-world context
    - Solve multi-step problems from scatter plots, real-world context
  - Histograms
    - Given various representations of data, determine histogram
  - Pictographs
    - Given bar graph, determine equivalent pictograph
    - Given pictograph, determine equivalent table
    - Given pictograph, determine equivalent bar graph
    - Condensed: Given pictograph, determine equivalent bar graph or table
  - 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
  - Mixed Charts & Graphs
    - Determine unit of measurement for data, various representations
    - Determine sample size, various representations
    - Condensed: Given table, determine equivalent bar graph or pictograph
    - Condensed: Given data, represent with dot plot or stem-and-leaf plot
    - Condensed: Determine equivalent visual representations of data
    - Determine solutions to problems involving bar graphs & line graphs
    - Condensed: Solve one-step problems from various plots, graphs, & tables, real-world context
    - Condensed: Solve multi-step problems from various plots, graphs, & tables, real-world context
Probability & Statistics
- Measures of Center & Spread
  - Calculating Measures of Center & Spread
    - 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
    - Given various representations of data, identify mean, median, mode, & range
    - Given mean, median, mode, or range, determine missing value in data set
    - Given additional value in data set, determine change in mean, median, mode, or range
    - Given mean, median, or range, determine missing or additional value in data set
    - Determine interquartile range of data
    - Determine mean absolute deviation
    - Determine mean absolute deviation, real-world context
    - Condensed: Solve problems involving interpretation of box plots & stem-&-leaf plots
  - Interpretting Measures of Center & Spread
    - Given various representations of data, identify outlier
    - Solve problems involving interpretation of histograms
    - Identify variability in real-world situations
    - Determine collection method, distribution shape, & unit of measure for data
    - Identify measures of center based on data distribution
    - Identify measures of variability based on data distribution
    - Identify & interpret measures of center
    - Identify & interpret measures of variability
    - Determine or interpret shapes & features of graphs
    - Determine or interpret measures of center & spread from graphs
- Box Plots
  - Determine characteristics of boxplots
  - Solve problems involving interpretation of box plots
  - Solve problems involving interpretation of stacked box plots, real-world context
  - Determine five-number summary
  - Given boxplot, determine values from five-number summary
  - Condensed: Determine five-number summary, including box plots
  - Solve problems involving five-number summary
- 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 side-by-side dot plots
- Statistical Data
  - Determine whether data was counted or measured
  - Determine whether data is categorical or numerical
  - Identify statistical questions
  - Identify biased samples & questions
  - Identify samples & populations
  - Identify variability in real-world situations
  - Determine definitions of data collection & distribution vocabulary, fill in the blank
- Basic Probability
  - Determine sample spaces
  - Classify probabilities by levels of likelihood
  - Determine probabilities of single events
  - Determine theoretical probabilities
  - Determine experimental probabilities
  - Determine theoretical probabilities, fraction answers
  - Determine experimental probabilities, fraction answers
  - Determine probabilities of flipping coins specified number of times
  - Determine probabilities & complementary probabilities of single events, including visual models
  - Determine predicted values, theoretical probability
  - Determine predicted values, experimental probability
Financial Literacy
- Identify positive & negative factors in establishing credit history
- Identify value of credit report
- Determine similarities & differences between debit & credit cards
- Identify methods of college payment
- Balance check register
- Determine budget allocations for spending, saving, & giving
- Solve problems involving information on credit report
- Given features & costs, determine best financial institution based on specified conditions
- Determine annual income
- Determine lifetime income
- Estimate costs of two-year college education
- Estimate costs of four-year college education