6th Grade Skills

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  • 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