5th Grade Skills

VIEW ALL SKILLS

  • Whole Numbers
    • Addition of Whole Numbers
      • Basic Addition of Whole Numbers
        • Add positive integers, up to two digits
        • 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 whole numbers, up to two digits, real-world context
        • Add three- & four-digit whole numbers, real-world context
        • Add four-digit whole numbers, real-world context
        • Add five-digit whole numbers, real-world context
        • Condensed: Add whole numbers, up to five digits, real-world context
        • Condensed: Add whole numbers, up to five digits, including real-world context
        • Add five- or six-digit whole numbers, real-world context
    • Subtraction of Whole Numbers
      • Basic Subtraction of Whole Numbers
        • Subtract positive integers, up to two digits, positive difference
        • Subtract whole numbers, four-digit & three-digit
        • Subtract whole numbers, four-digit & three-digit
        • Subtract whole numbers, three- or four-digit & two- to four-digit
        • Condensed: Subtract whole numbers, four-digit & three- or four-digit
        • Subtract whole numbers, four-digit & 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, seven-digit & six- or seven-digit
      • Application of Subtraction of Whole Numbers
        • 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
      • Modeling Multiplication of Whole Numbers
        • Multiply whole numbers using area models, up to four-digit & one-digit
        • Multiply whole numbers by decomposing factors, up to four-digit & one-digit
        • Condensed: Multiply whole numbers using area models or decomposition, up to four-digit & one-digit
        • Multiply whole numbers using area models, two-digit & two-digit
        • Condensed: Multiply whole numbers using area models or decomposition, two-digit & two-digit
      • Basic Multiplication of Whole Numbers
        • Multiply whole numbers, two-digit & one-digit
        • Multiply whole numbers, both up to 19
        • Multiply multiples of 10 & two-digit whole numbers
        • Multiply whole numbers, two-digit & two-digit
        • Multiply whole numbers by decomposing factors, two-digit & two-digit
      • Basic Multiplication of Whole Numbers, Three- or Four-Digit
        • Multiply whole numbers, three-digit & one-digit
        • Multiply whole numbers, four-digit & one-digit
        • Condensed: Multiply whole numbers, three- or four-digit & one-digit
        • Multiply whole numbers, two-digit & two- or three-digit
        • Multiply whole numbers, three-digit & two-digit 
        • Multiply whole numbers, both up to three digits
        • Condensed: Multiply whole numbers, three- or four-digit & two-digit
        • Condensed: Multiply whole numbers, up to four-digit & up to three-digit, no more than six total digits
      • Application of Multiplication of Whole Numbers
        • Multiply whole numbers, two-digit & one-digit, real-world context
        • Multiply whole numbers, three-digit & one-digit, real-world context
        • Multiply whole numbers, four-digit & one-digit, real-world context
        • Condensed: Multiply whole numbers, one-digit & up to four-digit, real-world context
        • Multiply whole numbers, two-digit & two-digit, real-world context
        • Condensed: Multiply whole numbers, one- or two-digit & up to four-digit, real-world context
        • Multiply whole numbers, three-digit & two-digit, including addition or subtraction step, real-world context
      • Products of Ten & One Hundred
        • Multiply 100 & two-digit whole numbers
        • Condensed: Multiply whole numbers, two-digit & 10 or 100
        • Multiply multiples of 10 & one-digit whole numbers, real-world context
        • Multiply multiples of 100 & one-digit whole numbers, real-world context
        • Condensed: Multiply multiples of 10 or 100 & one-digit whole numbers, real-world context
        • Condensed: Multiply multiples of 10 or 100 & one- or two-digit whole numbers, including real-world context
      • Multiplicative Comparisons
        • 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
      • Modeling Division of Whole Numbers
        • Determine equivalence between arrays & division equations
        • Determine equivalence between area models & division equations
        • Condensed: Determine equivalence between models & division equations
        • Apply divisibility rules to two-digit dividends, divisor 2, 3, 4, 5, 6, 9, 10
        • Determine division equations, real-world context 
      • Basic Division of Whole Numbers, One-Digit Divisor
        • Divide whole numbers, up to three-digit dividend, one-digit divisor
        • Determine quotient & remainder, one-digit dividend, one-digit divisor
        • Determine quotient & remainder, two-digit dividend, one-digit divisor
        • Determine quotient & remainder, three-digit dividend, one-digit divisor
        • Determine quotient & remainder, four-digit dividend, one-digit divisor
        • Determine quotient & remainder as fraction, one-digit dividend, one-digit divisor
        • Determine quotient & remainder as fraction, two-digit dividend, one-digit divisor
        • Determine quotient & remainder as fraction, three-digit dividend, one-digit divisor
        • Determine quotient & remainder as fraction, four-digit dividend, one-digit divisor
      • Basic Division of Whole Numbers, Up to Three-Digit Dividend & Two-Digit Divisor
        • Determine quotient & remainder, two-digit dividend, two-digit divisor
        • Condensed: Determine quotient & remainder, two-digit dividend, up to two-digit divisor
        • Determine quotient & remainder, three-digit dividend, two-digit divisor
        • Condensed: Determine quotient & remainder, three-digit dividend, up to two-digit divisor
        • Determine quotient & remainder as fraction, two-digit dividend, two-digit divisor
        • Condensed: Determine quotient & remainder as fraction, two-digit dividend, up two two-digit divisor
        • Determine quotient & remainder as fraction, three-digit dividend, two-digit divisor
        • Condensed: Determine quotient & remainder as fraction, three-digit dividend, up two two-digit divisor
      • Basic Division of Whole Numbers, Four- or Five-Digit Dividend & Two-Digit Divisor
        • Divide whole numbers, up to five-digit dividend, up to two-digit divisor
        • Determine quotient & remainder, four-digit dividend, two-digit divisor
        • Condensed: Determine quotient & remainder, up to four-digit dividend & two-digit divisor
        • Condensed: Determine quotient & remainder, four-digit dividend, up to two-digit divisor
        • Determine quotient & remainder as fraction, four-digit dividend, two-digit divisor
        • Condensed: Determine quotient & remainder as fraction, four-digit dividend, up two two-digit divisor
      • Application of Division of Whole Numbers
        • Divide positive integers, up to four-digit dividend, one-digit divisor, real-world context
        • Determine quotient or remainder, 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
        • Condensed: Divide whole numbers, up to four-digit dividend, up to two-digit divisor, including 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
        • Condensed: Solve multi-step problems involving equations, models, & whole number operations, real-world context
      • Equations of Mixed Operations of Whole Numbers
        • 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
      • Application of Mixed Operations of Whole Numbers
        • Add or subtract whole numbers, real-world context
        • Solve multi-step problems involving whole number operations, initially add, real-world context
        • Solve multi-step problems involving models & 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 & Estimating 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, real-world context
        • Condensed: Round whole numbers to nearest ten, hundred, & thousand, including real-world context
      • Application of Estimating Whole Numbers
        • Estimate sums of whole numbers, up to six digits, including real-world context
        • Estimate sum of rational numbers, round both to nearest whole, 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
        • Condensed: Estimate sums, differences, & products of whole numbers
        • Identify division expression to estimate quotient using compatible numbers, real-world context
        • Estimate quotients of whole numbers, up to six-digit dividend, up to three-digit divisor
        • Determine division expression to estimate quotient using compatible numbers
    • 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
      • Compare whole numbers up to 1,000,000,000
      • 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
      • Given various models, determine fraction, denominators 2, 3, 4, 6, 8
      • Identify fractions on strip diagrams
      • Identify fractions or mixed numbers on decimal grid
      • Identify common fractions or mixed numbers on number line
    • 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
    • Comparing & Ordering Fractions
      • Compare two fractions, different denominators, strip diagrams
      • Compare two fractions, different denominators, number lines
      • Compare two fractions, different denominators, area models
      • Compare fractions, different denominators, visual model
      • 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
    • Equivalent Fractions
      • Determine equivalent fractions, number lines
      • Determine equivalent fractions, area models
      • Determine equivalent fraction equations, area models
      • Determine equivalent fractions, strip diagrams
      • Determine equivalent fraction components
      • Identify or determine equivalent fraction components or fractions
      • Determine how many fraction parts are in whole
    • Decomposing Fractions
      • Decompose fractions into sum of fractions, visual models
      • Decompose fractions into sum of fractions
      • Decompose fractions or mixed numbers into sum of fractions, visual models
      • Decompose fractions or mixed numbers into sum of fractions, real-world context
      • Condensed: Decompose fractions or mixed numbers into sum of fractions, including visual models & real-world context
      • Decompose fractions or mixed numbers into sum of fractions & determine equivalent fractions & mixed numbers
    • Converting Fractions
      • Converting Fractions to Decimals
        • Identify decimal equivalent of fractions, real-world context
        • Given model, determine fraction & decimal equivalents, unreduced
        • Convert fractions to decimals, denominator power of 10
        • Convert fractions to decimals, denominator factor of power of 10
        • Condensed: Determine & identify equivalent fractions & decimals, including models, including real-world context
      • Converting Improper Fractions & Mixed Numbers
        • 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
        • Convert mixed numbers to improper fractions, denominators less than 10
        • Convert mixed numbers to improper fractions, includes denominators more than 10
        • Convert mixed numbers to unreduced improper fractions
        • Condensed: Convert between improper fractions & mixed numbers
    • Addition of Fractions
      • Basic Addition of Fractions, Common Denominators
        • Add fractions, common denominators, unreduced
        • Add fractions, common denominators, proper fraction sum
        • Add fractions, common denominators, sums greater than one
        • Add fractions, common denominators, mixed number sum
        • Add mixed numbers, common denominators
      • Application of Addition of Fractions, Common Denominators
        • Condensed: Add fractions, common denominators, including real-world context
        • Add fractions, common denominators, real-world context
      • Basic Addition of Fractions, Different Denominators
        • 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 mixed number sums
        • Add mixed numbers, different denominators
        • Add mixed numbers, different denominators, fractional sum greater than one
        • Given addition expression of two fractions, identify expression using fourths that best estimates sum
    • Subtraction of Fractions
      • Basic Subtraction of Fractions, Common Denominators
        • Subtract fractions, same denominator, positive difference, including unreduced fractions
        • Subtract fractions, common denominators, unreduced
        • Subtract fractions, common denominators, proper fraction difference
        • Subtract mixed numbers, common denominators
      • Application of Subtraction of Fractions, Common Denominators
        • Condensed: Subtract fractions, common denominators, including real-world context
        • Subtract fractions, common denominators, real-world context
      • Basic Subtraction of Fractions, Different Denominators
        • 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
        • Given subtraction expression of two fractions, identify expression using fourths that best estimates difference
    • Addition & Subtraction of Fractions
      • Modeling Addition & Subtraction of Fractions, Common Denominators
        • Identify expressions that represent addition or subtraction of unreduced fractions modeled on number lines
        • Identify expressions that represent addition or subtraction of unreduced fractions modeled by area models
        • Determine & evaluate expressions representing sums & differences of fractions
      • Basic Addition & Subtraction of Fractions, Common Denominators
        • Condensed: Add or subtract fractions, common denominators, unreduced
      • Application of Addition & Subtraction of Fractions, Common Denominators
        • Condensed: Add fractions, common denominators, including real-world context
        • Condensed: Add or subtract fractions, common denominators, real-world context
      • Modeling Addition & Subtraction of Fractions, Different Denominators
        • Add & subtract fractions, number lines
        • Add & subtract fractions, area models
        • Add & subtract fractions, fraction strips
        • Add & subtract fractions, various models
        • Condensed: Given model, determine or interpret addition & subtraction of fractions
      • Basic Addition & Subtraction of Fractions, Different Denominators
        • Condensed: Add or subtract fractions
        • Given subtraction expression of two fractions, identify expression using fourths that best estimates difference
        • Condensed: Given addition or subtraction expression of two fractions, identify expression using fourths that best estimates result
      • Application of Addition & Subtraction of Fractions, Different Denominators
        • Add & subtract fractions, real-world context
        • Add or subtract fractions, including estimation, real-world context
    • Multiplication of Fractions
      • Application & Modeling Multiplication of Fractions
        • Multiply whole numbers & fractions, area models
        • Multiply whole numbers & fractions, including visual models
        • Multiply whole numbers & fractions, real-world context
        • Multiply fractions, positive, real-world context
        • Multiply mixed numbers & proper fractions, visual models, real-world context
        • Multiply mixed numbers & proper fractions, real-world context
        • Condensed: Identify models or multiply whole numbers & fractions using area models
        • Determine part of whole using fraction multiplication, including visual models, including 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
        • Multiply proper & improper fractions, positive
        • Multiply fractions, positive, mixed number directions
        • Multiply mixed numbers, positive
      • 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
        • Interpret fractional parts & fraction multiplication, real-world context
        • Compare products of fractions, mixed numbers, & whole numbers, including 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 by unit fractions, models
        • Divide whole numbers & unit fractions, area models
        • Divide whole numbers & unit fractions, fraction strips
        • Divide whole numbers by unit fractions, number lines
        • 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
        • Divide fractions, positive, mixed number directions
        • Divide mixed numbers, positive
      • Application of Division of Fractions
        • Divide whole numbers & unit fractions, including unit fraction multiplication, real-world context
        • Condensed: Divide whole numbers & fractions, various models
        • Divide fractions & mixed numbers, positive, real-world context
        • 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
  • 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
      • Modeling, Comparing, & Ordering Decimals
        • Compare decimal models
        • Compare decimal models, up to three models
        • Order decimal models
        • Condensed: Compare or order decimal models
      • Basic Comparing & Ordering Decimals
        • 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
        • Compare decimals on number line
        • Identify & compare rational numbers on number lines, positive
        • Compare decimals written in word form, up to four decimal places
        • Order decimals up to 1,000,000,000
        • Condensed: Compare three- to six-digit whole numbers
      • Application of Comparing & Ordering Decimals
        • 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 up to three decimal places, including real-world context
        • Order decimals from table of place values, 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
        • Condensed: Compare or order decimals, up to three decimal places, including real-world context
    • Converting Decimals
      • Convert decimals to fractions
      • Convert decimals to fractions, real-world context
      • Convert decimals to mixed numbers
      • Convert decimals to fractions or mixed numbers
      • Condensed: Determine & identify equivalent fractions & decimals, including models, including real-world context
    • Addition of Decimals
      • Basic Addition of Decimals
        • Add decimals, positive, up to two decimal places
        • Add positive decimals, up to three 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
      • Condensed: Add & subtract decimals, up to two decimal places
      • Add & subtract decimals, up to two decimal places, real-world context
      • Condensed: Add & subtract decimals, up to two decimal places, including real-world context
      • Condensed: Add & subtract decimals, up to two decimal places, real-world context
      • Condensed: Add & subtract rational numbers, real-world context
    • Multiplication of Decimals
      • Basic Multiplication of Decimals
        • Multiply decimals times one-digit whole numbers
        • Multiply positive decimals, each factor up to two decimal places, factors up to 10 after decimal shift
        • Multiply positive decimals, each factor up to two decimal places, factors up to 20
        • Multiply positive decimals, each factor up to two decimal places
        • Multiply decimals, products limited to two decimal places
      • Application 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
    • Division of Decimals
      • Basic Division of Decimals
        • Divide four-digit dividends by two-digit whole number divisors
        • Divide decimals by whole numbers, up to two decimal places
      • Application of Division of Decimals
        • Divide decimals, up to three decimal places, real-world context
        • Divide four-digit dividends by two-digit whole number divisors, including real-world context
        • 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 model representing decimal division, interpret model & determine quotient, including money
        • 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
        • Condensed: Given model representing decimal division, interpret model & determine quotient, including real-world context
    • Rounding & Estimating Decimals
      • Basic Rounding & Estimating Decimals
        • Round decimal numbers to nearest whole, tenth, & hundredth
        • Round decimal numbers to nearest tenth & hundredth, including real-world context
        • Round decimal numbers to nearest whole, tenth, hundredth, & thousandth
        • Round decimal numbers to nearest whole, tenth, hundredth, & thousandth, including real-world context
        • Round decimal & whole numbers to specified place value
        • Estimate sums, differences, & products of decimals & whole numbers by rounding to specified place values
      • Application of Rounding & Estimating Decimals
        • Round decimal numbers to nearest whole, tenth, & hundredth, real-world context
        • Round decimal numbers to nearest tenth & hundredth, real-world context
        • Round numbers to nearest whole, ten, hundred, & thousand, real-world context
        • Round decimal numbers to nearest tenth, hundredth, & thousandth, real-world context
        • Condensed: Round decimal numbers to nearest whole, tenth, & hundredth, including real-world context
        • Determine sums & differences of decimals then round solution, real-world context
        • Estimate quotients of decimals & whole numbers using compatible numbers
        • Estimate solutions involving all operations, real-world context
        • Estimate sums, differences, products, or quotients of rational numbers
        • Estimate sums, differences, products, or quotients of rational numbers, real-world context
  • Number Lines
    • Given range & increment, identify blank number line
    • Identify or plot decimals on number lines, increment 0.5
    • Identify or plot decimals on number lines, increment 0.1
    • Identify or plot decimals on number lines, increment 0.2
    • Plot decimals on number lines, increment 0.1 or 0.01
    • Identify decimals on number lines, positive
    • Identify decimals on number lines, positive, vertical number lines
    • Identify or plot decimals or determine lengths on number line, increment 0.01
    • Identify or plot fractions or determine lengths on number line
    • Compare decimals on number line
    • Identify & compare rational numbers on number lines, positive
    • Determine location of rational numbers on number line
  • Number Sense
    • Place Value
      • Basic Place Value
        • Identify place value of specific digit
        • Identify place value of specific digit, decimals
        • Determine numerical value of specific digit
        • Determine product of number & power of 10
      • Application of Place Value, Determine Value
        • Determine values of digit in hundreds place, including comparison to other place values
        • Determine values of digit in thousands place, including comparison to other place values
        • Determine values of digit in ten-thousands place, including comparison to other place values
        • Determine values of digit in hundred-thousands place, including comparison to other place values
        • Condensed: Determine values of specific digits, including comparison to other place values
      • Application of Place Value, Identify Number with Specific Digit
        • Identify numbers with specific digit equal to 10 times digit to right
        • Identify numbers with specific digit equal to digit to right divided by 10
        • Identify numbers with ones digit equal to 100 times hundredths digit
        • Identify numbers with hundredths value equal to ones value divided by 100
        • Identify numbers with specific digit equal to digit to right divided by 10, 100, or 1,000
        • Identify whole numbers with specific digit equal to digit to right divided by 10, expanded notation
        • Identify numbers with specific digit equal to digit to right divided by 10, standard notation
        • Identify decimal numbers with specific digit equal to digit to right divided by 10, expanded notation
        • Condensed: Identify numbers with specific digit equal to digit to right divided by 10, including expanded notation
    • Number Forms
      • Expanded Number Forms
        • Determine equivalent representations of standard & expanded notations, whole numbers
        • Convert between standard & expanded notations, whole numbers
        • Convert between standard & expanded notations, whole numbers, real-world context
        • Determine equivalent representations of standard & expanded notations, decimals
        • Convert between standard & expanded notations, up to three decimal places
        • Convert between standard & expanded notations, up to three decimal places, real-world context
        • Convert between word, standard, & expanded notations, including real-world context
        • Condensed: Convert between standard & expanded notations, including place value words
      • Standard Number Forms
        • Given whole number in word form, determine standard notation
      • Word Number Forms
        • Given number in word form, determine standard notation
        • Convert numbers to word form, up to 1,000,000
      • Mixed Number Forms
        • Condensed: Convert between word & expanded notations of decimals
        • Condensed: Convert between word, standard, & expanded notations
        • Convert between standard & expanded notation, fraction expansions, including real-world context
        • Convert between word, standard, & expanded notation, fraction expansions, including real-world context
    • Powers of Ten
      • Multiply whole numbers & powers of 10
      • Multiply decimal numbers & powers of 10
      • Multiply powers of 10 & products of one-digit whole numbers
      • Condensed: Multiply powers of 10 & products involving one-digit whole numbers, including real-world context
      • Multiply powers of 10 & product involving one-digit whole numbers, real-world context
      • Divide decimal numbers by powers of 10
      • Multiply & divide decimal numbers & powers of 10
      • Determine magnitudes of products of powers of 10
      • Determine magnitudes of products & quotients of powers of 10
      • Determine magnitudes of products of powers of 10, including negative exponents
      • Determine magnitudes of products & quotients of powers of 10, including negative exponents
  • Number Theory
    • Prime & Composite Numbers
      • Identify prime & composite numbers
      • Identify prime & composite numbers, real-world context
    • 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
    • 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
    • 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
    • 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
    • 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
  • Expressions
    • Translating Expressions
      • Identify words or phrases that indicate specified operation or comparison
      • Determine definitions of arithmetic vocabulary, fill in the blank
      • Interpret numerical expressions
      • Given phrase, determine one-step algebraic expression
      • Determine algebraic expressions that represent real-world situations
      • Determine algebraic expressions that represent real-world situations, including two-variable expressions
    • Simplifying Expressions
      • Basic Simplifying Expressions
        • Evaluate numerical expressions, #/# + #
        • Evaluate numerical expressions, # + #(#)
        • Evaluate numerical expressions, including rationals & up to two sets of grouping symbols
      • Application of Simplifying Expressions
        • Identify first steps in evaluating numerical expressions using grouping symbols
        • Identify equivalent expressions using order of operations
        • Identify equivalent algebraic expressions, including real-world context
        • Evaluate & identify equivalent numerical expressions, including real-world context
        • Evaluate numerical expressions, up to two sets of grouping symbols, real-world context
  • Equations
    • Properties of Equations
      • Identify properties used in numerical expressions
      • Identify properties used in numerical & algebraic expressions
    • Checking Equation 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 & constant on right side
      • Identify values that solve equations
    • Solving Equations
      • Basic Solving Equations
        • 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
        • Determine unknown whole number in multiplication & division equations
        • Solve one-step linear equations, rationals
      • Application of Solving Equations
        • Solve two-step equation with isolated variable, real-world context
    • Writing Equations
      • Determine one-step linear equations, real-world context
      • Determine one-step linear equations, real-world context
      • Determine one-step equations, including decimals, real-world context
      • Given one-step equation, identify real-world situation represented by equation
      • Identify multi-step equations, real-world context
    • Writing & Solving Equations
      • Determine, solve, & apply addition equations, real-world context
      • Determine & solve multiplication equations, real-world context
      • Determine, solve, & apply multiplication equations, real-world context
  • Patterns & Sequences
    • Verbal Descriptions
      • Identify relationships between patterns
      • Given description of pattern, determine first five terms
      • Given description of patterns, determine first five terms for each pattern
    • Function Tables
      • Determine missing elements in tables, addition
      • Determine missing elements in tables, subtraction
      • Determine missing elements in tables, multiplication
      • Determine specific element from pattern represented in table
      • Given table, determine relationship between input & output
      • Given table, determine & extend patterns, addition
      • Given table, determine & extend patterns, subtraction
      • Given table, determine & extend patterns, multiplication
      • Condensed: Given table, determine & extend patterns
    • Graphs
      • Given graph of linear points, identify table 
      • Given graph of linear points, identify table, real-world context
      • Given graph or table, identify additive or multiplicative patterns
      • Determine & complete equivalent representations of linear equations, tables, & graphs
    • Equations
      • Given linear equation, identify table, real-world context
      • Given linear equation, identify table, including decimals
      • Given linear equation, identify table, including decimals & fractions 
      • Given linear equation, identify table, including decimals & fractions, real-world context
      • Condensed: Identify equivalent linear equations, tables, & graphs, including real-world context
      • Given multiplicative relationship in table, determine equation, real-world context
  • Geometry
    • 2D Figures
      • Classify angles from figure
      • Classify triangle based on given angle measures
      • Classify triangles based on angles & sides
      • Classify quadrilaterals shapes based on attributes
      • Classify polygons based on angles & parallel or perpendicular lines
      • Classify polygons based on number of sides or relationship to other shapes
      • 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
    • Angles, Lines, & Rays
      • Identify angle names
      • Identify 90°, 180°, 270°, & 360° angles
      • Estimate angle measures
      • Identify types of angles in figures
      • Determine angle measures in figures
      • Given two angle measures in triangle, determine angle measure
      • Identify angles, lines, & segments in figures
      • Identify characteristics of points, lines, segments & rays from diagrams
      • Identify characteristics of points, lines, segments & rays from descriptions
      • Condensed: Identify characteristics of points, lines, segments & rays
    • Measure Angles
      • Identify angles with specified measures
      • Measure angles using protractor 
      • Measure angles using protractor, real-world context
    • Perimeter
      • Basic Perimeter
        • Determine perimeter of rectangles
        • Given sides of rectangle, determine perimeter
        • Condensed: Determine perimeter of rectangles, including real-world context
        • 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
        • Determine perimeter of rectangles, real-world context
        • Determine perimeter of rectangles, including decimal dimensions, real-world context
        • Given model, identify formula & determine perimeter of rectangles
        • Given model, identify formula & determine perimeter of rectangles, including decimal dimensions
        • Determine perimeter of polygons, including real-world context
        • Determine side length or perimeter of squares
        • Determine perimeter of composite figures containing rectangles & squares, including real-world context
    • Area
      • Rectangle & Parallelogram Area
        • Basic Area of Rectangles & Paralleograms
          • Given sides of rectangle, determine area, model provided
          • Given sides of rectangle, determine area
          • Given length & width of rectangle, determine area
          • Determine area of rectangles with fractional dimensions
          • Given area & one dimension of rectangle, determine missing dimension
          • Given area of rectangle & one dimension, determine other dimension
          • Determine area of parallelograms, model provided
          • Determine area of parallelograms
          • Given area & one dimension of parallelogram, determine missing dimension
          • Determine areas of rectangles & parallelograms
          • Given area, determine dimensions of rectangles & parallelograms
          • Condensed: Determine areas & dimensions of rectangles & parallelograms
        • Application of Area of Rectangles & Parallelograms
          • 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
          • Given sides of rectangle & cost per square unit, determine area & total cost, real-world context
          • Determine area of parallelograms using models that decompose & rearrange parts
          • Determine equations that represent area of parallelograms, real-world context
          • Determine area of missing dimension of rectangles, real-world context
          • Determine area of shaded region between nested rectangles
          • Given perimeter & relationship between sides, determine specific dimension
      • Triangle Area
        • Determine area of triangles using models that decompose & rearrange parts
        • Determine area of triangles, internal height
        • Determine area of triangles, external height
        • Determine area of triangles
        • Determine area of triangles, internal height, mixed numbers
        • Determine area of triangles, external height, mixed numbers
        • Determine area of triangles, mixed numbers
        • Determine equations that represent area of triangles, real-world context
        • Given area & one dimension of triangle, determine missing dimension
        • Given area & one dimension of triangle, determine missing dimension, mixed numbers
      • Trapezoid Area
        • Determine area of trapezoids using models that decompose & rearrange parts
        • Determine area of trapezoids
        • Determine equations that represent area of trapezoids, real-world context
        • Given area & base lengths of trapezoid, determine height
      • Mixed & Composite Figure Area
        • Determine areas of triangles & trapezoids
        • Condensed: Determine area using models that decompose & rearrange parts
        • Determine area of polygons in coordinate plane
        • Determine area of polygons in coordinate plane, real-world context
        • Given area, determine dimensions of triangles
        • Condensed: Determine areas & dimensions of triangles & trapezoids
        • Determine area of composite figures, rectangle with various figures attached, no circular parts
    • Area & Perimeter
      • Determine area or perimeter of parallelograms
      • Condensed: Identify formula & determine perimeter or area of rectangles & squares
      • Condensed: Determine equations that represent area of triangles & quadrilaterals, real-world context
      • Determine dimension of rectangles, including real-world context
    • Volume
      • Unit Cube Volume
        • Determine relationship between area, volume, & dimensions
        • Determine relationship between area, volume, square units, & cubic units
        • Determine volume of rectangular prisms using unit cubes
        • Determine volume of rectangular prisms using unit cubes
        • Determine volume of rectangular 3D figures using unit cubes
      • Basic Volume
        • Determine volume of rectangular prisms, whole numbers, volume less than 10,000
        • Determine volume of rectangular prisms, various representations
        • Determine volumes of rectangular prisms, fractional dimensions
        • Given base area & edge or all edges, determine volume of rectangular prism
        • Given volume, determine edges of rectangular prisms
        • Given volume, determine edge of rectangular prisms, up to four-digit dividend, up to two-digit divisor
        • Given volume, determine dimension of rectangular prism, fractional dimensions
        • Determine volume or edge of rectangular prisms, whole numbers, volume less than 10,000
        • Determine volume or edge of rectangular prisms, whole numbers
      • Application of Volume
        • Interpret volume of rectangular prisms, various representations
        • Determine volume of rectangular prisms, whole numbers, including real-world context
        • 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 & apply associative property to volume expressions
        • Condensed: Determine volume or dimension of rectangular prisms, fractional dimensions
        • Determine volume of composite rectangular prisms
    • Coordinate Plane
      • Basic Coordinate Plane
        • Determine coordinates of first quadrant points
        • Determine coordinates of first quadrant point, various scales
        • Plot first quadrant points
        • Plot first quadrant points, various scales
        • Determine coordinates of first quadrant rational points
        • 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
        • Identify description of process to plot first quadrant points
        • Identify first quadrant points or parts of coordinate plane
        • Identify locations or parts of coordinate plane using first quadrant points
        • 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
  • Measurement & Data
    • Conversions
      • Basic Conversions
        • Convert between metric units of weight & mass
        • Convert between metric units
        • Convert between metric units, real-world context
        • Convert between customary units of weight & mass
        • Convert between customary units of weight & mass
        • Convert between customary units of volume & capacity
        • Convert between customary units of volume & capacity
        • Convert between customary units of capacity
        • Convert between customary units of length
      • Application of One-Step Conversions
        • Convert between metric units, including real-world context
        • Given conversion chart, convert between metric units, real-world context
        • Convert between customary units, including real-world context
        • Convert between customary units of weight
        • Convert between metric units of weight & determine appropriate relative units
        • Convert between metric units of capacity & determine appropriate relative units
        • Determine equivalent measurements using table
      • Application of Multi-Step Conversions
        • Convert between customary units of length & determine appropriate relative units
        • Convert between metric units of length & determine appropriate relative units
        • Convert between customary units, real-world context
        • Condensed: Convert between customary units of length, weight, & capacity
        • Convert between metric units of weight & mass, real-world context
        • Convert between metric units of volume & capacity
        • Convert between metric units of length, real-world context
        • Condensed: Convert customary & metric units, real-world context
        • Convert between customary units to find sums or differences, including real-world context
    • Application of Measurement
      • Determine appropriate units or estimated measurement for specified situation
      • Add, subtract, & multiply integer masses, metric units, real-world context
      • Solve problems involving interpretation of various visual diagrams
      • Add & subtract decimal distances, metric units, real-world context
      • Perform operations with money
      • Add, subtract, multiply, & divide liquid volumes, real-world context
      • Condensed: Perform operations with money or units of measurement, real-world context
    • Time
      • Determine time intervals
      • Convert between units of time, days, hours, minutes, & seconds
      • Convert between units of time, days, weeks, months, & years
      • Condensed: Convert between units of time
      • Condensed: Convert between units of time & determine time intervals
  • Charts & Graphs
    • Translating Charts & Graphs
      • Given data, identify stem-and-leaf plot
      • Given data, identify stem-and-leaf plot
      • Given data represented in various ways, identify dot plot
      • Given bar graph, determine equivalent table
      • Given table, determine equivalent bar graph
      • Given table, determine equivalent bar graph, including double bar graphs
      • Condensed: Given bar graph, determine equivalent table or pictograph
      • Identify equivalent representations of data in tables & scatter plots
      • Given data, identify frequency table or determine missing element of table
      • Given data, determine statistical display
      • Given data, determine scatter plot
    • Interpreting Charts & Graphs
      • Stem-&-Leaf Plots
        • Solve one-step problems from stem-and-leaf plots, real-world context
        • Solve multi-step problems from stem-and-leaf plots, real-world context
      • Frequency Tables
        • Solve one-step problems from frequency tables, real-world context
        • Solve one-step problems from frequency & relative frequency tables, real-world context
        • Solve problems from frequency tables, real-world context
        • Solve multi-step problems from frequency tables, real-world context
      • Line Plots
        • Solve one-step problems from dot plots, real-world context
        • Solve problems involving dot plots
        • Add or subtract fractions from line plots, common denominator
        • Solve problems involving line plots & fractions
        • Solve multi-step problems from dot plots, real-world context
      • Bar & Double 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
      • Scatter Plots
        • Solve one-step problems from scatter plots, real-world context
        • Solve multi-step problems from scatter plots, real-world context
      • Mixed Charts & Graphs
        • Solve problems involving interpretation of various 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
    • Mean, Median, Mode, & Range
      • Identify definition of mean, median, mode, or range
      • Determine mean from dot plots
      • Determine median from dot plots
      • Determine mean, median, mode, or range
      • Determine mean, median, mode, or range from stem-&-leaf plots
      • Determine mean, median, mode, or range from various graphs
      • Condensed: Determine mean, median, mode, or range, including graphs
      • Determine mean, median, mode, & range
      • Determine mean, median, mode, & range from stem-&-leaf plots
    • Statistical Data
      • Identify statistical questions
      • Determine whether data was counted or measured
      • Determine whether data is categorical or numerical
      • Identify biased samples & questions
      • Identify samples & populations
    • Basic Probability
      • Classify probabilities by levels of likelihood
      • Determine sample spaces
      • Determine probabilities of single events
      • Determine theoretical probabilities, fraction answers
      • Determine experimental probabilities, fraction answers
      • Determine probabilities & complementary probabilities of single events, including visual models
      • Determine predicted values, experimental probability
      • Determine number of combinations using fundamental counting principle, real-world context
      • Determine number of combinations using fundamental counting principle, including repeated letters & digits, real-world context
  • Financial Literacy
    • Identify various types of taxes
    • Identify & determine gross & net incomes
    • Balance & determine components of transaction register
    • Identify actions to balance budget
    • Determine amounts to balance budget
    • Identify advantages & disadvantages of various payment methods