5th Grade Skills

Whole Numbers

Addition of Whole Numbers

Basic Addition of Whole Numbers
 Add positive integers, up to two digits
 Add three & fourdigit whole numbers
 Condensed: Add fourdigit & three or fourdigit whole numbers
 Add fourdigit whole numbers

Application of Addition of Whole Numbers
 Add whole numbers, up to two digits, realworld context
 Add three & fourdigit whole numbers, realworld context
 Add fourdigit whole numbers, realworld context
 Add fivedigit whole numbers, realworld context
 Condensed: Add whole numbers, up to five digits, realworld context
 Condensed: Add whole numbers, up to five digits, including realworld context
 Add five or sixdigit whole numbers, realworld context


Subtraction of Whole Numbers

Basic Subtraction of Whole Numbers
 Subtract positive integers, up to two digits, positive difference
 Subtract whole numbers, fourdigit & threedigit
 Subtract whole numbers, fourdigit & threedigit
 Subtract whole numbers, three or fourdigit & two to fourdigit
 Condensed: Subtract whole numbers, fourdigit & three or fourdigit
 Subtract whole numbers, fourdigit & fourdigit
 Subtract whole numbers, fivedigit & four or fivedigit
 Condensed: Subtract whole numbers, four to sixdigit & two to fivedigit
 Subtract whole numbers, sevendigit & six or sevendigit

Application of Subtraction of Whole Numbers
 Subtract whole numbers, fivedigit & four or fivedigit, realworld context
 Subtract whole numbers, sixdigit & five or sixdigit, realworld context
 Subtract whole numbers, sevendigit & six or sevendigit, realworld context
 Condensed: Subtract whole numbers, four to sevendigit & three to sixdigit, including realworld context
 Condensed: Subtract whole numbers, four to sevendigit & three to sixdigit, including realworld context
 Condensed: Subtract whole numbers, four to sevendigit & three to sixdigit, realworld context


Multiplication of Whole Numbers

Modeling Multiplication of Whole Numbers
 Multiply whole numbers using area models, up to fourdigit & onedigit
 Multiply whole numbers by decomposing factors, up to fourdigit & onedigit
 Condensed: Multiply whole numbers using area models or decomposition, up to fourdigit & onedigit
 Multiply whole numbers using area models, twodigit & twodigit
 Condensed: Multiply whole numbers using area models or decomposition, twodigit & twodigit

Basic Multiplication of Whole Numbers
 Multiply whole numbers, twodigit & onedigit
 Multiply whole numbers, both up to 19
 Multiply multiples of 10 & twodigit whole numbers
 Multiply whole numbers, twodigit & twodigit
 Multiply whole numbers by decomposing factors, twodigit & twodigit

Basic Multiplication of Whole Numbers, Three or FourDigit
 Multiply whole numbers, threedigit & onedigit
 Multiply whole numbers, fourdigit & onedigit
 Condensed: Multiply whole numbers, three or fourdigit & onedigit
 Multiply whole numbers, twodigit & two or threedigit
 Multiply whole numbers, threedigit & twodigit
 Multiply whole numbers, both up to three digits
 Condensed: Multiply whole numbers, three or fourdigit & twodigit
 Condensed: Multiply whole numbers, up to fourdigit & up to threedigit, no more than six total digits

Application of Multiplication of Whole Numbers
 Multiply whole numbers, twodigit & onedigit, realworld context
 Multiply whole numbers, threedigit & onedigit, realworld context
 Multiply whole numbers, fourdigit & onedigit, realworld context
 Condensed: Multiply whole numbers, onedigit & up to fourdigit, realworld context
 Multiply whole numbers, twodigit & twodigit, realworld context
 Condensed: Multiply whole numbers, one or twodigit & up to fourdigit, realworld context
 Multiply whole numbers, threedigit & twodigit, including addition or subtraction step, realworld context

Products of Ten & One Hundred
 Multiply 100 & twodigit whole numbers
 Condensed: Multiply whole numbers, twodigit & 10 or 100
 Multiply multiples of 10 & onedigit whole numbers, realworld context
 Multiply multiples of 100 & onedigit whole numbers, realworld context
 Condensed: Multiply multiples of 10 or 100 & onedigit whole numbers, realworld context
 Condensed: Multiply multiples of 10 or 100 & one or twodigit whole numbers, including realworld 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, realworld 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 twodigit dividends, divisor 2, 3, 4, 5, 6, 9, 10
 Determine division equations, realworld context

Basic Division of Whole Numbers, OneDigit Divisor
 Divide whole numbers, up to threedigit dividend, onedigit divisor
 Determine quotient & remainder, onedigit dividend, onedigit divisor
 Determine quotient & remainder, twodigit dividend, onedigit divisor
 Determine quotient & remainder, threedigit dividend, onedigit divisor
 Determine quotient & remainder, fourdigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, onedigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, twodigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, threedigit dividend, onedigit divisor
 Determine quotient & remainder as fraction, fourdigit dividend, onedigit divisor

Basic Division of Whole Numbers, Up to ThreeDigit Dividend & TwoDigit Divisor
 Determine quotient & remainder, twodigit dividend, twodigit divisor
 Condensed: Determine quotient & remainder, twodigit dividend, up to twodigit divisor
 Determine quotient & remainder, threedigit dividend, twodigit divisor
 Condensed: Determine quotient & remainder, threedigit dividend, up to twodigit divisor
 Determine quotient & remainder as fraction, twodigit dividend, twodigit divisor
 Condensed: Determine quotient & remainder as fraction, twodigit dividend, up two twodigit divisor
 Determine quotient & remainder as fraction, threedigit dividend, twodigit divisor
 Condensed: Determine quotient & remainder as fraction, threedigit dividend, up two twodigit divisor

Basic Division of Whole Numbers, Four or FiveDigit Dividend & TwoDigit Divisor
 Divide whole numbers, up to fivedigit dividend, up to twodigit divisor
 Determine quotient & remainder, fourdigit dividend, twodigit divisor
 Condensed: Determine quotient & remainder, up to fourdigit dividend & twodigit divisor
 Condensed: Determine quotient & remainder, fourdigit dividend, up to twodigit divisor
 Determine quotient & remainder as fraction, fourdigit dividend, twodigit divisor
 Condensed: Determine quotient & remainder as fraction, fourdigit dividend, up two twodigit divisor

Application of Division of Whole Numbers
 Divide positive integers, up to fourdigit dividend, onedigit divisor, realworld context
 Determine quotient or remainder, up to fourdigit dividend, onedigit divisor, realworld context
 Divide positive integers, up to fourdigit dividend, up to twodigit divisor, realworld context
 Determine quotient, up to fourdigit dividend, up to twodigit divisor, realworld context
 Condensed: Divide whole numbers, up to fourdigit dividend, up to twodigit divisor, including realworld context
 Divide positive integers for decimal result, realworld context


Mixed Operations of Whole Numbers

Diagrams of Mixed Operations of Whole Numbers
 Solve multistep problems involving models & whole number operations, initially add, realworld context
 Solve multistep problems involving models & whole number operations, initially subtract, realworld context
 Solve multistep problems involving models & whole number operations, initially multiply, realworld context
 Solve multistep problems involving models & whole number operations, initially divide, realworld context
 Condensed: Solve multistep problems involving models & whole number operations, realworld context
 Condensed: Solve multistep problems involving equations, models, & whole number operations, realworld context

Equations of Mixed Operations of Whole Numbers
 Solve multistep problems involving equations & whole number operations, initially add, realworld context
 Solve multistep problems involving equations & whole number operations, initially subtract, realworld context
 Solve multistep problems involving equations & whole number operations, initially multiply, realworld context
 Solve multistep problems involving equations & whole number operations, initially divide, realworld context
 Condensed: Solve multistep problems involving equations & whole number operations, realworld context

Application of Mixed Operations of Whole Numbers
 Add or subtract whole numbers, realworld context
 Solve multistep problems involving whole number operations, initially add, realworld context
 Solve multistep problems involving models & whole number operations, initially add, realworld context
 Solve multistep problems involving whole number operations, initially subtract, realworld context
 Solve multistep problems involving whole number operations, initially multiply, realworld context
 Solve multistep problems involving whole number operations, initially divide, realworld context
 Solve multistep problems involving division of positive integers, realworld context
 Solve multistep problems involving operations with whole numbers
 Condensed: Solve multistep problems involving whole number operations, realworld 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 frontend rounding
 Round whole numbers to specified place value, up to hundredthousand

Application of Rounding & Estimating Whole Numbers
 Round whole numbers to nearest ten, realworld context
 Round whole numbers to nearest hundred, realworld context
 Round whole numbers to nearest thousand, realworld context
 Condensed: Round whole numbers to nearest ten, hundred, & thousand, realworld context
 Condensed: Round whole numbers to nearest ten, hundred, & thousand, including realworld context

Application of Estimating Whole Numbers
 Estimate sums of whole numbers, up to six digits, including realworld context
 Estimate sum of rational numbers, round both to nearest whole, realworld context
 Estimate differences of whole numbers, up to six digits, including realworld context
 Estimate sums & differences of whole numbers by rounding to specified place values
 Estimate products of whole numbers, twodigit factor times onedigit factor
 Condensed: Estimate sums, differences, & products of whole numbers
 Identify division expression to estimate quotient using compatible numbers, realworld context
 Estimate quotients of whole numbers, up to sixdigit dividend, up to threedigit divisor
 Determine division expression to estimate quotient using compatible numbers


Comparing & Ordering Whole Numbers
 Compare two positive integers
 Compare threedigit whole numbers
 Compare fourdigit whole numbers
 Compare fivedigit whole numbers
 Compare sixdigit whole numbers
 Compare whole numbers up to 1,000,000,000
 Order whole numbers up to 1,000,000,000, including realworld context
 Condensed: Order whole numbers, up to 1,000,000,000, including realworld context
 Order whole numbers up to 1,000,000,000, realworld 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 onehalf & 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, realworld context
 Condensed: Decompose fractions or mixed numbers into sum of fractions, including visual models & realworld 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, realworld 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 realworld 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 realworld context
 Add fractions, common denominators, realworld 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 realworld context
 Subtract fractions, common denominators, realworld 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 realworld context
 Condensed: Add or subtract fractions, common denominators, realworld 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, realworld context
 Add or subtract fractions, including estimation, realworld 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, realworld context
 Multiply fractions, positive, realworld context
 Multiply mixed numbers & proper fractions, visual models, realworld context
 Multiply mixed numbers & proper fractions, realworld context
 Condensed: Identify models or multiply whole numbers & fractions using area models
 Determine part of whole using fraction multiplication, including visual models, including realworld 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, realworld context
 Compare products of fractions, mixed numbers, & whole numbers, including realworld 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, realworld context
 Condensed: Divide whole numbers & fractions, various models
 Divide fractions & mixed numbers, positive, realworld context
 Determine fraction & mixed number equivalence of division problems, realworld 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 realworld context
 Compare decimals up to two decimal places & justify relationship, including realworld context
 Compare decimals written in word form, up to three decimal places
 Compare numbers, up to fourdigit whole numbers or threedigit 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 sixdigit whole numbers

Application of Comparing & Ordering Decimals
 Compare decimals up to three decimal places
 Compare decimals up to three decimal places, realworld context
 Order decimals up to two decimal places, including realworld context
 Order decimals up to three decimal places, including realworld context
 Order decimals from table of place values, realworld context
 Condensed: Compare or order numbers up to 1,000,000,000
 Compare & order decimals up to 1,000,000,000, realworld context
 Condensed: Compare or order decimals, up to three decimal places, including realworld context


Converting Decimals
 Convert decimals to fractions
 Convert decimals to fractions, realworld context
 Convert decimals to mixed numbers
 Convert decimals to fractions or mixed numbers
 Condensed: Determine & identify equivalent fractions & decimals, including models, including realworld 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 realworld context
 Add decimals, positive, up to two decimal places, realworld 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 realworld context
 Subtract decimals, up to two decimal places, realworld context
 Make change


Addition & Subtraction of Decimals
 Condensed: Add & subtract decimals, up to two decimal places
 Add & subtract decimals, up to two decimal places, realworld context
 Condensed: Add & subtract decimals, up to two decimal places, including realworld context
 Condensed: Add & subtract decimals, up to two decimal places, realworld context
 Condensed: Add & subtract rational numbers, realworld context

Multiplication of Decimals

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

Application of Multiplication of Decimals
 Determine equivalence between area models & multiplication equations
 Determine equivalence between base10 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, realworld context


Division of Decimals

Basic Division of Decimals
 Divide fourdigit dividends by twodigit 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, realworld context
 Divide fourdigit dividends by twodigit whole number divisors, including realworld context
 Identify base10 model that represents quotient of decimal division
 Determine equivalence of base10 model & components of decimal division
 Determine equivalence of base10 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 realworld context
 Given number line model representing decimal division, interpret model & determine quotient, including realworld context
 Condensed: Given model representing decimal division, interpret model & determine quotient, including realworld context


Rounding & Estimating Decimals

Basic Rounding & Estimating Decimals
 Round decimal numbers to nearest whole, tenth, & hundredth
 Round decimal numbers to nearest tenth & hundredth, including realworld context
 Round decimal numbers to nearest whole, tenth, hundredth, & thousandth
 Round decimal numbers to nearest whole, tenth, hundredth, & thousandth, including realworld 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, realworld context
 Round decimal numbers to nearest tenth & hundredth, realworld context
 Round numbers to nearest whole, ten, hundred, & thousand, realworld context
 Round decimal numbers to nearest tenth, hundredth, & thousandth, realworld context
 Condensed: Round decimal numbers to nearest whole, tenth, & hundredth, including realworld context
 Determine sums & differences of decimals then round solution, realworld context
 Estimate quotients of decimals & whole numbers using compatible numbers
 Estimate solutions involving all operations, realworld context
 Estimate sums, differences, products, or quotients of rational numbers
 Estimate sums, differences, products, or quotients of rational numbers, realworld 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 tenthousands place, including comparison to other place values
 Determine values of digit in hundredthousands 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, realworld 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, realworld context
 Convert between word, standard, & expanded notations, including realworld 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 realworld context
 Convert between word, standard, & expanded notation, fraction expansions, including realworld context


Powers of Ten
 Multiply whole numbers & powers of 10
 Multiply decimal numbers & powers of 10
 Multiply powers of 10 & products of onedigit whole numbers
 Condensed: Multiply powers of 10 & products involving onedigit whole numbers, including realworld context
 Multiply powers of 10 & product involving onedigit whole numbers, realworld 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, realworld 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 nonfactors of whole numbers
 Identify multiples or nonmultiples of whole numbers
 Identify factors or multiples of whole numbers
 Condensed: Identify factors, nonfactors, multiples, & nonmultiples 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, realworld context

Least Common Multiples
 Determine LCM of two numbers up to 100
 Determine LCM of two numbers up to 100 or multiples of 10
 Determine LCMs, realworld context

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


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 onestep algebraic expression
 Determine algebraic expressions that represent realworld situations
 Determine algebraic expressions that represent realworld situations, including twovariable 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 realworld context
 Evaluate & identify equivalent numerical expressions, including realworld context
 Evaluate numerical expressions, up to two sets of grouping symbols, realworld 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 onestep linear equations, rationals

Application of Solving Equations
 Solve twostep equation with isolated variable, realworld context


Writing Equations
 Determine onestep linear equations, realworld context
 Determine onestep linear equations, realworld context
 Determine onestep equations, including decimals, realworld context
 Given onestep equation, identify realworld situation represented by equation
 Identify multistep equations, realworld context

Writing & Solving Equations
 Determine, solve, & apply addition equations, realworld context
 Determine & solve multiplication equations, realworld context
 Determine, solve, & apply multiplication equations, realworld 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, realworld 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, realworld context
 Given linear equation, identify table, including decimals
 Given linear equation, identify table, including decimals & fractions
 Given linear equation, identify table, including decimals & fractions, realworld context
 Condensed: Identify equivalent linear equations, tables, & graphs, including realworld context
 Given multiplicative relationship in table, determine equation, realworld 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, realworld context

Perimeter

Basic Perimeter
 Determine perimeter of rectangles
 Given sides of rectangle, determine perimeter
 Condensed: Determine perimeter of rectangles, including realworld 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, realworld context
 Determine perimeter of rectangles, including decimal dimensions, realworld 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 realworld context
 Determine side length or perimeter of squares
 Determine perimeter of composite figures containing rectangles & squares, including realworld 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, realworld context
 Determine area of parallelograms using models that decompose & rearrange parts
 Determine equations that represent area of parallelograms, realworld context
 Determine area of missing dimension of rectangles, realworld 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, realworld 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, realworld 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, realworld 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, realworld context
 Determine dimension of rectangles, including realworld 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 fourdigit dividend, up to twodigit 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 realworld context
 Determine volume of rectangular prisms using repeated layers of base area, realworld context
 Determine volume of rectangular prisms using various representations of cubic units, realworld context
 Determine volume of rectangular prisms & apply associative property to volume expressions
 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, realworld context
 Determine or identify first quadrant points, including cardinal directions, realworld 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, realworld 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 OneStep Conversions
 Convert between metric units, including realworld context
 Given conversion chart, convert between metric units, realworld context
 Convert between customary units, including realworld 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 MultiStep 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, realworld context
 Condensed: Convert between customary units of length, weight, & capacity
 Convert between metric units of weight & mass, realworld context
 Convert between metric units of volume & capacity
 Convert between metric units of length, realworld context
 Condensed: Convert customary & metric units, realworld context
 Convert between customary units to find sums or differences, including realworld context


Application of Measurement
 Determine appropriate units or estimated measurement for specified situation
 Add, subtract, & multiply integer masses, metric units, realworld context
 Solve problems involving interpretation of various visual diagrams
 Add & subtract decimal distances, metric units, realworld context
 Perform operations with money
 Add, subtract, multiply, & divide liquid volumes, realworld context
 Condensed: Perform operations with money or units of measurement, realworld 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 stemandleaf plot
 Given data, identify stemandleaf 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 onestep problems from stemandleaf plots, realworld context
 Solve multistep problems from stemandleaf plots, realworld context

Frequency Tables
 Solve onestep problems from frequency tables, realworld context
 Solve onestep problems from frequency & relative frequency tables, realworld context
 Solve problems from frequency tables, realworld context
 Solve multistep problems from frequency tables, realworld context

Line Plots
 Solve onestep problems from dot plots, realworld context
 Solve problems involving dot plots
 Add or subtract fractions from line plots, common denominator
 Solve problems involving line plots & fractions
 Solve multistep problems from dot plots, realworld context

Bar & Double Bar Graphs
 Solve onestep problems from bar graphs, realworld context
 Solve onestep problems from double bar graphs, realworld context
 Add, subtract, & multiply fractions in bar graphs, common denominator
 Solve multistep problems from bar graphs, realworld context
 Solve multistep problems from double bar graphs, realworld context

Scatter Plots
 Solve onestep problems from scatter plots, realworld context
 Solve multistep problems from scatter plots, realworld context

Mixed Charts & Graphs
 Solve problems involving interpretation of various graphs
 Condensed: Solve onestep problems from various plots, graphs, & tables, realworld context
 Condensed: Solve multistep problems from various plots, graphs, & tables, realworld 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, realworld context
 Determine number of combinations using fundamental counting principle, including repeated letters & digits, realworld 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