5th Grade Skills
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Whole Numbers
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Addition of Whole Numbers
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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
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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
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Subtraction of Whole Numbers
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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
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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
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Multiplication of Whole Numbers
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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
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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
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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
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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
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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
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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
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Division of Whole Numbers
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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
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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
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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
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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
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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
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Mixed Operations of Whole Numbers
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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
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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
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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
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Rounding & Estimating Whole Numbers
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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
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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
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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
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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
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Fractions
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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
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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
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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
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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
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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
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Converting Fractions
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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
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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
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Addition of Fractions
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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
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Application of Addition of Fractions, Common Denominators
- Condensed: Add fractions, common denominators, including real-world context
- Add fractions, common denominators, real-world context
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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
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Subtraction of Fractions
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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
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Application of Subtraction of Fractions, Common Denominators
- Condensed: Subtract fractions, common denominators, including real-world context
- Subtract fractions, common denominators, real-world context
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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
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Addition & Subtraction of Fractions
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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
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Basic Addition & Subtraction of Fractions, Common Denominators
- Condensed: Add or subtract fractions, common denominators, unreduced
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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
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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
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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
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Application of Addition & Subtraction of Fractions, Different Denominators
- Add & subtract fractions, real-world context
- Add or subtract fractions, including estimation, real-world context
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Multiplication of Fractions
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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
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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
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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
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Division of Fractions
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Reciprocals
- Determine reciprocals of whole numbers or fractions
- Determine equivalent division & multiplication expressions using reciprocals
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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
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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
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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
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Decimals
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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
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Comparing & Ordering Decimals
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Modeling, Comparing, & Ordering Decimals
- Compare decimal models
- Compare decimal models, up to three models
- Order decimal models
- Condensed: Compare or order decimal models
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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
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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
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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
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Addition of Decimals
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Basic Addition of Decimals
- Add decimals, positive, up to two decimal places
- Add positive decimals, up to three decimal places
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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
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Subtraction of Decimals
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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
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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
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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
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Multiplication of Decimals
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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
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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
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Division of Decimals
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Basic Division of Decimals
- Divide four-digit dividends by two-digit whole number divisors
- Divide decimals by whole numbers, up to two decimal places
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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
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Rounding & Estimating Decimals
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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
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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
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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
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Number Sense
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Place Value
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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
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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
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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
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Number Forms
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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
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Standard Number Forms
- Given whole number in word form, determine standard notation
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Word Number Forms
- Given number in word form, determine standard notation
- Convert numbers to word form, up to 1,000,000
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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
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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
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Number Theory
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Prime & Composite Numbers
- Identify prime & composite numbers
- Identify prime & composite numbers, real-world context
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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
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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
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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
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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
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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
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Expressions
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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
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Simplifying Expressions
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Basic Simplifying Expressions
- Evaluate numerical expressions, #/# + #
- Evaluate numerical expressions, # + #(#)
- Evaluate numerical expressions, including rationals & up to two sets of grouping symbols
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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
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Equations
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Properties of Equations
- Identify properties used in numerical expressions
- Identify properties used in numerical & algebraic expressions
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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
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Solving Equations
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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
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Application of Solving Equations
- Solve two-step equation with isolated variable, real-world context
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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
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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
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Patterns & Sequences
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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
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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
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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
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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
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Geometry
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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
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3D Figures
- Identify 3D figures & their bases
- Identify equivalent representations of 3D figures & nets
- Determine 2D orthographic representation of 3D blocks
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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
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Measure Angles
- Identify angles with specified measures
- Measure angles using protractor
- Measure angles using protractor, real-world context
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Perimeter
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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
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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
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Area
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Rectangle & Parallelogram Area
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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
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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
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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
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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
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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
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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
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Volume
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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
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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
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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
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Coordinate Plane
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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
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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
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Measurement & Data
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Conversions
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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
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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
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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
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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
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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
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Charts & Graphs
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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
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Interpreting Charts & Graphs
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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
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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
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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
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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
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Scatter Plots
- Solve one-step problems from scatter plots, real-world context
- Solve multi-step problems from scatter plots, real-world context
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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
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Probability & Statistics
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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
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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
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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
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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