6th 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 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 three- & four-digit whole numbers, real-world context
- Add four-digit whole numbers, real-world context
- Condensed: Add whole numbers, up to five digits, including real-world context
- Condensed: Add whole numbers, up to five digits, real-world context
- Add five-digit whole numbers, real-world context
- Add five- or six-digit whole numbers, real-world context
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Subtraction of Whole Numbers
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Basic Subtraction of Whole Numbers
- Subtract whole numbers, four-digit & three-digit
- Condensed: Subtract whole numbers, four-digit & three- or four-digit
- Subtract whole numbers, five-digit & four- or five-digit
- Condensed: Subtract whole numbers, four- to six-digit & two- to five-digit
- Subtract whole numbers, six- or seven-digit & up to six digits
- Subtract whole numbers, seven-digit & six- or seven-digit
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Application of Subtraction of Whole Numbers
- Subtract whole numbers, four-digit & three- or four-digit, real-world context
- Subtract whole numbers, five-digit & four- or five-digit, real-world context
- Subtract whole numbers, six-digit & five- or six-digit, real-world context
- Subtract whole numbers, seven-digit & six- or seven-digit, real-world context
- Condensed: Subtract whole numbers, four- to seven-digit & three- to six-digit, including real-world context
- Condensed: Subtract whole numbers, four- to seven-digit & three- to six-digit, including real-world context
- Condensed: Subtract whole numbers, four- to seven-digit & three- to six-digit, real-world context
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Multiplication of Whole Numbers
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Application & Modeling of Multiplication of Whole Numbers
- Condensed: Multiply whole numbers, one-digit & up to four-digit, real-world context
- Condensed: Multiply whole numbers, one- or two-digit & up to four-digit, real-world context
- Condensed: Multiply whole numbers using area models or decomposition, up to four-digit & one-digit
- Condensed: Multiply whole numbers using area models or decomposition, two-digit & two-digit
- Multiply whole numbers, three-digit & two-digit, including addition or subtraction step, real-world context
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Basic Multiplication of Whole Numbers
- Condensed: Multiply whole numbers, three- or four-digit & one-digit
- Multiply whole numbers, two-digit & two-digit
- Multiply whole numbers by decomposing factors, two-digit & two-digit
- Multiply whole numbers, two-digit & two- or three-digit
- Multiply whole numbers, three-digit & two-digit
- Condensed: Multiply whole numbers, three- or four-digit & two-digit
- Multiply whole numbers, four-digit & two-digit
- Multiply whole numbers, both up to three digits
- Condensed: Multiply whole numbers, up to four-digit & up to three-digit, no more than six total digits
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Multiplicative Comparisons of Whole Numbers
- Solve problems involving multiplicative comparisons
- Solve problems involving multiplicative & additive comparisons of whole numbers
- Solve problems involving multiplicative & additive comparisons
- Condensed: Solve problems involving division of positive integers & multiplicative & additive comparisons, real-world context
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Division of Whole Numbers
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Basic Division of Whole Numbers
- Apply divisibility rules to two-digit dividends, divisor 2, 3, 4, 5, 6, 9, 10
- Condensed: Determine quotient & remainder, two-digit dividend, up to two-digit divisor
- Condensed: Determine quotient & remainder, three-digit dividend, up to two-digit divisor
- Condensed: Determine quotient & remainder, four-digit dividend, up to two-digit divisor
- Condensed: Determine quotient & remainder as fraction, two-digit dividend, up two two-digit divisor
- Condensed: Determine quotient & remainder as fraction, three-digit dividend, up two two-digit divisor
- Condensed: Determine quotient & remainder as fraction, four-digit dividend, up two two-digit divisor
- Divide whole numbers with decimal quotient, up to three-digit dividend, up to three-digit divisor
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Application of Division of Whole Numbers
- Determine division equations, real-world context
- Determine equivalence between area models & division equations
- Determine equivalence between arrays & division equations
- Condensed: Determine equivalence between models & division equations
- Divide positive integers, up to four-digit dividend, one-digit divisor, real-world context
- Divide positive integers, up to four-digit dividend, up to two-digit divisor, real-world context
- Determine quotient, up to four-digit dividend, up to two-digit divisor, real-world context
- Determine quotient or remainder, up to four-digit dividend, one-digit divisor, real-world context
- Divide positive integers for decimal result, real-world context
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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
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Equations of Mixed Operations of Whole Numbers
- Solve two-step equation with isolated variable, real-world context
- Identify multi-step equations, real-world context
- Solve multi-step problems involving equations & whole number operations, initially add, real-world context
- Solve multi-step problems involving equations & whole number operations, initially subtract, real-world context
- Solve multi-step problems involving equations & whole number operations, initially multiply, real-world context
- Solve multi-step problems involving equations & whole number operations, initially divide, real-world context
- Condensed: Solve multi-step problems involving equations & whole number operations, real-world context
- Determine & solve two-step equations with isolated variable, real-world context
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Diagrams & Equations of Mixed Operations of Whole Numbers
- Condensed: Solve multi-step problems involving equations, models, & whole number operations, real-world context
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Application of Mixed Operations of Whole Numbers
- Determine & evaluate addition or subtraction expressions, real-world context
- Solve multi-step problems involving whole number operations, initially add, real-world context
- Solve multi-step problems involving whole number operations, initially subtract, real-world context
- Solve multi-step problems involving whole number operations, initially multiply, real-world context
- Solve multi-step problems involving whole number operations, initially divide, real-world context
- Solve multi-step problems involving division of positive integers, real-world context
- Solve multi-step problems involving operations with whole numbers
- Condensed: Solve multi-step problems involving whole number operations, real-world context
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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 Whole Numbers
- Round whole numbers to nearest ten, real-world context
- Round whole numbers to nearest hundred, real-world context
- Round whole numbers to nearest thousand, real-world context
- Condensed: Round whole numbers to nearest ten, hundred, & thousand, including real-world context
- Condensed: Round whole numbers to nearest ten, hundred, & thousand, real-world context
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Application of Estimating Whole Numbers
- Estimate sums of whole numbers, up to six digits, including real-world context
- Estimate differences of whole numbers, up to six digits, including real-world context
- Estimate sums & differences of whole numbers by rounding to specified place values
- Estimate products of whole numbers, two-digit factor times one-digit factor
- Estimate quotients of whole numbers, up to six-digit dividend, up to three-digit divisor
- Condensed: Estimate sums, differences, & products of whole numbers
- Estimate sum of rational numbers, round both to nearest whole, real-world context
- Determine division expression to estimate quotient using compatible numbers
- Identify division expression to estimate quotient using compatible numbers, real-world context
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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
- 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
- Identify fractions or mixed numbers on decimal grid
- Identify fractions on strip diagrams
- Identify common fractions or mixed numbers on number line
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Equivalent Fractions
- Determine how many fraction parts are in whole
- Determine equivalent fractions, strip diagrams
- Determine equivalent fractions, number lines
- Determine equivalent fractions, area models
- Determine equivalent fraction equations, area models
- Determine equivalent fraction components
- Identify or determine equivalent fraction components or fractions
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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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Converting Fractions
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Converting Fractions to Decimals
- Given model, determine fraction & decimal equivalents, unreduced
- Identify decimal equivalent of fractions, real-world context
- Convert fractions to decimals, denominator power of 10
- Convert fractions to decimals, denominator factor of power of 10
- Convert fractions to decimals, denominator factor of 100
- Convert fractions to decimals, real-world context
- Convert fractions to decimals, up to two decimal places, real-world context
- Convert fractions to rounded decimals
- Convert fractions to decimals, including improper fractions, including repeating decimals
- Convert mixed numbers to decimals, including repeating decimals
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Converting Improper Fractions & Mixed Numbers
- Convert mixed numbers to improper fractions, denominators less than 10
- Convert mixed numbers to improper fractions, includes denominators more than 10
- Convert whole numbers to improper fractions
- Convert improper fractions to mixed numbers, whole part up to 3
- Convert improper fractions to mixed numbers, whole part up to 12
- Condensed: Convert between improper fractions & mixed numbers
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Converting Fractions to Percents
- Convert fractions to percents, denominator factor of 100
- Convert fractions to percents, denominator factor of 100, rounding directions
- Convert fractions to rounded percents
- Convert improper fractions to rounded percents
- Convert fractions to mixed number percents
- Convert fractions to mixed number percents over 100
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Comparing & Ordering Fractions
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Modeling Comparing Fractions
- Determine equivalent fractions, strip diagrams
- Compare two fractions, different denominators, number lines
- Compare two fractions, different denominators, strip diagrams
- Compare two fractions, different denominators, area models
- Compare fractions, different denominators, visual model
- Compare fractions, denominators less than 10
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Basic Comparing & Ordering Fractions
- Compare fractions, denominators less than 10
- Compare fractions, denominators less than 30
- Compare fractions between one-half & one
- Compare fractions, same numerators, denominators differ by one, denominators less than 10,000
- Compare fractions, different denominators
- Order positive fractions
- Determine equivalent fractions, strip diagrams
- Compare two fractions, different denominators, area models
- Compare two fractions, different denominators, number lines
- Compare two fractions, different denominators, strip diagrams
- Compare fractions, denominators less than 10
- Compare fractions, denominators less than 30
- Compare fractions between one-half & one
- Compare fractions, same numerators, denominators differ by one, denominators less than 10,000
- Compare fractions, different denominators
- Compare fractions, different denominators, visual model
- Order positive fractions
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Addition of Fractions
- Condensed: Add fractions, common denominators, including real-world context
- Add fractions, common denominators, real-world context
- Add fractions, denominators of 10 & 100
- Add fractions, one denominator multiple of other, including improper sums
- Add fractions, one denominator multiple of other, including mixed number sums
- Add fractions, different denominators, including improper sums
- Add fractions, different denominators, including mixed number sums
- Add mixed numbers, different denominators
- Add mixed numbers, different denominators, fractional sum greater than one
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Subtraction of Fractions
- Subtract fractions, one denominator multiple of other, proper fraction difference
- Subtract fractions, one denominator multiple of other, including improper differences
- Subtract fractions, different denominators, positive proper differences
- Subtract fractions, different denominators, including mixed number differences
- Subtract mixed numbers, different denominators
- Subtract mixed numbers, different denominators, borrowing required
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Mixed Addition & Subtraction of Fractions
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Modeling & Application of Mixed Addition & Subtraction of Fractions
- Identify expressions that represent addition or subtraction of unreduced fractions modeled by area models
- Identify expressions that represent addition or subtraction of unreduced fractions modeled on number lines
- Condensed: Given model, determine or interpret addition & subtraction of fractions
- Add & subtract fractions, fraction strips
- Add & subtract fractions, area models
- Add & subtract fractions, number lines
- Add & subtract fractions, various models
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Basic Mixed Addition & Subtraction of Fractions
- Condensed: Add or subtract fractions, common denominators, unreduced
- Condensed: Add or subtract fractions, common denominators, real-world context
- Condensed: Add or subtract fractions, different denominators
- Add or subtract fractions, including estimation, real-world context
- Add & subtract fractions, real-world context
- Given subtraction expression of two fractions, identify expression using fourths that best estimates difference
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Multiplication of Fractions
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Modeling Multiplication of Fractions
- Identify model representation of multiplication of fraction & whole number
- Condensed: Identify models or multiply whole numbers & fractions using area models
- Multiply whole numbers & fractions, area models
- Multiply whole numbers & fractions, including visual models
- Multiply mixed numbers & proper fractions, visual models, real-world context
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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, mixed number directions
- Multiply proper & improper fractions, positive
- Multiply fractions, positive
- Multiply mixed numbers, positive
- Condensed: Multiply fraction & mixed numbers, including mixed signs, mixed number directions
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Application of Multiplication of Fractions
- Multiply whole numbers & fractions, real-world context
- Multiply fractions, positive, real-world context
- Multiply mixed numbers & proper fractions, real-world context
- Determine part of whole using fraction multiplication, including visual models, including real-world context
- Estimate products of rational numbers, no decimals, round both factors to nearest whole number, real-world context
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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
- Compare products of fractions, mixed numbers, & whole numbers, including real-world context
- Interpret fractional parts & fraction multiplication, 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 & unit fractions, area models
- Divide whole numbers by unit fractions, number lines
- Divide whole numbers & unit fractions, fraction strips
- Divide whole numbers by unit fractions, models
- Condensed: Divide whole numbers & fractions, various models
- Identify division models & divide unit fractions by unit fractions
- Determine visual representation & fraction quotient of division problems
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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, mixed number directions
- Divide mixed numbers, positive
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Application of Division of Fractions
- Determine fraction & mixed number equivalence of division problems, real-world context
- Determine or estimate quotients of whole numbers, fraction quotients
- Estimate & determine quotients as fraction representation of division problem
- Divide whole numbers & unit fractions, including unit fraction multiplication, real-world context
- Divide fractions & mixed numbers, positive, real-world context
- Divide fractions, mixed numbers, & whole numbers, multi-step, real-world context
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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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Basic Comparing & Ordering Decimals
- Compare whole numbers up to 1,000,000,000
- Given decimals, identify locations on number line
- Compare decimals on number line
- Compare decimals up to two decimal places, including real-world context
- Compare decimals up to two decimal places & justify relationship, including real-world context
- Compare decimals written in word form, up to three decimal places
- Compare numbers, up to four-digit whole numbers or three-digit decimals
- Identify & compare rational numbers on number lines, positive
- Compare decimals written in word form, up to four decimal places
- Order positive decimals
- Order decimals up to 1,000,000,000
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Application of Comparing & Ordering Decimals
- Compare decimals up to two decimal places, including real-world context
- Compare decimals up to three decimal places
- Compare decimals up to three decimal places, real-world context
- Order decimals up to two decimal places, including real-world context
- Order decimals from table of place values, real-world context
- Order decimals up to three decimal places, including real-world context
- Condensed: Compare or order numbers up to 1,000,000,000
- Compare & order decimals up to 1,000,000,000, real-world context
- Compare or order positive & negative decimals, up to three decimal places
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Converting Decimals
- Convert decimals to percents
- Convert decimals to percents over 100
- Given model, determine fraction & decimal equivalents, unreduced
- Convert decimals to fractions
- Convert decimals to fractions, real-world context
- Convert decimals to mixed numbers
- Convert decimals to fractions or mixed numbers
- Convert decimals to fractions or mixed numbers, including repeating decimals of thirds
- Convert decimals to fractions or mixed numbers, including repeating decimals
- Condensed: Convert decimals to fractions & percents
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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
- Add decimals, positive, up to four 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
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Basic Addition & Subtraction of Decimals
- Condensed: Add & subtract decimals, up to two decimal places
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Application of Addition & Subtraction of Decimals
- Condensed: Add & subtract decimals, up to two decimal places, including real-world context
- Add & subtract decimals, up to two decimal places, real-world context
- Condensed: Add & subtract decimals, up to two decimal places, real-world context
- Add & subtract decimals, up to three decimal places, real-world context
- Add or subtract whole numbers or decimals, real-world context
- Condensed: Add & subtract rational numbers, real-world context
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Multiplication of Decimals
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Application & Modeling of Multiplication of Decimals
- Determine equivalence between area models & multiplication equations
- Determine equivalence between base-10 models & multiplication equations
- Determine equivalence between number line models & multiplication equations
- Condensed: Determine equivalence between models & multiplication equations
- Multiply decimals, products limited to two decimal places, real-world context
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Basic Multiplication of Decimals
- Multiply decimals times one-digit whole numbers
- Multiply decimals, products limited to two decimal places
- Multiply positive decimals, each factor up to two decimal places, factors up to 10 after decimal shift
- Multiply positive decimals, each factor up to two decimal places, factors up to 20
- Multiply positive decimals, each factor up to two decimal places
- Multiply positive decimals, each factor up to three decimal places
- Condensed: Multiply decimals
- Multiply three positive decimals, products limited to three decimal places
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Division of Decimals
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Application & Modeling of Division of Decimals
- Identify expressions & equations representing multiplication & division of rational numbers
- Identify base-10 model that represents quotient of decimal division
- Determine equivalence of base-10 model & components of decimal division
- Determine equivalence of base-10 model & components of decimal division, quotient limited to tenths
- Given area model representing decimal division, interpret model & determine quotient, including real-world context
- Given number line model representing decimal division, interpret model & determine quotient, including real-world context
- Given model representing decimal division, interpret model & determine quotient, including money
- Condensed: Given model representing decimal division, interpret model & determine quotient, including real-world context
- Divide decimals, up to three decimal places, real-world context
- Divide four-digit dividends by two-digit whole number divisors, including real-world context
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Basic Division of Decimals
- Divide whole numbers by decimals, up to two decimal places, integer quotients
- Divide decimals by whole numbers, up to two decimal places
- Divide decimals, up to two decimal places in quotients
- Divide decimals, up to three decimal places in dividend & divisor
- Divide decimals, up to three decimal places
- Divide four-digit dividends by two-digit whole number divisors
- Condensed: Divide decimals or whole numbers
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Mixed Operations with Decimals
- Condensed: Solve problems with decimal & whole numbers, real-world context
- Condensed: Add, subtract, multiply, & divide decimals, up to two decimal places
- Solve multi-step problems with rational numbers, including percents, real-world context
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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 whole, tenth, hundredth, & thousandth
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Application of Rounding & Estimating Decimals
- Round numbers to nearest whole, ten, hundred, & thousand, real-world context
- Round decimal numbers to nearest tenth & hundredth, including real-world context
- Round decimal numbers to nearest tenth & hundredth, real-world context
- Round decimal numbers to nearest tenth, hundredth, & thousandth, real-world context
- Round decimal numbers to nearest whole, tenth, hundredth, & thousandth, including real-world context
- Round decimal & whole numbers to specified place value
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Rounding & Operations with Decimals
- Round decimal numbers to nearest whole, tenth, & hundredth, real-world context
- Condensed: Round decimal numbers to nearest whole, tenth, & hundredth, including real-world context
- Estimate sum by rounding addends to nearest whole number, up to two decimal places
- Estimate differences of decimals by rounding to nearest whole number
- Condensed: Estimate sum or difference by rounding addends, minuend, & subtrahend, up to two decimal places
- Estimate quotients of decimals & whole numbers using compatible numbers
- Estimate solutions involving all operations, real-world context
- Determine sums & differences of decimals then round solution, real-world context
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Integers
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Classifying Numbers
- Classify rational numbers by definitions
- Classify rational numbers using graphic organizers
- Classify rational numbers, including graphic organizers
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Absolute Value & Opposites
- Determine opposites of numbers
- Identify opposite integers on number line
- Add opposite integers, up to two digits
- Identify situations represented by positive & negative numbers, real-world context
- Determine representations of quantities using positive & negative numbers, real-world context
- Determine change, opposite integers, real-world context
- Determine absolute value of integers
- Determine absolute value of integers, including real-world context
- Determine absolute value of rational numbers
- Determine absolute value of numeric expression
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Comparing Integers
- Compare two positive integers
- Compare two integers, one positive & one negative
- Compare two negative integers
- Interpret inequalities as statements about position
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Addition of Integers
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Modeling Addition of Integers
- Determine number represented by counters
- Add integers using counters
- Classify sum of integers on number line
- Given number line model, determine or interpret integer sum expression, same signs
- Given number line model, determine or interpret integer sum expression, mixed signs
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Basic Addition of Integers
- Add opposite integers
- Add opposite integers, up to two digits
- Add integers with same sign, start one digit & advance to two digits
- Add integers, one digit
- Add integers, positive sum
- Add integers, negative sum
- Add integers, start one digit & advance to two digits
- Add negative integers
- Add integers, up to two digits, positive sum
- Add integers, up to two digits, negative sum
- Add negative integers, up to two digits
- Condensed: Add positive & negative integers
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Application of Addition of Integers
- Add integers with same sign, up to three digits, real-world context
- Add integers, up to three digits, real-world context
- Given model or table, add integers, real-world context
- Condensed: Add integers, real-world context
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Subtraction of Integers
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Modeling Subtraction of Integers
- Subtract integers using counters
- Given variables on number line, classify difference
- Subtract integers on number line, same signs
- Subtract integers on number line, mixed signs
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Basic Subtraction of Integers, Positive Difference
- Subtract integers, positive difference
- Subtract negative integers, positive difference
- Subtract negative integers, up to two digits, positive difference
- Subtract integers, opposite signs, up to two digits, positive difference
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Basic Subtraction of Integers, Negative Difference
- Subtract integers, negative difference
- Subtract positive integers, negative difference
- Subtract negative integers, negative difference
- Subtract positive integers, up to two digits, negative difference
- Subtract negative integers, up to two digits, negative difference
- Subtract integers, opposite signs, up to two digits, negative difference
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Basic Subtraction of Integers, Mixed Differences
- Rewrite subtraction as addition & evaluate expression
- Subtract positive integers, one-digit & one-digit
- Subtract integers, various signs
- Condensed: Subtract integers, various signs, up to two digits
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Application of Subtraction of Integers
- Determine differences between integers, same signs, real-world context
- Determine differences between integers, mixed signs, real-world context
- Determine differences between integers, various signs, real-world context
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Multiplication of Integers
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Modeling Multiplication of Integers
- Multiply integers using counters
- Multiply positive integers using number line models, includes negatives shown on number line
- Multiply positive integers times negative integers using number line models
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Basic Multiplication of Integers
- Multiply negative integers
- Multiply integers, opposite signs
- Multiply integers, start one digit & advance to two digits
- Multiply negative integers, two-digit times two-digit
- Multiply integers, opposite signs, two-digit times two-digit
- Multiply negative integers, two-digit times two- or three-digit
- Multiply integers, opposite signs, two-digit times two- or three-digit
- Multiply three integers
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Application of Multiplication of Integers
- Multiply positive integers, real-world context
- Multiply integers, mixed signs, real-world context
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Division of Integers
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Modeling Division of Integers
- Divide integers using counters
- Divide integers, both positive, up to two-digit dividend, number line model
- Divide integers, opposite signs, up to two-digit dividend, number line model
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Basic Division of Integers
- Divide integers, one or both negative, start one-digit, advance up to three-digits
- Divide integers, one or both negative, start one-digit, advance up to three-digits, includes undefined
- Divide integers, both negative, up to three-digit dividend, up to two-digit divisor
- Divide integers, opposite signs, up to three-digit dividend, up to two-digit divisor
- Divide integers, both negative, up to five-digit dividend, up to two-digit divisor
- Divide integers, opposite signs, up to five-digit dividend, up to two-digit divisor
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Application of Division of Integers
- Divide integers, same signs, real-world context
- Divide integers, opposite signs, real-world context
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Mixed Operations of Integers
- Determine number of zero pairs or evaluate expressions using counters
- Estimate sums & differences of integers using front-end rounding
- Condensed: Add or subtract integers using counters
- Condensed: Multiply & divide integers
- Condensed: Add, subtract, multiply, & divide integers
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Percents
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Representing Percents
- Identify percents, decimal grids
- Identify percents, strip diagrams, real-world context
- Identify percents, area models
- Determine percents & specified quantities, double number lines, real-world context
- Condensed: Determine ratios & percents, decimal grids
- Condensed: Determine ratios & percents, strip diagrams, real-world context
- Condensed: Determine ratios & percents, various models
- Condensed: Determine ratios & percents, double number lines, including real-world context
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Converting Percents
- Convert percents to decimals
- Convert decimal percents to decimals
- Convert decimal percents less than one to decimals
- Convert percents to fractions
- Convert percents to fractions, real-world context
- Convert percents to mixed numbers
- Condensed: Convert percents to decimals & fractions
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Finding Tip, Tax, Markup, Markdown, & Commission
- Given percent, identify table that shows percent
- Determine tips
- Determine tax
- Determine markups
- Determine increases involving tips, tax, & markups
- Determine commissions
- Determine income tax for earned wages
- Determine discount, tax, or total cost
- Determine decreases involving sales, discounts, & markdowns
- Condensed: Determine tip, tax, discount, or markup
- Determine & compare savings from sales, rebates, & coupons
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Finding Total, Part, or Percent of a Number
- Given model, determine & identify fractions, decimals, & percents
- Given percent & whole, determine part, whole number answers
- Given percent & whole, determine part, exact answers
- Given percent & whole, determine rounded part
- Given percent & whole, determine part, real-world context
- Given part & percent, determine whole, exact answers
- Given part & percent, determine whole
- Given part & percent, determine whole, real-world context
- Given part & whole, determine percent
- Given part & whole, determine percent, real-world context
- Determine specified values in tables involving percents
-
Finding Percent of Change
- Determine percent of change, whole numbers, including real-world context
- Determine percent of change, including real-world context
-
Calculating Simple Interest
- Determine simple interest
- Determine simple interest & total amount
- Given simple interest earned, determine principal, rate, or time
-
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Fractions, Decimals, & Percents Combined
-
Comparing & Ordering Fractions & Decimals Combined
- Condensed: Order positive decimals & fractions
- Order positive rational numbers, no radicals, no exponents
- Given set or list, order rational numbers, real-world context
- Given table, order rational numbers, real-world context
-
Fraction, Decimal, & Percent Conversions
- Identify part of whole, real-world context
- Given model, determine & identify fractions, decimals, & percents
- Condensed: Convert proper & improper fractions to rounded percents
- Condensed: Convert fractions to decimals & percents
-
Basic Fractions & Decimals Combined
- Multiply decimals times fractions, both positive
- Multiply fractions times decimals, both positive
-
Application of Fractions & Decimals Combined
- Multiply decimals & fractions, real-world context
- Add or subtract whole numbers, fractions, or decimals, real-world context
- Condensed: Add & subtract rational numbers, real-world context
- Solve multi-step problems with rational numbers, including percents, real-world context
-
-
Ratios, Rates, & Proportions
-
Ratios
-
Basic Representing Ratios
- Determine part to part ratio, decimal grids
- Determine part to whole ratio, decimal grids
- Condensed: Determine ratios & percents, decimal grids
- Determine part to part ratio, various models
- Determine part to whole ratio, various models
- Condensed: Determine ratios & percents, various models
-
Representing Ratios Real-World
- Given part & percent, identify model & determine whole, real-world context
- Given double number line model, determine percent or specified quantity, real-world context
- Determine part to part ratio, strip diagrams, real-world context
- Determine part to whole ratio, strip diagrams, real-world context
- Condensed: Determine ratios & percents, strip diagrams, real-world context
- Determine part to part ratio, including double number lines, including real-world context
- Determine part to whole ratio, double number lines, real-world context
- Condensed: Determine ratios & percents, double number lines, including real-world context
-
Basic Ratios
- Rewrite ratios
- Given ratio, determine reduced form
- Identify equivalent ratios or determine missing component of proportion
- Given table, determine ratios, integers
- Determine ratios, various forms, real-world context
- Determine ratios, real-world context
-
Application of Ratios
- Given ratio, determine relationship between ratio terms, real-world context
- Interpret & apply ratios
- Given proportional relationship as ratio, determine specified quantity, real-world context
- Determine specified quantity in proportional relationship, including mixed numbers, real-world context
- Condensed: Determine ratios, relationship between ratio terms, & specified quantities, real-world context
- Given ratios a : b & b : c, determine a : c, real-world context
- Given ratios a : b & b : c, determine specified quantity, real-world context
- Condensed: Given extended ratio, determine ratio or specified quantity, real-world context
- Given proportional relationship & extended ratio, determine specified quantity, real-world context
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-
Rates
-
Basic Unit Rates
- Identify unit rates
- Determine unit rates, ratio tables, real-world context
- Determine unit rates, strip diagrams, real-world context
- Given double number line, determine unit rate, real-world context
- Identify measurement conversion unit rates
-
Application of Rates
- Determine unit rates, whole numbers, real-world context
- Determine unit rates, fractions, real-world context
- Determine unit rates, mixed numbers, real-world context
- Condensed: Determine or apply unit rates, real-world context
- Determine & compare unit rates, real-world context
- Given proportional relationship, determine specified quantity, real-world context
- Given rate, convert time unit to determine quantity over time interval, real-world context
- Given rate of travel, determine distance or time
- Given unit conversion rate, convert measurement units
- Identify measurement conversion rates
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-
Proportions
- Solve proportions, whole numbers
- Solve proportions
- Solve proportions, mixed number components
- Solve proportions to convert measurement units
- Solve proportions, exact answers, real-world context
- Solve proportions, rounded answers, real-world context
- Compare rates or determine specified values in proportional relationships, real-world context
-
-
Number Lines
-
Number Lines, Only Positives
- Given range & increment, identify blank number line
- Identify decimals on number lines, positive
- Identify decimals on number lines, vertical number lines, positive
- Identify or plot decimals on number lines, increment 0.5
- Identify or plot decimals on number lines, increment 0.2
- Condensed: Identify or plot decimals on number lines
- Plot or locate percents on number line
- Identify or plot fractions or determine lengths on number line
- Determine location of rational numbers on number line
- Determine location of rational numbers on number line, including negatives
- Condensed: Identify or plot decimals or fractions on number lines
-
Number Lines, Including Negatives
- Identify integers on number lines, negative
- Identify rational numbers on number lines, negative
- Identify rational numbers on number lines, vertical number lines
- Identify rational numbers on number lines, negative, vertical number lines
- Condensed: Identify rational numbers on number lines, vertical
- Condensed: Identify rational numbers on number lines, including vertical number lines
- Identify or determine rational values on number line, vertical number lines
- Plot rational numbers on number lines, negative
- Identify or plot rational numbers on number lines & interpret, real-world context
- Condensed: Identify or plot rational numbers on number lines
- Identify & compare rational numbers on number lines
-
-
Number Theory
-
Prime & Composite Numbers
- Identify prime & composite numbers
- Identify prime & composite numbers, real-world context
-
Factors & Multiples
- Identify factors or non-factors of whole numbers
- Identify multiples or non-multiples of whole numbers
- Identify factors or multiples of whole numbers
- Condensed: Identify factors, non-factors, multiples, & non-multiples of whole numbers
-
Prime Factorization
- Determine prime factorization of numbers up to 50
- Determine prime factorization of numbers up to 100
- Identify or complete prime factorization of numbers up to 144
- Identify equivalent expressions involving prime factorization
-
Greatest Common Factors
- Determine GCF of two numbers up to 100
- Determine GCF of two numbers up to 100 or multiples of 10
- Determine GCFs, real-world context
- Apply GCFs to determine number of items in groups, real-world context
-
Least Common Multiples
- Determine LCM of two numbers up to 100
- Determine LCM of two numbers up to 100 or multiples of 10
- Determine LCMs, real-world context
- Apply LCMs to determine number of items in groups, real-world context
-
Greatest Common Factors & Least Common Multiples
- Condensed: Determine GCF or LCM of two numbers up to 100 or multiples of 10
- Condensed: Determine GCFs & LCMs, real-world context
- Condensed: Apply GCFs & LCMs to determine number of items in groups, real-world context
-
-
Expressions
-
Expression Vocabulary
- Determine definitions of coefficient, fill in the blank
- Determine definitions of constant, fill in the blank
- Determine definitions of variable, fill in the blank
- Determine definitions of term, fill in the blank
- Determine definitions of expression, fill in the blank
- Determine definitions of evaluate, fill in the blank
- Determine definitions of operation, fill in the blank
- Determine definitions of arithmetic vocabulary, fill in the blank
- Determine definitions of relationship vocabulary, fill in the blank
- Identify parts of expressions
- Identify multiple parts of expressions
-
Whole Number Exponents
- Convert expanded numerical expressions to exponential form
- Convert exponential numerical expressions to expanded form
- Convert descriptions of numerical exponential expressions to exponential form
- Determine components & properties of whole-number exponents
- Square positive integers up to 10
- Simplify or evaluate numerical exponential expressions
-
Translating Expressions
- Identify words or phrases that indicate specified operation or comparison
- Determine algebraic expressions that represent real-world situations
- Given phrase, determine one-step algebraic expression
- Interpret numerical expressions
- Identify equivalent multi-step algebraic expressions & phrases
- Given phrase, determine multi-step algebraic expression
- Given phrase, determine & evaluate multi-step algebraic expression
- Determine algebraic expressions that represent real-world situations, including two-variable expressions
-
Equivalent Expressions
- Identify equivalent numerical expressions using counters
- Identify equivalent algebraic expressions using algebra tiles
- Identify equivalent expressions or determine simplified expressions
- Identify equivalent algebraic expressions, including real-world context
- Evaluate & identify equivalent numerical expressions, including real-world context
-
Evaluating Expressions
-
Basic Evaluating Expressions, Addition & Subtraction
- Evaluate addition expressions for specified value, one variable, whole numbers
- Evaluate subtraction expressions for specified value, one variable, whole numbers
- Evaluate addition expressions for specified value, one variable, at least one fraction
- Evaluate addition expressions for specified value, one variable, at least one decimal
- Evaluate subtraction expressions for specified value, one variable, at least one fraction
- Evaluate subtraction expressions for specified value, one variable, at least one decimal
- Evaluate expressions for specified value, one variable, only sums, at least one decimal
- Evaluate subtraction expressions for specified value, one variable, at least one decimal
-
Basic Evaluating Expressions, Multiplication & Division
- Evaluate multiplication expressions for specified value, one variable
- Evaluate division expressions for specified value, one variable
- Evaluate multiplication expressions for specified value, one variable, at least one fraction
- Evaluate multiplication expressions for specified value, one variable, at least one decimal
- Evaluate division expressions for specified value, one variable, at least one fraction
- Evaluate division expressions for specified value, one variable, at least one decimal
-
Application of Evaluating Expressions
- Condensed: Evaluate expressions for specified value, one variable
- Evaluate expressions for specified values, two variables, multiple operations, including powers & real-world context
- Condensed: Evaluate expressions, including powers, fractions, whole numbers, & decimals, including real-world context
- Evaluate or identify expressions that represent situations from descriptions, real-world context
- Evaluate expressions for specified value, one variable, including multiple operations, at least one decimal
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Distributing or Factoring Expressions
- Identify equivalent expressions involving distribution
- Identify equivalent expressions involving distribution, two or more terms
- Identify algebraic expressions, involving distribution, real-world context
- Apply distributive property to numerical expressions, real-world context
- Factor GCF from linear binomial expressions, both terms positive
- Distribute or factor, linear binomial expressions
-
Simplifying Variable Expressions
- Simplify algebraic expressions, combine two terms, positives
- Simplify algebraic expressions, one variable, product of two factors, positives
- Simplify algebraic expressions, one variable, product of three factors, positives
- Simplify algebraic expressions, one variable, positive integer coefficients
- Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
- Simplify algebraic expressions, two variables, positive integer coefficients
-
-
Equations & Inequalities
-
Equations
-
Equivalent Equations
- Identify missing operations in numerical sentences
-
Solving Equations, Only Positives
- Solve x + a = b, a > 0, b > 0, x > 0
- Solve x – a = b, a > 0, b > 0, x > 0
- Solve ax = b, a > 0, b > 0
- Solve x/a = b, a > 0, b > 0
- Solve one-step linear equations, rationals
-
Properties of Equations
- Identify properties used in numerical expressions
- Identify properties used in numerical & algebraic expressions
- Identify properties used to solve linear equations
-
Solving Addition & Subtraction Equations, Including Negatives
- Solve x + a = b, a > 0, b > 0, x < 0
- Solve x + a = b, a > 0, b < 0, x < 0
- Solve x + a = b, a < 0, b > 0, x > 0
- Solve x + a = b, a < 0, b < 0, x > 0
- Solve x + a = b, a < 0, b < 0, x < 0
- Solve a + x = b
- Solve x – a = b, a < 0, b > 0, x > 0
- Solve x – a = b, a < 0, b > 0, x < 0
- Solve x – a = b, a < 0, b < 0, x < 0
- Solve x – a = b, a > 0, b < 0, x > 0
- Solve x – a = b, a > 0, b > 0, x < 0
- Condensed: Solve one-step linear equations, addition or subtraction
-
Solving Multiplication & Division Equations, Including Negatives
- Solve ax = b, a > 0, b < 0
- Solve ax = b, a < 0, b < 0
- Solve ax = b, a < 0, b > 0
- Solve -x = b
- Solve x/a = b, a > 0, b < 0
- Solve x/a = b, a < 0, b > 0
- Solve x/a = b, a < 0, b < 0
- Condensed: Solve one-step linear equations, multiplication or division
-
Checking Solutions
- Identify values that solve equations, variable & constant on left side
- Identify values that solve equations, constant times variable
- Identify values that solve equations, variable divided by constant
- Identify values that solve equations, variable & constant on right side
- Identify values that solve equations
- Identify equations with given solution
-
Writing & Solving Equations, Addition
- Determine addition equations, real-world context
- Determine & solve addition equations, including real-world context
- Determine, solve, & apply addition equations, real-world context
- Solve addition equations, real-world context
- Determine & solve or apply addition equations, real-world context
-
Writing & Solving Equations, Multiplication
- Determine multiplication equations, real-world context
- Determine & solve multiplication equations, real-world context
- Determine & solve multiplication equations, including real-world context
- Determine & solve multiplication equations, including required rounding, real-world context
- Determine, solve, & apply multiplication equations, real-world context
- Determine, solve, & apply multiplication equations, including required rounding, real-world context
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Writing & Solving Equations, Mixed
- Determine one-step equations, including decimals, real-world context
- Given one-step linear equation, identify real-world situation represented by equation
- Given rate & time, determine distance
- Given distance & rate or time, determine missing quantity
- Determine solutions to problems using common formulas, including simple interest, area & perimeter, & d = rt, real-world context
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Inequalities
-
Checking Solutions
- Identify values that solve inequalities, variable & constant on left side
- Identify values that solve inequalities, variable & constant on right side
- Identify values that solve inequalities, constant minus variable on left side
- Identify values that solve inequalities, constant minus variable on right side
- Identify values that solve inequalities
-
Solving Inequalities, Only Positives
- Solve one-step inequalities, x + #
- Solve one-step inequalities, x – #
- Condensed: Solve one-step inequalities, x ± #
- Solve one-step inequalities, a * x, a > 0
- Solve & graph one-step inequalities, x + #
- Solve & graph one-step inequalities, x – #
- Condensed: Solve & graph one-step inequalities, x ± #
- Solve & graph one-step inequalities, a * x, a > 0
-
Solving Inequalities, Including Negatives
- Solve one-step inequalities, a * x, a < 0
- Solve one-step inequalities, x/a, a > 0
- Solve one-step inequalities, x/a, a < 0
- Condensed: Solve one-step inequalities, x/a
-
Solving & Graphing Inequalities, Including Negatives
- Condensed: Solve & graph one-step inequalities, x ± #
- Solve & graph one-step inequalities, a * x, a < 0
- Condensed: Solve & graph one-step inequalities, a * x
- Solve & graph one-step inequalities, x/a, a > 0
- Solve & graph one-step inequalities, x/a, a < 0
- Condensed: Solve & graph one-step inequalities, x/a
- Solve & graph one-step inequalities, whole number coefficients
- Solve & graph one-step inequalities, integer coefficients
- Solve & graph one-step inequalities, including fractional coefficients
- Solve & graph one-step inequalities, including negative & fractional coefficients
-
Basic Writing & Graphing Inequalities
- Determine graph from inequality or inequality from graph
- Graph inequalities on number line
- Given graph, determine inequality
-
Application of Writing Inequalities
- Represent real-world problems as inequalities
- Determine one-step inequalities, including real-world context
- Determine one-step inequalities, rational numbers, including real-world context
- Given description, determine inequality, graph, & possible solutions
- Given inequality, identify phrase or real-world problem that represents inequality
- Given one-step inequality, identify real-world problem modeled by inequality
- Given one-step inequality, identify real-world problem modeled by inequality, rational numbers
- Identify one-step inequalities that model real-world problems or interpret inequality components
- Determine, solve, & graph one-step inequalities, including real-world context
-
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-
Linear Relationships
-
Linear Relationships, Only Proportional
-
Identifying Independent & Dependent Variables
- Given description, identify dependent or independent variable
- Given equation, identify dependent or independent variable
- Given table, identify dependent or independent variable
- Given table or graph, identify dependent or independent variable
-
Interpreting Points
- Determine or interpret points on graphs showing proportional relationships
- Given constant of proportionality, determine or interpret point, real-world context
-
Writing Equations, Completing Tables & Graphs
- Given unit rate, determine graph of proportional relationship, real-world context
- Determine graph of proportional relationship, real-world context
- Given two points, determine linear graph & constant of proportionality
- Given constant of proportionality, determine table, graph, or equation
- Given table, determine constant of proportionality, graph, or equation
- Given equation, determine constant of proportionality, graph, or table
- Given graph, determine constant of proportionality, table, or equation
- Condensed: Determine equivalent representations of proportional relationships
- Determine or identify equivalent representations of proportional relationships
- Determine equations, tables, & graphs for proportional relationships, real-world context
- Given visual representation of proportional relationship, determine equation, table, & graph, real-world context
- Identify representation of proportional relationship, various representations, real-world context
-
-
Linear Relationships, Proportional & Non-Proportional
-
Additive & Multiplicative Relationships
- Identify graphs of additive & multiplicative relationships
- Given table, determine additive or multiplicative equation
- Identify components of additive & multiplicative equations
- Identify equivalent representations of additive & multiplicative relationships
- Identify equivalent representations of additive & multiplicative relationships, including decimals & fractions
- Identify situations modeled by additive & multiplicative relationships
- Identify situations modeled by tables or equations, y = mx or y = x + b
- Identify proportional & non-proportional relationships, real-world context
- Identify tables that represent real-world situations, y = mx or y = x + b
- Determine equations that represent real-world situations, y = mx or y = x + b
-
Finding Constant of Proportionality
- Given equation, determine constant of proportionality
- Given equation, determine constant of proportionality, real-world context
- Given table, determine constant of proportionality
- Given graph, determine constant of proportionality, including real-world context
- Determine constants of proportionality, real-world context
- Condensed: Determine constants of proportionality
- Given table, determine graph & constant of proportionality
-
Identifying Proportional vs. Non-Proportional
- Identify tables showing proportional relationship
- Identify graphs showing proportional relationship
- Identify equations showing proportional relationship
- Identify tables, graphs, or equations showing proportional relationship
-
Writing Equations, Completing Tables & Graphs
- Given linear equation & table, identify graph
- Given linear equation & table, determine graph
- Given linear graph, determine y-values in table
- Given linear graph, determine y-values in table & equation
- Given linear equation, determine y-values in table & graph, first quadrant
- Determine equations that represent real-world situations, including two-step equations
- Determine additive & multiplicative equations that represent real-world situations
- Given graph of proportional relationship, determine table & equation, real-world context
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-
Geometry
-
2D Figures
- Classify angles from figure
- Classify triangles by sides
- Classify triangles by angles
- Classify triangle based on given angle measures
- Classify triangles based on angles & sides
- Classify quadrilaterals shapes based on attributes
- Classify polygons based on number of sides or relationship to other shapes
- Classify polygons based on angles & parallel or perpendicular lines
- Classify polygons using graphic organizers
- Classify polygons using graphic organizers, including types of triangles
-
3D Figures
- Identify 3D figures & their bases
- Identify equivalent representations of 3D figures & nets
- Determine 2D orthographic representation of 3D blocks
-
Triangle Angle-Side Relationships
- Given two angle measures in triangle, determine angle measure
- Determine smallest & largest sides or angles in triangle
- Order angles in triangles
- Given congruent sides, identify congruent angles of isosceles triangle
- Given congruent angles, identify congruent sides of isosceles triangle
- Apply triangle inequality theorem to determine range of values for unknown side
- Apply triangle inequality theorem to determine side lengths
- Apply triangle angle sum theorem to determine appropriate equation & angles, algebraic expressions
-
Perimeter
-
Modeling Perimeter
- Given model, identify formula & determine perimeter of rectangles
- Given model, identify formula & determine perimeter of rectangles, including decimal dimensions
- Condensed: Identify formula & determine perimeter of rectangles & squares
-
Basic Perimeter
- Determine perimeter of rectangles
- Given sides of rectangle, determine perimeter
- Determine perimeter of rectangles, including decimal dimensions
- Determine side length or perimeter of squares
- Given perimeter & one dimension of rectangle, determine missing dimension
- Given perimeter of rectangle & one side, determine dimension
- Given perimeter of rectangle & one side, determine dimension, including decimals
-
Application of Perimeter
- Given sides of rectangle, determine perimeter
- Condensed: Determine perimeter of rectangles, including real-world context
- Determine perimeter of rectangles, real-world context
- Determine perimeter of rectangles, including decimal dimensions, real-world context
- Given perimeter & relationship between sides, determine specific dimension
- Determine perimeter of polygons, including real-world context
- Determine circumference of circle, exact answers, multiple choice, including real-world context
- Given radius or diameter, determine circumference
- Estimate diameter or circumference & identify equations using π
-
-
Area
-
Trapezoid Area
-
Basic Trapezoid Area
- Determine area of trapezoids
- Given area & base lengths of trapezoid, determine height
-
Application & Modeling of Trapezoid Area
- Determine area of triangles using models that decompose & rearrange parts
- Given height & bases of trapezoid, determine area
- Determine equations that represent area of trapezoids, real-world context
- Given area & bases of trapezoid, determine height
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Composite & Mixed Figure Area
- Determine algebraic expressions that represent area of rectangles & triangles
- Determine areas of triangles & trapezoids
- Given area, determine dimensions of triangles
- Condensed: Determine areas & dimensions of triangles & trapezoids
- Condensed: Determine equations that represent area of triangles & quadrilaterals, real-world context
- Determine perimeter of composite figures containing rectangles & squares, including real-world context
- Determine area of composite figures on coordinate plane, no circular shapes
- Determine area of polygons in coordinate plane
- Determine area of polygons in coordinate plane, real-world context
- Determine area of composite figures, rectangle with various figures attached, no circular parts
- Determine area of composite figures, no circular shapes
- Condensed: Determine area using models that decompose & rearrange parts
-
Triangle Area
-
Basic Triangle Area
- Determine area of triangles, internal height
- Determine area of triangles, external height
- Determine area of triangles
- Determine area of triangles, internal height, mixed numbers
- Determine area of triangles, external height, mixed numbers
- Determine area of triangles, mixed numbers
- Given area & one dimension of triangle, determine missing dimension
- Given area & one dimension of triangle, determine missing dimension, mixed numbers
-
Application & Modeling of Triangle Area
- Given base & height of triangle, determine area
- Determine area of triangles using models that decompose & rearrange parts
- Determine equations that represent area of triangles, real-world context
- Given area & one dimension of triangle, determine missing dimension
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Circle Area
- Determine area of circle, exact answers, including real-world context
- Given radius or diameter, determine area
- Given radius or diameter, determine area or circumference
- Condensed: Determine area or circumference of circle
- Identify approximate formulas for circumference & area of circles
-
Rectangle & Parallelogram Area
-
Modeling Area of Rectangles & Parallelograms
- Given sides of rectangle, determine area, model provided
- Given model, identify formula & determine area of square
- Given model, identify formula & determine area of rectangle
- Condensed: Given model, identify formula & determine area of square or rectangle
- Determine area of rectangles with fractional dimensions using tiling method
- Determine area of parallelograms, model provided
- Determine area of parallelograms using models that decompose & rearrange parts
-
Basic Area of Rectangles & Parallelograms
- Given length & width of rectangle, determine area
- Given sides of rectangle, determine area
- Determine area of rectangles with fractional dimensions
- Determine area of parallelograms
- Determine areas of rectangles & parallelograms
- Given area & one dimension of rectangle, determine missing dimension
- Given area of rectangle & one dimension, determine other dimension
- Given area & one dimension of parallelogram, determine missing dimension
- Given area, determine dimensions of rectangles & parallelograms
- Condensed: Determine areas & dimensions of rectangles & parallelograms
-
Application of Area of Rectangles & Parallelograms
- Determine equations that represent area of rectangles, real-world context
- Condensed: Determine area of rectangles, including real-world context
- Given sides of rectangle & cost per square unit, determine area & total cost, real-world context
- Determine area of shaded region between nested rectangles
- Given perimeter or side length, determine area of square, including real-world context
- Determine equations that represent area of parallelograms, real-world context
- Given base & height of rectangle or parallelogram, determine area
- Determine area of missing dimension of rectangles, real-world context
- Given area & one dimension of rectangle or parallelogram, determine missing dimension
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-
Area & Perimeter
- Condensed: Identify formula & determine perimeter of rectangles & squares
- Determine area or perimeter of parallelograms
- Condensed: Determine equations that represent area of triangles & quadrilaterals, real-world context
- Determine dimension of rectangles, including real-world context
-
Surface Area
-
Calculating Surface Area with Nets
- Identify equivalent representations of 3D figures & nets
- Given net, determine surface area of rectangular prism
- Given net, determine surface area of prisms
- Given net, determine lateral surface area of prisms
-
Surface Area of Rectangular & Triangular Prisms
- Determine surface area of rectangular prisms
- Determine surface area of triangular prisms
- Determine surface areas of 3D figures, no circles
-
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Volume
-
Unit Cube Volume
- Determine relationship between area, volume, & dimensions
- Determine relationship between area, volume, square units, & cubic units
- Determine volume of rectangular 3D figures using unit cubes
- Determine volume of rectangular prisms using unit cubes
- Determine volume of rectangular prisms using unit cubes
- Determine volume of rectangular prisms, various representations
-
Basic Volume, Cubes
- Determine volume of cubes, whole numbers or decimals
- Determine volume of cubes, whole numbers, decimals, or fractions, no visual provided
- Determine volume of cubes, whole numbers, decimals, or fractions
-
Basic Volume, Rectangular Prisms
- Determine volume of rectangular prisms, whole numbers, volume less than 10,000
- Determine volume of rectangular prisms, whole numbers or decimals
- Determine volume of rectangular prisms, whole numbers, decimals, or fractions
- Given base area & edge or all edges, determine volume of rectangular prism
- Determine volumes of rectangular & triangular prisms, fractional dimensions
- Given volume, determine edges of rectangular prisms
- Determine volume or edge of rectangular prisms, whole numbers, volume less than 10,000
- Determine volume or edge of rectangular prisms, whole numbers
- Condensed: Determine volume or dimension of rectangular prisms, fractional dimensions
- Determine volume of rectangular prisms, whole numbers or decimals
- Determine volumes of rectangular prisms, fractional dimensions
- Given volume, determine edge of rectangular prisms, up to four-digit dividend, up to two-digit divisor
-
Application of Volume, Cubes
- Determine volume of cubes, whole numbers or decimals, real-world context
- Determine volume of cubes, whole numbers, decimals, or fractions, real-world context
- Condensed: Determine volume or side length of cubes, whole numbers, decimals, or fractions, including real-world context
-
Application of Volume, Rectangular Prisms
- Determine volume of rectangular prisms using repeated layers of base area, real-world context
- Determine volume of rectangular prisms using various representations of cubic units, real-world context
- Determine volume of rectangular prisms, whole numbers, including real-world context
- Determine volumes of rectangular prisms, rational dimensions, real-world context
- Determine volumes of cubes & rectangular prisms
- Determine volume of triangular prisms
- Given volume & two dimensions of rectangular prism, determine missing dimension
- Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, real-world context
- Determine volume or edge of rectangular prisms, whole numbers or decimals, real-world context
- Determine volume of composite rectangular prisms
- Determine volume of rectangular prisms & apply associative property to volume expressions
- Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including real-world context
-
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Coordinate Plane
-
Basic Coordinate Plane, Only First Quadarant
- Determine coordinates of first quadrant points
- Determine coordinates of first quadrant point, various scales
- Determine coordinates of first quadrant rational points
- Plot first quadrant points
- Plot first quadrant points, various scales
- Plot first quadrant rational points
- Plot or determine coordinates of first quadrant points
- Condensed: Plot or determine coordinates of first quadrant points
- Condensed: Plot or determine coordinates of first quadrant rational points, various scales
-
Application of Coordinate Plane, Only First Quadrant
- Identify description of process to plot first quadrant points
- Identify locations or parts of coordinate plane using first quadrant points
- Identify first quadrant points or parts of coordinate plane
- Determine or identify first quadrant points, real-world context
- Determine or identify first quadrant points, including cardinal directions, real-world context
- Condensed: Plot or determine coordinates of first quadrant rational points
-
Basic Coordinate Plane, All Quadrants
- Given integer point on graph, determine coordinates, point on axis
- Given integer point on graph, determine coordinates
- Given lattice point, determine coordinates
- Given rational point, determine location on coordinate plane
- Plot integer points on coordinate plane, point on axis
- Plot integer points
- Plot points on coordinate plane, student selects scales
- Plot rational points on coordinate plane
- Plot rational points on coordinate plane, graph scale at most one-half
- Condensed: Plot integer points or determine coordinates
- Condensed: Plot or identify points on coordinate plane
- Plot or identify rational points on coordinate plane
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Reflections & Distance Between Points
- Determine coordinates of reflected points
- Determine distance between points on coordinate plane, horizontal or vertical
- Determine distance between points on coordinate plane, horizontal or vertical, real-world context
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Measurement & Data
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Conversions
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Basic Customary Conversions
- Convert between customary units of weight & mass
- Convert between customary units of volume & capacity
- Convert between customary units of length
- Convert between customary units of length
- Given unit conversion rate, convert measurement units
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Application of Customary Conversions
- Convert between customary units of volume & capacity
- Convert between customary units of weight & mass
- Condensed: Convert between customary units
- Convert between customary units, including real-world context
- Convert between customary units, real-world context
- Convert between customary units to find sums or differences, including real-world context
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Basic Metric Conversions
- Convert between metric units of length
- Convert between metric units
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Application of Metric Conversions
- Convert between metric units of weight & mass
- Convert between metric units of volume & capacity
- Convert between metric units of length, real-world context
- Convert between metric units of weight & mass, real-world context
- Convert between metric units of volume & capacity, real-world context
- Convert between metric units, including real-world context
- Given conversion chart, convert between metric units, real-world context
- Condensed: Convert between metric units
- Convert between metric units, real-world context
- Condensed: Convert between customary or metric units
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Basic Customary & Metric Conversions
- Convert customary to metric units of length, calculator expected
- Convert metric to customary units of length, calculator expected
- Convert customary to metric units of volume & capacity, calculator expected
- Convert metric to customary units of volume & capacity, calculator expected
- Convert customary to metric units of weight & mass, calculator expected
- Convert metric to customary units of weight & mass, calculator expected
- Condensed: Convert between customary & metric, calculator expected
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Application of Customary to Metric & Metric to Customary
- Convert customary to metric units of length
- Convert customary to metric units of weight & mass
- Convert customary to metric units of volume & capacity
- Convert metric to customary units of length
- Convert metric to customary units of weight & mass
- Convert metric to customary units of volume & capacity
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Application of One-Step Customary & Metric Conversions
- Condensed: Convert between customary & metric
- Convert between customary & metric using conversion graphs
- Convert between customary & metric using unit rates
- Convert between customary & metric using dimensional analysis
- Convert between customary & metric, proportion bias
- Condensed: Convert between customary & metric using multiple representations of conversion factor
- Convert between customary & metric, real-world context
- Convert between customary & metric using scale factors
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Application of Multi-Step Customary & Metric Conversions
- Convert customary to metric units of length, including multi-step
- Convert customary to metric units of weight & mass, including multi-step
- Convert customary to metric units of volume & capacity, including multi-step
- Convert metric to customary units of length, including multi-step
- Convert metric to customary units of weight & mass, including multi-step
- Convert metric to customary units of volume & capacity, including multi-step
- Condensed: Convert between customary & metric, including multi-step
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Charts & Graphs
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Frequency Tables
- Given data, identify frequency table or determine missing element of table
- Solve one-step problems from frequency tables, real-world context
- Solve problems from frequency tables, real-world context
- Solve one-step problems from frequency & relative frequency tables, real-world context
- Solve multi-step problems from frequency tables, real-world context
- Condensed: Interpret two-way frequency tables
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Line Plots
- Given data represented in various ways, identify dot plot
- Determine equivalent fraction data sets & line plots
- Solve one-step problems from dot plots, real-world context
- Solve problems involving dot plots
- Solve problems involving line plots & fractions
- Add or subtract fractions from line plots, common denominator
- Solve multi-step problems from dot plots, real-world context
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Bar & Double Bar Graphs
- Given table, determine equivalent bar graph
- Given bar graph, determine equivalent table
- Given table, determine equivalent bar graph, including double bar graphs
- Condensed: Given bar graph, determine equivalent table or pictograph
- Determine or interpret percentage bar graphs
- Solve problems involving bar graphs
- Solve one-step problems from bar graphs, real-world context
- Solve one-step problems from double bar graphs, real-world context
- Add, subtract, & multiply fractions in bar graphs, common denominator
- Solve multi-step problems from bar graphs, real-world context
- Solve multi-step problems from double bar graphs, real-world context
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Stem-&-Leaf Plots
- Given data, identify stem-and-leaf plot
- Given data, identify stem-and-leaf plot
- Solve one-step problems from stem-and-leaf plots, real-world context
- Solve multi-step problems from stem-and-leaf plots, real-world context
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Scatter Plots
- Given data, determine scatter plot
- Identify equivalent representations of data in tables & scatter plots
- Solve one-step problems from scatter plots, real-world context
- Solve multi-step problems from scatter plots, real-world context
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Histograms
- Given various representations of data, determine histogram
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Pictographs
- Given bar graph, determine equivalent pictograph
- Given pictograph, determine equivalent table
- Given pictograph, determine equivalent bar graph
- Condensed: Given pictograph, determine equivalent bar graph or table
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Pie Charts
- Solve problems involving interpretation of pie charts
- Solve problems involving interpretation of pie charts displayed using fractions, decimals, or percents
- Determine percent of category in pie charts
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Mixed Charts & Graphs
- Determine unit of measurement for data, various representations
- Determine sample size, various representations
- Condensed: Given table, determine equivalent bar graph or pictograph
- Condensed: Given data, represent with dot plot or stem-and-leaf plot
- Condensed: Determine equivalent visual representations of data
- Determine solutions to problems involving bar graphs & line graphs
- Condensed: Solve one-step problems from various plots, graphs, & tables, real-world context
- Condensed: Solve multi-step problems from various plots, graphs, & tables, real-world context
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Probability & Statistics
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Measures of Center & Spread
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Calculating Measures of Center & Spread
- Determine mean, median, mode, or range
- Determine mean, median, mode, or range from stem-&-leaf plots
- Determine mean, median, mode, or range from various graphs
- Condensed: Determine mean, median, mode, or range, including graphs
- Given various representations of data, identify mean, median, mode, & range
- Given mean, median, mode, or range, determine missing value in data set
- Given additional value in data set, determine change in mean, median, mode, or range
- Given mean, median, or range, determine missing or additional value in data set
- Determine interquartile range of data
- Determine mean absolute deviation
- Determine mean absolute deviation, real-world context
- Condensed: Solve problems involving interpretation of box plots & stem-&-leaf plots
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Interpretting Measures of Center & Spread
- Given various representations of data, identify outlier
- Solve problems involving interpretation of histograms
- Identify variability in real-world situations
- Determine collection method, distribution shape, & unit of measure for data
- Identify measures of center based on data distribution
- Identify measures of variability based on data distribution
- Identify & interpret measures of center
- Identify & interpret measures of variability
- Determine or interpret shapes & features of graphs
- Determine or interpret measures of center & spread from graphs
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Box Plots
- Determine characteristics of boxplots
- Solve problems involving interpretation of box plots
- Solve problems involving interpretation of stacked box plots, real-world context
- Determine five-number summary
- Given boxplot, determine values from five-number summary
- Condensed: Determine five-number summary, including box plots
- Solve problems involving five-number summary
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Dot Plots
- Determine mean from dot plots
- Determine median from dot plots
- Determine & compare means from two dot plots
- Determine & compare medians from two dot plots
- Determine mean absolute deviation from dot plots
- Compare mean absolute deviations from two dot plots
- Compare characteristics of side-by-side dot plots
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Statistical Data
- Determine whether data was counted or measured
- Determine whether data is categorical or numerical
- Identify statistical questions
- Identify biased samples & questions
- Identify samples & populations
- Identify variability in real-world situations
- Determine definitions of data collection & distribution vocabulary, fill in the blank
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Basic Probability
- Determine sample spaces
- Classify probabilities by levels of likelihood
- Determine probabilities of single events
- Determine theoretical probabilities
- Determine experimental probabilities
- Determine theoretical probabilities, fraction answers
- Determine experimental probabilities, fraction answers
- Determine probabilities of flipping coins specified number of times
- Determine probabilities & complementary probabilities of single events, including visual models
- Determine predicted values, theoretical probability
- Determine predicted values, experimental probability
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Financial Literacy
- Identify positive & negative factors in establishing credit history
- Identify value of credit report
- Determine similarities & differences between debit & credit cards
- Identify methods of college payment
- Balance check register
- Determine budget allocations for spending, saving, & giving
- Solve problems involving information on credit report
- Given features & costs, determine best financial institution based on specified conditions
- Determine annual income
- Determine lifetime income
- Estimate costs of two-year college education
- Estimate costs of four-year college education