7th Grade Skills
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Integers
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Integer Vocabulary & Scenarios
- Identify situations represented by positive & negative numbers, real-world context
- Determine representations of quantities using positive & negative numbers, real-world context
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Opposites
- Determine opposites of numbers
- Identify opposite integers on number line
- Determine change, opposite integers, real-world context
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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
- 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 negative integers
- Add integers, positive sum
- Add integers, negative sum
- Add integers, start one digit & advance to two digits
- Add negative integers, up to two digits
- Add integers, up to two digits, positive sum
- Add integers, up to two digits, negative sum
- 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 Differences
- 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 Differences
- Subtract positive integers, negative difference
- Subtract negative integers, negative difference
- Subtract 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
- Subtract positive integers, one-digit & one-digit
- Rewrite subtraction as addition & evaluate expression
- 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 integers, start one digit & advance to two digits
- Multiply integers, opposite signs
- Multiply negative integers
- Multiply integers, opposite signs, two-digit times two-digit
- Multiply negative integers, two-digit times two-digit
- Multiply integers, opposite signs, two-digit times two- or three-digit
- Multiply negative integers, 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, opposite signs, up to three-digit dividend, up to two-digit divisor
- Divide integers, both negative, up to three-digit dividend, up to two-digit divisor
- Divide integers, opposite signs, up to five-digit dividend, up to two-digit divisor
- Divide integers, both negative, up to five-digit dividend, up to two-digit divisor
- 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
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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
- Condensed: Add or subtract integers using counters
- Estimate sums & differences of integers using front-end rounding
- Add or subtract three integers
- Add or subtract four integers
- Multiply & divide three integers
- Condensed: Multiply & divide integers
- Condensed: Add, subtract, multiply, & divide integers
- Evaluate numerical expressions, real-world context
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Order of Operations of Integers, Sum & Difference Only
- Evaluate sum or difference of three integers, at least one difference
- Evaluate sum or difference of four integers, at least one difference
- Evaluate sum or difference of four integers, two grouped in parentheses, at least one difference
- Evaluate sum or difference of four integers, two grouped in absolute value, at least one difference
- Evaluate sum or difference of six integers, two grouped in parentheses, two grouped in absolute value, at least one difference
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Order of Operations of Integers
- Evaluate numerical expressions, three or four integers, including multiplication & division
- Evaluate numerical expressions, three or four integers, including multiplication & division as fraction
- Evaluate numerical expressions, three or four integers, one exponent, including multiplication
- Evaluate numerical expressions, four integers, including multiplication & exponents
- Evaluate numerical expressions, five integers, two grouped in parentheses, including multiplication & division
- Evaluate numerical expressions, five integers, two grouped in absolute value, including multiplication & division
- Evaluate numerical expressions, five integers, one exponent, two grouped in parentheses, including multiplication & division
- Evaluate numerical expression quotients, five to seven integers, one exponent, including multiplication, division, & absolute value
- Evaluate numerical expression quotients, five to seven integers, including multiplication, division, & absolute value
- Condensed: Evaluate numerical expressions
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Fractions
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Converting Fractions
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Converting Fractions to Decimals
- Identify & determine decimal equivalent of fractions, denominator less than 10
- 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 rounded decimals
- Convert fractions to decimals, including improper fractions, including repeating decimals
- Convert mixed numbers to decimals, including repeating decimals
- Convert fractions to decimals, up to two decimal places, real-world context
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Converting Fractions to Percents or Decimals
- 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
- Condensed: Convert proper & improper fractions to rounded percents
- Convert fractions to mixed number percents
- Convert fractions to mixed number percents over 100
- Condensed: Convert fractions to decimals & percents
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Addition of Fractions
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Basic Addition of Fractions, Only Positives
- 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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Basic Addition of Fractions, Including Negatives
- Add fractions, common denominators, at least one negative
- Add fractions, common denominators, at least one negative, including improper differences
- Condensed: Add fractions, common denominators
- Condensed: Add fractions, common denominators, including improper sums
- Add fractions, different denominators, at least one negative
- Condensed: Add fractions, different denominators
- Condensed: Add fractions, no mixed numbers
- Add fractions, different denominators, at least one negative, including improper differences
- Condensed: Add fractions, including improper sums
- Condensed: Add fractions, different denominators, including improper sums
- Condensed: Add fractions, including mixed numbers
- Add mixed numbers, different denominators, at least one negative
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Application of Addition of Fractions
- Add fractions, mixed signs, real-world context
- Add fractions, mixed signs, including improper sums, real-world context
- Add mixed numbers, mixed signs, real-world context
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Subtraction of Fractions
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Basic Subtraction of Fractions, Only Positives
- 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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Basic Subtraction of Fractions, Common Denominators
- Subtract fractions, common denominators, at least one negative
- Subtract fractions, common denominators, including improper differences
- Subtract fractions, common denominators, at least one negative, including improper differences
- Condensed: Subtract fractions, common denominators
- Condensed: Subtract fractions, common denominators, including improper differences
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Basic Subtraction of Fractions, Including Negatives
- Subtract fractions, different denominators, at least one negative
- Condensed: Subtract fractions, different denominators
- Condensed: Subtract fractions, no mixed numbers
- Subtract fractions, different denominators, at least one negative, including improper differences
- Subtract fractions, different denominators, negative proper differences
- Condensed: Subtract fractions, different denominators, including improper differences
- Condensed: Subtract fractions, including improper differences
- Subtract mixed numbers, different denominators, at least one negative
- Subtract mixed numbers, different denominators, borrowing required, negative difference
- Condensed: Subtract fractions, including mixed numbers
- Subtract fractions, different denominators, negative difference
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Application of Subtraction of Fractions
- Subtract fractions, mixed signs, including improper differences, real-world context
- Subtract mixed numbers, mixed signs, real-world context
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Multiplication of Fractions
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Application & Modeling of Multiplication of Fractions
- Multiply whole numbers & fractions, area models
- Multiply whole numbers & fractions, real-world context
- Multiply fractions, positive, real-world context
- Multiply fractions & mixed numbers, mixed signs, real-world context
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Basic Multiplication of Fractions, Only Positives
- Multiply whole numbers & unit fractions, whole number first
- Multiply whole numbers & unit fractions
- Multiply whole numbers & fractions, positive
- Multiply proper & improper fractions, positive
- Multiply fractions, positive
- Multiply fractions, positive, mixed number directions
- Multiply mixed numbers, positive
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Basic Multiplication of Fractions, Including Negatives
- Multiply whole numbers & fractions, mixed signs
- Multiply fractions, mixed signs
- Multiply proper & improper fractions, mixed signs
- Condensed: Multiply fractions, including mixed signs
- Multiply fractions, mixed signs, mixed number directions
- Condensed: Multiply fractions, including mixed signs, mixed number directions
- Multiply mixed numbers, mixed signs
- Condensed: Multiply fraction & mixed numbers, including mixed signs, mixed number directions
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Division of Fractions
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Basic Division of Fractions, Only Positives
- Divide whole numbers by unit fractions
- Divide fractions, positive
- Divide fractions, positive, mixed number directions
- Divide mixed numbers, positive
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Basic Division of Fractions, Including Negatives
- Divide fractions, mixed signs
- Condensed: Divide fractions, including mixed signs
- Divide fractions, mixed signs, mixed number directions
- Condensed: Divide fractions, including mixed signs, mixed number directions
- Divide mixed numbers, mixed signs
- Condensed: Divide fractions & mixed numbers, including mixed signs, mixed number directions
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Application of Division of Fractions
- Determine or estimate quotients of whole numbers, fraction quotients
- Divide whole numbers & unit fractions, including unit fraction multiplication, real-world context
- Divide fractions & whole numbers, mixed signs, 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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Mixed Operations of Fractions
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Basic Mixed Operations of Fractions
- Add or subtract fractions, different denominators, at least one negative, including improper results
- Add or subtract fractions, different denominators, at least one negative, including mixed number results
- Condensed: Add or subtract fractions
- Condensed: Add or subtract fractions, different denominators
- Add or subtract mixed numbers, different denominators, at least one negative, fractional sum greater than one
- Multiply & divide three fractions, mixed signs
- Add or subtract three fractions, positive & negative, different denominators
- Add or subtract four fractions, positive & negative, different denominators
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Application of Mixed Operations of Fractions
- Add or subtract fractions, including estimation, real-world context
- Add & subtract fractions, real-world context
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Decimals
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Converting Decimals
- Convert decimals to percents
- Convert decimals to percents over 100
- Convert decimals to fractions
- 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, Only Positives
- 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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Basic Addition of Decimals, Including Negatives
- Add positive decimals, up to three decimal places
- Add negative decimals, up to three decimal places
- Add positive & negative decimals, up to three decimal places, positive sum
- Add positive & negative decimals, up to three decimal places, negative sum
- Condensed: Add decimals, up to three decimal places
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Application of Addition of Decimals
- Add decimals, positive, up to two decimal places, real-world context
- Condensed: Add decimals, positive, up to two decimal places, including real-world context
- Add decimals, up to hundredths, same signs, real-world context
- Add decimals, up to two decimal places, mixed signs, real-world context
- Condensed: Add decimals, up to three decimal places, real-world context
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Subtraction of Decimals
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Basic Subtraction of Decimals, Only Positives
- 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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Basic Subtraction of Decimals, Including Negatives
- Subtract decimals, up to three decimal places, negative difference
- Subtract decimals, both negative, up to three decimal places, positive difference
- Subtract decimals, both negative, up to three decimal places, negative difference
- Subtract decimals, opposite signs, up to three decimal places, positive difference
- Subtract decimals, opposite signs, up to three decimal places, negative difference
- Condensed: Subtract decimals, up to three decimal places
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Application of Subtraction of Decimals
- Subtract decimals, same signs, up to two decimal places, real-world context
- Subtract decimals, mixed signs, up to two decimal places, real-world context
- Subtract decimals, up to two decimal places, real-world context
- Condensed: Subtract decimals, up to two decimal places, including real-world context
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Multiplication of Decimals
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Basic Multiplication of Decimals, Only Positives
- 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
- Multiply positive decimals, each factor up to three decimal places
- Multiply three positive decimals, products limited to three decimal places
- Condensed: Multiply decimals
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Basic Multiplicaition of Decimals, Including Negatives
- Multiply decimals, both negative, each factor up to two decimal places with one non-zero digit
- Multiply decimals, opposite signs, each factor up to two decimal places with one non-zero digit
- Multiply decimals, both negative, each factor up to two decimal places, including integers up to 19
- Multiply decimals, opposite signs, each factor up to two decimal places, including integers up to 19
- Multiply decimals, both negative, each factor up to two decimal places
- Multiply decimals, opposite signs, each factor up to two decimal places, including integers up to 99
- Multiply decimals, both negative, each factor up to three decimal places
- Multiply decimals, opposite signs, each factor up to three decimal places
- Condensed: Multiply decimals, mixed signs
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Application of Multiplication of Decimals
- Multiply decimals, products limited to two decimal places, real-world context
- Multiply decimals, mixed signs, real-world context
- Multiply decimals, real-world context
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Division of Decimals
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Basic Division of Decimals, Only Positives
- 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
- Divide decimals, up to three decimal places in dividend & divisor
- Condensed: Divide decimals or whole numbers
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Basic Division of Decimals, Including Negatives
- Divide integers by decimals, two-digit dividend, divisor up to two decimal places, both negative
- Divide integers by decimals, two-digit dividend, divisor up to two decimal places, opposite signs
- Divide integers by decimals, two-digit dividend, divisor up to two decimal places, mixed signs
- Divide decimals, up to three decimal places, both negative
- Divide decimals, up to three decimal places, opposite signs
- Divide decimals, up to three decimal places
- Divide decimals, dividend up to four decimal places, divisor integer or up to two decimal places, both negative
- Divide decimals, dividend up to four decimal places, divisor integer or up to two decimal places, opposite signs
- Divide decimals, up to four decimal places
- Condensed: Divide decimals, mixed signs
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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
- Divide decimals, same signs, real-world context
- Divide decimals, mixed signs, real-world context
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Mixed Operations of Decimals
- Condensed: Add & subtract decimals, up to two decimal places
- 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 or subtract three decimals, positive & negative, hundredths
- Add or subtract four decimals, positive & negative, hundredths
- Multiply & divide three decimals, mixed signs
- Condensed: Add, subtract, multiply, & divide decimals, up to two decimal places
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Rational Numbers
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Classifying Rational Numbers
- Classify rational numbers by definitions
- Classify rational numbers using graphic organizers
- Classify rational numbers, including graphic organizers
- Determine relationships between subsets of real numbers
- Determine relationships between subsets of rational numbers
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Absolute Value of Rational Numbers
- Determine absolute value of integers
- Determine absolute value of rational numbers
- Determine absolute value of integers, including real-world context
- Determine absolute value of numeric expression
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Comparing & Ordering Rational Numbers
- Condensed: Order positive decimals & fractions
- Order decimals & fractions
- Order positive rational numbers, no radicals, no exponents
- Order rational numbers, no radicals, no exponents
- Given table, order rational numbers, real-world context
- Given set or list, order rational numbers, real-world context
- Order real numbers, exponents are positive
- Order real numbers, positive exponents, percents are whole, including real-world context
- Order real numbers, positive exponents, percents are whole, including real-world context
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Estimating Rational Numbers
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Basic Estimating of Rational Numbers
- Estimate sum of rational numbers, round both to nearest whole
- Estimate differences of rational numbers
- Estimate products of mixed numbers
- Estimate products of rational numbers, no decimals, round both factors to same place value
- Estimate products of rational numbers
- Estimate quotients of rational numbers, no decimals
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Application of Estimating Rational Numbers
- Estimate sum of rational numbers, round both to nearest whole, real-world context
- Estimate differences of rational numbers, real-world context
- Estimate products of positive rational numbers, real-world contexts
- Estimate products of rational numbers, no decimals, round both factors to nearest whole number, real-world context
- Estimate quotients of rational numbers, no decimals, real-world context
- Estimate quotients of rational numbers, real-world context
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Order of Operations of Rational Numbers
- Evaluate numerical expressions, # ± #(#), decimals
- Evaluate numerical expressions, #/# + #, decimals
- Evaluate numerical expressions, #(# + #), decimals
- Evaluate numerical expressions, decimals, no exponents
- Evaluate numerical expressions, fractions, no exponents
- Evaluate numerical expressions, decimals & fractions, no exponents
- Evaluate numerical expressions, decimals
- Evaluate numerical expressions, fractions
- Evaluate numerical expressions, decimals & fractions
- Evaluate numerical expressions, including rationals & up to two sets of grouping symbols
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Mixed Operations of Rational Numbers
- Multiply decimals times fractions, at least one negative
- Multiply fractions times decimals, at least one negative
- Condensed: Multiply decimals & fractions
- Divide decimal by fraction, both less than one, both positive
- Divide fraction by decimal, both less than one, both positive
- Divide decimal by fraction, both less than one, mixed signs
- Divide fraction by decimal, both less than one, mixed signs
- Condensed: Divide decimals & fractions, both less than one
- Solve multi-step problems with rational numbers, including percents, real-world context
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Scientific Notation
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Basic Scientific Notation
- Identify correct conversion of number from scientific notation with positive exponent to standard form
- Identify correct conversion of number from scientific notation with negative exponent to standard form
- Identify correct conversion of number from standard form to scientific notation with positive exponent
- Identify correct conversion of number from standard form to scientific notation with negative exponent
- Convert number from scientific notation with positive exponent to standard form
- Convert number from scientific notation with negative exponent to standard form
- Multiply decimal or whole number & 10 to negative exponent
- Convert number from standard form to scientific notation with positive exponent
- Convert number from standard form to scientific notation with negative exponent
- Condensed: Identify correct conversion of number between scientific notation & standard form
- Condensed: Convert number between scientific notation & standard form
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Application of Scientific Notation
- Convert numbers between standard form & scientific notation, real-world context
- Convert number from standard form to scientific notation, real-world context
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Operations with Scientific Notation
- Add numbers in scientific notation
- Subtract numbers in scientific notation
- Multiply numbers in scientific notation
- Divide numbers in scientific notation
- Condensed: Add, subtract, multiply, & divide numbers in scientific notation
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Powers of Ten
- Determine equivalent powers of 10 & fractions, decimals, or whole numbers
- Round & convert number from standard form to scientific notation with positive exponent
- Round & convert number from standard form to scientific notation with negative exponent
- Condensed: Round & convert number from standard form to scientific notation
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Comparing & Ordering Scientific Notation
- Compare two numbers in scientific notation
- Compare magnitude of numbers in scientific notation, real-world context
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Radicals & Roots
- Determine square roots of perfect squares
- Solve perfect square root equations
- Condensed: Determine square roots of perfect squares
- Evaluate perfect cube roots
- Solve perfect cube root equations
- Condensed: Determine cube roots of perfect cubes
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Expressions
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Translating Expressions
- Interpret numerical expressions
- Given phrase, determine one-step algebraic expression
- Determine algebraic expressions that represent real-world situations
- Identify equivalent multi-step algebraic expressions & phrases
- Determine algebraic expressions that represent real-world situations, including two-variable expressions
- Identify algebraic expressions, involving distribution, real-world context
- Identify equivalent expressions involving distribution, two or more terms
- Given phrase, determine multi-step algebraic expression
- Given phrase, determine & evaluate multi-step algebraic expression
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Equivalent Expressions
- Identify equivalent numerical expressions using counters
- Identify equivalent algebraic expressions using algebra tiles
- Identify equivalent expressions involving distribution
- Identify equivalent expressions or determine simplified expressions
- Identify equivalent numerical & algebraic expressions, including distribution, including real-world context
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Evaluating Expressions
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Basic Evaluating Expressions, Addition & Subtraction Only
- Evaluate addition 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, whole numbers
- Evaluate subtraction expressions for specified value, one variable, at least one fraction
- Evaluate subtraction expressions for specified value, one variable, at least one decimal
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Basic Evaluating Expressions
- Evaluate expressions for specified value, one variable, one term, two factors
- Evaluate expressions for specified value, one variable, one term, three factors
- Evaluate expressions for specified value, one variable, two terms
- Evaluate expressions for specified values, two variables, two terms
- Evaluate expressions for specified value, one variable, two terms, only sums & differences
- Evaluate expressions for specified values, two variables, two terms, one term with three factors
- Evaluate expressions for specified value, one variable, two terms, multiple operations, including absolute value & powers
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Application of Evaluating Expressions
- Evaluate or identify expressions that represent situations from descriptions, real-world context
- 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
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Distributing or Factoring Expressions
- Simplify algebraic expressions, one variable, distribute once, integer multiplier
- Simplify algebraic expressions, one variable, distribute once, decimal multiplier
- Simplify algebraic expressions, one variable, distribute once, fraction multiplier
- Condensed: Simplify algebraic expressions, one variable, distribute once, including fraction & decimal multipliers
- Simplify algebraic expressions, one variable, distribute once, three or four grouped terms
- Factor GCF from linear binomial expressions, both terms positive
- Factor GCF from linear binomial expressions, both terms negative
- Factor GCF from linear binomial expressions, mixed signs
- Condensed: Factor GCF from linear binomial expressions
- Distribute or factor, linear binomial expressions
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Simplifying Variable Expressions
- Simplify algebraic expressions, combine two terms, positives
- Simplify algebraic expressions, combine two terms
- Simplify algebraic expressions, one variable, positive integer coefficients
- Simplify algebraic expressions, one variable, integer coefficients
- Simplify algebraic expressions, one variable, rational coefficients
- Simplify algebraic expressions, one variable, product of two factors
- Simplify algebraic expressions, one variable, product of two or three factors, one variable factor
- Simplify algebraic expressions, one variable, product of two or three factors
- Simplify algebraic expressions, product of two variable factors
- Simplify algebraic expressions, one variable, product of three factors, two variable factors
- Simplify algebraic expressions, two variables, positive integer coefficients
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Equations
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Solving One-Step Equations
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Addition One-Step Equations
- 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 x + a = b, a < 0, b < 0, x < 0
- Solve a + x = b
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Subtraction One-Step Equations
- 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 x – a = b, a < 0, b < 0, x < 0
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Multiplication One-Step Equations
- Solve ax = b, a > 0, b > 0
- 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
- Solve x/a = b, a < 0, b < 0
- Condensed: Solve one-step linear equations, multiplication or division
- Condensed: Solve one-step linear equations, including fractional coefficients & fractional answers
- Solve one-step linear equations, fractional coefficients & constants
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Division One-Step Equations
- Solve x/a = b, a > 0, b > 0
- Solve x/a = b, a > 0, b < 0
- Solve x/a = b, a < 0, b > 0
- Solve x/a = b, a < 0, b < 0
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Solving One-Step Equations
- Condensed: Solve one-step linear equations, addition or subtraction
- Condensed: Solve one-step linear equations, multiplication or division
- Solve one-step linear equations, fractional coefficients
- Solve one-step linear equations, fractional answers
- Solve one-step linear equations, fractional coefficients & constants
- Condensed: Solve one-step linear equations, including fractional coefficients & fractional answers
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Application of One-Step Equations, Addition
- Determine addition equations, real-world context
- Solve addition equations, real-world context
- Determine & solve addition equations, including real-world context
- Determine & solve or apply addition equations, real-world context
- Determine, solve, & apply addition equations, real-world context
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Appllication of One-Step 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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Application of One-Step 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
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Solving Two-Step Equations
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Application & Modeling of Two-Step Equations
- Solve two-step linear equations, algebra tiles, positive coefficients
- Solve two-step linear equations, algebra tiles
- Determine two-step linear equations, real-world context
- Determine equations or identify real-world situations represented by one-step or two-step equations
- Given two-step linear equation, identify real-world situation represented by equation
- Solve problems that can be represented by two-step equations, real-world context
- Determine solutions to problems using common formulas, including simple interest, area & perimeter, & d = rt, real-world context
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Multiplication Two-Step Equations with Addition
- Solve ax + b = c, a > 0, b > 0, c > 0, x > 0
- Solve ax + b = c, a > 0, b > 0, c < 0, x < 0
- Solve ax + b = c, a > 0, b < 0, c > 0, x > 0
- Solve ax + b = c, a < 0, b > 0, c > 0, x > 0
- Solve ax + b = c, a < 0, b < 0, c > 0, x < 0
- Solve ax + b = c, b > 0, c > 0, x < 0
- Solve ax + b = c, b < 0, c < 0, x < 0
- Solve ax + b = c, a < 0, b < 0, c < 0, x < 0
- Solve ax + b = c, a > 0, b < 0, c < 0, x > 0
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Multliplication Two-Step Equations with Subtraction
- Solve ax – b = c, a > 0, b < 0, c > 0, x > 0
- Solve ax – b = c, a > 0, b < 0, c < 0, x < 0
- Solve ax – b = c, a > 0, b > 0, c < 0, x > 0
- Solve ax – b = c, a < 0, b > 0, c > 0, x < 0
- Solve ax – b = c, a < 0, b > 0, c < 0, x < 0
- Solve ax – b = c, b < 0, c > 0, x < 0
- Solve ax – b = c, b > 0, c < 0, x < 0
- Solve ax – b = c, a < 0, b < 0, c > 0, x > 0
- Solve ax – b = c, a > 0, b > 0, c > 0, x > 0
- Solve ax ± b = c
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Division Two-Step Equations with Addition
- Solve x/a + b = c, a > 0, b > 0, c > 0, x > 0
- Solve x/a + b = c, a > 0, b > 0, c < 0, x < 0
- Solve x/a + b = c, a > 0, b < 0, c > 0, x > 0
- Solve x/a + b = c, a < 0, b > 0, c > 0, x > 0
- Solve x/a + b = c, a < 0, b < 0, c > 0, x < 0
- Solve x/a + b = c, b > 0, c > 0, x < 0
- Solve x/a + b = c, a > 0, b < 0, c < 0, x > 0
- Solve x/a + b = c, b < 0, c < 0, x < 0
- Solve x/a + b = c, a < 0, b < 0, c < 0, x < 0
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Division Two-Step Equations with Subtraction
- Solve x/a – b = c, a > 0, b < 0, c > 0, x > 0
- Solve x/a – b = c, a > 0, b < 0, c < 0, x < 0
- Solve x/a – b = c, a > 0, b > 0, c > 0, x > 0
- Solve x/a – b = c, a < 0, b < 0, c > 0, x > 0
- Solve x/a – b = c, a < 0, b > 0, c > 0, x < 0
- Condensed: Solve x/a ± b = c
- Solve x/a – b = c, b < 0, c > 0, x < 0
- Solve x/a – b = c, a > 0, b > 0, c < 0, x > 0
- Solve x/a – b = c, b > 0, c < 0, x < 0
- Solve x/a – b = c, a < 0, b > 0, c < 0, x < 0
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Rational Coefficient Two-Step Equations
- Determine if given value is solution to two-step linear equations
- Solve two-step linear equations, decimal coefficients
- Solve two-step linear equations, fractional coefficients
- Condensed: Solve one- or two-step linear equations, fractional coefficients
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Solving Multi-Step Equations
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Application & Modeling of Multi-Step Equations
- Given algebra tiles, determine & solve one-variable equations with variables on both sides
- Solve problems that can be represented by one-step equations, including algebra tiles, real-world context
- Determine linear equations & solve problems that can be represented by equations with distributive property on one side, real-world context
- Determine & solve linear equations with variables on both sides, real-world context
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Basic Multi-Step Equations
- Solve linear equations, distributive property on one side
- Solve three-step linear equations involving distribution of decimal multiplier
- Solve three-step linear equations involving distribution, fractional multiplier cancels if distributed
- Solve three-step linear equations involving distribution, fractional multiplier doesn’t cancel if distributed
- Condensed: Solve three-step linear equations involving distribution, including fractional & decimal answers
- Solve (ax ± b)/c = d
- Solve linear equations, variables as numerators on both sides
- Solve linear equations, binomials on both sides, decimals
- Solve linear equations, binomials on both sides, fractions
- Solve multi-step linear equations
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Inequalities
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Identifying & Graphing Inequalities
- Graph inequalities on number line
- Given graph, determine inequality
- Determine graph from inequality or inequality from graph
- Identify solutions to inequalities, including real-world context
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Solving One-Step Inequalities
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Basic One-Step Inequalities
- 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 one-step inequalities, a * x, a < 0
- Condensed: Solve one-step inequalities, a * x
- Solve one-step inequalities, x/a, a > 0
- Solve one-step inequalities, x/a, a < 0
- Condensed: Solve one-step inequalities, x/a
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Basic Solving & Graphing of One-Step Inequalities, Addition & Subtraction
- Solve & graph one-step inequalities, x + #
- Solve & graph one-step inequalities, x – #
- Condensed: Solve & graph one-step inequalities, x ± #
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Basic Solving & Graphing One-Step Inequalities, Multiplication & Division
- Solve & graph one-step inequalities, a * x, a > 0
- 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
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Basic Solving & Graphing of One-Step Inequalities, Mixed Operations
- 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
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Application of One-Step Inequalities
- Given inequality, identify phrase or real-world problem that represents inequality
- Represent real-world problems as inequalities
- Determine one-step inequalities, including real-world context
- Determine one-step inequalities, rational numbers, including real-world context
- Identify one-step inequalities that model real-world problems or interpret inequality components
- Given one-step inequality, identify real-world problem modeled by inequality
- Given one-step inequality, identify real-world problem modeled by inequality, rational numbers
- Determine, solve, & graph one-step inequalities, including real-world context
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Solving Two-Step Inequalities
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Application & Modeling of Two-Step Inequalities
- Determine if given value is solution to two-step inequality
- Solve two-step inequalities modeled with algebra tiles
- Determine two-step inequalities, rational numbers, including real-world context
- Given two-step inequality, identify real-world problem modeled by inequality
- Determine & solve two-step inequalities, greater than, real-world context
- Determine & solve two-step inequalities, less than, real-world context
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Basic Two-Step Inequalities
- Solve two-step inequalities, integers
- Solve two-step inequalities, decimals
- Solve two-step inequalities, fractions
- Condensed: Solve two-step inequalities
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Basic Solving & Graphing of Two-Step Inequalities
- Solve & graph two-step inequalities, integers
- Solve & graph two-step inequalities
- Solve & graph two-step inequalities, decimals
- Solve & graph two-step inequalities, fractions
- Condensed: Solve & graph two-step inequalities
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Linear Concepts
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Slope of a Line
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Identifying Slope Category
- Given linear graph, identify type of slope
- Identify linear graph with specific type of slope
- Given linear equation, identify type of slope
- Given table of linear equation, identify type of slope
- Condensed: Identify type of slope
- Given graph of horizontal or vertical line, determine rate of change
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Finding Slope, Given Equation
- Given equation in slope-intercept form, determine rate of change, integer solution
- Given equation in slope-intercept form, determine rate of change
- Given equation of horizontal or vertical line, determine rate of change
- Given equation in point-slope form, identify slope
- Given linear equation in standard form, determine rate of change
- Given table of linear equation, determine rate of change
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Finding Slope, Given Points Or Graph
- Given two points, determine rate of change, one coordinate is fraction
- Given two points with integer coordinates, determine rate of change
- Given two points, determine rate of change, integer solution, including undefined
- Given two points, determine rate of change, two coordinates are fractions
- Given linear graph, determine rate of change, integer solution
- Given linear graph, determine rate of change
- Given linear graph, determine rate of change, various scales
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Comparing Slopes
- Identify linear graph with most extreme rate of change
- Identify linear table with most extreme rate of change
- Given description, compare rates of change, real-world context
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Finding & Using Slope
- Given equation in slope-intercept form, determine next value in table, Δx = 1
- Given equation in slope-intercept form, determine next value in table
- Given equation in slope-intercept form, determine values in table
- Given table, determine rate of change & specific value, function notation, integer rate of change
- Given table, determine rate of change & specific value, function notation
- Given table of linear equation, determine rate of change & specific value
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Intercepts, Given Graph
- Given linear graph, plot y-intercept
- Given linear graph, plot x-intercept
- Given linear graph, determine coordinates of y-intercept
- Given linear graph, determine coordinates of x-intercept
- Given linear graph, locate intercept or determine coordinates, various scales
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Intercepts, Given Equation
- Given linear equation in slope-intercept form, determine coordinates of y-intercept
- Given equation of horizontal or vertical line, determine coordinates of y-intercept
- Given linear equation in slope-intercept form, determine coordinates of x-intercept
- Given equation of horizontal or vertical line, determine coordinates of x-intercept
- Given linear equation in slope-intercept form, plot y-intercept
- Given equation of horizontal or vertical line, plot y-intercept
- Given linear equation, determine intercepts
- Given linear equation in standard form, determine coordinates of y-intercept
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Writing Equation of a Line
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Writing Equation Given Point & Slope
- Given point & integer slope, determine linear equation in point-slope form, including slope-intercept form conversion
- Given slope & y-intercept, determine equation
- Given point & integer slope, determine linear equation in slope-intercept form
- Given point & integer slope or rate of change, determine linear equation in slope-intercept form
- Given point & fractional slope, determine linear equation in point-slope form, including slope-intercept form conversion
- Given point & fractional slope, determine linear equation in slope-intercept form, integer y-intercept
- Given point & fractional slope, determine linear equation in slope-intercept form, fractional y-intercept
- Given positive point & whole number slope, determine y-intercept, equation, & specific value
- Given point & integer slope, determine y-intercept, equation, & specific value
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Writing Equation Given Two Points
- Given two points, determine linear equation in point-slope form, integer slope, including slope-intercept form conversion
- Given two points, determine linear equation in point-slope form, fractional slope, including slope-intercept form conversion
- Given two points, determine linear equation, undefined slope
- Given two points, determine linear equation, zero slope
- Given two points, determine linear equation in slope-intercept form, integer slope
- Given two points, determine linear equation in slope-intercept form, fractional slope
- Given two points, determine linear equation in standard form, integer slope, including slope-intercept form conversion
- Given two points, determine linear equation in standard form, fractional slope, including slope-intercept form conversion
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Writing Equation Given Various Components
- Identify equivalent linear graphs & equations in slope-intercept form
- Identify equivalent linear graphs & equations in slope-intercept form, various scales
- Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
- Given points or slope & point, determine linear equation in point-slope or standard form
- Given points or slope & point, determine linear equation in standard form
- Given points or slope & point, determine linear equation in various forms
- Given intercepts, determine linear equation in slope-intercept form
- Condensed: Given two points, determine linear equation in slope-intercept form, including horizontal & vertical lines
- Condensed: Given linear graph, determine equation in slope-intercept form & specific value, various scales, including real-world context
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Writing Equation Given Graph
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Given Graph of y-Intercept of Zero, Write Equation
- Given linear graph through origin with points shown on line, determine equation in slope-intercept form, integer slopes
- Given linear graph through origin, determine equation in slope-intercept form, integer slope, 1 ≤ |m| ≤ 3
- Given linear graph through origin, determine equation in slope-intercept form, integer slope
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Given Graph with Varying y-Intercepts, Write Equation
- Given linear graph, determine equation in point-slope form
- Given linear graph, determine equation in slope-intercept form, m = 1
- Given linear graph, determine equation in slope-intercept form, integer slopes
- Given linear graph, determine equation in slope-intercept form, fractional slopes
- Given linear graph, determine slope, y-intercept, & equation
- Given linear graph, determine equation in standard form
- Given linear graph, identify equation, slope-intercept form
- Given linear graph, identify equation, various forms
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Given Graph with Varying y-Intercepts & Scales, Write Equation
- Given linear graph, determine equation in slope-intercept form, m = 1, various scales
- Given linear graph, determine equation in slope-intercept form, integer slopes, various scales
- Given linear graph, determine equation in slope-intercept form, m = ±1, various scales
- Given linear graph, determine equation in slope-intercept form & specific value, various scales
- Given linear graph, identify equation in slope-intercept form, integer slopes, various scales
- Given equation in slope-intercept form, identify graph, integer slopes, various scales
- Condensed: Identify equivalent linear graphs & equations in slope-intercept form, integers slopes, various scales
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Identifying Key Features of a Linear Function
- Given linear graph, determine slope & y-intercept, integer slope
- Given linear graph, determine slope & y-intercept
- Given graph of linear equation, determine slope & intercepts
- Given table of linear equation, determine slope & intercepts
- Given linear equation, determine slope & intercepts
- Given linear equation in standard form, solve for y
- Given linear equation in standard form, determine slope
- Condensed: Given linear equation in standard form, solve for y or determine slope
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Determining Solution of Linear Equation
- Given horizontal or vertical linear equation, determine if point is on line
- Given linear equation in slope-intercept form, determine if point is on line
- Given linear equation in standard form, determine if point is on line
- Given horizontal or vertical linear equation, identify point on line
- Given linear equation in slope-intercept form, identify point on line
- Given linear equation in standard form, identify point on line
- Given graph of linear equation, identify point on line
- Condensed: Given linear equation in slope-intercept form & graph, identify point on line
- Identify linear & non-linear relationships, various representations
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Equations, Graphs, & Tables
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Equation to Table, m=1
- Given linear equation, fill missing value in table, m = 1
- Given linear equation & table, determine another point, m = 1
- Given linear equation, fill missing value in table, m = 1, Δx ≥ 5
- Given linear equation, fill table, m = 1
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Equation to Table
- Given horizontal or vertical linear equation, fill table
- Given linear equation & two x-values, determine y-values in table
- Given linear equation, fill missing value in table, integer slope
- Given linear equation, fill missing value in table, integer slope, b = 0, Δx ≥ 5
- Given linear equation, fill missing value in table, integer slope, Δx ≥ 5
- Given linear equation, fill table, integer slope, b = 0
- Given linear equation, fill table, integer slope
- Given linear equation, determine table values
- Given linear equation & one x-value, determine y-value in table
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Equation to Graph
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Standard Form to Graph
- Given linear equation in standard form, graph
- Given linear equation in standard form, graph, scrambled variable terms
- Condensed: Determine linear equation in standard form & graph, including real-world context
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Slope-Intercept Form to Graph
- Given linear equation & table, determine graph
- Graph linear equations, m = 1
- Graph linear equations, m = 1, various scales
- Given equation in slope-intercept form, graph line, m = ±1, various scales
- Graph linear equations, integer slope, various scales
- Graph linear equations, integer slope not including one & negative one, b = 0
- Graph linear equations, integer slope not including one & negative one
- Graph linear equations, including horizontal & vertical, integer slope, various scales
- Graph linear equations, fractional slope
- Graph linear equations, fractional slope, various scales
- Condensed: Graph linear equations, including horizontal & vertical, various scales
- Condensed: Given linear equation or description, determine graph, fractional slope, including real-world context
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Basic Graphing
- Given point & integer slope, graph line
- Given point & slope, graph line
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Graph to Table
- Given linear graph with points shown on line, determine table value
- Given linear graph through origin with points shown on line, determine table values, one table point off graph
- Given linear graph through origin with points shown on line, determine table value, table point off graph
- Given linear graph through origin, determine table value
- Given linear graph, determine table value, m = 1, table point off graph
- Given linear graph through origin, determine table values, one table point off graph
- Given linear graph through origin, determine table value, table point off graph
- Given linear graph, determine table value, table point off graph
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Table to Equation
- Given table, identify linear equation in slope-intercept form, rational constants & coefficients
- Given table representing horizontal linear equation, determine equation
- Given table representing vertical linear equation, determine equation
- Given table, determine linear equation, m = 1
- Given table, determine linear equation, integer slope, b = 0
- Given table, determine linear equation, integer slope
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Linear Word Problems
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Identifying Key Features Given Verbal Description
- Given graph or table of linear function, determine slope or y-intercept, real-world context
- Given description of linear relationship, determine slope, y-intercept, & equation, real-world context
- Given description of linear equation, identify graph, fractional slope, real-world context
- Form 1 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope, only input to output questions
- Form 2 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, positive slope
- Form 3 – Given slope & intercept, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
- Form 4 – Given point & slope, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
- Form 5 – Given two points, interpret linear relationship, determine slope-intercept equation, & graph, including negative slope
- Condensed: Forms 3 to 5 – Given linear word problem, interpret linear relationship, determine slope-intercept equation, & graph
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Choosing Correct Model Given Verbal Description
- Given description of linear equation, identify graph, integer slope, real-world context
- Given linear word problem, identify graph
- Given linear equation, interpret slope & y-intercept, real-world context
- Given description of linear relationship, identify graph, table, or equation, real-world context
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Proportional Relationships
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Graphing Proportional Relationships
- Given unit rate, determine graph of proportional relationship, real-world context
- Given table, graph proportional linear equation
- Graph proportional linear equation
- Determine graph of proportional relationship, real-world context
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Identifying Independent & Dependent Variables
- Given table, identify dependent or independent variable
- Given equation, identify dependent or independent variable
- Given table or graph, identify dependent or independent variable
- Given description, identify dependent or independent variable
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Writing Equations, Completing Tables, or Graphing
- Given constant of proportionality, determine table, graph, or equation
- Given table, determine constant of proportionality, graph, or equation
- Given graph, determine constant of proportionality, table, or equation
- Given equation, determine constant of proportionality, graph, or table
- 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
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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
- Identify linear graph with most extreme rate of change
- Identify linear table with most extreme rate of change
- Compare rates of changes represented differently
- Given description, compare rates of change, real-world context
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Proportional & Non-Proportional
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Additive & Multiplicative Relationships
- Given table, determine additive or multiplicative equation
- Identify graphs of additive & multiplicative relationships
- Condensed: Given additive or multiplicative relationship in table, determine equation
- Identify equivalent representations of additive & multiplicative relationships, including decimals & fractions
- Identify situations modeled by additive & multiplicative relationships
- Identify components of additive & multiplicative equations
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Completing Tables or Graphing
- Given linear equation & table, identify graph
- Identify tables that represent real-world situations, y = mx or y = x + b
- Given linear equation, determine y-values in table, real-world context
- Given linear equation, determine y-values in table & identify graph, first quadrant
- Given slope-intercept equation, determine table & identify graph
- Given linear equation & table, determine graph
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Writing Equations
- Given linear graph & table, determine equation
- Determine equations that represent real-world situations, y = mx or y = x + b
- Determine equations that represent real-world situations, including two-step equations
- Given additive relationship in table, determine equation
- Given multiplicative relationship in table, determine equation
- Identify equivalent representations of additive & multiplicative relationships
- Identify situations modeled by tables or equations, y = mx or y = x + b
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Writing Equations, Completing Tables, or Graphing Mixed
- Condensed: Determine tables or equations of additive & multiplicative relationships
- Condensed: Determine equations & graphs of additive & multiplicative relationships
- Identify representation of proportional relationship, various representations, real-world context
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Identifying Proportional vs. Non-Proportional
- Identify equations showing proportional relationship
- Identify graphs showing proportional relationship
- Identify tables showing proportional relationship
- Identify tables, graphs, or equations showing proportional relationship
- Identify proportional & non-proportional relationships, real-world context
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Geometry
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Perimeter & Area
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Rectangle Perimeter
- Determine perimeter of rectangles
- Given sides of rectangle, determine perimeter
- Given sides of rectangle, determine perimeter
- Determine perimeter of rectangles, including decimal dimensions
- Determine perimeter of rectangles, real-world context
- Determine perimeter of rectangles, including decimal dimensions, real-world context
- Condensed: Determine perimeter of rectangles, including real-world context
- Given perimeter of rectangle & one side, determine dimension
- Given perimeter of rectangle & one side, determine dimension, including decimals
- Given perimeter & relationship between sides, determine specific dimension
- Given perimeter & one dimension of rectangle, determine missing dimension
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Rectangle Area
- Given sides of rectangle, determine area, model provided
- Given sides of rectangle, determine area
- Given area & one dimension of rectangle, determine missing dimension
- Determine area of missing dimension of rectangles, real-world context
- Given sides of rectangle & cost per square unit, determine area & total cost, real-world context
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Parallelogram Perimeter & Area
- Determine area of parallelograms, model provided
- Determine area of parallelograms
- Determine area or perimeter of parallelograms
- Given area & one dimension of parallelogram, determine missing dimension
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Trapezoid Area
- Determine area of trapezoids
- Given area & base lengths of trapezoid, determine height
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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
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Circle Circumference & Area
- Determine circumference of circle, exact answers, multiple choice, including real-world context
- Given radius or diameter, determine circumference
- 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
- Determine areas of semicircles & quarter circles
- Given circumference of circle, determine radius or diameter
- Condensed: Given area or circumference of circle, determine radius or diameter
- Identify approximate formulas for circumference & area of circles
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Compound Figure Area
- Determine area of shaded region between nested rectangles
- Determine area of shaded region between nested shapes
- Determine area of composite figures, rectangle with various figures attached, no circular parts
- Determine area of composite figures, no circular shapes
- Determine area of composite figures, rectangle with various figures attached
- Determine area of composite figures, at least three subdivisions
- Determine area of composite figures
- Determine area of composite figures, real-world context
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Mixed Figures Perimeter & Area
- Identify formulas for area & perimeter of basic shapes
- Determine perimeter of polygons, including real-world context
- Determine areas of rectangles & parallelograms
- Determine areas of triangles & trapezoids
- Determine area of polygons in coordinate plane, real-world context
- Determine area of shaded region between nested shapes
- Given coordinates of vertices, determine side lengths & perimeter of polygons
- Given area, determine dimensions of rectangles & parallelograms
- Given area, determine dimensions of triangles
- Condensed: Determine areas & dimensions of rectangles & parallelograms
- Condensed: Determine areas & dimensions of triangles & trapezoids
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Surface Area & Volume
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Net Surface Area
- Given net, determine surface area of prisms
- Given net, determine surface area of pyramids
- Given net, determine surface area of prisms & pyramids
- Given net, determine surface area of rectangular & triangular prisms & pyramids
- Given net, determine lateral surface area of prisms
- Given net, determine lateral surface area of pyramids
- Given net, determine lateral surface area of prisms & pyramids, real-world context
- Condensed: Given net, determine surface area & lateral surface area of prisms & pyramids, including real-world context
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Rectangular Prism Surface Area & Volume
- Determine surface area of rectangular prisms
- Given base area & edge or all edges, determine volume of rectangular prism
- Determine volume of rectangular prisms, whole numbers or decimals
- Determine volume of rectangular prisms, whole numbers, decimals, or fractions
- Determine volumes of rectangular prisms, rational dimensions, real-world context
- Determine equations for volume of rectangular prisms, rational dimensions, 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
- Given volume, determine edges of rectangular prisms
- Determine volume or edge of rectangular prisms, whole numbers
- Determine volume or edge of rectangular prisms, whole numbers, decimals, or fractions, real-world context
- Condensed: Determine volumes or edges of rectangular prisms, whole numbers, decimals, or fractions, including real-world context
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Cube Volume
- Determine volume of cubes, whole numbers or decimals
- Determine volume of rectangular prisms, whole numbers or decimals
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Cylinder Surface Area & Volume
- Given base area & height, determine volume of cylinder
- Determine volume of cylinders
- Determine surface area of cylinders
- Determine lateral surface area of cylinders
- Given volume, determine dimension of cylinder
- Given surface area, determine dimension of cylinder
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Pyramid Surface Area & Volume
- Determine volume of pyramids
- Determine surface area of pyramids
- Given volume, determine dimension of pyramid
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Mixed Figures Surface Area & Volume
- Determine volumes of rectangular & triangular prisms, fractional dimensions
- Determine surface areas of 3D figures, no circles
- Determine surface area of 3D figures, real-world context
- Identify & determine relationship between volumes of rectangular prisms & pyramids
- Identify & determine relationship between volumes of triangular prisms & pyramids
- Condensed: Identify & determine relationship between volumes of prisms & pyramids
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Properties of Quadrilaterals & Triangles
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Classifying Triangles
- Given three sides, classify triangles
- Classify triangles based on angles & sides
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Triangle Angle Sum Theorem
- Given two angle measures in triangle, determine angle measure
- Apply triangle angle sum theorem to determine angles, multiple algebraic expressions
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Triangle Angle-Side Relationships
- Determine smallest & largest sides or angles in triangle
- Order angles in triangles
- Condensed: Determine angles & order side lengths & angles in triangles, including algebraic expressions
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Triangle Inequality Theorem
- Apply triangle inequality theorem to determine side lengths
- Apply triangle inequality theorem to determine range of values for unknown side
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Equilateral & Isosceles Triangles
- Solve problems involving perimeter of equilateral triangles
- Solve problems involving perimeter of isosceles triangles
- Condensed: Solve problems involving perimeter of equilateral & isosceles triangles
- Determine angle measure in isosceles triangle, at most one algebraic expression
- Given equilateral triangle & algebraic expression for angle, solve for variable
- Determine angle measure in isosceles triangle, up to two algebraic expressions
- Given equilateral triangle & algebraic expressions for sides, solve for variable or determine side length
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Similar Figures
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Similar Triangles
- Determine similar triangles using SAS similarity
- Determine similar triangles using SSS similarity
- Condensed: Determine similar triangles using SAS or SSS similarity
- Determine angles of similar triangles using AA similarity
- Determine sides of similar triangles using AA similarity
- Determine similarity of triangles using AA similarity
- Given similar triangles, determine perimeter
- Given similar triangles, determine area
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Similar Polygons
- Identify corresponding parts of similar figures
- Given similar figures, identify proportion of side lengths, triangles & quadrilaterals
- Given similar figures, identify proportion of side lengths, image orientations differ
- Identify similar polygons
- Determine dimensions in similar figures, whole number dimensions
- Determine dimensions using similar figures & indirect measurements
- Determine dimensions in similar figures
- Determine parts using similar triangles, including real-world context
- Given similar rectangles, determine perimeter
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Coordinate Plane
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Basic Coordinates, First Quadrant
- 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
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Application of Coordinates, 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
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Integral Coordinates, All Quadrants
- Given integer point on graph, determine coordinates, point on axis
- Given integer point on graph, determine coordinates
- Given lattice point, determine coordinates
- Plot integer points on coordinate plane, point on axis
- Plot integer points
- Plot points on coordinate plane, student selects scales
- Condensed: Plot integer points or determine coordinates
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Rational Coordinates, All Quadrants
- Given rational point, determine location on coordinate plane
- Plot rational points on coordinate plane
- Plot rational points on coordinate plane, graph scale at most one-half
- Plot or identify rational points on coordinate plane
- Condensed: Plot or identify points on coordinate plane
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Distance
- 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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Transformations
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Reflections
- Determine coordinates of reflected points
- Identify rule or reflected point on coordinate plane
- Given figure on coordinate plane, determine reflected coordinates
- Given coordinate vertices of figure, determine reflected image
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Translations
- Identify rule or determine translated point on coordinate plane
- Given figure on coordinate plane, determine translated coordinates
- Given coordinate vertices of figure, determine translated image
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Rotations
- Identify rule or rotated point on coordinate plane
- Given figure on coordinate plane, determine rotated coordinates
- Given coordinate vertices of figure, determine rotated image
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Dilations
- Identify rule or dilated point on coordinate plane, including variable scale factors
- Identify characteristics of dilations
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Mixed Transformations
- Identify characteristics of transformed lines
- Identify characteristics of transformed parallel lines
- Identify characteristics of transformed line segments
- Identify characteristics of transformed angles
- Identify characteristics of transformed lines, segments, & angles
- Identify characteristics of transformations
- Identify rule or determine transformed point on coordinate plane
- Identify rule for transformed shape on coordinate plane
- Composition of transformations on coordinate plane
- Identify reflections & rotations on coordinate plane
- Condensed: Identify rule or determine transformed point on coordinate plane
- Condensed: Given figure on coordinate plane or coordinate vertices, determine transformed image or coordinates
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Mixed Transformations, Congruence
- Given similar figures, identify description of transformations
- Identify congruence transformations
- Given congruent figures, identify description of transformations
- Condensed: Given similar or congruent figures, identify description of transformations
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3D Figures
- Identify 3D figures & their bases
- Determine 2D orthographic representation of 3D blocks
- Identify equivalent representations of 3D figures & nets
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Angles
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Classifying Angles
- Identify angle names
- Identify angle pairs
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Vertical Angles & Adjacent Angles
- Given vertical angles, determine angle measure
- Given parallel lines with transversal & angle, determine vertical angle
- Given figure, determine missing part of adjacent angle
- Given vertical angles, determine angle measure, one algebraic expression
- Given parallel lines with transversal & angle, determine vertical angle, algebraic expressions
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Complementary Angles
- Given complementary angles, determine angle measure
- Given complementary angles, determine angle measure, one algebraic expression
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Supplementary Angles
- Given supplementary angles, determine angle measure
- Given vertical angles, determine supplementary angle measure
- Given supplementary angles, determine angle measure, one algebraic expression
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Alternate Interior & Alternate Exterior Angles
- Given parallel lines with transversal & angle, determine alternate interior angle
- Given parallel lines with transversal & angle, determine alternate exterior angle
- Given parallel lines with transversal & angle, determine alternate interior angle, algebraic expressions
- Given parallel lines with transversal & angle, determine alternate exterior angle, algebraic expressions
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Corresponding & Same-Side Interior Angles
- Given parallel lines with transversal & angle, determine corresponding angle
- Given parallel lines with transversal & angle, determine same-side interior angle
- Given parallel lines with transversal & angle, determine corresponding angle, algebraic expressions
- Given parallel lines with transversal & angle, determine same-side interior angle, algebraic expressions
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Adjacent, Vertical, Supplementary, & Complementary Angles
- Determine angle measures, including figures or descriptions
- Determine complementary, supplementary, or equivalent angle measures
- Given vertical, complementary, or supplementary angles, determine angle measure, one algebraic expression
- Determine angle measures in figures, one-step algebraic expressions
- Given vertical angles, determine supplementary angle measure, algebraic expressions
- Determine complementary, supplementary, or equivalent angle measures, algebraic expressions
- Determine angle measures in figures, algebraic expressions
- Determine angle measures in figures, two algebraic expressions
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Mixed Angles Formed by Transversals
- Given parallel lines with transversal & angle, identify specified angle pairs, uses “consecutive” terminology
- Given parallel lines with transversal, identify specified angle pairs, only numbered angles, uses “consecutive” terminology
- Given parallel lines with transversal & angle, determine supplement to corresponding angle
- Given parallel lines with transversal & angle, determine specified angle
- Determine angle measures involving parallel lines, one-step algebraic expressions
- Given parallel lines with transversal & angle, determine specified angle, algebraic expressions
- Determine angle measures involving parallel lines, algebraic expressions
- Determine angle measures involving parallel lines, algebraic expressions
- Given parallel lines with transversal & angle, determine supplement to corresponding angle, algebraic expressions
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Scale
- Given scale, determine specified dimension in scaled figure, real-world context
- Given scale, determine area in scaled figure, real-world context
- Compare measurements drawn with different scale factors
- Compare measurements of scaled shapes, including 3D shapes
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Ratios, Rates, & Proportions
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Ratios
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Simplifying Ratios
- Given ratio, identify table
- Condensed: Simplify ratios, identify equivalent ratios, & determine missing components of proportions
- Condensed: Determine ratios, relationship between ratio terms, & specified quantities, real-world context
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Representing Ratios
- Determine part to whole ratio, strip diagrams, real-world context
- Determine part to part ratio, strip diagrams, real-world context
- Determine part to whole ratio, decimal grids
- Determine part to part ratio, decimal grids
- Determine part to whole ratio, double number lines, real-world context
- Determine part to part ratio, including double number lines, including real-world context
- Determine part to whole ratio, various models
- Determine part to part ratio, various models
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Application of Ratios
- Given table, determine ratios, integers
- Compare rates or determine specified values in proportional relationships, real-world context
- Compare rates
- Determine specified values in proportional relationships, real-world context
- Given double number line model, determine percent or specified quantity, real-world context
- Condensed: Given extended ratio, determine ratio or specified quantity, real-world context
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Rates
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Basic Unit Rates
- Identify unit rates
- Given unit rate, determine specified value in proportional relationship, real-world context
- 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
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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
- Given rate, convert time unit to determine quantity over time interval, real-world context
- Given rate of travel, determine distance or time
- Determine & compare unit rates, real-world context
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Proportions
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Basic Proportions
- Solve proportions, whole numbers
- Solve proportions
- Solve proportions, mixed number components, whole number cross products
- Solve proportions, mixed number components
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Application of Proportions
- Solve proportions to convert measurement units
- Given proportional relationship, determine specified quantity, real-world context
- Solve proportions, exact answers, real-world context
- Solve proportions, rounded answers, real-world context
- Solve proportions involving time, real-world context
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Percents
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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
- Convert repeating decimals to fractions
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Basic Finding Total, Part, or Percent of Number
- Given percent & whole, determine part, exact answers
- Given part & percent, determine whole, exact answers
- Given percent & whole, determine part, whole number answers
- Given part & percent, determine whole
- Given part & whole, determine percent
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Application of Finding Total, Part, or Percent of Number
- Given percent & whole, determine part, real-world context
- Given part & percent, determine whole, real-world context
- Given part & whole, determine percent, real-world context
- Determine percent of change, whole numbers, including real-world context
- Determine percent of change, including real-world context
- Given percent, identify table that shows percent
- Determine specified values in tables involving percents
- Identify part of whole, real-world context
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Finding Tip, Tax, Markup, Markdown, & Commission
- Determine tips
- Determine tax
- Determine markups
- Determine commissions
- Condensed: Determine tip, tax, discount, or markup
- Determine discount, tax, or total cost
- Determine increases involving tips, tax, & markups
- Determine decreases involving sales, discounts, & markdowns
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Finding Percent of Change
- Determine percent of change, whole numbers, including real-world context
- Determine percent of change, including real-world context
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Calculating Simple & Compound Interest
- Determine simple interest
- Determine simple interest & total amount
- Given simple interest earned, determine principal, rate, or time
- Determine income tax for earned wages
- Determine savings in loan repayment based on various lengths of repayment
- Determine compound interest
- Determine annually compounded interest
- Condensed: Determine compound interest on savings & loans
- Determine & compare simple & compound interest
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Probability & Statistics
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Measures of Center & Spread
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Calculating Measures of Center & Spread
- Identify definition of mean, median, mode, or range
- 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
- Given various representations of data, identify mean, median, mode, & range
- Given mean, median, mode, or range, determine missing value in data set
- Given mean, median, or range, determine missing or additional value in data set
- Given additional value in data set, determine change in mean, median, mode, or range
- Determine interquartile range of data
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Interpreting Measures of Center & Spread
- Given various representations of data, identify outlier
- Identify measures of center based on data distribution
- Identify & interpret measures of center
- Identify & interpret measures of variability
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Graphical Displays of Data
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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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Box Plots
- Determine characteristics of boxplots
- Solve problems involving interpretation of box plots
- Solve problems involving interpretation of stacked box plots, real-world context
- Given boxplot, determine values from five-number summary
- Solve problems involving five-number summary
- Condensed: Determine five-number summary, including box plots
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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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Frequency Tables
- Interpret two-way frequency tables, conditional distribution
- Interpret two-way frequency tables, marginal distribution
- Interpret two-way frequency tables, joint distribution
- Condensed: Interpret two-way frequency tables
- Determine two-way frequency tables
- Given two-way frequency tables, identify associations
- Determine specified probabilities in two-way frequency tables
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Histograms
- Given various representations of data, determine histogram
- Solve problems involving interpretation of histograms
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Mixed Graphical Displays
- Given data, determine statistical display
- Determine or interpret shapes & features of graphs
- Determine or interpret measures of center & spread from graphs
- Condensed: Solve problems involving interpretation of box plots & stem-&-leaf plots
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Statistical Data
- Determine sample size, various representations
- Identify biased samples & questions
- Identify samples & populations
- Compare data from two samples, various representations
- Identify simulations used to acquire simple random samples
- Identify simulations to model probability events
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Probability
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Basic Probability
- Determine sample spaces
- Classify probabilities by levels of likelihood
- Determine probabilities of single events
- Determine theoretical probabilities, fraction answers
- Determine probabilities & complementary probabilities of single events, including visual models
- Determine experimental probabilities, fraction answers
- Determine probabilities of flipping coins specified number of times
- Determine probabilities of flipping coins & rolling die
- Determine probabilities & odds, including visual models
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Compound Probability
- Determine sample spaces
- Determine size of sample spaces, compound events
- Given visual model, determine “or” probability as fraction, decimal, or percent
- Determine “or” probabilities
- Determine “or” probabilities as fractions, decimals, or percents
- Determine “and” probabilities, independent events, visuals provided
- Determine “and” probabilities, independent events, same sample space
- Determine “and” probabilities, independent events, two distinct sample spaces
- Determine “and” probabilities, independent & dependent events
- Determine “and” probabilities, independent & dependent events, including complementary events
- Condensed: Determine probabilities
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Predictions Using Probability
- Determine predicted values, theoretical probability
- Determine predicted values, experimental probability
- Determine predicted values or compare likelihood of events
- Determine predicted values, theoretical probability, compound events
- Determine predicted values, experimental probability, compound events
- Determine inferences from samples
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Conditional Probability
- Determine conditional probabilities from two-way frequency tables
- Determine conditional probabilities, including two-way frequency tables
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Conversions
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Metric to Customary Conversions
- Convert metric to customary units of length
- Convert metric to customary units of weight & mass
- Convert metric to customary units of volume & capacity
- Convert metric to customary units of length, calculator expected
- Convert metric to customary units of weight & mass, calculator expected
- Convert metric to customary units of volume & capacity, calculator expected
- 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
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Customary to Metric Conversions
- Convert customary to metric units of length
- Convert customary to metric units of weight & mass
- Convert customary to metric units of length, calculator expected
- Convert customary to metric units of weight & mass, calculator expected
- Convert customary to metric units of volume & capacity, calculator expected
- Convert customary to metric units of length, including multi-step
- Convert customary to metric units of weight & mass, including multi-step
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Customary & Metric Conversions
- Convert between customary & metric using dimensional analysis
- Convert between customary & metric using unit rates
- Convert between customary & metric using scale factors
- Convert between customary & metric, proportion bias
- Convert between customary & metric using conversion graphs
- Convert between customary & metric, real-world context
- Condensed: Convert between customary & metric
- Condensed: Convert between customary & metric using multiple representations of conversion factor
- Condensed: Convert between customary & metric, including multi-step
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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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Factors & Multiples
- Identify multiples or non-multiples of whole numbers
- Identify factors or non-factors 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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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
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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
- Apply GCFs to determine number of items in groups, 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
- Apply LCMs to determine number of items in groups, 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
- Condensed: Apply GCFs & LCMs to determine number of items in groups, real-world context
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Financial Literacy
- Classify assets & liabilities
- Determine net worth, assets, & liabilities
- Determine minimum income necessary to balance budget
- Determine minimum hourly wage necessary to balance budget
- Determine budget allocations
- Determine savings in loan repayment based on various lengths of repayment