842 Combined Parent + Subtopic Reinforced Index

Parent-level topic navigation and subtopic deep dives are combined. Each topic page now includes prerequisite and post-topic links at both the parent-topic and selected-subtopic level.

Loading topics...Optional filters use primary grade plus course/strand groups such as Pre-Algebra, Algebra 1, Geometry, Calculus, Statistics, and Linear Algebra.
#0002Count objects with one-to-one correspondenceCounting and Early Number Sense • Counting and Cardinality • arithmetic
Show 5 reinforced subtopics
  • 0002.1: Concept meaning of Count objects with one-to-one correspondence
  • 0002.2: Core skill or procedure for Count objects with one-to-one correspondence
  • 0002.3: Representation or model for Count objects with one-to-one correspondence
  • 0002.4: Application of Count objects with one-to-one correspondence
  • 0002.5: Common misconception or error check for Count objects with one-to-one correspondence
#0006Represent a number with objects, fingers, or drawingsCounting and Early Number Sense • Counting and Cardinality • arithmetic
Show 5 reinforced subtopics
  • 0006.1: Concept meaning of Represent a number with objects, fingers, or drawings
  • 0006.2: Core skill or procedure for Represent a number with objects, fingers, or drawings
  • 0006.3: Representation or model for Represent a number with objects, fingers, or drawings
  • 0006.4: Application of Represent a number with objects, fingers, or drawings
  • 0006.5: Common misconception or error check for Represent a number with objects, fingers, or drawings
#0009Count objects arranged in an array or scattered setCounting and Early Number Sense • Counting and Cardinality • arithmetic
Show 5 reinforced subtopics
  • 0009.1: Concept meaning of Count objects arranged in an array or scattered set
  • 0009.2: Core skill or procedure for Count objects arranged in an array or scattered set
  • 0009.3: Representation or model for Count objects arranged in an array or scattered set
  • 0009.4: Application of Count objects arranged in an array or scattered set
  • 0009.5: Common misconception or error check for Count objects arranged in an array or scattered set
#0010Count on from a known number to solve a small addition problemCounting and Early Number Sense • Counting and Cardinality • arithmetic
Show 5 reinforced subtopics
  • 0010.1: Concept meaning of Count on from a known number to solve a small addition problem
  • 0010.2: Core skill or procedure for Count on from a known number to solve a small addition problem
  • 0010.3: Representation or model for Count on from a known number to solve a small addition problem
  • 0010.4: Application of Count on from a known number to solve a small addition problem
  • 0010.5: Common misconception or error check for Count on from a known number to solve a small addition problem
#0011Count back to solve a small subtraction problemCounting and Early Number Sense • Counting and Cardinality • arithmetic
Show 5 reinforced subtopics
  • 0011.1: Concept meaning of Count back to solve a small subtraction problem
  • 0011.2: Core skill or procedure for Count back to solve a small subtraction problem
  • 0011.3: Representation or model for Count back to solve a small subtraction problem
  • 0011.4: Application of Count back to solve a small subtraction problem
  • 0011.5: Common misconception or error check for Count back to solve a small subtraction problem
#0012Identify one more and one less within a small rangeCounting and Early Number Sense • Counting and Cardinality • generic_math
Show 5 reinforced subtopics
  • 0012.1: Concept meaning of Identify one more and one less within a small range
  • 0012.2: Core skill or procedure for Identify one more and one less within a small range
  • 0012.3: Representation or model for Identify one more and one less within a small range
  • 0012.4: Application of Identify one more and one less within a small range
  • 0012.5: Common misconception or error check for Identify one more and one less within a small range
#0013Compare sets using greater than, less than, and equalCounting and Early Number Sense • Counting and Cardinality • generic_math
Show 5 reinforced subtopics
  • 0013.1: Concept meaning of Compare sets using greater than, less than, and equal
  • 0013.2: Core skill or procedure for Compare sets using greater than, less than, and equal
  • 0013.3: Representation or model for Compare sets using greater than, less than, and equal
  • 0013.4: Application of Compare sets using greater than, less than, and equal
  • 0013.5: Common misconception or error check for Compare sets using greater than, less than, and equal
#0014Conserve number when objects are rearrangedCounting and Early Number Sense • Counting and Cardinality • arithmetic
Show 5 reinforced subtopics
  • 0014.1: Concept meaning of Conserve number when objects are rearranged
  • 0014.2: Core skill or procedure for Conserve number when objects are rearranged
  • 0014.3: Representation or model for Conserve number when objects are rearranged
  • 0014.4: Application of Conserve number when objects are rearranged
  • 0014.5: Common misconception or error check for Conserve number when objects are rearranged
#0020Decompose teen numbers into ten and onesCounting and Early Number Sense • Number Recognition and Representation • arithmetic
Show 5 reinforced subtopics
  • 0020.1: Concept meaning of Decompose teen numbers into ten and ones
  • 0020.2: Core skill or procedure for Decompose teen numbers into ten and ones
  • 0020.3: Representation or model for Decompose teen numbers into ten and ones
  • 0020.4: Application of Decompose teen numbers into ten and ones
  • 0020.5: Common misconception or error check for Decompose teen numbers into ten and ones
#0024Read number words for small whole numbersCounting and Early Number Sense • Number Recognition and Representation • arithmetic
Show 5 reinforced subtopics
  • 0024.1: Concept meaning of Read number words for small whole numbers
  • 0024.2: Core skill or procedure for Read number words for small whole numbers
  • 0024.3: Representation or model for Read number words for small whole numbers
  • 0024.4: Application of Read number words for small whole numbers
  • 0024.5: Common misconception or error check for Read number words for small whole numbers
#0026Connect numeral, number word, and quantityCounting and Early Number Sense • Number Recognition and Representation • arithmetic
Show 5 reinforced subtopics
  • 0026.1: Concept meaning of Connect numeral, number word, and quantity
  • 0026.2: Core skill or procedure for Connect numeral, number word, and quantity
  • 0026.3: Representation or model for Connect numeral, number word, and quantity
  • 0026.4: Application of Connect numeral, number word, and quantity
  • 0026.5: Common misconception or error check for Connect numeral, number word, and quantity
#0027Place numbers in order on a short number pathCounting and Early Number Sense • Number Recognition and Representation • arithmetic
Show 5 reinforced subtopics
  • 0027.1: Concept meaning of Place numbers in order on a short number path
  • 0027.2: Core skill or procedure for Place numbers in order on a short number path
  • 0027.3: Representation or model for Place numbers in order on a short number path
  • 0027.4: Application of Place numbers in order on a short number path
  • 0027.5: Common misconception or error check for Place numbers in order on a short number path
#0028Identify missing numbers in a sequenceCounting and Early Number Sense • Number Recognition and Representation • arithmetic
Show 5 reinforced subtopics
  • 0028.1: Concept meaning of Identify missing numbers in a sequence
  • 0028.2: Core skill or procedure for Identify missing numbers in a sequence
  • 0028.3: Representation or model for Identify missing numbers in a sequence
  • 0028.4: Application of Identify missing numbers in a sequence
  • 0028.5: Common misconception or error check for Identify missing numbers in a sequence
#0034Find an unknown in a simple equation boxCounting and Early Number Sense • Early Addition and Subtraction • generic_math
Show 5 reinforced subtopics
  • 0034.1: Concept meaning of Find an unknown in a simple equation box
  • 0034.2: Core skill or procedure for Find an unknown in a simple equation box
  • 0034.3: Representation or model for Find an unknown in a simple equation box
  • 0034.4: Application of Find an unknown in a simple equation box
  • 0034.5: Common misconception or error check for Find an unknown in a simple equation box
#0036Compose and decompose numbers within 10Counting and Early Number Sense • Early Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0036.1: Concept meaning of Compose and decompose numbers within 10
  • 0036.2: Core skill or procedure for Compose and decompose numbers within 10
  • 0036.3: Representation or model for Compose and decompose numbers within 10
  • 0036.4: Application of Compose and decompose numbers within 10
  • 0036.5: Common misconception or error check for Compose and decompose numbers within 10
#0037Act out joining and separating situationsCounting and Early Number Sense • Early Addition and Subtraction • generic_math
Show 5 reinforced subtopics
  • 0037.1: Concept meaning of Act out joining and separating situations
  • 0037.2: Core skill or procedure for Act out joining and separating situations
  • 0037.3: Representation or model for Act out joining and separating situations
  • 0037.4: Application of Act out joining and separating situations
  • 0037.5: Common misconception or error check for Act out joining and separating situations
#0038Represent addition with objects, drawings, and equationsCounting and Early Number Sense • Early Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0038.1: Concept meaning of Represent addition with objects, drawings, and equations
  • 0038.2: Core skill or procedure for Represent addition with objects, drawings, and equations
  • 0038.3: Representation or model for Represent addition with objects, drawings, and equations
  • 0038.4: Application of Represent addition with objects, drawings, and equations
  • 0038.5: Common misconception or error check for Represent addition with objects, drawings, and equations
#0039Represent subtraction with objects, drawings, and equationsCounting and Early Number Sense • Early Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0039.1: Concept meaning of Represent subtraction with objects, drawings, and equations
  • 0039.2: Core skill or procedure for Represent subtraction with objects, drawings, and equations
  • 0039.3: Representation or model for Represent subtraction with objects, drawings, and equations
  • 0039.4: Application of Represent subtraction with objects, drawings, and equations
  • 0039.5: Common misconception or error check for Represent subtraction with objects, drawings, and equations
#0040Find an unknown addend in a small equationCounting and Early Number Sense • Early Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0040.1: Concept meaning of Find an unknown addend in a small equation
  • 0040.2: Core skill or procedure for Find an unknown addend in a small equation
  • 0040.3: Representation or model for Find an unknown addend in a small equation
  • 0040.4: Application of Find an unknown addend in a small equation
  • 0040.5: Common misconception or error check for Find an unknown addend in a small equation
#0041Understand part-part-whole structureCounting and Early Number Sense • Early Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0041.1: Concept meaning of Understand part-part-whole structure
  • 0041.2: Core skill or procedure for Understand part-part-whole structure
  • 0041.3: Representation or model for Understand part-part-whole structure
  • 0041.4: Application of Understand part-part-whole structure
  • 0041.5: Common misconception or error check for Understand part-part-whole structure
#0042Fluently add and subtract within tenCounting and Early Number Sense • Early Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0042.1: Concept meaning of Fluently add and subtract within ten
  • 0042.2: Core skill or procedure for Fluently add and subtract within ten
  • 0042.3: Representation or model for Fluently add and subtract within ten
  • 0042.4: Application of Fluently add and subtract within ten
  • 0042.5: Common misconception or error check for Fluently add and subtract within ten
#0044Identify the core of a repeating patternCounting and Early Number Sense • Early Patterns and Structure • generic_math
Show 5 reinforced subtopics
  • 0044.1: Concept meaning of Identify the core of a repeating pattern
  • 0044.2: Core skill or procedure for Identify the core of a repeating pattern
  • 0044.3: Representation or model for Identify the core of a repeating pattern
  • 0044.4: Application of Identify the core of a repeating pattern
  • 0044.5: Common misconception or error check for Identify the core of a repeating pattern
#0050Extend repeating patterns with numbersCounting and Early Number Sense • Early Patterns and Structure • arithmetic
Show 5 reinforced subtopics
  • 0050.1: Concept meaning of Extend repeating patterns with numbers
  • 0050.2: Core skill or procedure for Extend repeating patterns with numbers
  • 0050.3: Representation or model for Extend repeating patterns with numbers
  • 0050.4: Application of Extend repeating patterns with numbers
  • 0050.5: Common misconception or error check for Extend repeating patterns with numbers
#0051Create a repeating pattern from a ruleCounting and Early Number Sense • Early Patterns and Structure • generic_math
Show 5 reinforced subtopics
  • 0051.1: Concept meaning of Create a repeating pattern from a rule
  • 0051.2: Core skill or procedure for Create a repeating pattern from a rule
  • 0051.3: Representation or model for Create a repeating pattern from a rule
  • 0051.4: Application of Create a repeating pattern from a rule
  • 0051.5: Common misconception or error check for Create a repeating pattern from a rule
#0054Describe a growing pattern informallyCounting and Early Number Sense • Early Patterns and Structure • generic_math
Show 5 reinforced subtopics
  • 0054.1: Concept meaning of Describe a growing pattern informally
  • 0054.2: Core skill or procedure for Describe a growing pattern informally
  • 0054.3: Representation or model for Describe a growing pattern informally
  • 0054.4: Application of Describe a growing pattern informally
  • 0054.5: Common misconception or error check for Describe a growing pattern informally
#0055Find a missing term in a repeating patternCounting and Early Number Sense • Early Patterns and Structure • generic_math
Show 5 reinforced subtopics
  • 0055.1: Concept meaning of Find a missing term in a repeating pattern
  • 0055.2: Core skill or procedure for Find a missing term in a repeating pattern
  • 0055.3: Representation or model for Find a missing term in a repeating pattern
  • 0055.4: Application of Find a missing term in a repeating pattern
  • 0055.5: Common misconception or error check for Find a missing term in a repeating pattern
#0065Read and write whole numbers in standard formWhole Numbers and Arithmetic • Place Value • arithmetic
Show 5 reinforced subtopics
  • 0065.1: Concept meaning of Read and write whole numbers in standard form
  • 0065.2: Core skill or procedure for Read and write whole numbers in standard form
  • 0065.3: Representation or model for Read and write whole numbers in standard form
  • 0065.4: Application of Read and write whole numbers in standard form
  • 0065.5: Common misconception or error check for Read and write whole numbers in standard form
#0066Read and write whole numbers in word formWhole Numbers and Arithmetic • Place Value • arithmetic
Show 5 reinforced subtopics
  • 0066.1: Concept meaning of Read and write whole numbers in word form
  • 0066.2: Core skill or procedure for Read and write whole numbers in word form
  • 0066.3: Representation or model for Read and write whole numbers in word form
  • 0066.4: Application of Read and write whole numbers in word form
  • 0066.5: Common misconception or error check for Read and write whole numbers in word form
#0067Read and write whole numbers in expanded formWhole Numbers and Arithmetic • Place Value • arithmetic
Show 5 reinforced subtopics
  • 0067.1: Concept meaning of Read and write whole numbers in expanded form
  • 0067.2: Core skill or procedure for Read and write whole numbers in expanded form
  • 0067.3: Representation or model for Read and write whole numbers in expanded form
  • 0067.4: Application of Read and write whole numbers in expanded form
  • 0067.5: Common misconception or error check for Read and write whole numbers in expanded form
#0071Decompose numbers in multiple place-value waysWhole Numbers and Arithmetic • Place Value • percent
Show 5 reinforced subtopics
  • 0071.1: Concept meaning of Decompose numbers in multiple place-value ways
  • 0071.2: Core skill or procedure for Decompose numbers in multiple place-value ways
  • 0071.3: Representation or model for Decompose numbers in multiple place-value ways
  • 0071.4: Application of Decompose numbers in multiple place-value ways
  • 0071.5: Common misconception or error check for Decompose numbers in multiple place-value ways
#0079Check reasonableness using inverse operationsWhole Numbers and Arithmetic • Addition and Subtraction • ratio_rate
Show 5 reinforced subtopics
  • 0079.1: Concept meaning of Check reasonableness using inverse operations
  • 0079.2: Core skill or procedure for Check reasonableness using inverse operations
  • 0079.3: Representation or model for Check reasonableness using inverse operations
  • 0079.4: Application of Check reasonableness using inverse operations
  • 0079.5: Common misconception or error check for Check reasonableness using inverse operations
#0080Add multi-digit whole numbers with the standard algorithmWhole Numbers and Arithmetic • Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0080.1: Concept meaning of Add multi-digit whole numbers with the standard algorithm
  • 0080.2: Core skill or procedure for Add multi-digit whole numbers with the standard algorithm
  • 0080.3: Representation or model for Add multi-digit whole numbers with the standard algorithm
  • 0080.4: Application of Add multi-digit whole numbers with the standard algorithm
  • 0080.5: Common misconception or error check for Add multi-digit whole numbers with the standard algorithm
#0081Subtract multi-digit whole numbers with regroupingWhole Numbers and Arithmetic • Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0081.1: Concept meaning of Subtract multi-digit whole numbers with regrouping
  • 0081.2: Core skill or procedure for Subtract multi-digit whole numbers with regrouping
  • 0081.3: Representation or model for Subtract multi-digit whole numbers with regrouping
  • 0081.4: Application of Subtract multi-digit whole numbers with regrouping
  • 0081.5: Common misconception or error check for Subtract multi-digit whole numbers with regrouping
#0082Estimate sums using rounding or front-end estimationWhole Numbers and Arithmetic • Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0082.1: Concept meaning of Estimate sums using rounding or front-end estimation
  • 0082.2: Core skill or procedure for Estimate sums using rounding or front-end estimation
  • 0082.3: Representation or model for Estimate sums using rounding or front-end estimation
  • 0082.4: Application of Estimate sums using rounding or front-end estimation
  • 0082.5: Common misconception or error check for Estimate sums using rounding or front-end estimation
#0083Check addition and subtraction with inverse operationsWhole Numbers and Arithmetic • Addition and Subtraction • ratio_rate
Show 5 reinforced subtopics
  • 0083.1: Concept meaning of Check addition and subtraction with inverse operations
  • 0083.2: Core skill or procedure for Check addition and subtraction with inverse operations
  • 0083.3: Representation or model for Check addition and subtraction with inverse operations
  • 0083.4: Application of Check addition and subtraction with inverse operations
  • 0083.5: Common misconception or error check for Check addition and subtraction with inverse operations
#0084Solve addition and subtraction word problemsWhole Numbers and Arithmetic • Addition and Subtraction • arithmetic
Show 5 reinforced subtopics
  • 0084.1: Concept meaning of Solve addition and subtraction word problems
  • 0084.2: Core skill or procedure for Solve addition and subtraction word problems
  • 0084.3: Representation or model for Solve addition and subtraction word problems
  • 0084.4: Application of Solve addition and subtraction word problems
  • 0084.5: Common misconception or error check for Solve addition and subtraction word problems
#0085Represent comparison situations with equationsWhole Numbers and Arithmetic • Addition and Subtraction • generic_math
Show 5 reinforced subtopics
  • 0085.1: Concept meaning of Represent comparison situations with equations
  • 0085.2: Core skill or procedure for Represent comparison situations with equations
  • 0085.3: Representation or model for Represent comparison situations with equations
  • 0085.4: Application of Represent comparison situations with equations
  • 0085.5: Common misconception or error check for Represent comparison situations with equations
#0086Choose mental math, paper method, or calculator appropriatelyWhole Numbers and Arithmetic • Addition and Subtraction • generic_math
Show 5 reinforced subtopics
  • 0086.1: Concept meaning of Choose mental math, paper method, or calculator appropriately
  • 0086.2: Core skill or procedure for Choose mental math, paper method, or calculator appropriately
  • 0086.3: Representation or model for Choose mental math, paper method, or calculator appropriately
  • 0086.4: Application of Choose mental math, paper method, or calculator appropriately
  • 0086.5: Common misconception or error check for Choose mental math, paper method, or calculator appropriately
#0087Interpret multiplication as equal groupsWhole Numbers and Arithmetic • Multiplication and Division • percent
Show 5 reinforced subtopics
  • 0087.1: Concept meaning of Interpret multiplication as equal groups
  • 0087.2: Core skill or procedure for Interpret multiplication as equal groups
  • 0087.3: Representation or model for Interpret multiplication as equal groups
  • 0087.4: Application of Interpret multiplication as equal groups
  • 0087.5: Common misconception or error check for Interpret multiplication as equal groups
#0090Interpret division as sharing equallyWhole Numbers and Arithmetic • Multiplication and Division • generic_math
Show 5 reinforced subtopics
  • 0090.1: Concept meaning of Interpret division as sharing equally
  • 0090.2: Core skill or procedure for Interpret division as sharing equally
  • 0090.3: Representation or model for Interpret division as sharing equally
  • 0090.4: Application of Interpret division as sharing equally
  • 0090.5: Common misconception or error check for Interpret division as sharing equally
#0094Interpret multiplication as repeated additionWhole Numbers and Arithmetic • Multiplication and Division • percent
Show 5 reinforced subtopics
  • 0094.1: Concept meaning of Interpret multiplication as repeated addition
  • 0094.2: Core skill or procedure for Interpret multiplication as repeated addition
  • 0094.3: Representation or model for Interpret multiplication as repeated addition
  • 0094.4: Application of Interpret multiplication as repeated addition
  • 0094.5: Common misconception or error check for Interpret multiplication as repeated addition
#0098Multiply multi-digit numbers with standard algorithmsWhole Numbers and Arithmetic • Multiplication and Division • percent
Show 5 reinforced subtopics
  • 0098.1: Concept meaning of Multiply multi-digit numbers with standard algorithms
  • 0098.2: Core skill or procedure for Multiply multi-digit numbers with standard algorithms
  • 0098.3: Representation or model for Multiply multi-digit numbers with standard algorithms
  • 0098.4: Application of Multiply multi-digit numbers with standard algorithms
  • 0098.5: Common misconception or error check for Multiply multi-digit numbers with standard algorithms
#0107Use the commutative property of additionWhole Numbers and Arithmetic • Properties and Mental Strategies • arithmetic
Show 5 reinforced subtopics
  • 0107.1: Concept meaning of Use the commutative property of addition
  • 0107.2: Core skill or procedure for Use the commutative property of addition
  • 0107.3: Representation or model for Use the commutative property of addition
  • 0107.4: Application of Use the commutative property of addition
  • 0107.5: Common misconception or error check for Use the commutative property of addition
#0108Use the commutative property of multiplicationWhole Numbers and Arithmetic • Properties and Mental Strategies • percent
Show 5 reinforced subtopics
  • 0108.1: Concept meaning of Use the commutative property of multiplication
  • 0108.2: Core skill or procedure for Use the commutative property of multiplication
  • 0108.3: Representation or model for Use the commutative property of multiplication
  • 0108.4: Application of Use the commutative property of multiplication
  • 0108.5: Common misconception or error check for Use the commutative property of multiplication
#0109Use the associative property of additionWhole Numbers and Arithmetic • Properties and Mental Strategies • arithmetic
Show 5 reinforced subtopics
  • 0109.1: Concept meaning of Use the associative property of addition
  • 0109.2: Core skill or procedure for Use the associative property of addition
  • 0109.3: Representation or model for Use the associative property of addition
  • 0109.4: Application of Use the associative property of addition
  • 0109.5: Common misconception or error check for Use the associative property of addition
#0110Use the associative property of multiplicationWhole Numbers and Arithmetic • Properties and Mental Strategies • percent
Show 5 reinforced subtopics
  • 0110.1: Concept meaning of Use the associative property of multiplication
  • 0110.2: Core skill or procedure for Use the associative property of multiplication
  • 0110.3: Representation or model for Use the associative property of multiplication
  • 0110.4: Application of Use the associative property of multiplication
  • 0110.5: Common misconception or error check for Use the associative property of multiplication
#0111Use the distributive property to decompose productsWhole Numbers and Arithmetic • Properties and Mental Strategies • generic_math
Show 5 reinforced subtopics
  • 0111.1: Concept meaning of Use the distributive property to decompose products
  • 0111.2: Core skill or procedure for Use the distributive property to decompose products
  • 0111.3: Representation or model for Use the distributive property to decompose products
  • 0111.4: Application of Use the distributive property to decompose products
  • 0111.5: Common misconception or error check for Use the distributive property to decompose products
#0112Use identity properties of addition and multiplicationWhole Numbers and Arithmetic • Properties and Mental Strategies • percent
Show 5 reinforced subtopics
  • 0112.1: Concept meaning of Use identity properties of addition and multiplication
  • 0112.2: Core skill or procedure for Use identity properties of addition and multiplication
  • 0112.3: Representation or model for Use identity properties of addition and multiplication
  • 0112.4: Application of Use identity properties of addition and multiplication
  • 0112.5: Common misconception or error check for Use identity properties of addition and multiplication
#0113Understand zero property of multiplicationWhole Numbers and Arithmetic • Properties and Mental Strategies • percent
Show 5 reinforced subtopics
  • 0113.1: Concept meaning of Understand zero property of multiplication
  • 0113.2: Core skill or procedure for Understand zero property of multiplication
  • 0113.3: Representation or model for Understand zero property of multiplication
  • 0113.4: Application of Understand zero property of multiplication
  • 0113.5: Common misconception or error check for Understand zero property of multiplication
#0114Select properties to simplify computationWhole Numbers and Arithmetic • Properties and Mental Strategies • generic_math
Show 5 reinforced subtopics
  • 0114.1: Concept meaning of Select properties to simplify computation
  • 0114.2: Core skill or procedure for Select properties to simplify computation
  • 0114.3: Representation or model for Select properties to simplify computation
  • 0114.4: Application of Select properties to simplify computation
  • 0114.5: Common misconception or error check for Select properties to simplify computation
#0115Justify arithmetic steps with propertiesWhole Numbers and Arithmetic • Properties and Mental Strategies • generic_math
Show 5 reinforced subtopics
  • 0115.1: Concept meaning of Justify arithmetic steps with properties
  • 0115.2: Core skill or procedure for Justify arithmetic steps with properties
  • 0115.3: Representation or model for Justify arithmetic steps with properties
  • 0115.4: Application of Justify arithmetic steps with properties
  • 0115.5: Common misconception or error check for Justify arithmetic steps with properties
#0117Identify prime and composite numbersWhole Numbers and Arithmetic • Factors, Multiples, and Divisibility • arithmetic
Show 5 reinforced subtopics
  • 0117.1: Concept meaning of Identify prime and composite numbers
  • 0117.2: Core skill or procedure for Identify prime and composite numbers
  • 0117.3: Representation or model for Identify prime and composite numbers
  • 0117.4: Application of Identify prime and composite numbers
  • 0117.5: Common misconception or error check for Identify prime and composite numbers
#0122Use exponents in prime factorizationWhole Numbers and Arithmetic • Factors, Multiples, and Divisibility • polynomial
Show 5 reinforced subtopics
  • 0122.1: Concept meaning of Use exponents in prime factorization
  • 0122.2: Core skill or procedure for Use exponents in prime factorization
  • 0122.3: Representation or model for Use exponents in prime factorization
  • 0122.4: Application of Use exponents in prime factorization
  • 0122.5: Common misconception or error check for Use exponents in prime factorization
#0124Determine whether one number is a multiple of anotherWhole Numbers and Arithmetic • Factors, Multiples, and Divisibility • percent
Show 5 reinforced subtopics
  • 0124.1: Concept meaning of Determine whether one number is a multiple of another
  • 0124.2: Core skill or procedure for Determine whether one number is a multiple of another
  • 0124.3: Representation or model for Determine whether one number is a multiple of another
  • 0124.4: Application of Determine whether one number is a multiple of another
  • 0124.5: Common misconception or error check for Determine whether one number is a multiple of another
#0125Write a prime factorization using exponentsWhole Numbers and Arithmetic • Factors, Multiples, and Divisibility • polynomial
Show 5 reinforced subtopics
  • 0125.1: Concept meaning of Write a prime factorization using exponents
  • 0125.2: Core skill or procedure for Write a prime factorization using exponents
  • 0125.3: Representation or model for Write a prime factorization using exponents
  • 0125.4: Application of Write a prime factorization using exponents
  • 0125.5: Common misconception or error check for Write a prime factorization using exponents
#0126Find common factors of two or more numbersWhole Numbers and Arithmetic • Factors, Multiples, and Divisibility • polynomial
Show 5 reinforced subtopics
  • 0126.1: Concept meaning of Find common factors of two or more numbers
  • 0126.2: Core skill or procedure for Find common factors of two or more numbers
  • 0126.3: Representation or model for Find common factors of two or more numbers
  • 0126.4: Application of Find common factors of two or more numbers
  • 0126.5: Common misconception or error check for Find common factors of two or more numbers
#0127Find common multiples of two or more numbersWhole Numbers and Arithmetic • Factors, Multiples, and Divisibility • percent
Show 5 reinforced subtopics
  • 0127.1: Concept meaning of Find common multiples of two or more numbers
  • 0127.2: Core skill or procedure for Find common multiples of two or more numbers
  • 0127.3: Representation or model for Find common multiples of two or more numbers
  • 0127.4: Application of Find common multiples of two or more numbers
  • 0127.5: Common misconception or error check for Find common multiples of two or more numbers
#0128Use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10Whole Numbers and Arithmetic • Factors, Multiples, and Divisibility • generic_math
Show 5 reinforced subtopics
  • 0128.1: Concept meaning of Use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10
  • 0128.2: Core skill or procedure for Use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10
  • 0128.3: Representation or model for Use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10
  • 0128.4: Application of Use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10
  • 0128.5: Common misconception or error check for Use divisibility rules for 2, 3, 4, 5, 6, 8, 9, and 10
#0129Evaluate expressions with parenthesesWhole Numbers and Arithmetic • Expressions with Whole Numbers • generic_math
Show 5 reinforced subtopics
  • 0129.1: Concept meaning of Evaluate expressions with parentheses
  • 0129.2: Core skill or procedure for Evaluate expressions with parentheses
  • 0129.3: Representation or model for Evaluate expressions with parentheses
  • 0129.4: Application of Evaluate expressions with parentheses
  • 0129.5: Common misconception or error check for Evaluate expressions with parentheses
#0130Evaluate expressions using order of operationsWhole Numbers and Arithmetic • Expressions with Whole Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0130.1: Concept meaning of Evaluate expressions using order of operations
  • 0130.2: Core skill or procedure for Evaluate expressions using order of operations
  • 0130.3: Representation or model for Evaluate expressions using order of operations
  • 0130.4: Application of Evaluate expressions using order of operations
  • 0130.5: Common misconception or error check for Evaluate expressions using order of operations
#0131Translate words to numeric expressionsWhole Numbers and Arithmetic • Expressions with Whole Numbers • generic_math
Show 5 reinforced subtopics
  • 0131.1: Concept meaning of Translate words to numeric expressions
  • 0131.2: Core skill or procedure for Translate words to numeric expressions
  • 0131.3: Representation or model for Translate words to numeric expressions
  • 0131.4: Application of Translate words to numeric expressions
  • 0131.5: Common misconception or error check for Translate words to numeric expressions
#0132Identify operation symbols in contextWhole Numbers and Arithmetic • Expressions with Whole Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0132.1: Concept meaning of Identify operation symbols in context
  • 0132.2: Core skill or procedure for Identify operation symbols in context
  • 0132.3: Representation or model for Identify operation symbols in context
  • 0132.4: Application of Identify operation symbols in context
  • 0132.5: Common misconception or error check for Identify operation symbols in context
#0136Evaluate numerical expressions with parenthesesWhole Numbers and Arithmetic • Expressions with Whole Numbers • generic_math
Show 5 reinforced subtopics
  • 0136.1: Concept meaning of Evaluate numerical expressions with parentheses
  • 0136.2: Core skill or procedure for Evaluate numerical expressions with parentheses
  • 0136.3: Representation or model for Evaluate numerical expressions with parentheses
  • 0136.4: Application of Evaluate numerical expressions with parentheses
  • 0136.5: Common misconception or error check for Evaluate numerical expressions with parentheses
#0137Evaluate numerical expressions with exponentsWhole Numbers and Arithmetic • Expressions with Whole Numbers • generic_math
Show 5 reinforced subtopics
  • 0137.1: Concept meaning of Evaluate numerical expressions with exponents
  • 0137.2: Core skill or procedure for Evaluate numerical expressions with exponents
  • 0137.3: Representation or model for Evaluate numerical expressions with exponents
  • 0137.4: Application of Evaluate numerical expressions with exponents
  • 0137.5: Common misconception or error check for Evaluate numerical expressions with exponents
#0138Apply order of operations with all four operationsWhole Numbers and Arithmetic • Expressions with Whole Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0138.1: Concept meaning of Apply order of operations with all four operations
  • 0138.2: Core skill or procedure for Apply order of operations with all four operations
  • 0138.3: Representation or model for Apply order of operations with all four operations
  • 0138.4: Application of Apply order of operations with all four operations
  • 0138.5: Common misconception or error check for Apply order of operations with all four operations
#0139Distinguish grouping symbols from multiplication notationWhole Numbers and Arithmetic • Expressions with Whole Numbers • percent
Show 5 reinforced subtopics
  • 0139.1: Concept meaning of Distinguish grouping symbols from multiplication notation
  • 0139.2: Core skill or procedure for Distinguish grouping symbols from multiplication notation
  • 0139.3: Representation or model for Distinguish grouping symbols from multiplication notation
  • 0139.4: Application of Distinguish grouping symbols from multiplication notation
  • 0139.5: Common misconception or error check for Distinguish grouping symbols from multiplication notation
#0140Write an expression that matches a verbal phraseWhole Numbers and Arithmetic • Expressions with Whole Numbers • generic_math
Show 5 reinforced subtopics
  • 0140.1: Concept meaning of Write an expression that matches a verbal phrase
  • 0140.2: Core skill or procedure for Write an expression that matches a verbal phrase
  • 0140.3: Representation or model for Write an expression that matches a verbal phrase
  • 0140.4: Application of Write an expression that matches a verbal phrase
  • 0140.5: Common misconception or error check for Write an expression that matches a verbal phrase
#0141Insert grouping symbols to change a value intentionallyWhole Numbers and Arithmetic • Expressions with Whole Numbers • generic_math
Show 5 reinforced subtopics
  • 0141.1: Concept meaning of Insert grouping symbols to change a value intentionally
  • 0141.2: Core skill or procedure for Insert grouping symbols to change a value intentionally
  • 0141.3: Representation or model for Insert grouping symbols to change a value intentionally
  • 0141.4: Application of Insert grouping symbols to change a value intentionally
  • 0141.5: Common misconception or error check for Insert grouping symbols to change a value intentionally
#0142Detect and explain common order-of-operations errorsWhole Numbers and Arithmetic • Expressions with Whole Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0142.1: Concept meaning of Detect and explain common order-of-operations errors
  • 0142.2: Core skill or procedure for Detect and explain common order-of-operations errors
  • 0142.3: Representation or model for Detect and explain common order-of-operations errors
  • 0142.4: Application of Detect and explain common order-of-operations errors
  • 0142.5: Common misconception or error check for Detect and explain common order-of-operations errors
#0143Evaluate expressions with repeated operations left to rightWhole Numbers and Arithmetic • Expressions with Whole Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0143.1: Concept meaning of Evaluate expressions with repeated operations left to right
  • 0143.2: Core skill or procedure for Evaluate expressions with repeated operations left to right
  • 0143.3: Representation or model for Evaluate expressions with repeated operations left to right
  • 0143.4: Application of Evaluate expressions with repeated operations left to right
  • 0143.5: Common misconception or error check for Evaluate expressions with repeated operations left to right
#0144Identify numerator and denominatorFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0144.1: Concept meaning of Identify numerator and denominator
  • 0144.2: Core skill or procedure for Identify numerator and denominator
  • 0144.3: Representation or model for Identify numerator and denominator
  • 0144.4: Application of Identify numerator and denominator
  • 0144.5: Common misconception or error check for Identify numerator and denominator
#0145Represent fractions on number linesFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0145.1: Concept meaning of Represent fractions on number lines
  • 0145.2: Core skill or procedure for Represent fractions on number lines
  • 0145.3: Representation or model for Represent fractions on number lines
  • 0145.4: Application of Represent fractions on number lines
  • 0145.5: Common misconception or error check for Represent fractions on number lines
#0146Represent fractions with area modelsFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0146.1: Concept meaning of Represent fractions with area models
  • 0146.2: Core skill or procedure for Represent fractions with area models
  • 0146.3: Representation or model for Represent fractions with area models
  • 0146.4: Application of Represent fractions with area models
  • 0146.5: Common misconception or error check for Represent fractions with area models
#0148Compare fractions with common denominatorsFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0148.1: Concept meaning of Compare fractions with common denominators
  • 0148.2: Core skill or procedure for Compare fractions with common denominators
  • 0148.3: Representation or model for Compare fractions with common denominators
  • 0148.4: Application of Compare fractions with common denominators
  • 0148.5: Common misconception or error check for Compare fractions with common denominators
#0149Compare fractions with common numeratorsFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0149.1: Concept meaning of Compare fractions with common numerators
  • 0149.2: Core skill or procedure for Compare fractions with common numerators
  • 0149.3: Representation or model for Compare fractions with common numerators
  • 0149.4: Application of Compare fractions with common numerators
  • 0149.5: Common misconception or error check for Compare fractions with common numerators
#0150Understand mixed numbers and improper fractionsFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0150.1: Concept meaning of Understand mixed numbers and improper fractions
  • 0150.2: Core skill or procedure for Understand mixed numbers and improper fractions
  • 0150.3: Representation or model for Understand mixed numbers and improper fractions
  • 0150.4: Application of Understand mixed numbers and improper fractions
  • 0150.5: Common misconception or error check for Understand mixed numbers and improper fractions
#0151Represent fractions with set modelsFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0151.1: Concept meaning of Represent fractions with set models
  • 0151.2: Core skill or procedure for Represent fractions with set models
  • 0151.3: Representation or model for Represent fractions with set models
  • 0151.4: Application of Represent fractions with set models
  • 0151.5: Common misconception or error check for Represent fractions with set models
#0153Generate equivalent fractions by scalingFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • ratio_rate
Show 5 reinforced subtopics
  • 0153.1: Concept meaning of Generate equivalent fractions by scaling
  • 0153.2: Core skill or procedure for Generate equivalent fractions by scaling
  • 0153.3: Representation or model for Generate equivalent fractions by scaling
  • 0153.4: Application of Generate equivalent fractions by scaling
  • 0153.5: Common misconception or error check for Generate equivalent fractions by scaling
#0154Simplify a fraction to lowest termsFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0154.1: Concept meaning of Simplify a fraction to lowest terms
  • 0154.2: Core skill or procedure for Simplify a fraction to lowest terms
  • 0154.3: Representation or model for Simplify a fraction to lowest terms
  • 0154.4: Application of Simplify a fraction to lowest terms
  • 0154.5: Common misconception or error check for Simplify a fraction to lowest terms
#0155Convert between mixed numbers and improper fractionsFractions, Decimals, Percents, and Rational Numbers • Fraction Meaning and Representation • fractions
Show 5 reinforced subtopics
  • 0155.1: Concept meaning of Convert between mixed numbers and improper fractions
  • 0155.2: Core skill or procedure for Convert between mixed numbers and improper fractions
  • 0155.3: Representation or model for Convert between mixed numbers and improper fractions
  • 0155.4: Application of Convert between mixed numbers and improper fractions
  • 0155.5: Common misconception or error check for Convert between mixed numbers and improper fractions
#0156Add fractions with like denominatorsFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0156.1: Concept meaning of Add fractions with like denominators
  • 0156.2: Core skill or procedure for Add fractions with like denominators
  • 0156.3: Representation or model for Add fractions with like denominators
  • 0156.4: Application of Add fractions with like denominators
  • 0156.5: Common misconception or error check for Add fractions with like denominators
#0157Subtract fractions with like denominatorsFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0157.1: Concept meaning of Subtract fractions with like denominators
  • 0157.2: Core skill or procedure for Subtract fractions with like denominators
  • 0157.3: Representation or model for Subtract fractions with like denominators
  • 0157.4: Application of Subtract fractions with like denominators
  • 0157.5: Common misconception or error check for Subtract fractions with like denominators
#0158Add fractions with unlike denominatorsFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0158.1: Concept meaning of Add fractions with unlike denominators
  • 0158.2: Core skill or procedure for Add fractions with unlike denominators
  • 0158.3: Representation or model for Add fractions with unlike denominators
  • 0158.4: Application of Add fractions with unlike denominators
  • 0158.5: Common misconception or error check for Add fractions with unlike denominators
#0159Subtract fractions with unlike denominatorsFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0159.1: Concept meaning of Subtract fractions with unlike denominators
  • 0159.2: Core skill or procedure for Subtract fractions with unlike denominators
  • 0159.3: Representation or model for Subtract fractions with unlike denominators
  • 0159.4: Application of Subtract fractions with unlike denominators
  • 0159.5: Common misconception or error check for Subtract fractions with unlike denominators
#0160Multiply a fraction by a whole numberFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • percent
Show 5 reinforced subtopics
  • 0160.1: Concept meaning of Multiply a fraction by a whole number
  • 0160.2: Core skill or procedure for Multiply a fraction by a whole number
  • 0160.3: Representation or model for Multiply a fraction by a whole number
  • 0160.4: Application of Multiply a fraction by a whole number
  • 0160.5: Common misconception or error check for Multiply a fraction by a whole number
#0163Find a common denominator for unlike fractionsFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0163.1: Concept meaning of Find a common denominator for unlike fractions
  • 0163.2: Core skill or procedure for Find a common denominator for unlike fractions
  • 0163.3: Representation or model for Find a common denominator for unlike fractions
  • 0163.4: Application of Find a common denominator for unlike fractions
  • 0163.5: Common misconception or error check for Find a common denominator for unlike fractions
#0164Divide a fraction by a whole numberFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0164.1: Concept meaning of Divide a fraction by a whole number
  • 0164.2: Core skill or procedure for Divide a fraction by a whole number
  • 0164.3: Representation or model for Divide a fraction by a whole number
  • 0164.4: Application of Divide a fraction by a whole number
  • 0164.5: Common misconception or error check for Divide a fraction by a whole number
#0165Divide a whole number by a unit fractionFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0165.1: Concept meaning of Divide a whole number by a unit fraction
  • 0165.2: Core skill or procedure for Divide a whole number by a unit fraction
  • 0165.3: Representation or model for Divide a whole number by a unit fraction
  • 0165.4: Application of Divide a whole number by a unit fraction
  • 0165.5: Common misconception or error check for Divide a whole number by a unit fraction
#0166Divide fractions using reciprocal reasoningFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • fractions
Show 5 reinforced subtopics
  • 0166.1: Concept meaning of Divide fractions using reciprocal reasoning
  • 0166.2: Core skill or procedure for Divide fractions using reciprocal reasoning
  • 0166.3: Representation or model for Divide fractions using reciprocal reasoning
  • 0166.4: Application of Divide fractions using reciprocal reasoning
  • 0166.5: Common misconception or error check for Divide fractions using reciprocal reasoning
#0167Solve word problems with fraction operationsFractions, Decimals, Percents, and Rational Numbers • Fraction Operations • ratio_rate
Show 5 reinforced subtopics
  • 0167.1: Concept meaning of Solve word problems with fraction operations
  • 0167.2: Core skill or procedure for Solve word problems with fraction operations
  • 0167.3: Representation or model for Solve word problems with fraction operations
  • 0167.4: Application of Solve word problems with fraction operations
  • 0167.5: Common misconception or error check for Solve word problems with fraction operations
#0175Read and write decimals to thousandthsFractions, Decimals, Percents, and Rational Numbers • Decimal Place Value and Operations • decimals
Show 5 reinforced subtopics
  • 0175.1: Concept meaning of Read and write decimals to thousandths
  • 0175.2: Core skill or procedure for Read and write decimals to thousandths
  • 0175.3: Representation or model for Read and write decimals to thousandths
  • 0175.4: Application of Read and write decimals to thousandths
  • 0175.5: Common misconception or error check for Read and write decimals to thousandths
#0178Add decimals using place value alignmentFractions, Decimals, Percents, and Rational Numbers • Decimal Place Value and Operations • decimals
Show 5 reinforced subtopics
  • 0178.1: Concept meaning of Add decimals using place value alignment
  • 0178.2: Core skill or procedure for Add decimals using place value alignment
  • 0178.3: Representation or model for Add decimals using place value alignment
  • 0178.4: Application of Add decimals using place value alignment
  • 0178.5: Common misconception or error check for Add decimals using place value alignment
#0179Subtract decimals using place value alignmentFractions, Decimals, Percents, and Rational Numbers • Decimal Place Value and Operations • decimals
Show 5 reinforced subtopics
  • 0179.1: Concept meaning of Subtract decimals using place value alignment
  • 0179.2: Core skill or procedure for Subtract decimals using place value alignment
  • 0179.3: Representation or model for Subtract decimals using place value alignment
  • 0179.4: Application of Subtract decimals using place value alignment
  • 0179.5: Common misconception or error check for Subtract decimals using place value alignment
#0180Multiply decimals by powers of tenFractions, Decimals, Percents, and Rational Numbers • Decimal Place Value and Operations • percent
Show 5 reinforced subtopics
  • 0180.1: Concept meaning of Multiply decimals by powers of ten
  • 0180.2: Core skill or procedure for Multiply decimals by powers of ten
  • 0180.3: Representation or model for Multiply decimals by powers of ten
  • 0180.4: Application of Multiply decimals by powers of ten
  • 0180.5: Common misconception or error check for Multiply decimals by powers of ten
#0184Convert between fractions and terminating decimalsFractions, Decimals, Percents, and Rational Numbers • Decimal Place Value and Operations • fractions
Show 5 reinforced subtopics
  • 0184.1: Concept meaning of Convert between fractions and terminating decimals
  • 0184.2: Core skill or procedure for Convert between fractions and terminating decimals
  • 0184.3: Representation or model for Convert between fractions and terminating decimals
  • 0184.4: Application of Convert between fractions and terminating decimals
  • 0184.5: Common misconception or error check for Convert between fractions and terminating decimals
#0193Find the whole given the part and percentFractions, Decimals, Percents, and Rational Numbers • Percents • percent
Show 5 reinforced subtopics
  • 0193.1: Concept meaning of Find the whole given the part and percent
  • 0193.2: Core skill or procedure for Find the whole given the part and percent
  • 0193.3: Representation or model for Find the whole given the part and percent
  • 0193.4: Application of Find the whole given the part and percent
  • 0193.5: Common misconception or error check for Find the whole given the part and percent
#0194Find the percent given part and wholeFractions, Decimals, Percents, and Rational Numbers • Percents • percent
Show 5 reinforced subtopics
  • 0194.1: Concept meaning of Find the percent given part and whole
  • 0194.2: Core skill or procedure for Find the percent given part and whole
  • 0194.3: Representation or model for Find the percent given part and whole
  • 0194.4: Application of Find the percent given part and whole
  • 0194.5: Common misconception or error check for Find the percent given part and whole
#0197Solve discount, tax, and tip problemsFractions, Decimals, Percents, and Rational Numbers • Percents • percent
Show 5 reinforced subtopics
  • 0197.1: Concept meaning of Solve discount, tax, and tip problems
  • 0197.2: Core skill or procedure for Solve discount, tax, and tip problems
  • 0197.3: Representation or model for Solve discount, tax, and tip problems
  • 0197.4: Application of Solve discount, tax, and tip problems
  • 0197.5: Common misconception or error check for Solve discount, tax, and tip problems
#0206Find absolute value of a rational numberFractions, Decimals, Percents, and Rational Numbers • Integers and Rational Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0206.1: Concept meaning of Find absolute value of a rational number
  • 0206.2: Core skill or procedure for Find absolute value of a rational number
  • 0206.3: Representation or model for Find absolute value of a rational number
  • 0206.4: Application of Find absolute value of a rational number
  • 0206.5: Common misconception or error check for Find absolute value of a rational number
#0208Add integers with different signsFractions, Decimals, Percents, and Rational Numbers • Integers and Rational Numbers • arithmetic
Show 5 reinforced subtopics
  • 0208.1: Concept meaning of Add integers with different signs
  • 0208.2: Core skill or procedure for Add integers with different signs
  • 0208.3: Representation or model for Add integers with different signs
  • 0208.4: Application of Add integers with different signs
  • 0208.5: Common misconception or error check for Add integers with different signs
#0209Subtract integers as adding the oppositeFractions, Decimals, Percents, and Rational Numbers • Integers and Rational Numbers • arithmetic
Show 5 reinforced subtopics
  • 0209.1: Concept meaning of Subtract integers as adding the opposite
  • 0209.2: Core skill or procedure for Subtract integers as adding the opposite
  • 0209.3: Representation or model for Subtract integers as adding the opposite
  • 0209.4: Application of Subtract integers as adding the opposite
  • 0209.5: Common misconception or error check for Subtract integers as adding the opposite
#0210Interpret rational numbers in real contextsFractions, Decimals, Percents, and Rational Numbers • Integers and Rational Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0210.1: Concept meaning of Interpret rational numbers in real contexts
  • 0210.2: Core skill or procedure for Interpret rational numbers in real contexts
  • 0210.3: Representation or model for Interpret rational numbers in real contexts
  • 0210.4: Application of Interpret rational numbers in real contexts
  • 0210.5: Common misconception or error check for Interpret rational numbers in real contexts
#0211Compare and order rational numbers in different formsFractions, Decimals, Percents, and Rational Numbers • Integers and Rational Numbers • ratio_rate
Show 5 reinforced subtopics
  • 0211.1: Concept meaning of Compare and order rational numbers in different forms
  • 0211.2: Core skill or procedure for Compare and order rational numbers in different forms
  • 0211.3: Representation or model for Compare and order rational numbers in different forms
  • 0211.4: Application of Compare and order rational numbers in different forms
  • 0211.5: Common misconception or error check for Compare and order rational numbers in different forms
#0214Convert repeating decimals to fractionsFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • fractions
Show 5 reinforced subtopics
  • 0214.1: Concept meaning of Convert repeating decimals to fractions
  • 0214.2: Core skill or procedure for Convert repeating decimals to fractions
  • 0214.3: Representation or model for Convert repeating decimals to fractions
  • 0214.4: Application of Convert repeating decimals to fractions
  • 0214.5: Common misconception or error check for Convert repeating decimals to fractions
#0215Order rational numbers in different formsFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • ratio_rate
Show 5 reinforced subtopics
  • 0215.1: Concept meaning of Order rational numbers in different forms
  • 0215.2: Core skill or procedure for Order rational numbers in different forms
  • 0215.3: Representation or model for Order rational numbers in different forms
  • 0215.4: Application of Order rational numbers in different forms
  • 0215.5: Common misconception or error check for Order rational numbers in different forms
#0218Reason about distance and directionFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • generic_math
Show 5 reinforced subtopics
  • 0218.1: Concept meaning of Reason about distance and direction
  • 0218.2: Core skill or procedure for Reason about distance and direction
  • 0218.3: Representation or model for Reason about distance and direction
  • 0218.4: Application of Reason about distance and direction
  • 0218.5: Common misconception or error check for Reason about distance and direction
#0219Recognize that every integer is a rational numberFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • ratio_rate
Show 5 reinforced subtopics
  • 0219.1: Concept meaning of Recognize that every integer is a rational number
  • 0219.2: Core skill or procedure for Recognize that every integer is a rational number
  • 0219.3: Representation or model for Recognize that every integer is a rational number
  • 0219.4: Application of Recognize that every integer is a rational number
  • 0219.5: Common misconception or error check for Recognize that every integer is a rational number
#0220Write equivalent forms of a rational numberFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • ratio_rate
Show 5 reinforced subtopics
  • 0220.1: Concept meaning of Write equivalent forms of a rational number
  • 0220.2: Core skill or procedure for Write equivalent forms of a rational number
  • 0220.3: Representation or model for Write equivalent forms of a rational number
  • 0220.4: Application of Write equivalent forms of a rational number
  • 0220.5: Common misconception or error check for Write equivalent forms of a rational number
#0221Represent terminating decimals as fractionsFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • fractions
Show 5 reinforced subtopics
  • 0221.1: Concept meaning of Represent terminating decimals as fractions
  • 0221.2: Core skill or procedure for Represent terminating decimals as fractions
  • 0221.3: Representation or model for Represent terminating decimals as fractions
  • 0221.4: Application of Represent terminating decimals as fractions
  • 0221.5: Common misconception or error check for Represent terminating decimals as fractions
#0222Represent repeating decimals as rational numbersFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • ratio_rate
Show 5 reinforced subtopics
  • 0222.1: Concept meaning of Represent repeating decimals as rational numbers
  • 0222.2: Core skill or procedure for Represent repeating decimals as rational numbers
  • 0222.3: Representation or model for Represent repeating decimals as rational numbers
  • 0222.4: Application of Represent repeating decimals as rational numbers
  • 0222.5: Common misconception or error check for Represent repeating decimals as rational numbers
#0223Classify numbers as natural, whole, integer, or rationalFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • ratio_rate
Show 5 reinforced subtopics
  • 0223.1: Concept meaning of Classify numbers as natural, whole, integer, or rational
  • 0223.2: Core skill or procedure for Classify numbers as natural, whole, integer, or rational
  • 0223.3: Representation or model for Classify numbers as natural, whole, integer, or rational
  • 0223.4: Application of Classify numbers as natural, whole, integer, or rational
  • 0223.5: Common misconception or error check for Classify numbers as natural, whole, integer, or rational
#0224Plot rational numbers on a number lineFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • ratio_rate
Show 5 reinforced subtopics
  • 0224.1: Concept meaning of Plot rational numbers on a number line
  • 0224.2: Core skill or procedure for Plot rational numbers on a number line
  • 0224.3: Representation or model for Plot rational numbers on a number line
  • 0224.4: Application of Plot rational numbers on a number line
  • 0224.5: Common misconception or error check for Plot rational numbers on a number line
#0225Compare magnitude using benchmarksFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • generic_math
Show 5 reinforced subtopics
  • 0225.1: Concept meaning of Compare magnitude using benchmarks
  • 0225.2: Core skill or procedure for Compare magnitude using benchmarks
  • 0225.3: Representation or model for Compare magnitude using benchmarks
  • 0225.4: Application of Compare magnitude using benchmarks
  • 0225.5: Common misconception or error check for Compare magnitude using benchmarks
#0226Understand density of rational numbersFractions, Decimals, Percents, and Rational Numbers • Rational Number Structure • ratio_rate
Show 5 reinforced subtopics
  • 0226.1: Concept meaning of Understand density of rational numbers
  • 0226.2: Core skill or procedure for Understand density of rational numbers
  • 0226.3: Representation or model for Understand density of rational numbers
  • 0226.4: Application of Understand density of rational numbers
  • 0226.5: Common misconception or error check for Understand density of rational numbers
#0234Interpret a ratio as part-to-part or part-to-wholeRatios, Proportions, Expressions, and Algebraic Thinking • Ratios, Rates, and Unit Rates • ratio_rate
Show 5 reinforced subtopics
  • 0234.1: Concept meaning of Interpret a ratio as part-to-part or part-to-whole
  • 0234.2: Core skill or procedure for Interpret a ratio as part-to-part or part-to-whole
  • 0234.3: Representation or model for Interpret a ratio as part-to-part or part-to-whole
  • 0234.4: Application of Interpret a ratio as part-to-part or part-to-whole
  • 0234.5: Common misconception or error check for Interpret a ratio as part-to-part or part-to-whole
#0238Compute unit rate from a contextRatios, Proportions, Expressions, and Algebraic Thinking • Ratios, Rates, and Unit Rates • ratio_rate
Show 5 reinforced subtopics
  • 0238.1: Concept meaning of Compute unit rate from a context
  • 0238.2: Core skill or procedure for Compute unit rate from a context
  • 0238.3: Representation or model for Compute unit rate from a context
  • 0238.4: Application of Compute unit rate from a context
  • 0238.5: Common misconception or error check for Compute unit rate from a context
#0239Compare rates in real-world situationsRatios, Proportions, Expressions, and Algebraic Thinking • Ratios, Rates, and Unit Rates • ratio_rate
Show 5 reinforced subtopics
  • 0239.1: Concept meaning of Compare rates in real-world situations
  • 0239.2: Core skill or procedure for Compare rates in real-world situations
  • 0239.3: Representation or model for Compare rates in real-world situations
  • 0239.4: Application of Compare rates in real-world situations
  • 0239.5: Common misconception or error check for Compare rates in real-world situations
#0242Determine whether a relationship is proportionalRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0242.1: Concept meaning of Determine whether a relationship is proportional
  • 0242.2: Core skill or procedure for Determine whether a relationship is proportional
  • 0242.3: Representation or model for Determine whether a relationship is proportional
  • 0242.4: Application of Determine whether a relationship is proportional
  • 0242.5: Common misconception or error check for Determine whether a relationship is proportional
#0243Represent proportional relationships in tablesRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0243.1: Concept meaning of Represent proportional relationships in tables
  • 0243.2: Core skill or procedure for Represent proportional relationships in tables
  • 0243.3: Representation or model for Represent proportional relationships in tables
  • 0243.4: Application of Represent proportional relationships in tables
  • 0243.5: Common misconception or error check for Represent proportional relationships in tables
#0244Represent proportional relationships on graphsRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0244.1: Concept meaning of Represent proportional relationships on graphs
  • 0244.2: Core skill or procedure for Represent proportional relationships on graphs
  • 0244.3: Representation or model for Represent proportional relationships on graphs
  • 0244.4: Application of Represent proportional relationships on graphs
  • 0244.5: Common misconception or error check for Represent proportional relationships on graphs
#0245Write equations of proportional relationshipsRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0245.1: Concept meaning of Write equations of proportional relationships
  • 0245.2: Core skill or procedure for Write equations of proportional relationships
  • 0245.3: Representation or model for Write equations of proportional relationships
  • 0245.4: Application of Write equations of proportional relationships
  • 0245.5: Common misconception or error check for Write equations of proportional relationships
#0248Interpret constant of proportionalityRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0248.1: Concept meaning of Interpret constant of proportionality
  • 0248.2: Core skill or procedure for Interpret constant of proportionality
  • 0248.3: Representation or model for Interpret constant of proportionality
  • 0248.4: Application of Interpret constant of proportionality
  • 0248.5: Common misconception or error check for Interpret constant of proportionality
#0249Recognize a proportional relationship from a tableRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0249.1: Concept meaning of Recognize a proportional relationship from a table
  • 0249.2: Core skill or procedure for Recognize a proportional relationship from a table
  • 0249.3: Representation or model for Recognize a proportional relationship from a table
  • 0249.4: Application of Recognize a proportional relationship from a table
  • 0249.5: Common misconception or error check for Recognize a proportional relationship from a table
#0250Recognize a proportional relationship from a graphRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0250.1: Concept meaning of Recognize a proportional relationship from a graph
  • 0250.2: Core skill or procedure for Recognize a proportional relationship from a graph
  • 0250.3: Representation or model for Recognize a proportional relationship from a graph
  • 0250.4: Application of Recognize a proportional relationship from a graph
  • 0250.5: Common misconception or error check for Recognize a proportional relationship from a graph
#0251Recognize a proportional relationship from an equationRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0251.1: Concept meaning of Recognize a proportional relationship from an equation
  • 0251.2: Core skill or procedure for Recognize a proportional relationship from an equation
  • 0251.3: Representation or model for Recognize a proportional relationship from an equation
  • 0251.4: Application of Recognize a proportional relationship from an equation
  • 0251.5: Common misconception or error check for Recognize a proportional relationship from an equation
#0252Find the constant of proportionalityRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0252.1: Concept meaning of Find the constant of proportionality
  • 0252.2: Core skill or procedure for Find the constant of proportionality
  • 0252.3: Representation or model for Find the constant of proportionality
  • 0252.4: Application of Find the constant of proportionality
  • 0252.5: Common misconception or error check for Find the constant of proportionality
#0254Solve proportions by cross multiplicationRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • percent
Show 5 reinforced subtopics
  • 0254.1: Concept meaning of Solve proportions by cross multiplication
  • 0254.2: Core skill or procedure for Solve proportions by cross multiplication
  • 0254.3: Representation or model for Solve proportions by cross multiplication
  • 0254.4: Application of Solve proportions by cross multiplication
  • 0254.5: Common misconception or error check for Solve proportions by cross multiplication
#0255Interpret slope as unit rate in proportional contextsRatios, Proportions, Expressions, and Algebraic Thinking • Proportional Relationships • ratio_rate
Show 5 reinforced subtopics
  • 0255.1: Concept meaning of Interpret slope as unit rate in proportional contexts
  • 0255.2: Core skill or procedure for Interpret slope as unit rate in proportional contexts
  • 0255.3: Representation or model for Interpret slope as unit rate in proportional contexts
  • 0255.4: Application of Interpret slope as unit rate in proportional contexts
  • 0255.5: Common misconception or error check for Interpret slope as unit rate in proportional contexts
#0257Use distributive property on algebraic expressionsRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • generic_math
Show 5 reinforced subtopics
  • 0257.1: Concept meaning of Use distributive property on algebraic expressions
  • 0257.2: Core skill or procedure for Use distributive property on algebraic expressions
  • 0257.3: Representation or model for Use distributive property on algebraic expressions
  • 0257.4: Application of Use distributive property on algebraic expressions
  • 0257.5: Common misconception or error check for Use distributive property on algebraic expressions
#0258Factor out a greatest common factor from an expressionRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • polynomial
Show 5 reinforced subtopics
  • 0258.1: Concept meaning of Factor out a greatest common factor from an expression
  • 0258.2: Core skill or procedure for Factor out a greatest common factor from an expression
  • 0258.3: Representation or model for Factor out a greatest common factor from an expression
  • 0258.4: Application of Factor out a greatest common factor from an expression
  • 0258.5: Common misconception or error check for Factor out a greatest common factor from an expression
#0259Evaluate expressions with substitutionRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • generic_math
Show 5 reinforced subtopics
  • 0259.1: Concept meaning of Evaluate expressions with substitution
  • 0259.2: Core skill or procedure for Evaluate expressions with substitution
  • 0259.3: Representation or model for Evaluate expressions with substitution
  • 0259.4: Application of Evaluate expressions with substitution
  • 0259.5: Common misconception or error check for Evaluate expressions with substitution
#0260Simplify expressions with rational numbersRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • ratio_rate
Show 5 reinforced subtopics
  • 0260.1: Concept meaning of Simplify expressions with rational numbers
  • 0260.2: Core skill or procedure for Simplify expressions with rational numbers
  • 0260.3: Representation or model for Simplify expressions with rational numbers
  • 0260.4: Application of Simplify expressions with rational numbers
  • 0260.5: Common misconception or error check for Simplify expressions with rational numbers
#0261Translate verbal phrases into algebraic expressionsRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • generic_math
Show 5 reinforced subtopics
  • 0261.1: Concept meaning of Translate verbal phrases into algebraic expressions
  • 0261.2: Core skill or procedure for Translate verbal phrases into algebraic expressions
  • 0261.3: Representation or model for Translate verbal phrases into algebraic expressions
  • 0261.4: Application of Translate verbal phrases into algebraic expressions
  • 0261.5: Common misconception or error check for Translate verbal phrases into algebraic expressions
#0262Identify terms, coefficients, and constantsRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • generic_math
Show 5 reinforced subtopics
  • 0262.1: Concept meaning of Identify terms, coefficients, and constants
  • 0262.2: Core skill or procedure for Identify terms, coefficients, and constants
  • 0262.3: Representation or model for Identify terms, coefficients, and constants
  • 0262.4: Application of Identify terms, coefficients, and constants
  • 0262.5: Common misconception or error check for Identify terms, coefficients, and constants
#0263Translate algebraic expressions to verbal phrasesRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • generic_math
Show 5 reinforced subtopics
  • 0263.1: Concept meaning of Translate algebraic expressions to verbal phrases
  • 0263.2: Core skill or procedure for Translate algebraic expressions to verbal phrases
  • 0263.3: Representation or model for Translate algebraic expressions to verbal phrases
  • 0263.4: Application of Translate algebraic expressions to verbal phrases
  • 0263.5: Common misconception or error check for Translate algebraic expressions to verbal phrases
#0264Use order of operations with variablesRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • ratio_rate
Show 5 reinforced subtopics
  • 0264.1: Concept meaning of Use order of operations with variables
  • 0264.2: Core skill or procedure for Use order of operations with variables
  • 0264.3: Representation or model for Use order of operations with variables
  • 0264.4: Application of Use order of operations with variables
  • 0264.5: Common misconception or error check for Use order of operations with variables
#0265Simplify expressions with exponentsRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • generic_math
Show 5 reinforced subtopics
  • 0265.1: Concept meaning of Simplify expressions with exponents
  • 0265.2: Core skill or procedure for Simplify expressions with exponents
  • 0265.3: Representation or model for Simplify expressions with exponents
  • 0265.4: Application of Simplify expressions with exponents
  • 0265.5: Common misconception or error check for Simplify expressions with exponents
#0266Interpret parts of an algebraic expressionRatios, Proportions, Expressions, and Algebraic Thinking • Expressions and Simplification • generic_math
Show 5 reinforced subtopics
  • 0266.1: Concept meaning of Interpret parts of an algebraic expression
  • 0266.2: Core skill or procedure for Interpret parts of an algebraic expression
  • 0266.3: Representation or model for Interpret parts of an algebraic expression
  • 0266.4: Application of Interpret parts of an algebraic expression
  • 0266.5: Common misconception or error check for Interpret parts of an algebraic expression
#0270Solve equations with variables on both sidesRatios, Proportions, Expressions, and Algebraic Thinking • Linear Equations and Inequalities • equations
Show 5 reinforced subtopics
  • 0270.1: Concept meaning of Solve equations with variables on both sides
  • 0270.2: Core skill or procedure for Solve equations with variables on both sides
  • 0270.3: Representation or model for Solve equations with variables on both sides
  • 0270.4: Application of Solve equations with variables on both sides
  • 0270.5: Common misconception or error check for Solve equations with variables on both sides
#0271Solve one-variable inequalitiesRatios, Proportions, Expressions, and Algebraic Thinking • Linear Equations and Inequalities • generic_math
Show 5 reinforced subtopics
  • 0271.1: Concept meaning of Solve one-variable inequalities
  • 0271.2: Core skill or procedure for Solve one-variable inequalities
  • 0271.3: Representation or model for Solve one-variable inequalities
  • 0271.4: Application of Solve one-variable inequalities
  • 0271.5: Common misconception or error check for Solve one-variable inequalities
#0272Graph solutions to inequalitiesRatios, Proportions, Expressions, and Algebraic Thinking • Linear Equations and Inequalities • generic_math
Show 5 reinforced subtopics
  • 0272.1: Concept meaning of Graph solutions to inequalities
  • 0272.2: Core skill or procedure for Graph solutions to inequalities
  • 0272.3: Representation or model for Graph solutions to inequalities
  • 0272.4: Application of Graph solutions to inequalities
  • 0272.5: Common misconception or error check for Graph solutions to inequalities
#0273Model real situations with linear equationsRatios, Proportions, Expressions, and Algebraic Thinking • Linear Equations and Inequalities • equations
Show 5 reinforced subtopics
  • 0273.1: Concept meaning of Model real situations with linear equations
  • 0273.2: Core skill or procedure for Model real situations with linear equations
  • 0273.3: Representation or model for Model real situations with linear equations
  • 0273.4: Application of Model real situations with linear equations
  • 0273.5: Common misconception or error check for Model real situations with linear equations
#0274Solve equations with rational coefficientsRatios, Proportions, Expressions, and Algebraic Thinking • Linear Equations and Inequalities • ratio_rate
Show 5 reinforced subtopics
  • 0274.1: Concept meaning of Solve equations with rational coefficients
  • 0274.2: Core skill or procedure for Solve equations with rational coefficients
  • 0274.3: Representation or model for Solve equations with rational coefficients
  • 0274.4: Application of Solve equations with rational coefficients
  • 0274.5: Common misconception or error check for Solve equations with rational coefficients
#0275Write an equation from a word problemRatios, Proportions, Expressions, and Algebraic Thinking • Linear Equations and Inequalities • generic_math
Show 5 reinforced subtopics
  • 0275.1: Concept meaning of Write an equation from a word problem
  • 0275.2: Core skill or procedure for Write an equation from a word problem
  • 0275.3: Representation or model for Write an equation from a word problem
  • 0275.4: Application of Write an equation from a word problem
  • 0275.5: Common misconception or error check for Write an equation from a word problem
#0276Write and solve compound inequalitiesRatios, Proportions, Expressions, and Algebraic Thinking • Linear Equations and Inequalities • generic_math
Show 5 reinforced subtopics
  • 0276.1: Concept meaning of Write and solve compound inequalities
  • 0276.2: Core skill or procedure for Write and solve compound inequalities
  • 0276.3: Representation or model for Write and solve compound inequalities
  • 0276.4: Application of Write and solve compound inequalities
  • 0276.5: Common misconception or error check for Write and solve compound inequalities
#0277Interpret a system of two equationsRatios, Proportions, Expressions, and Algebraic Thinking • Systems and Simultaneous Relationships • generic_math
Show 5 reinforced subtopics
  • 0277.1: Concept meaning of Interpret a system of two equations
  • 0277.2: Core skill or procedure for Interpret a system of two equations
  • 0277.3: Representation or model for Interpret a system of two equations
  • 0277.4: Application of Interpret a system of two equations
  • 0277.5: Common misconception or error check for Interpret a system of two equations
#0281Interpret solution meaning in contextRatios, Proportions, Expressions, and Algebraic Thinking • Systems and Simultaneous Relationships • statistics
Show 5 reinforced subtopics
  • 0281.1: Concept meaning of Interpret solution meaning in context
  • 0281.2: Core skill or procedure for Interpret solution meaning in context
  • 0281.3: Representation or model for Interpret solution meaning in context
  • 0281.4: Application of Interpret solution meaning in context
  • 0281.5: Common misconception or error check for Interpret solution meaning in context
#0282Recognize no solution and infinitely many solutionsRatios, Proportions, Expressions, and Algebraic Thinking • Systems and Simultaneous Relationships • generic_math
Show 5 reinforced subtopics
  • 0282.1: Concept meaning of Recognize no solution and infinitely many solutions
  • 0282.2: Core skill or procedure for Recognize no solution and infinitely many solutions
  • 0282.3: Representation or model for Recognize no solution and infinitely many solutions
  • 0282.4: Application of Recognize no solution and infinitely many solutions
  • 0282.5: Common misconception or error check for Recognize no solution and infinitely many solutions
#0283Write a system from a word problemRatios, Proportions, Expressions, and Algebraic Thinking • Systems and Simultaneous Relationships • generic_math
Show 5 reinforced subtopics
  • 0283.1: Concept meaning of Write a system from a word problem
  • 0283.2: Core skill or procedure for Write a system from a word problem
  • 0283.3: Representation or model for Write a system from a word problem
  • 0283.4: Application of Write a system from a word problem
  • 0283.5: Common misconception or error check for Write a system from a word problem
#0284Solve simple systems of inequalities graphicallyRatios, Proportions, Expressions, and Algebraic Thinking • Systems and Simultaneous Relationships • generic_math
Show 5 reinforced subtopics
  • 0284.1: Concept meaning of Solve simple systems of inequalities graphically
  • 0284.2: Core skill or procedure for Solve simple systems of inequalities graphically
  • 0284.3: Representation or model for Solve simple systems of inequalities graphically
  • 0284.4: Application of Solve simple systems of inequalities graphically
  • 0284.5: Common misconception or error check for Solve simple systems of inequalities graphically
#0285Interpret the meaning of an intersection pointRatios, Proportions, Expressions, and Algebraic Thinking • Systems and Simultaneous Relationships • statistics
Show 5 reinforced subtopics
  • 0285.1: Concept meaning of Interpret the meaning of an intersection point
  • 0285.2: Core skill or procedure for Interpret the meaning of an intersection point
  • 0285.3: Representation or model for Interpret the meaning of an intersection point
  • 0285.4: Application of Interpret the meaning of an intersection point
  • 0285.5: Common misconception or error check for Interpret the meaning of an intersection point
#0292Compare linear and exponential pattern growthRatios, Proportions, Expressions, and Algebraic Thinking • Patterns and Introductory Sequences • exponential_log
Show 5 reinforced subtopics
  • 0292.1: Concept meaning of Compare linear and exponential pattern growth
  • 0292.2: Core skill or procedure for Compare linear and exponential pattern growth
  • 0292.3: Representation or model for Compare linear and exponential pattern growth
  • 0292.4: Application of Compare linear and exponential pattern growth
  • 0292.5: Common misconception or error check for Compare linear and exponential pattern growth
#0293Identify a recursive pattern ruleRatios, Proportions, Expressions, and Algebraic Thinking • Patterns and Introductory Sequences • generic_math
Show 5 reinforced subtopics
  • 0293.1: Concept meaning of Identify a recursive pattern rule
  • 0293.2: Core skill or procedure for Identify a recursive pattern rule
  • 0293.3: Representation or model for Identify a recursive pattern rule
  • 0293.4: Application of Identify a recursive pattern rule
  • 0293.5: Common misconception or error check for Identify a recursive pattern rule
#0294Identify an explicit pattern ruleRatios, Proportions, Expressions, and Algebraic Thinking • Patterns and Introductory Sequences • generic_math
Show 5 reinforced subtopics
  • 0294.1: Concept meaning of Identify an explicit pattern rule
  • 0294.2: Core skill or procedure for Identify an explicit pattern rule
  • 0294.3: Representation or model for Identify an explicit pattern rule
  • 0294.4: Application of Identify an explicit pattern rule
  • 0294.5: Common misconception or error check for Identify an explicit pattern rule
#0296Find a term of an arithmetic sequenceRatios, Proportions, Expressions, and Algebraic Thinking • Patterns and Introductory Sequences • arithmetic_sequence
Show 5 reinforced subtopics
  • 0296.1: Concept meaning of Find a term of an arithmetic sequence
  • 0296.2: Core skill or procedure for Find a term of an arithmetic sequence
  • 0296.3: Representation or model for Find a term of an arithmetic sequence
  • 0296.4: Application of Find a term of an arithmetic sequence
  • 0296.5: Common misconception or error check for Find a term of an arithmetic sequence
#0299Find a term of a geometric sequenceRatios, Proportions, Expressions, and Algebraic Thinking • Patterns and Introductory Sequences • geometric_sequence
Show 5 reinforced subtopics
  • 0299.1: Concept meaning of Find a term of a geometric sequence
  • 0299.2: Core skill or procedure for Find a term of a geometric sequence
  • 0299.3: Representation or model for Find a term of a geometric sequence
  • 0299.4: Application of Find a term of a geometric sequence
  • 0299.5: Common misconception or error check for Find a term of a geometric sequence
#0301Model pattern growth with tables and graphsRatios, Proportions, Expressions, and Algebraic Thinking • Patterns and Introductory Sequences • generic_math
Show 5 reinforced subtopics
  • 0301.1: Concept meaning of Model pattern growth with tables and graphs
  • 0301.2: Core skill or procedure for Model pattern growth with tables and graphs
  • 0301.3: Representation or model for Model pattern growth with tables and graphs
  • 0301.4: Application of Model pattern growth with tables and graphs
  • 0301.5: Common misconception or error check for Model pattern growth with tables and graphs
#0303Determine whether a relation is a functionFunctions and Mathematical Modeling • Function Concept and Representations • generic_math
Show 5 reinforced subtopics
  • 0303.1: Concept meaning of Determine whether a relation is a function
  • 0303.2: Core skill or procedure for Determine whether a relation is a function
  • 0303.3: Representation or model for Determine whether a relation is a function
  • 0303.4: Application of Determine whether a relation is a function
  • 0303.5: Common misconception or error check for Determine whether a relation is a function
#0306Interpret a function from an equationFunctions and Mathematical Modeling • Function Concept and Representations • generic_math
Show 5 reinforced subtopics
  • 0306.1: Concept meaning of Interpret a function from an equation
  • 0306.2: Core skill or procedure for Interpret a function from an equation
  • 0306.3: Representation or model for Interpret a function from an equation
  • 0306.4: Application of Interpret a function from an equation
  • 0306.5: Common misconception or error check for Interpret a function from an equation
#0310Evaluate a function from an equationFunctions and Mathematical Modeling • Function Concept and Representations • generic_math
Show 5 reinforced subtopics
  • 0310.1: Concept meaning of Evaluate a function from an equation
  • 0310.2: Core skill or procedure for Evaluate a function from an equation
  • 0310.3: Representation or model for Evaluate a function from an equation
  • 0310.4: Application of Evaluate a function from an equation
  • 0310.5: Common misconception or error check for Evaluate a function from an equation
#0313Find domain in simple discrete settingsFunctions and Mathematical Modeling • Function Concept and Representations • generic_math
Show 5 reinforced subtopics
  • 0313.1: Concept meaning of Find domain in simple discrete settings
  • 0313.2: Core skill or procedure for Find domain in simple discrete settings
  • 0313.3: Representation or model for Find domain in simple discrete settings
  • 0313.4: Application of Find domain in simple discrete settings
  • 0313.5: Common misconception or error check for Find domain in simple discrete settings
#0314Find range in simple discrete settingsFunctions and Mathematical Modeling • Function Concept and Representations • generic_math
Show 5 reinforced subtopics
  • 0314.1: Concept meaning of Find range in simple discrete settings
  • 0314.2: Core skill or procedure for Find range in simple discrete settings
  • 0314.3: Representation or model for Find range in simple discrete settings
  • 0314.4: Application of Find range in simple discrete settings
  • 0314.5: Common misconception or error check for Find range in simple discrete settings
#0315Interpret average rate of change informallyFunctions and Mathematical Modeling • Function Concept and Representations • ratio_rate
Show 5 reinforced subtopics
  • 0315.1: Concept meaning of Interpret average rate of change informally
  • 0315.2: Core skill or procedure for Interpret average rate of change informally
  • 0315.3: Representation or model for Interpret average rate of change informally
  • 0315.4: Application of Interpret average rate of change informally
  • 0315.5: Common misconception or error check for Interpret average rate of change informally
#0321Write an equation in slope-intercept formFunctions and Mathematical Modeling • Linear Functions • linear
Show 5 reinforced subtopics
  • 0321.1: Concept meaning of Write an equation in slope-intercept form
  • 0321.2: Core skill or procedure for Write an equation in slope-intercept form
  • 0321.3: Representation or model for Write an equation in slope-intercept form
  • 0321.4: Application of Write an equation in slope-intercept form
  • 0321.5: Common misconception or error check for Write an equation in slope-intercept form
#0322Write an equation from a point and slopeFunctions and Mathematical Modeling • Linear Functions • linear
Show 5 reinforced subtopics
  • 0322.1: Concept meaning of Write an equation from a point and slope
  • 0322.2: Core skill or procedure for Write an equation from a point and slope
  • 0322.3: Representation or model for Write an equation from a point and slope
  • 0322.4: Application of Write an equation from a point and slope
  • 0322.5: Common misconception or error check for Write an equation from a point and slope
#0326Find parallel and perpendicular line relationshipsFunctions and Mathematical Modeling • Linear Functions • geometry
Show 5 reinforced subtopics
  • 0326.1: Concept meaning of Find parallel and perpendicular line relationships
  • 0326.2: Core skill or procedure for Find parallel and perpendicular line relationships
  • 0326.3: Representation or model for Find parallel and perpendicular line relationships
  • 0326.4: Application of Find parallel and perpendicular line relationships
  • 0326.5: Common misconception or error check for Find parallel and perpendicular line relationships
#0329Interpret vertex and axis of symmetryFunctions and Mathematical Modeling • Nonlinear Function Families • generic_math
Show 5 reinforced subtopics
  • 0329.1: Concept meaning of Interpret vertex and axis of symmetry
  • 0329.2: Core skill or procedure for Interpret vertex and axis of symmetry
  • 0329.3: Representation or model for Interpret vertex and axis of symmetry
  • 0329.4: Application of Interpret vertex and axis of symmetry
  • 0329.5: Common misconception or error check for Interpret vertex and axis of symmetry
#0334Compare linear, quadratic, and exponential behaviorFunctions and Mathematical Modeling • Nonlinear Function Families • quadratics
Show 5 reinforced subtopics
  • 0334.1: Concept meaning of Compare linear, quadratic, and exponential behavior
  • 0334.2: Core skill or procedure for Compare linear, quadratic, and exponential behavior
  • 0334.3: Representation or model for Compare linear, quadratic, and exponential behavior
  • 0334.4: Application of Compare linear, quadratic, and exponential behavior
  • 0334.5: Common misconception or error check for Compare linear, quadratic, and exponential behavior
#0335Recognize quadratic functions in multiple formsFunctions and Mathematical Modeling • Nonlinear Function Families • percent
Show 5 reinforced subtopics
  • 0335.1: Concept meaning of Recognize quadratic functions in multiple forms
  • 0335.2: Core skill or procedure for Recognize quadratic functions in multiple forms
  • 0335.3: Representation or model for Recognize quadratic functions in multiple forms
  • 0335.4: Application of Recognize quadratic functions in multiple forms
  • 0335.5: Common misconception or error check for Recognize quadratic functions in multiple forms
#0336Recognize exponential functions in multiple formsFunctions and Mathematical Modeling • Nonlinear Function Families • percent
Show 5 reinforced subtopics
  • 0336.1: Concept meaning of Recognize exponential functions in multiple forms
  • 0336.2: Core skill or procedure for Recognize exponential functions in multiple forms
  • 0336.3: Representation or model for Recognize exponential functions in multiple forms
  • 0336.4: Application of Recognize exponential functions in multiple forms
  • 0336.5: Common misconception or error check for Recognize exponential functions in multiple forms
#0337Recognize square root functions in multiple formsFunctions and Mathematical Modeling • Nonlinear Function Families • percent
Show 5 reinforced subtopics
  • 0337.1: Concept meaning of Recognize square root functions in multiple forms
  • 0337.2: Core skill or procedure for Recognize square root functions in multiple forms
  • 0337.3: Representation or model for Recognize square root functions in multiple forms
  • 0337.4: Application of Recognize square root functions in multiple forms
  • 0337.5: Common misconception or error check for Recognize square root functions in multiple forms
#0338Compare linear and exponential growthFunctions and Mathematical Modeling • Nonlinear Function Families • exponential_log
Show 5 reinforced subtopics
  • 0338.1: Concept meaning of Compare linear and exponential growth
  • 0338.2: Core skill or procedure for Compare linear and exponential growth
  • 0338.3: Representation or model for Compare linear and exponential growth
  • 0338.4: Application of Compare linear and exponential growth
  • 0338.5: Common misconception or error check for Compare linear and exponential growth
#0339Graph quadratic parent and transformationsFunctions and Mathematical Modeling • Nonlinear Function Families • quadratics
Show 5 reinforced subtopics
  • 0339.1: Concept meaning of Graph quadratic parent and transformations
  • 0339.2: Core skill or procedure for Graph quadratic parent and transformations
  • 0339.3: Representation or model for Graph quadratic parent and transformations
  • 0339.4: Application of Graph quadratic parent and transformations
  • 0339.5: Common misconception or error check for Graph quadratic parent and transformations
#0340Graph exponential parent and transformationsFunctions and Mathematical Modeling • Nonlinear Function Families • exponential_log
Show 5 reinforced subtopics
  • 0340.1: Concept meaning of Graph exponential parent and transformations
  • 0340.2: Core skill or procedure for Graph exponential parent and transformations
  • 0340.3: Representation or model for Graph exponential parent and transformations
  • 0340.4: Application of Graph exponential parent and transformations
  • 0340.5: Common misconception or error check for Graph exponential parent and transformations
#0341Interpret key features of nonlinear graphsFunctions and Mathematical Modeling • Nonlinear Function Families • geometry
Show 5 reinforced subtopics
  • 0341.1: Concept meaning of Interpret key features of nonlinear graphs
  • 0341.2: Core skill or procedure for Interpret key features of nonlinear graphs
  • 0341.3: Representation or model for Interpret key features of nonlinear graphs
  • 0341.4: Application of Interpret key features of nonlinear graphs
  • 0341.5: Common misconception or error check for Interpret key features of nonlinear graphs
#0342Choose an appropriate nonlinear model from dataFunctions and Mathematical Modeling • Nonlinear Function Families • statistics
Show 5 reinforced subtopics
  • 0342.1: Concept meaning of Choose an appropriate nonlinear model from data
  • 0342.2: Core skill or procedure for Choose an appropriate nonlinear model from data
  • 0342.3: Representation or model for Choose an appropriate nonlinear model from data
  • 0342.4: Application of Choose an appropriate nonlinear model from data
  • 0342.5: Common misconception or error check for Choose an appropriate nonlinear model from data
#0343Find average rate of change on an intervalFunctions and Mathematical Modeling • Nonlinear Function Families • ratio_rate
Show 5 reinforced subtopics
  • 0343.1: Concept meaning of Find average rate of change on an interval
  • 0343.2: Core skill or procedure for Find average rate of change on an interval
  • 0343.3: Representation or model for Find average rate of change on an interval
  • 0343.4: Application of Find average rate of change on an interval
  • 0343.5: Common misconception or error check for Find average rate of change on an interval
#0350Analyze asymptotes of rational functionsFunctions and Mathematical Modeling • Polynomial and Rational Functions • ratio_rate
Show 5 reinforced subtopics
  • 0350.1: Concept meaning of Analyze asymptotes of rational functions
  • 0350.2: Core skill or procedure for Analyze asymptotes of rational functions
  • 0350.3: Representation or model for Analyze asymptotes of rational functions
  • 0350.4: Application of Analyze asymptotes of rational functions
  • 0350.5: Common misconception or error check for Analyze asymptotes of rational functions
#0351Factor common monomial and polynomial factorsFunctions and Mathematical Modeling • Polynomial and Rational Functions • polynomial
Show 5 reinforced subtopics
  • 0351.1: Concept meaning of Factor common monomial and polynomial factors
  • 0351.2: Core skill or procedure for Factor common monomial and polynomial factors
  • 0351.3: Representation or model for Factor common monomial and polynomial factors
  • 0351.4: Application of Factor common monomial and polynomial factors
  • 0351.5: Common misconception or error check for Factor common monomial and polynomial factors
#0353Use special products and factoring patternsFunctions and Mathematical Modeling • Polynomial and Rational Functions • polynomial
Show 5 reinforced subtopics
  • 0353.1: Concept meaning of Use special products and factoring patterns
  • 0353.2: Core skill or procedure for Use special products and factoring patterns
  • 0353.3: Representation or model for Use special products and factoring patterns
  • 0353.4: Application of Use special products and factoring patterns
  • 0353.5: Common misconception or error check for Use special products and factoring patterns
#0356Apply vertical and horizontal shiftsFunctions and Mathematical Modeling • Transformations, Piecewise, and Inverse Functions • generic_math
Show 5 reinforced subtopics
  • 0356.1: Concept meaning of Apply vertical and horizontal shifts
  • 0356.2: Core skill or procedure for Apply vertical and horizontal shifts
  • 0356.3: Representation or model for Apply vertical and horizontal shifts
  • 0356.4: Application of Apply vertical and horizontal shifts
  • 0356.5: Common misconception or error check for Apply vertical and horizontal shifts
#0360Determine whether a function has an inverseFunctions and Mathematical Modeling • Transformations, Piecewise, and Inverse Functions • generic_math
Show 5 reinforced subtopics
  • 0360.1: Concept meaning of Determine whether a function has an inverse
  • 0360.2: Core skill or procedure for Determine whether a function has an inverse
  • 0360.3: Representation or model for Determine whether a function has an inverse
  • 0360.4: Application of Determine whether a function has an inverse
  • 0360.5: Common misconception or error check for Determine whether a function has an inverse
#0363Graph a piecewise-defined functionFunctions and Mathematical Modeling • Transformations, Piecewise, and Inverse Functions • generic_math
Show 5 reinforced subtopics
  • 0363.1: Concept meaning of Graph a piecewise-defined function
  • 0363.2: Core skill or procedure for Graph a piecewise-defined function
  • 0363.3: Representation or model for Graph a piecewise-defined function
  • 0363.4: Application of Graph a piecewise-defined function
  • 0363.5: Common misconception or error check for Graph a piecewise-defined function
#0364Find domain restrictions from contextFunctions and Mathematical Modeling • Transformations, Piecewise, and Inverse Functions • generic_math
Show 5 reinforced subtopics
  • 0364.1: Concept meaning of Find domain restrictions from context
  • 0364.2: Core skill or procedure for Find domain restrictions from context
  • 0364.3: Representation or model for Find domain restrictions from context
  • 0364.4: Application of Find domain restrictions from context
  • 0364.5: Common misconception or error check for Find domain restrictions from context
#0365Describe parent-function transformations preciselyFunctions and Mathematical Modeling • Transformations, Piecewise, and Inverse Functions • generic_math
Show 5 reinforced subtopics
  • 0365.1: Concept meaning of Describe parent-function transformations precisely
  • 0365.2: Core skill or procedure for Describe parent-function transformations precisely
  • 0365.3: Representation or model for Describe parent-function transformations precisely
  • 0365.4: Application of Describe parent-function transformations precisely
  • 0365.5: Common misconception or error check for Describe parent-function transformations precisely
#0366Combine vertical and horizontal transformationsFunctions and Mathematical Modeling • Transformations, Piecewise, and Inverse Functions • generic_math
Show 5 reinforced subtopics
  • 0366.1: Concept meaning of Combine vertical and horizontal transformations
  • 0366.2: Core skill or procedure for Combine vertical and horizontal transformations
  • 0366.3: Representation or model for Combine vertical and horizontal transformations
  • 0366.4: Application of Combine vertical and horizontal transformations
  • 0366.5: Common misconception or error check for Combine vertical and horizontal transformations
#0373Use models for prediction with constraintsFunctions and Mathematical Modeling • Function Modeling • generic_math
Show 5 reinforced subtopics
  • 0373.1: Concept meaning of Use models for prediction with constraints
  • 0373.2: Core skill or procedure for Use models for prediction with constraints
  • 0373.3: Representation or model for Use models for prediction with constraints
  • 0373.4: Application of Use models for prediction with constraints
  • 0373.5: Common misconception or error check for Use models for prediction with constraints
#0377Use exponential regression as a modelFunctions and Mathematical Modeling • Function Modeling • exponential_log
Show 5 reinforced subtopics
  • 0377.1: Concept meaning of Use exponential regression as a model
  • 0377.2: Core skill or procedure for Use exponential regression as a model
  • 0377.3: Representation or model for Use exponential regression as a model
  • 0377.4: Application of Use exponential regression as a model
  • 0377.5: Common misconception or error check for Use exponential regression as a model
#0384Identify parallel and perpendicular linesGeometry and Spatial Reasoning • Shapes and Properties • geometry
Show 5 reinforced subtopics
  • 0384.1: Concept meaning of Identify parallel and perpendicular lines
  • 0384.2: Core skill or procedure for Identify parallel and perpendicular lines
  • 0384.3: Representation or model for Identify parallel and perpendicular lines
  • 0384.4: Application of Identify parallel and perpendicular lines
  • 0384.5: Common misconception or error check for Identify parallel and perpendicular lines
#0390Compare attributes of prisms, pyramids, cylinders, cones, and spheresGeometry and Spatial Reasoning • Shapes and Properties • generic_math
Show 5 reinforced subtopics
  • 0390.1: Concept meaning of Compare attributes of prisms, pyramids, cylinders, cones, and spheres
  • 0390.2: Core skill or procedure for Compare attributes of prisms, pyramids, cylinders, cones, and spheres
  • 0390.3: Representation or model for Compare attributes of prisms, pyramids, cylinders, cones, and spheres
  • 0390.4: Application of Compare attributes of prisms, pyramids, cylinders, cones, and spheres
  • 0390.5: Common misconception or error check for Compare attributes of prisms, pyramids, cylinders, cones, and spheres
#0391Use Euler-type reasoning for polyhedra informallyGeometry and Spatial Reasoning • Shapes and Properties • generic_math
Show 5 reinforced subtopics
  • 0391.1: Concept meaning of Use Euler-type reasoning for polyhedra informally
  • 0391.2: Core skill or procedure for Use Euler-type reasoning for polyhedra informally
  • 0391.3: Representation or model for Use Euler-type reasoning for polyhedra informally
  • 0391.4: Application of Use Euler-type reasoning for polyhedra informally
  • 0391.5: Common misconception or error check for Use Euler-type reasoning for polyhedra informally
#0393Determine congruence from rigid motionsGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0393.1: Concept meaning of Determine congruence from rigid motions
  • 0393.2: Core skill or procedure for Determine congruence from rigid motions
  • 0393.3: Representation or model for Determine congruence from rigid motions
  • 0393.4: Application of Determine congruence from rigid motions
  • 0393.5: Common misconception or error check for Determine congruence from rigid motions
#0394Determine similarity from dilations and rigid motionsGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0394.1: Concept meaning of Determine similarity from dilations and rigid motions
  • 0394.2: Core skill or procedure for Determine similarity from dilations and rigid motions
  • 0394.3: Representation or model for Determine similarity from dilations and rigid motions
  • 0394.4: Application of Determine similarity from dilations and rigid motions
  • 0394.5: Common misconception or error check for Determine similarity from dilations and rigid motions
#0395Perform translations on a coordinate planeGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0395.1: Concept meaning of Perform translations on a coordinate plane
  • 0395.2: Core skill or procedure for Perform translations on a coordinate plane
  • 0395.3: Representation or model for Perform translations on a coordinate plane
  • 0395.4: Application of Perform translations on a coordinate plane
  • 0395.5: Common misconception or error check for Perform translations on a coordinate plane
#0396Perform reflections on a coordinate planeGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0396.1: Concept meaning of Perform reflections on a coordinate plane
  • 0396.2: Core skill or procedure for Perform reflections on a coordinate plane
  • 0396.3: Representation or model for Perform reflections on a coordinate plane
  • 0396.4: Application of Perform reflections on a coordinate plane
  • 0396.5: Common misconception or error check for Perform reflections on a coordinate plane
#0397Perform rotations on a coordinate planeGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0397.1: Concept meaning of Perform rotations on a coordinate plane
  • 0397.2: Core skill or procedure for Perform rotations on a coordinate plane
  • 0397.3: Representation or model for Perform rotations on a coordinate plane
  • 0397.4: Application of Perform rotations on a coordinate plane
  • 0397.5: Common misconception or error check for Perform rotations on a coordinate plane
#0398Perform dilations on a coordinate planeGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0398.1: Concept meaning of Perform dilations on a coordinate plane
  • 0398.2: Core skill or procedure for Perform dilations on a coordinate plane
  • 0398.3: Representation or model for Perform dilations on a coordinate plane
  • 0398.4: Application of Perform dilations on a coordinate plane
  • 0398.5: Common misconception or error check for Perform dilations on a coordinate plane
#0399Describe transformations with vectors or rulesGeometry and Spatial Reasoning • Transformations • vectors
Show 5 reinforced subtopics
  • 0399.1: Concept meaning of Describe transformations with vectors or rules
  • 0399.2: Core skill or procedure for Describe transformations with vectors or rules
  • 0399.3: Representation or model for Describe transformations with vectors or rules
  • 0399.4: Application of Describe transformations with vectors or rules
  • 0399.5: Common misconception or error check for Describe transformations with vectors or rules
#0401Identify symmetries using transformationsGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0401.1: Concept meaning of Identify symmetries using transformations
  • 0401.2: Core skill or procedure for Identify symmetries using transformations
  • 0401.3: Representation or model for Identify symmetries using transformations
  • 0401.4: Application of Identify symmetries using transformations
  • 0401.5: Common misconception or error check for Identify symmetries using transformations
#0402Distinguish rigid motions from dilationsGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0402.1: Concept meaning of Distinguish rigid motions from dilations
  • 0402.2: Core skill or procedure for Distinguish rigid motions from dilations
  • 0402.3: Representation or model for Distinguish rigid motions from dilations
  • 0402.4: Application of Distinguish rigid motions from dilations
  • 0402.5: Common misconception or error check for Distinguish rigid motions from dilations
#0403Connect transformations to congruence and similarityGeometry and Spatial Reasoning • Transformations • generic_math
Show 5 reinforced subtopics
  • 0403.1: Concept meaning of Connect transformations to congruence and similarity
  • 0403.2: Core skill or procedure for Connect transformations to congruence and similarity
  • 0403.3: Representation or model for Connect transformations to congruence and similarity
  • 0403.4: Application of Connect transformations to congruence and similarity
  • 0403.5: Common misconception or error check for Connect transformations to congruence and similarity
#0406Solve proportional sides in similar figuresGeometry and Spatial Reasoning • Congruence and Similarity • ratio_rate
Show 5 reinforced subtopics
  • 0406.1: Concept meaning of Solve proportional sides in similar figures
  • 0406.2: Core skill or procedure for Solve proportional sides in similar figures
  • 0406.3: Representation or model for Solve proportional sides in similar figures
  • 0406.4: Application of Solve proportional sides in similar figures
  • 0406.5: Common misconception or error check for Solve proportional sides in similar figures
#0407Reason with scale factor and perimeterGeometry and Spatial Reasoning • Congruence and Similarity • polynomial
Show 5 reinforced subtopics
  • 0407.1: Concept meaning of Reason with scale factor and perimeter
  • 0407.2: Core skill or procedure for Reason with scale factor and perimeter
  • 0407.3: Representation or model for Reason with scale factor and perimeter
  • 0407.4: Application of Reason with scale factor and perimeter
  • 0407.5: Common misconception or error check for Reason with scale factor and perimeter
#0411Set up proportions from similar figuresGeometry and Spatial Reasoning • Congruence and Similarity • ratio_rate
Show 5 reinforced subtopics
  • 0411.1: Concept meaning of Set up proportions from similar figures
  • 0411.2: Core skill or procedure for Set up proportions from similar figures
  • 0411.3: Representation or model for Set up proportions from similar figures
  • 0411.4: Application of Set up proportions from similar figures
  • 0411.5: Common misconception or error check for Set up proportions from similar figures
#0412Find missing lengths in similar figuresGeometry and Spatial Reasoning • Congruence and Similarity • generic_math
Show 5 reinforced subtopics
  • 0412.1: Concept meaning of Find missing lengths in similar figures
  • 0412.2: Core skill or procedure for Find missing lengths in similar figures
  • 0412.3: Representation or model for Find missing lengths in similar figures
  • 0412.4: Application of Find missing lengths in similar figures
  • 0412.5: Common misconception or error check for Find missing lengths in similar figures
#0413Use scale factor to enlarge or reduce a figureGeometry and Spatial Reasoning • Congruence and Similarity • polynomial
Show 5 reinforced subtopics
  • 0413.1: Concept meaning of Use scale factor to enlarge or reduce a figure
  • 0413.2: Core skill or procedure for Use scale factor to enlarge or reduce a figure
  • 0413.3: Representation or model for Use scale factor to enlarge or reduce a figure
  • 0413.4: Application of Use scale factor to enlarge or reduce a figure
  • 0413.5: Common misconception or error check for Use scale factor to enlarge or reduce a figure
#0414Identify corresponding parts in similar figuresGeometry and Spatial Reasoning • Congruence and Similarity • generic_math
Show 5 reinforced subtopics
  • 0414.1: Concept meaning of Identify corresponding parts in similar figures
  • 0414.2: Core skill or procedure for Identify corresponding parts in similar figures
  • 0414.3: Representation or model for Identify corresponding parts in similar figures
  • 0414.4: Application of Identify corresponding parts in similar figures
  • 0414.5: Common misconception or error check for Identify corresponding parts in similar figures
#0415Use congruence to justify equal measuresGeometry and Spatial Reasoning • Congruence and Similarity • generic_math
Show 5 reinforced subtopics
  • 0415.1: Concept meaning of Use congruence to justify equal measures
  • 0415.2: Core skill or procedure for Use congruence to justify equal measures
  • 0415.3: Representation or model for Use congruence to justify equal measures
  • 0415.4: Application of Use congruence to justify equal measures
  • 0415.5: Common misconception or error check for Use congruence to justify equal measures
#0416Apply similarity in indirect measurementGeometry and Spatial Reasoning • Congruence and Similarity • generic_math
Show 5 reinforced subtopics
  • 0416.1: Concept meaning of Apply similarity in indirect measurement
  • 0416.2: Core skill or procedure for Apply similarity in indirect measurement
  • 0416.3: Representation or model for Apply similarity in indirect measurement
  • 0416.4: Application of Apply similarity in indirect measurement
  • 0416.5: Common misconception or error check for Apply similarity in indirect measurement
#0421Analyze equations of circles in the planeGeometry and Spatial Reasoning • Coordinate Geometry • geometry
Show 5 reinforced subtopics
  • 0421.1: Concept meaning of Analyze equations of circles in the plane
  • 0421.2: Core skill or procedure for Analyze equations of circles in the plane
  • 0421.3: Representation or model for Analyze equations of circles in the plane
  • 0421.4: Application of Analyze equations of circles in the plane
  • 0421.5: Common misconception or error check for Analyze equations of circles in the plane
#0425Use slope to analyze line relationshipsGeometry and Spatial Reasoning • Coordinate Geometry • linear
Show 5 reinforced subtopics
  • 0425.1: Concept meaning of Use slope to analyze line relationships
  • 0425.2: Core skill or procedure for Use slope to analyze line relationships
  • 0425.3: Representation or model for Use slope to analyze line relationships
  • 0425.4: Application of Use slope to analyze line relationships
  • 0425.5: Common misconception or error check for Use slope to analyze line relationships
#0426Find equations of lines through given conditionsGeometry and Spatial Reasoning • Coordinate Geometry • geometry
Show 5 reinforced subtopics
  • 0426.1: Concept meaning of Find equations of lines through given conditions
  • 0426.2: Core skill or procedure for Find equations of lines through given conditions
  • 0426.3: Representation or model for Find equations of lines through given conditions
  • 0426.4: Application of Find equations of lines through given conditions
  • 0426.5: Common misconception or error check for Find equations of lines through given conditions
#0429Classify quadrilaterals with slope and distanceGeometry and Spatial Reasoning • Coordinate Geometry • linear
Show 5 reinforced subtopics
  • 0429.1: Concept meaning of Classify quadrilaterals with slope and distance
  • 0429.2: Core skill or procedure for Classify quadrilaterals with slope and distance
  • 0429.3: Representation or model for Classify quadrilaterals with slope and distance
  • 0429.4: Application of Classify quadrilaterals with slope and distance
  • 0429.5: Common misconception or error check for Classify quadrilaterals with slope and distance
#0430Prove geometric properties analyticallyGeometry and Spatial Reasoning • Coordinate Geometry • generic_math
Show 5 reinforced subtopics
  • 0430.1: Concept meaning of Prove geometric properties analytically
  • 0430.2: Core skill or procedure for Prove geometric properties analytically
  • 0430.3: Representation or model for Prove geometric properties analytically
  • 0430.4: Application of Prove geometric properties analytically
  • 0430.5: Common misconception or error check for Prove geometric properties analytically
#0434Justify statements with definitions and theoremsGeometry and Spatial Reasoning • Angle Relationships and Proof • generic_math
Show 5 reinforced subtopics
  • 0434.1: Concept meaning of Justify statements with definitions and theorems
  • 0434.2: Core skill or procedure for Justify statements with definitions and theorems
  • 0434.3: Representation or model for Justify statements with definitions and theorems
  • 0434.4: Application of Justify statements with definitions and theorems
  • 0434.5: Common misconception or error check for Justify statements with definitions and theorems
#0437Use complementary and supplementary relationshipsGeometry and Spatial Reasoning • Angle Relationships and Proof • generic_math
Show 5 reinforced subtopics
  • 0437.1: Concept meaning of Use complementary and supplementary relationships
  • 0437.2: Core skill or procedure for Use complementary and supplementary relationships
  • 0437.3: Representation or model for Use complementary and supplementary relationships
  • 0437.4: Application of Use complementary and supplementary relationships
  • 0437.5: Common misconception or error check for Use complementary and supplementary relationships
#0438Use angle pairs formed by parallel lines and a transversalGeometry and Spatial Reasoning • Angle Relationships and Proof • geometry
Show 5 reinforced subtopics
  • 0438.1: Concept meaning of Use angle pairs formed by parallel lines and a transversal
  • 0438.2: Core skill or procedure for Use angle pairs formed by parallel lines and a transversal
  • 0438.3: Representation or model for Use angle pairs formed by parallel lines and a transversal
  • 0438.4: Application of Use angle pairs formed by parallel lines and a transversal
  • 0438.5: Common misconception or error check for Use angle pairs formed by parallel lines and a transversal
#0440Justify a step in a geometric argumentGeometry and Spatial Reasoning • Angle Relationships and Proof • generic_math
Show 5 reinforced subtopics
  • 0440.1: Concept meaning of Justify a step in a geometric argument
  • 0440.2: Core skill or procedure for Justify a step in a geometric argument
  • 0440.3: Representation or model for Justify a step in a geometric argument
  • 0440.4: Application of Justify a step in a geometric argument
  • 0440.5: Common misconception or error check for Justify a step in a geometric argument
#0441Understand the structure of a two-column proofGeometry and Spatial Reasoning • Angle Relationships and Proof • generic_math
Show 5 reinforced subtopics
  • 0441.1: Concept meaning of Understand the structure of a two-column proof
  • 0441.2: Core skill or procedure for Understand the structure of a two-column proof
  • 0441.3: Representation or model for Understand the structure of a two-column proof
  • 0441.4: Application of Understand the structure of a two-column proof
  • 0441.5: Common misconception or error check for Understand the structure of a two-column proof
#0442Use triangle angle sum and exterior angle theoremsGeometry and Spatial Reasoning • Angle Relationships and Proof • geometry
Show 5 reinforced subtopics
  • 0442.1: Concept meaning of Use triangle angle sum and exterior angle theorems
  • 0442.2: Core skill or procedure for Use triangle angle sum and exterior angle theorems
  • 0442.3: Representation or model for Use triangle angle sum and exterior angle theorems
  • 0442.4: Application of Use triangle angle sum and exterior angle theorems
  • 0442.5: Common misconception or error check for Use triangle angle sum and exterior angle theorems
#0443Prove simple statements about parallel lines and trianglesGeometry and Spatial Reasoning • Angle Relationships and Proof • geometry
Show 5 reinforced subtopics
  • 0443.1: Concept meaning of Prove simple statements about parallel lines and triangles
  • 0443.2: Core skill or procedure for Prove simple statements about parallel lines and triangles
  • 0443.3: Representation or model for Prove simple statements about parallel lines and triangles
  • 0443.4: Application of Prove simple statements about parallel lines and triangles
  • 0443.5: Common misconception or error check for Prove simple statements about parallel lines and triangles
#0448Find volume of prisms and cylindersGeometry and Spatial Reasoning • Area, Surface Area, and Volume • measurement_geometry
Show 5 reinforced subtopics
  • 0448.1: Concept meaning of Find volume of prisms and cylinders
  • 0448.2: Core skill or procedure for Find volume of prisms and cylinders
  • 0448.3: Representation or model for Find volume of prisms and cylinders
  • 0448.4: Application of Find volume of prisms and cylinders
  • 0448.5: Common misconception or error check for Find volume of prisms and cylinders
#0449Find volume of pyramids, cones, and spheresGeometry and Spatial Reasoning • Area, Surface Area, and Volume • measurement_geometry
Show 5 reinforced subtopics
  • 0449.1: Concept meaning of Find volume of pyramids, cones, and spheres
  • 0449.2: Core skill or procedure for Find volume of pyramids, cones, and spheres
  • 0449.3: Representation or model for Find volume of pyramids, cones, and spheres
  • 0449.4: Application of Find volume of pyramids, cones, and spheres
  • 0449.5: Common misconception or error check for Find volume of pyramids, cones, and spheres
#0451Choose an appropriate measurement toolGeometry and Spatial Reasoning • Area, Surface Area, and Volume • generic_math
Show 5 reinforced subtopics
  • 0451.1: Concept meaning of Choose an appropriate measurement tool
  • 0451.2: Core skill or procedure for Choose an appropriate measurement tool
  • 0451.3: Representation or model for Choose an appropriate measurement tool
  • 0451.4: Application of Choose an appropriate measurement tool
  • 0451.5: Common misconception or error check for Choose an appropriate measurement tool
#0454Find area of parallelograms and trapezoidsGeometry and Spatial Reasoning • Area, Surface Area, and Volume • measurement_geometry
Show 5 reinforced subtopics
  • 0454.1: Concept meaning of Find area of parallelograms and trapezoids
  • 0454.2: Core skill or procedure for Find area of parallelograms and trapezoids
  • 0454.3: Representation or model for Find area of parallelograms and trapezoids
  • 0454.4: Application of Find area of parallelograms and trapezoids
  • 0454.5: Common misconception or error check for Find area of parallelograms and trapezoids
#0455Find surface area of prisms and cylindersGeometry and Spatial Reasoning • Area, Surface Area, and Volume • measurement_geometry
Show 5 reinforced subtopics
  • 0455.1: Concept meaning of Find surface area of prisms and cylinders
  • 0455.2: Core skill or procedure for Find surface area of prisms and cylinders
  • 0455.3: Representation or model for Find surface area of prisms and cylinders
  • 0455.4: Application of Find surface area of prisms and cylinders
  • 0455.5: Common misconception or error check for Find surface area of prisms and cylinders
#0456Solve composite-figure measurement problemsGeometry and Spatial Reasoning • Area, Surface Area, and Volume • generic_math
Show 5 reinforced subtopics
  • 0456.1: Concept meaning of Solve composite-figure measurement problems
  • 0456.2: Core skill or procedure for Solve composite-figure measurement problems
  • 0456.3: Representation or model for Solve composite-figure measurement problems
  • 0456.4: Application of Solve composite-figure measurement problems
  • 0456.5: Common misconception or error check for Solve composite-figure measurement problems
#0459Measure length with standard unitsMeasurement, Units, and Quantitative Reasoning • Attributes and Direct Measurement • generic_math
Show 5 reinforced subtopics
  • 0459.1: Concept meaning of Measure length with standard units
  • 0459.2: Core skill or procedure for Measure length with standard units
  • 0459.3: Representation or model for Measure length with standard units
  • 0459.4: Application of Measure length with standard units
  • 0459.5: Common misconception or error check for Measure length with standard units
#0464Identify measurable attributes of an objectMeasurement, Units, and Quantitative Reasoning • Attributes and Direct Measurement • generic_math
Show 5 reinforced subtopics
  • 0464.1: Concept meaning of Identify measurable attributes of an object
  • 0464.2: Core skill or procedure for Identify measurable attributes of an object
  • 0464.3: Representation or model for Identify measurable attributes of an object
  • 0464.4: Application of Identify measurable attributes of an object
  • 0464.5: Common misconception or error check for Identify measurable attributes of an object
#0465Compare lengths directly and indirectlyMeasurement, Units, and Quantitative Reasoning • Attributes and Direct Measurement • generic_math
Show 5 reinforced subtopics
  • 0465.1: Concept meaning of Compare lengths directly and indirectly
  • 0465.2: Core skill or procedure for Compare lengths directly and indirectly
  • 0465.3: Representation or model for Compare lengths directly and indirectly
  • 0465.4: Application of Compare lengths directly and indirectly
  • 0465.5: Common misconception or error check for Compare lengths directly and indirectly
#0466Estimate measurement before measuringMeasurement, Units, and Quantitative Reasoning • Attributes and Direct Measurement • generic_math
Show 5 reinforced subtopics
  • 0466.1: Concept meaning of Estimate measurement before measuring
  • 0466.2: Core skill or procedure for Estimate measurement before measuring
  • 0466.3: Representation or model for Estimate measurement before measuring
  • 0466.4: Application of Estimate measurement before measuring
  • 0466.5: Common misconception or error check for Estimate measurement before measuring
#0470Use dimensional reasoning informallyMeasurement, Units, and Quantitative Reasoning • Units and Conversions • generic_math
Show 5 reinforced subtopics
  • 0470.1: Concept meaning of Use dimensional reasoning informally
  • 0470.2: Core skill or procedure for Use dimensional reasoning informally
  • 0470.3: Representation or model for Use dimensional reasoning informally
  • 0470.4: Application of Use dimensional reasoning informally
  • 0470.5: Common misconception or error check for Use dimensional reasoning informally
#0473Choose appropriate measurement unitsMeasurement, Units, and Quantitative Reasoning • Units and Conversions • generic_math
Show 5 reinforced subtopics
  • 0473.1: Concept meaning of Choose appropriate measurement units
  • 0473.2: Core skill or procedure for Choose appropriate measurement units
  • 0473.3: Representation or model for Choose appropriate measurement units
  • 0473.4: Application of Choose appropriate measurement units
  • 0473.5: Common misconception or error check for Choose appropriate measurement units
#0476Convert within customary length unitsMeasurement, Units, and Quantitative Reasoning • Units and Conversions • generic_math
Show 5 reinforced subtopics
  • 0476.1: Concept meaning of Convert within customary length units
  • 0476.2: Core skill or procedure for Convert within customary length units
  • 0476.3: Representation or model for Convert within customary length units
  • 0476.4: Application of Convert within customary length units
  • 0476.5: Common misconception or error check for Convert within customary length units
#0478Convert within customary weight unitsMeasurement, Units, and Quantitative Reasoning • Units and Conversions • generic_math
Show 5 reinforced subtopics
  • 0478.1: Concept meaning of Convert within customary weight units
  • 0478.2: Core skill or procedure for Convert within customary weight units
  • 0478.3: Representation or model for Convert within customary weight units
  • 0478.4: Application of Convert within customary weight units
  • 0478.5: Common misconception or error check for Convert within customary weight units
#0479Convert within metric volume unitsMeasurement, Units, and Quantitative Reasoning • Units and Conversions • measurement_geometry
Show 5 reinforced subtopics
  • 0479.1: Concept meaning of Convert within metric volume units
  • 0479.2: Core skill or procedure for Convert within metric volume units
  • 0479.3: Representation or model for Convert within metric volume units
  • 0479.4: Application of Convert within metric volume units
  • 0479.5: Common misconception or error check for Convert within metric volume units
#0480Convert within customary capacity unitsMeasurement, Units, and Quantitative Reasoning • Units and Conversions • generic_math
Show 5 reinforced subtopics
  • 0480.1: Concept meaning of Convert within customary capacity units
  • 0480.2: Core skill or procedure for Convert within customary capacity units
  • 0480.3: Representation or model for Convert within customary capacity units
  • 0480.4: Application of Convert within customary capacity units
  • 0480.5: Common misconception or error check for Convert within customary capacity units
#0482Use conversion factors in one-step problemsMeasurement, Units, and Quantitative Reasoning • Units and Conversions • polynomial
Show 5 reinforced subtopics
  • 0482.1: Concept meaning of Use conversion factors in one-step problems
  • 0482.2: Core skill or procedure for Use conversion factors in one-step problems
  • 0482.3: Representation or model for Use conversion factors in one-step problems
  • 0482.4: Application of Use conversion factors in one-step problems
  • 0482.5: Common misconception or error check for Use conversion factors in one-step problems
#0483Use multiple conversion steps in applied problemsMeasurement, Units, and Quantitative Reasoning • Units and Conversions • percent
Show 5 reinforced subtopics
  • 0483.1: Concept meaning of Use multiple conversion steps in applied problems
  • 0483.2: Core skill or procedure for Use multiple conversion steps in applied problems
  • 0483.3: Representation or model for Use multiple conversion steps in applied problems
  • 0483.4: Application of Use multiple conversion steps in applied problems
  • 0483.5: Common misconception or error check for Use multiple conversion steps in applied problems
#0486Derive volume formulas from layersMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0486.1: Concept meaning of Derive volume formulas from layers
  • 0486.2: Core skill or procedure for Derive volume formulas from layers
  • 0486.3: Representation or model for Derive volume formulas from layers
  • 0486.4: Application of Derive volume formulas from layers
  • 0486.5: Common misconception or error check for Derive volume formulas from layers
#0487Use area and perimeter in design contextsMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0487.1: Concept meaning of Use area and perimeter in design contexts
  • 0487.2: Core skill or procedure for Use area and perimeter in design contexts
  • 0487.3: Representation or model for Use area and perimeter in design contexts
  • 0487.4: Application of Use area and perimeter in design contexts
  • 0487.5: Common misconception or error check for Use area and perimeter in design contexts
#0488Analyze additive vs multiplicative change in measurementMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • percent
Show 5 reinforced subtopics
  • 0488.1: Concept meaning of Analyze additive vs multiplicative change in measurement
  • 0488.2: Core skill or procedure for Analyze additive vs multiplicative change in measurement
  • 0488.3: Representation or model for Analyze additive vs multiplicative change in measurement
  • 0488.4: Application of Analyze additive vs multiplicative change in measurement
  • 0488.5: Common misconception or error check for Analyze additive vs multiplicative change in measurement
#0492Find area of rectangles and squaresMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0492.1: Concept meaning of Find area of rectangles and squares
  • 0492.2: Core skill or procedure for Find area of rectangles and squares
  • 0492.3: Representation or model for Find area of rectangles and squares
  • 0492.4: Application of Find area of rectangles and squares
  • 0492.5: Common misconception or error check for Find area of rectangles and squares
#0493Find area of composite figuresMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0493.1: Concept meaning of Find area of composite figures
  • 0493.2: Core skill or procedure for Find area of composite figures
  • 0493.3: Representation or model for Find area of composite figures
  • 0493.4: Application of Find area of composite figures
  • 0493.5: Common misconception or error check for Find area of composite figures
#0495Find volume of rectangular prismsMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0495.1: Concept meaning of Find volume of rectangular prisms
  • 0495.2: Core skill or procedure for Find volume of rectangular prisms
  • 0495.3: Representation or model for Find volume of rectangular prisms
  • 0495.4: Application of Find volume of rectangular prisms
  • 0495.5: Common misconception or error check for Find volume of rectangular prisms
#0496Find volume of prisms and cylindersMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0496.1: Concept meaning of Find volume of prisms and cylinders
  • 0496.2: Core skill or procedure for Find volume of prisms and cylinders
  • 0496.3: Representation or model for Find volume of prisms and cylinders
  • 0496.4: Application of Find volume of prisms and cylinders
  • 0496.5: Common misconception or error check for Find volume of prisms and cylinders
#0497Find volume of pyramids and conesMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0497.1: Concept meaning of Find volume of pyramids and cones
  • 0497.2: Core skill or procedure for Find volume of pyramids and cones
  • 0497.3: Representation or model for Find volume of pyramids and cones
  • 0497.4: Application of Find volume of pyramids and cones
  • 0497.5: Common misconception or error check for Find volume of pyramids and cones
#0499Interpret units for perimeter, area, and volume correctlyMeasurement, Units, and Quantitative Reasoning • Perimeter, Area, and Volume Quantitative Reasoning • measurement_geometry
Show 5 reinforced subtopics
  • 0499.1: Concept meaning of Interpret units for perimeter, area, and volume correctly
  • 0499.2: Core skill or procedure for Interpret units for perimeter, area, and volume correctly
  • 0499.3: Representation or model for Interpret units for perimeter, area, and volume correctly
  • 0499.4: Application of Interpret units for perimeter, area, and volume correctly
  • 0499.5: Common misconception or error check for Interpret units for perimeter, area, and volume correctly
#0501Use trig ratios to find side lengthsTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • ratio_rate
Show 5 reinforced subtopics
  • 0501.1: Concept meaning of Use trig ratios to find side lengths
  • 0501.2: Core skill or procedure for Use trig ratios to find side lengths
  • 0501.3: Representation or model for Use trig ratios to find side lengths
  • 0501.4: Application of Use trig ratios to find side lengths
  • 0501.5: Common misconception or error check for Use trig ratios to find side lengths
#0502Use trig ratios to find angle measuresTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • ratio_rate
Show 5 reinforced subtopics
  • 0502.1: Concept meaning of Use trig ratios to find angle measures
  • 0502.2: Core skill or procedure for Use trig ratios to find angle measures
  • 0502.3: Representation or model for Use trig ratios to find angle measures
  • 0502.4: Application of Use trig ratios to find angle measures
  • 0502.5: Common misconception or error check for Use trig ratios to find angle measures
#0503Solve applied right-triangle problemsTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • geometry
Show 5 reinforced subtopics
  • 0503.1: Concept meaning of Solve applied right-triangle problems
  • 0503.2: Core skill or procedure for Solve applied right-triangle problems
  • 0503.3: Representation or model for Solve applied right-triangle problems
  • 0503.4: Application of Solve applied right-triangle problems
  • 0503.5: Common misconception or error check for Solve applied right-triangle problems
#0504Recognize special right trianglesTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • geometry
Show 5 reinforced subtopics
  • 0504.1: Concept meaning of Recognize special right triangles
  • 0504.2: Core skill or procedure for Recognize special right triangles
  • 0504.3: Representation or model for Recognize special right triangles
  • 0504.4: Application of Recognize special right triangles
  • 0504.5: Common misconception or error check for Recognize special right triangles
#0505Use inverse trigonometric functions in right trianglesTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • trig
Show 5 reinforced subtopics
  • 0505.1: Concept meaning of Use inverse trigonometric functions in right triangles
  • 0505.2: Core skill or procedure for Use inverse trigonometric functions in right triangles
  • 0505.3: Representation or model for Use inverse trigonometric functions in right triangles
  • 0505.4: Application of Use inverse trigonometric functions in right triangles
  • 0505.5: Common misconception or error check for Use inverse trigonometric functions in right triangles
#0506Interpret angle of elevation and depressionTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • geometry
Show 5 reinforced subtopics
  • 0506.1: Concept meaning of Interpret angle of elevation and depression
  • 0506.2: Core skill or procedure for Interpret angle of elevation and depression
  • 0506.3: Representation or model for Interpret angle of elevation and depression
  • 0506.4: Application of Interpret angle of elevation and depression
  • 0506.5: Common misconception or error check for Interpret angle of elevation and depression
#0507Solve angle of depression problemsTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • geometry
Show 5 reinforced subtopics
  • 0507.1: Concept meaning of Solve angle of depression problems
  • 0507.2: Core skill or procedure for Solve angle of depression problems
  • 0507.3: Representation or model for Solve angle of depression problems
  • 0507.4: Application of Solve angle of depression problems
  • 0507.5: Common misconception or error check for Solve angle of depression problems
#0508Choose the correct trigonometric ratio from a diagramTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • ratio_rate
Show 5 reinforced subtopics
  • 0508.1: Concept meaning of Choose the correct trigonometric ratio from a diagram
  • 0508.2: Core skill or procedure for Choose the correct trigonometric ratio from a diagram
  • 0508.3: Representation or model for Choose the correct trigonometric ratio from a diagram
  • 0508.4: Application of Choose the correct trigonometric ratio from a diagram
  • 0508.5: Common misconception or error check for Choose the correct trigonometric ratio from a diagram
#0509Connect tangent to slope on a right triangleTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • linear
Show 5 reinforced subtopics
  • 0509.1: Concept meaning of Connect tangent to slope on a right triangle
  • 0509.2: Core skill or procedure for Connect tangent to slope on a right triangle
  • 0509.3: Representation or model for Connect tangent to slope on a right triangle
  • 0509.4: Application of Connect tangent to slope on a right triangle
  • 0509.5: Common misconception or error check for Connect tangent to slope on a right triangle
#0510Apply Pythagorean theorem with trigonometric contextsTrigonometry, Vectors, and Advanced Geometric Modeling • Right Triangle Trigonometry • trig
Show 5 reinforced subtopics
  • 0510.1: Concept meaning of Apply Pythagorean theorem with trigonometric contexts
  • 0510.2: Core skill or procedure for Apply Pythagorean theorem with trigonometric contexts
  • 0510.3: Representation or model for Apply Pythagorean theorem with trigonometric contexts
  • 0510.4: Application of Apply Pythagorean theorem with trigonometric contexts
  • 0510.5: Common misconception or error check for Apply Pythagorean theorem with trigonometric contexts
#0511Define trig functions on the unit circleTrigonometry, Vectors, and Advanced Geometric Modeling • Unit Circle and Trig Functions • trig
Show 5 reinforced subtopics
  • 0511.1: Concept meaning of Define trig functions on the unit circle
  • 0511.2: Core skill or procedure for Define trig functions on the unit circle
  • 0511.3: Representation or model for Define trig functions on the unit circle
  • 0511.4: Application of Define trig functions on the unit circle
  • 0511.5: Common misconception or error check for Define trig functions on the unit circle
#0512Find exact trig values for special anglesTrigonometry, Vectors, and Advanced Geometric Modeling • Unit Circle and Trig Functions • trig
Show 5 reinforced subtopics
  • 0512.1: Concept meaning of Find exact trig values for special angles
  • 0512.2: Core skill or procedure for Find exact trig values for special angles
  • 0512.3: Representation or model for Find exact trig values for special angles
  • 0512.4: Application of Find exact trig values for special angles
  • 0512.5: Common misconception or error check for Find exact trig values for special angles
#0517Interpret inverse trig functions on restricted domainsTrigonometry, Vectors, and Advanced Geometric Modeling • Unit Circle and Trig Functions • trig
Show 5 reinforced subtopics
  • 0517.1: Concept meaning of Interpret inverse trig functions on restricted domains
  • 0517.2: Core skill or procedure for Interpret inverse trig functions on restricted domains
  • 0517.3: Representation or model for Interpret inverse trig functions on restricted domains
  • 0517.4: Application of Interpret inverse trig functions on restricted domains
  • 0517.5: Common misconception or error check for Interpret inverse trig functions on restricted domains
#0518Use radian measure on the unit circleTrigonometry, Vectors, and Advanced Geometric Modeling • Unit Circle and Trig Functions • trig
Show 5 reinforced subtopics
  • 0518.1: Concept meaning of Use radian measure on the unit circle
  • 0518.2: Core skill or procedure for Use radian measure on the unit circle
  • 0518.3: Representation or model for Use radian measure on the unit circle
  • 0518.4: Application of Use radian measure on the unit circle
  • 0518.5: Common misconception or error check for Use radian measure on the unit circle
#0519Convert between degrees and radiansTrigonometry, Vectors, and Advanced Geometric Modeling • Unit Circle and Trig Functions • generic_math
Show 5 reinforced subtopics
  • 0519.1: Concept meaning of Convert between degrees and radians
  • 0519.2: Core skill or procedure for Convert between degrees and radians
  • 0519.3: Representation or model for Convert between degrees and radians
  • 0519.4: Application of Convert between degrees and radians
  • 0519.5: Common misconception or error check for Convert between degrees and radians
#0521Determine signs of trig functions by quadrantTrigonometry, Vectors, and Advanced Geometric Modeling • Unit Circle and Trig Functions • trig
Show 5 reinforced subtopics
  • 0521.1: Concept meaning of Determine signs of trig functions by quadrant
  • 0521.2: Core skill or procedure for Determine signs of trig functions by quadrant
  • 0521.3: Representation or model for Determine signs of trig functions by quadrant
  • 0521.4: Application of Determine signs of trig functions by quadrant
  • 0521.5: Common misconception or error check for Determine signs of trig functions by quadrant
#0522Interpret amplitude, period, and phase shiftTrigonometry, Vectors, and Advanced Geometric Modeling • Unit Circle and Trig Functions • generic_math
Show 5 reinforced subtopics
  • 0522.1: Concept meaning of Interpret amplitude, period, and phase shift
  • 0522.2: Core skill or procedure for Interpret amplitude, period, and phase shift
  • 0522.3: Representation or model for Interpret amplitude, period, and phase shift
  • 0522.4: Application of Interpret amplitude, period, and phase shift
  • 0522.5: Common misconception or error check for Interpret amplitude, period, and phase shift
#0524Use angle sum and difference identitiesTrigonometry, Vectors, and Advanced Geometric Modeling • Trig Identities and Equations • geometry
Show 5 reinforced subtopics
  • 0524.1: Concept meaning of Use angle sum and difference identities
  • 0524.2: Core skill or procedure for Use angle sum and difference identities
  • 0524.3: Representation or model for Use angle sum and difference identities
  • 0524.4: Application of Use angle sum and difference identities
  • 0524.5: Common misconception or error check for Use angle sum and difference identities
#0527Solve basic trigonometric equationsTrigonometry, Vectors, and Advanced Geometric Modeling • Trig Identities and Equations • equations
Show 5 reinforced subtopics
  • 0527.1: Concept meaning of Solve basic trigonometric equations
  • 0527.2: Core skill or procedure for Solve basic trigonometric equations
  • 0527.3: Representation or model for Solve basic trigonometric equations
  • 0527.4: Application of Solve basic trigonometric equations
  • 0527.5: Common misconception or error check for Solve basic trigonometric equations
#0530Verify basic trigonometric identitiesTrigonometry, Vectors, and Advanced Geometric Modeling • Trig Identities and Equations • trig
Show 5 reinforced subtopics
  • 0530.1: Concept meaning of Verify basic trigonometric identities
  • 0530.2: Core skill or procedure for Verify basic trigonometric identities
  • 0530.3: Representation or model for Verify basic trigonometric identities
  • 0530.4: Application of Verify basic trigonometric identities
  • 0530.5: Common misconception or error check for Verify basic trigonometric identities
#0533Solve basic trigonometric equations on an intervalTrigonometry, Vectors, and Advanced Geometric Modeling • Trig Identities and Equations • equations
Show 5 reinforced subtopics
  • 0533.1: Concept meaning of Solve basic trigonometric equations on an interval
  • 0533.2: Core skill or procedure for Solve basic trigonometric equations on an interval
  • 0533.3: Representation or model for Solve basic trigonometric equations on an interval
  • 0533.4: Application of Solve basic trigonometric equations on an interval
  • 0533.5: Common misconception or error check for Solve basic trigonometric equations on an interval
#0534Solve trigonometric equations on a general domainTrigonometry, Vectors, and Advanced Geometric Modeling • Trig Identities and Equations • equations
Show 5 reinforced subtopics
  • 0534.1: Concept meaning of Solve trigonometric equations on a general domain
  • 0534.2: Core skill or procedure for Solve trigonometric equations on a general domain
  • 0534.3: Representation or model for Solve trigonometric equations on a general domain
  • 0534.4: Application of Solve trigonometric equations on a general domain
  • 0534.5: Common misconception or error check for Solve trigonometric equations on a general domain
#0535Use sum and difference identitiesTrigonometry, Vectors, and Advanced Geometric Modeling • Trig Identities and Equations • generic_math
Show 5 reinforced subtopics
  • 0535.1: Concept meaning of Use sum and difference identities
  • 0535.2: Core skill or procedure for Use sum and difference identities
  • 0535.3: Representation or model for Use sum and difference identities
  • 0535.4: Application of Use sum and difference identities
  • 0535.5: Common misconception or error check for Use sum and difference identities
#0536Simplify trigonometric expressions strategicallyTrigonometry, Vectors, and Advanced Geometric Modeling • Trig Identities and Equations • ratio_rate
Show 5 reinforced subtopics
  • 0536.1: Concept meaning of Simplify trigonometric expressions strategically
  • 0536.2: Core skill or procedure for Simplify trigonometric expressions strategically
  • 0536.3: Representation or model for Simplify trigonometric expressions strategically
  • 0536.4: Application of Simplify trigonometric expressions strategically
  • 0536.5: Common misconception or error check for Simplify trigonometric expressions strategically
#0545Use dot product to find angle between vectorsTrigonometry, Vectors, and Advanced Geometric Modeling • Vectors • vectors
Show 5 reinforced subtopics
  • 0545.1: Concept meaning of Use dot product to find angle between vectors
  • 0545.2: Core skill or procedure for Use dot product to find angle between vectors
  • 0545.3: Representation or model for Use dot product to find angle between vectors
  • 0545.4: Application of Use dot product to find angle between vectors
  • 0545.5: Common misconception or error check for Use dot product to find angle between vectors
#0549Convert between polar and rectangular coordinatesTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • generic_math
Show 5 reinforced subtopics
  • 0549.1: Concept meaning of Convert between polar and rectangular coordinates
  • 0549.2: Core skill or procedure for Convert between polar and rectangular coordinates
  • 0549.3: Representation or model for Convert between polar and rectangular coordinates
  • 0549.4: Application of Convert between polar and rectangular coordinates
  • 0549.5: Common misconception or error check for Convert between polar and rectangular coordinates
#0551Interpret complex numbers geometricallyTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • complex
Show 5 reinforced subtopics
  • 0551.1: Concept meaning of Interpret complex numbers geometrically
  • 0551.2: Core skill or procedure for Interpret complex numbers geometrically
  • 0551.3: Representation or model for Interpret complex numbers geometrically
  • 0551.4: Application of Interpret complex numbers geometrically
  • 0551.5: Common misconception or error check for Interpret complex numbers geometrically
#0552Add and multiply complex numbersTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • percent
Show 5 reinforced subtopics
  • 0552.1: Concept meaning of Add and multiply complex numbers
  • 0552.2: Core skill or procedure for Add and multiply complex numbers
  • 0552.3: Representation or model for Add and multiply complex numbers
  • 0552.4: Application of Add and multiply complex numbers
  • 0552.5: Common misconception or error check for Add and multiply complex numbers
#0554Relate complex roots to the planeTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • complex
Show 5 reinforced subtopics
  • 0554.1: Concept meaning of Relate complex roots to the plane
  • 0554.2: Core skill or procedure for Relate complex roots to the plane
  • 0554.3: Representation or model for Relate complex roots to the plane
  • 0554.4: Application of Relate complex roots to the plane
  • 0554.5: Common misconception or error check for Relate complex roots to the plane
#0556Interpret parametric equationsTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • generic_math
Show 5 reinforced subtopics
  • 0556.1: Concept meaning of Interpret parametric equations
  • 0556.2: Core skill or procedure for Interpret parametric equations
  • 0556.3: Representation or model for Interpret parametric equations
  • 0556.4: Application of Interpret parametric equations
  • 0556.5: Common misconception or error check for Interpret parametric equations
#0557Eliminate a parameter to compare formsTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • generic_math
Show 5 reinforced subtopics
  • 0557.1: Concept meaning of Eliminate a parameter to compare forms
  • 0557.2: Core skill or procedure for Eliminate a parameter to compare forms
  • 0557.3: Representation or model for Eliminate a parameter to compare forms
  • 0557.4: Application of Eliminate a parameter to compare forms
  • 0557.5: Common misconception or error check for Eliminate a parameter to compare forms
#0558Interpret velocity from parametric motionTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • generic_math
Show 5 reinforced subtopics
  • 0558.1: Concept meaning of Interpret velocity from parametric motion
  • 0558.2: Core skill or procedure for Interpret velocity from parametric motion
  • 0558.3: Representation or model for Interpret velocity from parametric motion
  • 0558.4: Application of Interpret velocity from parametric motion
  • 0558.5: Common misconception or error check for Interpret velocity from parametric motion
#0559Represent complex numbers in rectangular formTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • complex
Show 5 reinforced subtopics
  • 0559.1: Concept meaning of Represent complex numbers in rectangular form
  • 0559.2: Core skill or procedure for Represent complex numbers in rectangular form
  • 0559.3: Representation or model for Represent complex numbers in rectangular form
  • 0559.4: Application of Represent complex numbers in rectangular form
  • 0559.5: Common misconception or error check for Represent complex numbers in rectangular form
#0560Represent complex numbers in polar formTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • complex
Show 5 reinforced subtopics
  • 0560.1: Concept meaning of Represent complex numbers in polar form
  • 0560.2: Core skill or procedure for Represent complex numbers in polar form
  • 0560.3: Representation or model for Represent complex numbers in polar form
  • 0560.4: Application of Represent complex numbers in polar form
  • 0560.5: Common misconception or error check for Represent complex numbers in polar form
#0561Multiply and divide complex numbers in polar formTrigonometry, Vectors, and Advanced Geometric Modeling • Polar, Parametric, and Complex Plane Connections • percent
Show 5 reinforced subtopics
  • 0561.1: Concept meaning of Multiply and divide complex numbers in polar form
  • 0561.2: Core skill or procedure for Multiply and divide complex numbers in polar form
  • 0561.3: Representation or model for Multiply and divide complex numbers in polar form
  • 0561.4: Application of Multiply and divide complex numbers in polar form
  • 0561.5: Common misconception or error check for Multiply and divide complex numbers in polar form
#0568Describe spread with range and IQRData, Probability, and Statistics • Data Displays and Descriptive Statistics • generic_math
Show 5 reinforced subtopics
  • 0568.1: Concept meaning of Describe spread with range and IQR
  • 0568.2: Core skill or procedure for Describe spread with range and IQR
  • 0568.3: Representation or model for Describe spread with range and IQR
  • 0568.4: Application of Describe spread with range and IQR
  • 0568.5: Common misconception or error check for Describe spread with range and IQR
#0572Choose an appropriate display for a data setData, Probability, and Statistics • Data Displays and Descriptive Statistics • statistics
Show 5 reinforced subtopics
  • 0572.1: Concept meaning of Choose an appropriate display for a data set
  • 0572.2: Core skill or procedure for Choose an appropriate display for a data set
  • 0572.3: Representation or model for Choose an appropriate display for a data set
  • 0572.4: Application of Choose an appropriate display for a data set
  • 0572.5: Common misconception or error check for Choose an appropriate display for a data set
#0574Describe positive negative and no associationData, Probability, and Statistics • Bivariate Data and Association • generic_math
Show 5 reinforced subtopics
  • 0574.1: Concept meaning of Describe positive negative and no association
  • 0574.2: Core skill or procedure for Describe positive negative and no association
  • 0574.3: Representation or model for Describe positive negative and no association
  • 0574.4: Application of Describe positive negative and no association
  • 0574.5: Common misconception or error check for Describe positive negative and no association
#0579Analyze linear vs nonlinear associationData, Probability, and Statistics • Bivariate Data and Association • geometry
Show 5 reinforced subtopics
  • 0579.1: Concept meaning of Analyze linear vs nonlinear association
  • 0579.2: Core skill or procedure for Analyze linear vs nonlinear association
  • 0579.3: Representation or model for Analyze linear vs nonlinear association
  • 0579.4: Application of Analyze linear vs nonlinear association
  • 0579.5: Common misconception or error check for Analyze linear vs nonlinear association
#0580Describe association in bivariate dataData, Probability, and Statistics • Bivariate Data and Association • statistics
Show 5 reinforced subtopics
  • 0580.1: Concept meaning of Describe association in bivariate data
  • 0580.2: Core skill or procedure for Describe association in bivariate data
  • 0580.3: Representation or model for Describe association in bivariate data
  • 0580.4: Application of Describe association in bivariate data
  • 0580.5: Common misconception or error check for Describe association in bivariate data
#0581Interpret slope and intercept in a contextData, Probability, and Statistics • Bivariate Data and Association • linear
Show 5 reinforced subtopics
  • 0581.1: Concept meaning of Interpret slope and intercept in a context
  • 0581.2: Core skill or procedure for Interpret slope and intercept in a context
  • 0581.3: Representation or model for Interpret slope and intercept in a context
  • 0581.4: Application of Interpret slope and intercept in a context
  • 0581.5: Common misconception or error check for Interpret slope and intercept in a context
#0582Distinguish correlation from causationData, Probability, and Statistics • Bivariate Data and Association • statistics
Show 5 reinforced subtopics
  • 0582.1: Concept meaning of Distinguish correlation from causation
  • 0582.2: Core skill or procedure for Distinguish correlation from causation
  • 0582.3: Representation or model for Distinguish correlation from causation
  • 0582.4: Application of Distinguish correlation from causation
  • 0582.5: Common misconception or error check for Distinguish correlation from causation
#0583Identify clusters and outliers in scatterplotsData, Probability, and Statistics • Bivariate Data and Association • generic_math
Show 5 reinforced subtopics
  • 0583.1: Concept meaning of Identify clusters and outliers in scatterplots
  • 0583.2: Core skill or procedure for Identify clusters and outliers in scatterplots
  • 0583.3: Representation or model for Identify clusters and outliers in scatterplots
  • 0583.4: Application of Identify clusters and outliers in scatterplots
  • 0583.5: Common misconception or error check for Identify clusters and outliers in scatterplots
#0590Distinguish independent and dependent eventsData, Probability, and Statistics • Probability Basics • generic_math
Show 5 reinforced subtopics
  • 0590.1: Concept meaning of Distinguish independent and dependent events
  • 0590.2: Core skill or procedure for Distinguish independent and dependent events
  • 0590.3: Representation or model for Distinguish independent and dependent events
  • 0590.4: Application of Distinguish independent and dependent events
  • 0590.5: Common misconception or error check for Distinguish independent and dependent events
#0591Describe probability as a number from zero to oneData, Probability, and Statistics • Probability Basics • probability
Show 5 reinforced subtopics
  • 0591.1: Concept meaning of Describe probability as a number from zero to one
  • 0591.2: Core skill or procedure for Describe probability as a number from zero to one
  • 0591.3: Representation or model for Describe probability as a number from zero to one
  • 0591.4: Application of Describe probability as a number from zero to one
  • 0591.5: Common misconception or error check for Describe probability as a number from zero to one
#0593Compare theoretical and experimental probabilityData, Probability, and Statistics • Probability Basics • probability
Show 5 reinforced subtopics
  • 0593.1: Concept meaning of Compare theoretical and experimental probability
  • 0593.2: Core skill or procedure for Compare theoretical and experimental probability
  • 0593.3: Representation or model for Compare theoretical and experimental probability
  • 0593.4: Application of Compare theoretical and experimental probability
  • 0593.5: Common misconception or error check for Compare theoretical and experimental probability
#0594Find probability of compound events with organized listsData, Probability, and Statistics • Probability Basics • probability
Show 5 reinforced subtopics
  • 0594.1: Concept meaning of Find probability of compound events with organized lists
  • 0594.2: Core skill or procedure for Find probability of compound events with organized lists
  • 0594.3: Representation or model for Find probability of compound events with organized lists
  • 0594.4: Application of Find probability of compound events with organized lists
  • 0594.5: Common misconception or error check for Find probability of compound events with organized lists
#0595Find probability of independent eventsData, Probability, and Statistics • Probability Basics • probability
Show 5 reinforced subtopics
  • 0595.1: Concept meaning of Find probability of independent events
  • 0595.2: Core skill or procedure for Find probability of independent events
  • 0595.3: Representation or model for Find probability of independent events
  • 0595.4: Application of Find probability of independent events
  • 0595.5: Common misconception or error check for Find probability of independent events
#0596Find probability of dependent events informallyData, Probability, and Statistics • Probability Basics • probability
Show 5 reinforced subtopics
  • 0596.1: Concept meaning of Find probability of dependent events informally
  • 0596.2: Core skill or procedure for Find probability of dependent events informally
  • 0596.3: Representation or model for Find probability of dependent events informally
  • 0596.4: Application of Find probability of dependent events informally
  • 0596.5: Common misconception or error check for Find probability of dependent events informally
#0606Distinguish combinations from permutations informallyData, Probability, and Statistics • Counting and Combinatorics • probability
Show 5 reinforced subtopics
  • 0606.1: Concept meaning of Distinguish combinations from permutations informally
  • 0606.2: Core skill or procedure for Distinguish combinations from permutations informally
  • 0606.3: Representation or model for Distinguish combinations from permutations informally
  • 0606.4: Application of Distinguish combinations from permutations informally
  • 0606.5: Common misconception or error check for Distinguish combinations from permutations informally
#0613Interpret margin of error conceptuallyData, Probability, and Statistics • Sampling and Statistical Inference • generic_math
Show 5 reinforced subtopics
  • 0613.1: Concept meaning of Interpret margin of error conceptually
  • 0613.2: Core skill or procedure for Interpret margin of error conceptually
  • 0613.3: Representation or model for Interpret margin of error conceptually
  • 0613.4: Application of Interpret margin of error conceptually
  • 0613.5: Common misconception or error check for Interpret margin of error conceptually
#0614Use simulation to estimate probabilityData, Probability, and Statistics • Sampling and Statistical Inference • probability
Show 5 reinforced subtopics
  • 0614.1: Concept meaning of Use simulation to estimate probability
  • 0614.2: Core skill or procedure for Use simulation to estimate probability
  • 0614.3: Representation or model for Use simulation to estimate probability
  • 0614.4: Application of Use simulation to estimate probability
  • 0614.5: Common misconception or error check for Use simulation to estimate probability
#0615Interpret confidence intervals conceptuallyData, Probability, and Statistics • Sampling and Statistical Inference • statistics
Show 5 reinforced subtopics
  • 0615.1: Concept meaning of Interpret confidence intervals conceptually
  • 0615.2: Core skill or procedure for Interpret confidence intervals conceptually
  • 0615.3: Representation or model for Interpret confidence intervals conceptually
  • 0615.4: Application of Interpret confidence intervals conceptually
  • 0615.5: Common misconception or error check for Interpret confidence intervals conceptually
#0617Identify random, stratified, and systematic samplesData, Probability, and Statistics • Sampling and Statistical Inference • generic_math
Show 5 reinforced subtopics
  • 0617.1: Concept meaning of Identify random, stratified, and systematic samples
  • 0617.2: Core skill or procedure for Identify random, stratified, and systematic samples
  • 0617.3: Representation or model for Identify random, stratified, and systematic samples
  • 0617.4: Application of Identify random, stratified, and systematic samples
  • 0617.5: Common misconception or error check for Identify random, stratified, and systematic samples
#0620Distinguish observational study from experimentData, Probability, and Statistics • Sampling and Statistical Inference • generic_math
Show 5 reinforced subtopics
  • 0620.1: Concept meaning of Distinguish observational study from experiment
  • 0620.2: Core skill or procedure for Distinguish observational study from experiment
  • 0620.3: Representation or model for Distinguish observational study from experiment
  • 0620.4: Application of Distinguish observational study from experiment
  • 0620.5: Common misconception or error check for Distinguish observational study from experiment
#0621Draw cautious conclusions from sample dataData, Probability, and Statistics • Sampling and Statistical Inference • statistics
Show 5 reinforced subtopics
  • 0621.1: Concept meaning of Draw cautious conclusions from sample data
  • 0621.2: Core skill or procedure for Draw cautious conclusions from sample data
  • 0621.3: Representation or model for Draw cautious conclusions from sample data
  • 0621.4: Application of Draw cautious conclusions from sample data
  • 0621.5: Common misconception or error check for Draw cautious conclusions from sample data
#0622Recognize normal distribution shapeData, Probability, and Statistics • Distributions, Normal Models, and Regression • generic_math
Show 5 reinforced subtopics
  • 0622.1: Concept meaning of Recognize normal distribution shape
  • 0622.2: Core skill or procedure for Recognize normal distribution shape
  • 0622.3: Representation or model for Recognize normal distribution shape
  • 0622.4: Application of Recognize normal distribution shape
  • 0622.5: Common misconception or error check for Recognize normal distribution shape
#0624Use normal distribution tables conceptuallyData, Probability, and Statistics • Distributions, Normal Models, and Regression • generic_math
Show 5 reinforced subtopics
  • 0624.1: Concept meaning of Use normal distribution tables conceptually
  • 0624.2: Core skill or procedure for Use normal distribution tables conceptually
  • 0624.3: Representation or model for Use normal distribution tables conceptually
  • 0624.4: Application of Use normal distribution tables conceptually
  • 0624.5: Common misconception or error check for Use normal distribution tables conceptually
#0625Build and interpret regression linesData, Probability, and Statistics • Distributions, Normal Models, and Regression • statistics
Show 5 reinforced subtopics
  • 0625.1: Concept meaning of Build and interpret regression lines
  • 0625.2: Core skill or procedure for Build and interpret regression lines
  • 0625.3: Representation or model for Build and interpret regression lines
  • 0625.4: Application of Build and interpret regression lines
  • 0625.5: Common misconception or error check for Build and interpret regression lines
#0626Interpret slope and intercept in regressionData, Probability, and Statistics • Distributions, Normal Models, and Regression • linear
Show 5 reinforced subtopics
  • 0626.1: Concept meaning of Interpret slope and intercept in regression
  • 0626.2: Core skill or procedure for Interpret slope and intercept in regression
  • 0626.3: Representation or model for Interpret slope and intercept in regression
  • 0626.4: Application of Interpret slope and intercept in regression
  • 0626.5: Common misconception or error check for Interpret slope and intercept in regression
#0628Distinguish correlation from causationData, Probability, and Statistics • Distributions, Normal Models, and Regression • statistics
Show 5 reinforced subtopics
  • 0628.1: Concept meaning of Distinguish correlation from causation
  • 0628.2: Core skill or procedure for Distinguish correlation from causation
  • 0628.3: Representation or model for Distinguish correlation from causation
  • 0628.4: Application of Distinguish correlation from causation
  • 0628.5: Common misconception or error check for Distinguish correlation from causation
#0629Describe shape, center, and spread of a distributionData, Probability, and Statistics • Distributions, Normal Models, and Regression • generic_math
Show 5 reinforced subtopics
  • 0629.1: Concept meaning of Describe shape, center, and spread of a distribution
  • 0629.2: Core skill or procedure for Describe shape, center, and spread of a distribution
  • 0629.3: Representation or model for Describe shape, center, and spread of a distribution
  • 0629.4: Application of Describe shape, center, and spread of a distribution
  • 0629.5: Common misconception or error check for Describe shape, center, and spread of a distribution
#0630Recognize symmetric and skewed distributionsData, Probability, and Statistics • Distributions, Normal Models, and Regression • generic_math
Show 5 reinforced subtopics
  • 0630.1: Concept meaning of Recognize symmetric and skewed distributions
  • 0630.2: Core skill or procedure for Recognize symmetric and skewed distributions
  • 0630.3: Representation or model for Recognize symmetric and skewed distributions
  • 0630.4: Application of Recognize symmetric and skewed distributions
  • 0630.5: Common misconception or error check for Recognize symmetric and skewed distributions
#0633Compute correlation coefficient in contextData, Probability, and Statistics • Distributions, Normal Models, and Regression • statistics
Show 5 reinforced subtopics
  • 0633.1: Concept meaning of Compute correlation coefficient in context
  • 0633.2: Core skill or procedure for Compute correlation coefficient in context
  • 0633.3: Representation or model for Compute correlation coefficient in context
  • 0633.4: Application of Compute correlation coefficient in context
  • 0633.5: Common misconception or error check for Compute correlation coefficient in context
#0634Distinguish explanatory and response variablesData, Probability, and Statistics • Distributions, Normal Models, and Regression • generic_math
Show 5 reinforced subtopics
  • 0634.1: Concept meaning of Distinguish explanatory and response variables
  • 0634.2: Core skill or procedure for Distinguish explanatory and response variables
  • 0634.3: Representation or model for Distinguish explanatory and response variables
  • 0634.4: Application of Distinguish explanatory and response variables
  • 0634.5: Common misconception or error check for Distinguish explanatory and response variables
#0644Apply continuity to polynomial, rational, and root functionsCalculus and Analysis Pathway • Limits and Continuity • ratio_rate
Show 5 reinforced subtopics
  • 0644.1: Concept meaning of Apply continuity to polynomial, rational, and root functions
  • 0644.2: Core skill or procedure for Apply continuity to polynomial, rational, and root functions
  • 0644.3: Representation or model for Apply continuity to polynomial, rational, and root functions
  • 0644.4: Application of Apply continuity to polynomial, rational, and root functions
  • 0644.5: Common misconception or error check for Apply continuity to polynomial, rational, and root functions
#0646Interpret derivative as slope of tangent lineCalculus and Analysis Pathway • Derivatives • linear
Show 5 reinforced subtopics
  • 0646.1: Concept meaning of Interpret derivative as slope of tangent line
  • 0646.2: Core skill or procedure for Interpret derivative as slope of tangent line
  • 0646.3: Representation or model for Interpret derivative as slope of tangent line
  • 0646.4: Application of Interpret derivative as slope of tangent line
  • 0646.5: Common misconception or error check for Interpret derivative as slope of tangent line
#0649Differentiate composite functions with chain ruleCalculus and Analysis Pathway • Derivatives • calculus_derivative
Show 5 reinforced subtopics
  • 0649.1: Concept meaning of Differentiate composite functions with chain rule
  • 0649.2: Core skill or procedure for Differentiate composite functions with chain rule
  • 0649.3: Representation or model for Differentiate composite functions with chain rule
  • 0649.4: Application of Differentiate composite functions with chain rule
  • 0649.5: Common misconception or error check for Differentiate composite functions with chain rule
#0650Differentiate exponential and logarithmic functionsCalculus and Analysis Pathway • Derivatives • exponential_log
Show 5 reinforced subtopics
  • 0650.1: Concept meaning of Differentiate exponential and logarithmic functions
  • 0650.2: Core skill or procedure for Differentiate exponential and logarithmic functions
  • 0650.3: Representation or model for Differentiate exponential and logarithmic functions
  • 0650.4: Application of Differentiate exponential and logarithmic functions
  • 0650.5: Common misconception or error check for Differentiate exponential and logarithmic functions
#0651Differentiate trigonometric functionsCalculus and Analysis Pathway • Derivatives • trig
Show 5 reinforced subtopics
  • 0651.1: Concept meaning of Differentiate trigonometric functions
  • 0651.2: Core skill or procedure for Differentiate trigonometric functions
  • 0651.3: Representation or model for Differentiate trigonometric functions
  • 0651.4: Application of Differentiate trigonometric functions
  • 0651.5: Common misconception or error check for Differentiate trigonometric functions
#0657Analyze increasing and decreasing intervalsCalculus and Analysis Pathway • Applications of Derivatives • generic_math
Show 5 reinforced subtopics
  • 0657.1: Concept meaning of Analyze increasing and decreasing intervals
  • 0657.2: Core skill or procedure for Analyze increasing and decreasing intervals
  • 0657.3: Representation or model for Analyze increasing and decreasing intervals
  • 0657.4: Application of Analyze increasing and decreasing intervals
  • 0657.5: Common misconception or error check for Analyze increasing and decreasing intervals
#0664Analyze motion with velocity and accelerationCalculus and Analysis Pathway • Applications of Derivatives • ratio_rate
Show 5 reinforced subtopics
  • 0664.1: Concept meaning of Analyze motion with velocity and acceleration
  • 0664.2: Core skill or procedure for Analyze motion with velocity and acceleration
  • 0664.3: Representation or model for Analyze motion with velocity and acceleration
  • 0664.4: Application of Analyze motion with velocity and acceleration
  • 0664.5: Common misconception or error check for Analyze motion with velocity and acceleration
#0667Interpret definite integral as accumulationCalculus and Analysis Pathway • Integrals • calculus_integral
Show 5 reinforced subtopics
  • 0667.1: Concept meaning of Interpret definite integral as accumulation
  • 0667.2: Core skill or procedure for Interpret definite integral as accumulation
  • 0667.3: Representation or model for Interpret definite integral as accumulation
  • 0667.4: Application of Interpret definite integral as accumulation
  • 0667.5: Common misconception or error check for Interpret definite integral as accumulation
#0672Solve separable accumulation-style problemsCalculus and Analysis Pathway • Integrals • calculus_integral
Show 5 reinforced subtopics
  • 0672.1: Concept meaning of Solve separable accumulation-style problems
  • 0672.2: Core skill or procedure for Solve separable accumulation-style problems
  • 0672.3: Representation or model for Solve separable accumulation-style problems
  • 0672.4: Application of Solve separable accumulation-style problems
  • 0672.5: Common misconception or error check for Solve separable accumulation-style problems
#0674Integrate polynomials and basic elementary functionsCalculus and Analysis Pathway • Integrals • ratio_rate
Show 5 reinforced subtopics
  • 0674.1: Concept meaning of Integrate polynomials and basic elementary functions
  • 0674.2: Core skill or procedure for Integrate polynomials and basic elementary functions
  • 0674.3: Representation or model for Integrate polynomials and basic elementary functions
  • 0674.4: Application of Integrate polynomials and basic elementary functions
  • 0674.5: Common misconception or error check for Integrate polynomials and basic elementary functions
#0676Use numerical approximation for integralsCalculus and Analysis Pathway • Integrals • calculus_integral
Show 5 reinforced subtopics
  • 0676.1: Concept meaning of Use numerical approximation for integrals
  • 0676.2: Core skill or procedure for Use numerical approximation for integrals
  • 0676.3: Representation or model for Use numerical approximation for integrals
  • 0676.4: Application of Use numerical approximation for integrals
  • 0676.5: Common misconception or error check for Use numerical approximation for integrals
#0680Compute volume by shells conceptuallyCalculus and Analysis Pathway • Applications of Integrals • measurement_geometry
Show 5 reinforced subtopics
  • 0680.1: Concept meaning of Compute volume by shells conceptually
  • 0680.2: Core skill or procedure for Compute volume by shells conceptually
  • 0680.3: Representation or model for Compute volume by shells conceptually
  • 0680.4: Application of Compute volume by shells conceptually
  • 0680.5: Common misconception or error check for Compute volume by shells conceptually
#0687Find volumes of revolution with disks and washersCalculus and Analysis Pathway • Applications of Integrals • measurement_geometry
Show 5 reinforced subtopics
  • 0687.1: Concept meaning of Find volumes of revolution with disks and washers
  • 0687.2: Core skill or procedure for Find volumes of revolution with disks and washers
  • 0687.3: Representation or model for Find volumes of revolution with disks and washers
  • 0687.4: Application of Find volumes of revolution with disks and washers
  • 0687.5: Common misconception or error check for Find volumes of revolution with disks and washers
#0688Find volumes of revolution with shellsCalculus and Analysis Pathway • Applications of Integrals • measurement_geometry
Show 5 reinforced subtopics
  • 0688.1: Concept meaning of Find volumes of revolution with shells
  • 0688.2: Core skill or procedure for Find volumes of revolution with shells
  • 0688.3: Representation or model for Find volumes of revolution with shells
  • 0688.4: Application of Find volumes of revolution with shells
  • 0688.5: Common misconception or error check for Find volumes of revolution with shells
#0689Model growth and decay with differential equations informallyCalculus and Analysis Pathway • Applications of Integrals • generic_math
Show 5 reinforced subtopics
  • 0689.1: Concept meaning of Model growth and decay with differential equations informally
  • 0689.2: Core skill or procedure for Model growth and decay with differential equations informally
  • 0689.3: Representation or model for Model growth and decay with differential equations informally
  • 0689.4: Application of Model growth and decay with differential equations informally
  • 0689.5: Common misconception or error check for Model growth and decay with differential equations informally
#0690Interpret integral results in contextCalculus and Analysis Pathway • Applications of Integrals • calculus_integral
Show 5 reinforced subtopics
  • 0690.1: Concept meaning of Interpret integral results in context
  • 0690.2: Core skill or procedure for Interpret integral results in context
  • 0690.3: Representation or model for Interpret integral results in context
  • 0690.4: Application of Interpret integral results in context
  • 0690.5: Common misconception or error check for Interpret integral results in context
#0691Determine convergence of a geometric seriesCalculus and Analysis Pathway • Series and Analysis Bridge • geometric_series
Show 5 reinforced subtopics
  • 0691.1: Concept meaning of Determine convergence of a geometric series
  • 0691.2: Core skill or procedure for Determine convergence of a geometric series
  • 0691.3: Representation or model for Determine convergence of a geometric series
  • 0691.4: Application of Determine convergence of a geometric series
  • 0691.5: Common misconception or error check for Determine convergence of a geometric series
#0696Understand epsilon-delta idea informallyCalculus and Analysis Pathway • Series and Analysis Bridge • generic_math
Show 5 reinforced subtopics
  • 0696.1: Concept meaning of Understand epsilon-delta idea informally
  • 0696.2: Core skill or procedure for Understand epsilon-delta idea informally
  • 0696.3: Representation or model for Understand epsilon-delta idea informally
  • 0696.4: Application of Understand epsilon-delta idea informally
  • 0696.5: Common misconception or error check for Understand epsilon-delta idea informally
#0697Distinguish pointwise and global behavior informallyCalculus and Analysis Pathway • Series and Analysis Bridge • generic_math
Show 5 reinforced subtopics
  • 0697.1: Concept meaning of Distinguish pointwise and global behavior informally
  • 0697.2: Core skill or procedure for Distinguish pointwise and global behavior informally
  • 0697.3: Representation or model for Distinguish pointwise and global behavior informally
  • 0697.4: Application of Distinguish pointwise and global behavior informally
  • 0697.5: Common misconception or error check for Distinguish pointwise and global behavior informally
#0699Determine convergence of a simple sequenceCalculus and Analysis Pathway • Series and Analysis Bridge • generic_math
Show 5 reinforced subtopics
  • 0699.1: Concept meaning of Determine convergence of a simple sequence
  • 0699.2: Core skill or procedure for Determine convergence of a simple sequence
  • 0699.3: Representation or model for Determine convergence of a simple sequence
  • 0699.4: Application of Determine convergence of a simple sequence
  • 0699.5: Common misconception or error check for Determine convergence of a simple sequence
#0702Understand series as sums of sequence termsCalculus and Analysis Pathway • Series and Analysis Bridge • generic_math
Show 5 reinforced subtopics
  • 0702.1: Concept meaning of Understand series as sums of sequence terms
  • 0702.2: Core skill or procedure for Understand series as sums of sequence terms
  • 0702.3: Representation or model for Understand series as sums of sequence terms
  • 0702.4: Application of Understand series as sums of sequence terms
  • 0702.5: Common misconception or error check for Understand series as sums of sequence terms
#0703Test convergence with comparison or ratio ideasCalculus and Analysis Pathway • Series and Analysis Bridge • ratio_rate
Show 5 reinforced subtopics
  • 0703.1: Concept meaning of Test convergence with comparison or ratio ideas
  • 0703.2: Core skill or procedure for Test convergence with comparison or ratio ideas
  • 0703.3: Representation or model for Test convergence with comparison or ratio ideas
  • 0703.4: Application of Test convergence with comparison or ratio ideas
  • 0703.5: Common misconception or error check for Test convergence with comparison or ratio ideas
#0708Compute double and triple integrals conceptuallyCalculus and Analysis Pathway • Multivariable and Vector Calculus • calculus_integral
Show 5 reinforced subtopics
  • 0708.1: Concept meaning of Compute double and triple integrals conceptually
  • 0708.2: Core skill or procedure for Compute double and triple integrals conceptually
  • 0708.3: Representation or model for Compute double and triple integrals conceptually
  • 0708.4: Application of Compute double and triple integrals conceptually
  • 0708.5: Common misconception or error check for Compute double and triple integrals conceptually
#0709Compute line integrals conceptuallyCalculus and Analysis Pathway • Multivariable and Vector Calculus • calculus_integral
Show 5 reinforced subtopics
  • 0709.1: Concept meaning of Compute line integrals conceptually
  • 0709.2: Core skill or procedure for Compute line integrals conceptually
  • 0709.3: Representation or model for Compute line integrals conceptually
  • 0709.4: Application of Compute line integrals conceptually
  • 0709.5: Common misconception or error check for Compute line integrals conceptually
#0710Compute divergence and curl conceptuallyCalculus and Analysis Pathway • Multivariable and Vector Calculus • generic_math
Show 5 reinforced subtopics
  • 0710.1: Concept meaning of Compute divergence and curl conceptually
  • 0710.2: Core skill or procedure for Compute divergence and curl conceptually
  • 0710.3: Representation or model for Compute divergence and curl conceptually
  • 0710.4: Application of Compute divergence and curl conceptually
  • 0710.5: Common misconception or error check for Compute divergence and curl conceptually
#0711Interpret level curves and contour mapsCalculus and Analysis Pathway • Multivariable and Vector Calculus • generic_math
Show 5 reinforced subtopics
  • 0711.1: Concept meaning of Interpret level curves and contour maps
  • 0711.2: Core skill or procedure for Interpret level curves and contour maps
  • 0711.3: Representation or model for Interpret level curves and contour maps
  • 0711.4: Application of Interpret level curves and contour maps
  • 0711.5: Common misconception or error check for Interpret level curves and contour maps
#0712Compute higher-order partial derivativesCalculus and Analysis Pathway • Multivariable and Vector Calculus • calculus_derivative
Show 5 reinforced subtopics
  • 0712.1: Concept meaning of Compute higher-order partial derivatives
  • 0712.2: Core skill or procedure for Compute higher-order partial derivatives
  • 0712.3: Representation or model for Compute higher-order partial derivatives
  • 0712.4: Application of Compute higher-order partial derivatives
  • 0712.5: Common misconception or error check for Compute higher-order partial derivatives
#0716Represent a system with an augmented matrixLinear Algebra • Matrices and Systems of Linear Equations • linear_algebra
Show 5 reinforced subtopics
  • 0716.1: Concept meaning of Represent a system with an augmented matrix
  • 0716.2: Core skill or procedure for Represent a system with an augmented matrix
  • 0716.3: Representation or model for Represent a system with an augmented matrix
  • 0716.4: Application of Represent a system with an augmented matrix
  • 0716.5: Common misconception or error check for Represent a system with an augmented matrix
#0723Solve a system by Gaussian eliminationLinear Algebra • Matrices and Systems of Linear Equations • generic_math
Show 5 reinforced subtopics
  • 0723.1: Concept meaning of Solve a system by Gaussian elimination
  • 0723.2: Core skill or procedure for Solve a system by Gaussian elimination
  • 0723.3: Representation or model for Solve a system by Gaussian elimination
  • 0723.4: Application of Solve a system by Gaussian elimination
  • 0723.5: Common misconception or error check for Solve a system by Gaussian elimination
#0724Solve a system by Gauss-Jordan eliminationLinear Algebra • Matrices and Systems of Linear Equations • generic_math
Show 5 reinforced subtopics
  • 0724.1: Concept meaning of Solve a system by Gauss-Jordan elimination
  • 0724.2: Core skill or procedure for Solve a system by Gauss-Jordan elimination
  • 0724.3: Representation or model for Solve a system by Gauss-Jordan elimination
  • 0724.4: Application of Solve a system by Gauss-Jordan elimination
  • 0724.5: Common misconception or error check for Solve a system by Gauss-Jordan elimination
#0725Connect linear systems to intersections of geometric objectsLinear Algebra • Matrices and Systems of Linear Equations • geometry
Show 5 reinforced subtopics
  • 0725.1: Concept meaning of Connect linear systems to intersections of geometric objects
  • 0725.2: Core skill or procedure for Connect linear systems to intersections of geometric objects
  • 0725.3: Representation or model for Connect linear systems to intersections of geometric objects
  • 0725.4: Application of Connect linear systems to intersections of geometric objects
  • 0725.5: Common misconception or error check for Connect linear systems to intersections of geometric objects
#0726Add and subtract matricesLinear Algebra • Matrix Operations • arithmetic
Show 5 reinforced subtopics
  • 0726.1: Concept meaning of Add and subtract matrices
  • 0726.2: Core skill or procedure for Add and subtract matrices
  • 0726.3: Representation or model for Add and subtract matrices
  • 0726.4: Application of Add and subtract matrices
  • 0726.5: Common misconception or error check for Add and subtract matrices
#0727Multiply matricesLinear Algebra • Matrix Operations • percent
Show 5 reinforced subtopics
  • 0727.1: Concept meaning of Multiply matrices
  • 0727.2: Core skill or procedure for Multiply matrices
  • 0727.3: Representation or model for Multiply matrices
  • 0727.4: Application of Multiply matrices
  • 0727.5: Common misconception or error check for Multiply matrices
#0728Multiply a matrix by a scalarLinear Algebra • Matrix Operations • percent
Show 5 reinforced subtopics
  • 0728.1: Concept meaning of Multiply a matrix by a scalar
  • 0728.2: Core skill or procedure for Multiply a matrix by a scalar
  • 0728.3: Representation or model for Multiply a matrix by a scalar
  • 0728.4: Application of Multiply a matrix by a scalar
  • 0728.5: Common misconception or error check for Multiply a matrix by a scalar
#0729Interpret matrix multiplication as compositionLinear Algebra • Matrix Operations • percent
Show 5 reinforced subtopics
  • 0729.1: Concept meaning of Interpret matrix multiplication as composition
  • 0729.2: Core skill or procedure for Interpret matrix multiplication as composition
  • 0729.3: Representation or model for Interpret matrix multiplication as composition
  • 0729.4: Application of Interpret matrix multiplication as composition
  • 0729.5: Common misconception or error check for Interpret matrix multiplication as composition
#0750Find coordinate vector relative to a basisLinear Algebra • Vectors, Vector Spaces, and Subspaces • vectors
Show 5 reinforced subtopics
  • 0750.1: Concept meaning of Find coordinate vector relative to a basis
  • 0750.2: Core skill or procedure for Find coordinate vector relative to a basis
  • 0750.3: Representation or model for Find coordinate vector relative to a basis
  • 0750.4: Application of Find coordinate vector relative to a basis
  • 0750.5: Common misconception or error check for Find coordinate vector relative to a basis
#0753Represent a linear transformation with a matrixLinear Algebra • Linear Independence and Linear Transformations • linear_algebra
Show 5 reinforced subtopics
  • 0753.1: Concept meaning of Represent a linear transformation with a matrix
  • 0753.2: Core skill or procedure for Represent a linear transformation with a matrix
  • 0753.3: Representation or model for Represent a linear transformation with a matrix
  • 0753.4: Application of Represent a linear transformation with a matrix
  • 0753.5: Common misconception or error check for Represent a linear transformation with a matrix
#0756Change coordinates relative to a basisLinear Algebra • Linear Independence and Linear Transformations • generic_math
Show 5 reinforced subtopics
  • 0756.1: Concept meaning of Change coordinates relative to a basis
  • 0756.2: Core skill or procedure for Change coordinates relative to a basis
  • 0756.3: Representation or model for Change coordinates relative to a basis
  • 0756.4: Application of Change coordinates relative to a basis
  • 0756.5: Common misconception or error check for Change coordinates relative to a basis
#0759Interpret column space and null spaceLinear Algebra • Linear Independence and Linear Transformations • generic_math
Show 5 reinforced subtopics
  • 0759.1: Concept meaning of Interpret column space and null space
  • 0759.2: Core skill or procedure for Interpret column space and null space
  • 0759.3: Representation or model for Interpret column space and null space
  • 0759.4: Application of Interpret column space and null space
  • 0759.5: Common misconception or error check for Interpret column space and null space
#0760Compute image of a vector under a linear transformationLinear Algebra • Linear Independence and Linear Transformations • vectors
Show 5 reinforced subtopics
  • 0760.1: Concept meaning of Compute image of a vector under a linear transformation
  • 0760.2: Core skill or procedure for Compute image of a vector under a linear transformation
  • 0760.3: Representation or model for Compute image of a vector under a linear transformation
  • 0760.4: Application of Compute image of a vector under a linear transformation
  • 0760.5: Common misconception or error check for Compute image of a vector under a linear transformation
#0761Connect invertibility to transformation propertiesLinear Algebra • Linear Independence and Linear Transformations • generic_math
Show 5 reinforced subtopics
  • 0761.1: Concept meaning of Connect invertibility to transformation properties
  • 0761.2: Core skill or procedure for Connect invertibility to transformation properties
  • 0761.3: Representation or model for Connect invertibility to transformation properties
  • 0761.4: Application of Connect invertibility to transformation properties
  • 0761.5: Common misconception or error check for Connect invertibility to transformation properties
#0769Find orthogonal complement informallyLinear Algebra • Orthogonality, Projections, and Least Squares • generic_math
Show 5 reinforced subtopics
  • 0769.1: Concept meaning of Find orthogonal complement informally
  • 0769.2: Core skill or procedure for Find orthogonal complement informally
  • 0769.3: Representation or model for Find orthogonal complement informally
  • 0769.4: Application of Find orthogonal complement informally
  • 0769.5: Common misconception or error check for Find orthogonal complement informally
#0770Decompose a vector into parallel and orthogonal partsLinear Algebra • Orthogonality, Projections, and Least Squares • vectors
Show 5 reinforced subtopics
  • 0770.1: Concept meaning of Decompose a vector into parallel and orthogonal parts
  • 0770.2: Core skill or procedure for Decompose a vector into parallel and orthogonal parts
  • 0770.3: Representation or model for Decompose a vector into parallel and orthogonal parts
  • 0770.4: Application of Decompose a vector into parallel and orthogonal parts
  • 0770.5: Common misconception or error check for Decompose a vector into parallel and orthogonal parts
#0771Apply Gram-Schmidt process in simple casesLinear Algebra • Orthogonality, Projections, and Least Squares • generic_math
Show 5 reinforced subtopics
  • 0771.1: Concept meaning of Apply Gram-Schmidt process in simple cases
  • 0771.2: Core skill or procedure for Apply Gram-Schmidt process in simple cases
  • 0771.3: Representation or model for Apply Gram-Schmidt process in simple cases
  • 0771.4: Application of Apply Gram-Schmidt process in simple cases
  • 0771.5: Common misconception or error check for Apply Gram-Schmidt process in simple cases
#0772Find an orthonormal basis in simple casesLinear Algebra • Orthogonality, Projections, and Least Squares • generic_math
Show 5 reinforced subtopics
  • 0772.1: Concept meaning of Find an orthonormal basis in simple cases
  • 0772.2: Core skill or procedure for Find an orthonormal basis in simple cases
  • 0772.3: Representation or model for Find an orthonormal basis in simple cases
  • 0772.4: Application of Find an orthonormal basis in simple cases
  • 0772.5: Common misconception or error check for Find an orthonormal basis in simple cases
#0778Use symmetric matrix properties conceptuallyLinear Algebra • Eigenvalues, Eigenvectors, and Diagonalization • linear_algebra
Show 5 reinforced subtopics
  • 0778.1: Concept meaning of Use symmetric matrix properties conceptually
  • 0778.2: Core skill or procedure for Use symmetric matrix properties conceptually
  • 0778.3: Representation or model for Use symmetric matrix properties conceptually
  • 0778.4: Application of Use symmetric matrix properties conceptually
  • 0778.5: Common misconception or error check for Use symmetric matrix properties conceptually
#0779Connect eigenanalysis to dynamical systemsLinear Algebra • Eigenvalues, Eigenvectors, and Diagonalization • linear_algebra
Show 5 reinforced subtopics
  • 0779.1: Concept meaning of Connect eigenanalysis to dynamical systems
  • 0779.2: Core skill or procedure for Connect eigenanalysis to dynamical systems
  • 0779.3: Representation or model for Connect eigenanalysis to dynamical systems
  • 0779.4: Application of Connect eigenanalysis to dynamical systems
  • 0779.5: Common misconception or error check for Connect eigenanalysis to dynamical systems
#0780Interpret eigenvector and eigenvalue definitionsLinear Algebra • Eigenvalues, Eigenvectors, and Diagonalization • linear_algebra
Show 5 reinforced subtopics
  • 0780.1: Concept meaning of Interpret eigenvector and eigenvalue definitions
  • 0780.2: Core skill or procedure for Interpret eigenvector and eigenvalue definitions
  • 0780.3: Representation or model for Interpret eigenvector and eigenvalue definitions
  • 0780.4: Application of Interpret eigenvector and eigenvalue definitions
  • 0780.5: Common misconception or error check for Interpret eigenvector and eigenvalue definitions
#0783Determine whether a matrix is diagonalizableLinear Algebra • Eigenvalues, Eigenvectors, and Diagonalization • linear_algebra
Show 5 reinforced subtopics
  • 0783.1: Concept meaning of Determine whether a matrix is diagonalizable
  • 0783.2: Core skill or procedure for Determine whether a matrix is diagonalizable
  • 0783.3: Representation or model for Determine whether a matrix is diagonalizable
  • 0783.4: Application of Determine whether a matrix is diagonalizable
  • 0783.5: Common misconception or error check for Determine whether a matrix is diagonalizable
#0784Use diagonalization to compute powers of a matrixLinear Algebra • Eigenvalues, Eigenvectors, and Diagonalization • linear_algebra
Show 5 reinforced subtopics
  • 0784.1: Concept meaning of Use diagonalization to compute powers of a matrix
  • 0784.2: Core skill or procedure for Use diagonalization to compute powers of a matrix
  • 0784.3: Representation or model for Use diagonalization to compute powers of a matrix
  • 0784.4: Application of Use diagonalization to compute powers of a matrix
  • 0784.5: Common misconception or error check for Use diagonalization to compute powers of a matrix
#0785Interpret trace and determinant in relation to eigenvaluesLinear Algebra • Eigenvalues, Eigenvectors, and Diagonalization • linear_algebra
Show 5 reinforced subtopics
  • 0785.1: Concept meaning of Interpret trace and determinant in relation to eigenvalues
  • 0785.2: Core skill or procedure for Interpret trace and determinant in relation to eigenvalues
  • 0785.3: Representation or model for Interpret trace and determinant in relation to eigenvalues
  • 0785.4: Application of Interpret trace and determinant in relation to eigenvalues
  • 0785.5: Common misconception or error check for Interpret trace and determinant in relation to eigenvalues
#0787Perform union intersection complementDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Logic, Sets, and Foundations • generic_math
Show 5 reinforced subtopics
  • 0787.1: Concept meaning of Perform union intersection complement
  • 0787.2: Core skill or procedure for Perform union intersection complement
  • 0787.3: Representation or model for Perform union intersection complement
  • 0787.4: Application of Perform union intersection complement
  • 0787.5: Common misconception or error check for Perform union intersection complement
#0788Interpret subset and element relationsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Logic, Sets, and Foundations • generic_math
Show 5 reinforced subtopics
  • 0788.1: Concept meaning of Interpret subset and element relations
  • 0788.2: Core skill or procedure for Interpret subset and element relations
  • 0788.3: Representation or model for Interpret subset and element relations
  • 0788.4: Application of Interpret subset and element relations
  • 0788.5: Common misconception or error check for Interpret subset and element relations
#0791Use implication and equivalenceDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Logic, Sets, and Foundations • generic_math
Show 5 reinforced subtopics
  • 0791.1: Concept meaning of Use implication and equivalence
  • 0791.2: Core skill or procedure for Use implication and equivalence
  • 0791.3: Representation or model for Use implication and equivalence
  • 0791.4: Application of Use implication and equivalence
  • 0791.5: Common misconception or error check for Use implication and equivalence
#0795Recognize logically equivalent statementsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Logic, Sets, and Foundations • generic_math
Show 5 reinforced subtopics
  • 0795.1: Concept meaning of Recognize logically equivalent statements
  • 0795.2: Core skill or procedure for Recognize logically equivalent statements
  • 0795.3: Representation or model for Recognize logically equivalent statements
  • 0795.4: Application of Recognize logically equivalent statements
  • 0795.5: Common misconception or error check for Recognize logically equivalent statements
#0801Understand existence and uniqueness claimsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Proof Methods • generic_math
Show 5 reinforced subtopics
  • 0801.1: Concept meaning of Understand existence and uniqueness claims
  • 0801.2: Core skill or procedure for Understand existence and uniqueness claims
  • 0801.3: Representation or model for Understand existence and uniqueness claims
  • 0801.4: Application of Understand existence and uniqueness claims
  • 0801.5: Common misconception or error check for Understand existence and uniqueness claims
#0802Distinguish conjecture from theoremDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Proof Methods • generic_math
Show 5 reinforced subtopics
  • 0802.1: Concept meaning of Distinguish conjecture from theorem
  • 0802.2: Core skill or procedure for Distinguish conjecture from theorem
  • 0802.3: Representation or model for Distinguish conjecture from theorem
  • 0802.4: Application of Distinguish conjecture from theorem
  • 0802.5: Common misconception or error check for Distinguish conjecture from theorem
#0808Model relationships with graphsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • generic_math
Show 5 reinforced subtopics
  • 0808.1: Concept meaning of Model relationships with graphs
  • 0808.2: Core skill or procedure for Model relationships with graphs
  • 0808.3: Representation or model for Model relationships with graphs
  • 0808.4: Application of Model relationships with graphs
  • 0808.5: Common misconception or error check for Model relationships with graphs
#0812Work with adjacency matrices conceptuallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • generic_math
Show 5 reinforced subtopics
  • 0812.1: Concept meaning of Work with adjacency matrices conceptually
  • 0812.2: Core skill or procedure for Work with adjacency matrices conceptually
  • 0812.3: Representation or model for Work with adjacency matrices conceptually
  • 0812.4: Application of Work with adjacency matrices conceptually
  • 0812.5: Common misconception or error check for Work with adjacency matrices conceptually
#0813Use recursion in simple settingsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • generic_math
Show 5 reinforced subtopics
  • 0813.1: Concept meaning of Use recursion in simple settings
  • 0813.2: Core skill or procedure for Use recursion in simple settings
  • 0813.3: Representation or model for Use recursion in simple settings
  • 0813.4: Application of Use recursion in simple settings
  • 0813.5: Common misconception or error check for Use recursion in simple settings
#0814Count recursively defined structures conceptuallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • arithmetic
Show 5 reinforced subtopics
  • 0814.1: Concept meaning of Count recursively defined structures conceptually
  • 0814.2: Core skill or procedure for Count recursively defined structures conceptually
  • 0814.3: Representation or model for Count recursively defined structures conceptually
  • 0814.4: Application of Count recursively defined structures conceptually
  • 0814.5: Common misconception or error check for Count recursively defined structures conceptually
#0816Count with recurrence ideas informallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • arithmetic
Show 5 reinforced subtopics
  • 0816.1: Concept meaning of Count with recurrence ideas informally
  • 0816.2: Core skill or procedure for Count with recurrence ideas informally
  • 0816.3: Representation or model for Count with recurrence ideas informally
  • 0816.4: Application of Count with recurrence ideas informally
  • 0816.5: Common misconception or error check for Count with recurrence ideas informally
#0817Analyze simple recursive algorithmsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • generic_math
Show 5 reinforced subtopics
  • 0817.1: Concept meaning of Analyze simple recursive algorithms
  • 0817.2: Core skill or procedure for Analyze simple recursive algorithms
  • 0817.3: Representation or model for Analyze simple recursive algorithms
  • 0817.4: Application of Analyze simple recursive algorithms
  • 0817.5: Common misconception or error check for Analyze simple recursive algorithms
#0818Work with binary representationsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • generic_math
Show 5 reinforced subtopics
  • 0818.1: Concept meaning of Work with binary representations
  • 0818.2: Core skill or procedure for Work with binary representations
  • 0818.3: Representation or model for Work with binary representations
  • 0818.4: Application of Work with binary representations
  • 0818.5: Common misconception or error check for Work with binary representations
#0819Represent relations and functions discretelyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Discrete Structures and Graph Ideas • generic_math
Show 5 reinforced subtopics
  • 0819.1: Concept meaning of Represent relations and functions discretely
  • 0819.2: Core skill or procedure for Represent relations and functions discretely
  • 0819.3: Representation or model for Represent relations and functions discretely
  • 0819.4: Application of Represent relations and functions discretely
  • 0819.5: Common misconception or error check for Represent relations and functions discretely
#0820Interpret a differential equationDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • generic_math
Show 5 reinforced subtopics
  • 0820.1: Concept meaning of Interpret a differential equation
  • 0820.2: Core skill or procedure for Interpret a differential equation
  • 0820.3: Representation or model for Interpret a differential equation
  • 0820.4: Application of Interpret a differential equation
  • 0820.5: Common misconception or error check for Interpret a differential equation
#0821Solve separable differential equationsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • equations
Show 5 reinforced subtopics
  • 0821.1: Concept meaning of Solve separable differential equations
  • 0821.2: Core skill or procedure for Solve separable differential equations
  • 0821.3: Representation or model for Solve separable differential equations
  • 0821.4: Application of Solve separable differential equations
  • 0821.5: Common misconception or error check for Solve separable differential equations
#0822Solve first-order linear differential equations conceptuallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • equations
Show 5 reinforced subtopics
  • 0822.1: Concept meaning of Solve first-order linear differential equations conceptually
  • 0822.2: Core skill or procedure for Solve first-order linear differential equations conceptually
  • 0822.3: Representation or model for Solve first-order linear differential equations conceptually
  • 0822.4: Application of Solve first-order linear differential equations conceptually
  • 0822.5: Common misconception or error check for Solve first-order linear differential equations conceptually
#0825Interpret stability qualitativelyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • generic_math
Show 5 reinforced subtopics
  • 0825.1: Concept meaning of Interpret stability qualitatively
  • 0825.2: Core skill or procedure for Interpret stability qualitatively
  • 0825.3: Representation or model for Interpret stability qualitatively
  • 0825.4: Application of Interpret stability qualitatively
  • 0825.5: Common misconception or error check for Interpret stability qualitatively
#0826Model growth and decay with differential equationsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • generic_math
Show 5 reinforced subtopics
  • 0826.1: Concept meaning of Model growth and decay with differential equations
  • 0826.2: Core skill or procedure for Model growth and decay with differential equations
  • 0826.3: Representation or model for Model growth and decay with differential equations
  • 0826.4: Application of Model growth and decay with differential equations
  • 0826.5: Common misconception or error check for Model growth and decay with differential equations
#0827Estimate solutions numerically step by stepDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • generic_math
Show 5 reinforced subtopics
  • 0827.1: Concept meaning of Estimate solutions numerically step by step
  • 0827.2: Core skill or procedure for Estimate solutions numerically step by step
  • 0827.3: Representation or model for Estimate solutions numerically step by step
  • 0827.4: Application of Estimate solutions numerically step by step
  • 0827.5: Common misconception or error check for Estimate solutions numerically step by step
#0828Recognize equilibrium solutionsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • generic_math
Show 5 reinforced subtopics
  • 0828.1: Concept meaning of Recognize equilibrium solutions
  • 0828.2: Core skill or procedure for Recognize equilibrium solutions
  • 0828.3: Representation or model for Recognize equilibrium solutions
  • 0828.4: Application of Recognize equilibrium solutions
  • 0828.5: Common misconception or error check for Recognize equilibrium solutions
#0829Estimate numerical error conceptuallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Differential Equations and Numerical Methods • generic_math
Show 5 reinforced subtopics
  • 0829.1: Concept meaning of Estimate numerical error conceptually
  • 0829.2: Core skill or procedure for Estimate numerical error conceptually
  • 0829.3: Representation or model for Estimate numerical error conceptually
  • 0829.4: Application of Estimate numerical error conceptually
  • 0829.5: Common misconception or error check for Estimate numerical error conceptually
#0830Reason about algebraic structures informallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0830.1: Concept meaning of Reason about algebraic structures informally
  • 0830.2: Core skill or procedure for Reason about algebraic structures informally
  • 0830.3: Representation or model for Reason about algebraic structures informally
  • 0830.4: Application of Reason about algebraic structures informally
  • 0830.5: Common misconception or error check for Reason about algebraic structures informally
#0832Interpret group operation examplesDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • ratio_rate
Show 5 reinforced subtopics
  • 0832.1: Concept meaning of Interpret group operation examples
  • 0832.2: Core skill or procedure for Interpret group operation examples
  • 0832.3: Representation or model for Interpret group operation examples
  • 0832.4: Application of Interpret group operation examples
  • 0832.5: Common misconception or error check for Interpret group operation examples
#0833Analyze sequence convergence rigorously in simple casesDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0833.1: Concept meaning of Analyze sequence convergence rigorously in simple cases
  • 0833.2: Core skill or procedure for Analyze sequence convergence rigorously in simple cases
  • 0833.3: Representation or model for Analyze sequence convergence rigorously in simple cases
  • 0833.4: Application of Analyze sequence convergence rigorously in simple cases
  • 0833.5: Common misconception or error check for Analyze sequence convergence rigorously in simple cases
#0834Interpret completeness conceptuallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0834.1: Concept meaning of Interpret completeness conceptually
  • 0834.2: Core skill or procedure for Interpret completeness conceptually
  • 0834.3: Representation or model for Interpret completeness conceptually
  • 0834.4: Application of Interpret completeness conceptually
  • 0834.5: Common misconception or error check for Interpret completeness conceptually
#0835Distinguish algebraic and transcendental numbers conceptuallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • arithmetic
Show 5 reinforced subtopics
  • 0835.1: Concept meaning of Distinguish algebraic and transcendental numbers conceptually
  • 0835.2: Core skill or procedure for Distinguish algebraic and transcendental numbers conceptually
  • 0835.3: Representation or model for Distinguish algebraic and transcendental numbers conceptually
  • 0835.4: Application of Distinguish algebraic and transcendental numbers conceptually
  • 0835.5: Common misconception or error check for Distinguish algebraic and transcendental numbers conceptually
#0836Understand proof-based definition styleDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0836.1: Concept meaning of Understand proof-based definition style
  • 0836.2: Core skill or procedure for Understand proof-based definition style
  • 0836.3: Representation or model for Understand proof-based definition style
  • 0836.4: Application of Understand proof-based definition style
  • 0836.5: Common misconception or error check for Understand proof-based definition style
#0837Work with functions as mappings between setsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0837.1: Concept meaning of Work with functions as mappings between sets
  • 0837.2: Core skill or procedure for Work with functions as mappings between sets
  • 0837.3: Representation or model for Work with functions as mappings between sets
  • 0837.4: Application of Work with functions as mappings between sets
  • 0837.5: Common misconception or error check for Work with functions as mappings between sets
#0838Analyze injective, surjective, and bijective functionsDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0838.1: Concept meaning of Analyze injective, surjective, and bijective functions
  • 0838.2: Core skill or procedure for Analyze injective, surjective, and bijective functions
  • 0838.3: Representation or model for Analyze injective, surjective, and bijective functions
  • 0838.4: Application of Analyze injective, surjective, and bijective functions
  • 0838.5: Common misconception or error check for Analyze injective, surjective, and bijective functions
#0839Understand equivalence relations informallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0839.1: Concept meaning of Understand equivalence relations informally
  • 0839.2: Core skill or procedure for Understand equivalence relations informally
  • 0839.3: Representation or model for Understand equivalence relations informally
  • 0839.4: Application of Understand equivalence relations informally
  • 0839.5: Common misconception or error check for Understand equivalence relations informally
#0840Reason with epsilon-style precision informallyDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0840.1: Concept meaning of Reason with epsilon-style precision informally
  • 0840.2: Core skill or procedure for Reason with epsilon-style precision informally
  • 0840.3: Representation or model for Reason with epsilon-style precision informally
  • 0840.4: Application of Reason with epsilon-style precision informally
  • 0840.5: Common misconception or error check for Reason with epsilon-style precision informally
#0841Distinguish sequence convergence from series convergenceDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0841.1: Concept meaning of Distinguish sequence convergence from series convergence
  • 0841.2: Core skill or procedure for Distinguish sequence convergence from series convergence
  • 0841.3: Representation or model for Distinguish sequence convergence from series convergence
  • 0841.4: Application of Distinguish sequence convergence from series convergence
  • 0841.5: Common misconception or error check for Distinguish sequence convergence from series convergence
#0842Recognize groups, rings, and fields as structuresDiscrete Mathematics, Logic, Proof, and Advanced University Foundations • Abstract Algebra and Real Analysis Bridges • generic_math
Show 5 reinforced subtopics
  • 0842.1: Concept meaning of Recognize groups, rings, and fields as structures
  • 0842.2: Core skill or procedure for Recognize groups, rings, and fields as structures
  • 0842.3: Representation or model for Recognize groups, rings, and fields as structures
  • 0842.4: Application of Recognize groups, rings, and fields as structures
  • 0842.5: Common misconception or error check for Recognize groups, rings, and fields as structures