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Math

Algebra

Functions

Geometry

Mathematical Practices

Mathematics Connections

Measurement

Measurement And Data

Number System

Absolute Value And Operations

Complex Numbers

Applications Of Complex Numbers

Proving Fundamental Theorem Of Algebra

Solving Quadratics With Complex Solutions

Understanding And Applying Conjugates Of Complex Numbers

Applying Conjugates To Find Quotients

Finding The Conjugate Of A Complex Number

Complex Number Fundamentals

Extend Polynomial Identities To Complex Numbers

Understanding Complex Numbers And I² = -1

Understanding And Using Complex Number Notation

Finding The Square Root Of A Negative Number

Knowing The Existence Of A Complex Number I And That I^2 = –1

Understanding That Every Complex Number Has The Form Of A + Bi Where A And B Are Real Numbers

Complex Number Operations

Adding And Subtracting Complex Numbers

Using Different Properties (commutative, Associative) To Add And/or Subtract Complex Numbers

Adding, Subtracting & Multiplying Complex Numbers

Applying Properties Of Operations On Complex Numbers To Solve Problems

Calculating The Distance Between Complex Numbers

Extending Algebraic Polynomial Identities To Complex Numbers

Finding The Midpoint Of A Segment Connecting Two Complex Numbers

Knowing The Fundamental Theorem Of Algebra

Solving Problems Involving A Mix Of Addition, Subtraction, Multiplication And/or Division Of Complex Numbers

Finding Conjugates & Moduli Of Complex Numbers

Multiplying Complex Numbers

Using I^2 = –1 And Different Properties (commutative, Associative, Distributive) To Multiply Complex Numbers (including Cases Where Addition/subtraction Are Involved)

Complex Numbers In The Coordinate Plane

Complex Plane: Distance & Midpoint Calculation

Geometric Representation Of Complex Numbers

Proving Fundamental Theorem Of Algebra

Representing Complex Numbers In Different Forms

Representing Complex Numbers

Finding The Modulus And/or Argument Of A Complex Number

Representing Complex Numbers In The Polar Form

Representing Complex Numbers In The Rectangular Form

Understanding Why The Rectangular And Polar Forms Of A Complex Number Represent The Same Number

Solving Quadratics With Complex Solutions

Operations With Complex Numbers

Adding And Subtracting Complex Numbers

Using Different Properties (commutative, Associative) To Add And/or Subtract Complex Numbers

Adding, Subtracting & Multiplying Complex Numbers

Applying Properties Of Operations On Complex Numbers To Solve Problems

Calculating The Distance Between Complex Numbers

Extending Algebraic Polynomial Identities To Complex Numbers

Finding The Midpoint Of A Segment Connecting Two Complex Numbers

Knowing The Fundamental Theorem Of Algebra

Solving Problems Involving A Mix Of Addition, Subtraction, Multiplication And/or Division Of Complex Numbers

Multiplying Complex Numbers

Using I^2 = –1 And Different Properties (commutative, Associative, Distributive) To Multiply Complex Numbers (including Cases Where Addition/subtraction Are Involved)

Understanding Complex Numbers

Extend Polynomial Identities To Complex Numbers

Finding Conjugates & Moduli Of Complex Numbers

Representing Complex Numbers

Finding The Modulus And/or Argument Of A Complex Number

Representing Complex Numbers In The Polar Form

Representing Complex Numbers In The Rectangular Form

Understanding Why The Rectangular And Polar Forms Of A Complex Number Represent The Same Number

Understanding Complex Numbers And I² = -1

Understanding And Applying Conjugates Of Complex Numbers

Applying Conjugates To Find Quotients

Finding The Conjugate Of A Complex Number

Understanding And Using Complex Number Notation

Finding The Square Root Of A Negative Number

Knowing The Existence Of A Complex Number I And That I^2 = –1

Understanding That Every Complex Number Has The Form Of A + Bi Where A And B Are Real Numbers

Decimal Numbers

Comparing Decimals

Comparing To Tenths Or Hundredths

Comparing Two Decimal Numbers To Thousandths Using The Symbols >, = And <

Comparing Two Decimal Numbers To Thousandths Using The Symbols >, = And <, Ordering Decimal Numbers

Operations With Decimal Numbers

Adding And Subtracting Decimal Numbers

Adding And Subtracting Decimal Numbers Using The Standard Algorithm

Adding Decimal Numbers Using Concrete Models Or Drawings

Adding Decimal Numbers Using Place Value Strategies

Estimating Sums And Differences Using Rounding

Subtracting Decimal Numbers Using Concrete Models Or Drawings

Subtracting Decimal Numbers Using Place Value Strategies

Multiplying And Dividing Decimal Numbers

Dividing Decimal Numbers Using Place Value Strategies

Dividing Decimal Numbers Using Properties Of Operations

Estimating Products And Quotients Using Rounding

Multiplying And/or Dividing Decimal Numbers Using The Standard Algorithm

Multiplying Decimal Numbers Using Place Value Strategies

Multiplying Decimal Numbers Using Properties Of Operations

Understanding Decimals

Applying Place Value Understanding (decimal Numbers)

Explaining Patterns In The Placement Of The Decimal Point When Multiplying Or Dividing By Powers Of 10

Reading And Writing Decimal Numbers To Thousandths Using Base-ten Numerals

Reading And Writing Decimal Numbers To Thousandths Using Number Names

Reading And Writing Decimal Numbers To Thousandths Using The Expanded Form

Using Place Value Understanding To Round Decimal Numbers To Any Place

Expressing Fractions As Decimals

Tenths And Hundredths

Exponents And Radicals

Radicals

Concepts In Irrational Numbers

Understanding Irrational Numbers

Writing A Radical In Its Simplest Form

Rational Exponents

Rewriting Radicals & Rational Exponents

Understanding Rational Exponents & Radicals

Understanding And Applying The Laws Of Exponents To Numerical Expressions (rational Exponents)

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

Understanding That The Definition Of Rational Exponents Follows From Extending Understanding Of Integer Exponents

Fractions

Comparing Fractions

Different Numerators And Denominators

Ordering Fractions

Same Denominator

Same Numerator

Using Benchmarks

Using Equivalent Fractions

Equal Parts

Identifying Fourths

Identifying Halves

Making Fourths

Making Halves

Recognizing 2, 3, And 4 Equal Parts

Equivalent Fractions

Generating Equivalent Fractions

Recognizing Equivalent Fractions

Understanding Equivalence Using Models

Operations With Fractions

Adding And Subtracting Unlike Fractions

Adding And/or Subtracting Mixed Numbers With Unlike Denominators

Adding And/or Subtracting Unlike Fractions

Solving Word Problems Involving Addition And/or Subtraction Of Unlike Fractions Referring To The Same Whole

Dividing Fractions And/or Mixed Numbers

Calculating And Interpreting The Quotient Of The Division Of A Non-zero Whole Number By A Unit Fraction

Calculating And Interpreting The Quotient Of The Division Of A Unit Fraction By A Non-zero Whole Number

Solving Real-world Problems Involving Division Of Unit Fractions By Whole Numbers

Solving Real-world Problems Involving Division Of Whole Numbers By Unit Fractions

Solving Word Problems Involving Division Of Whole Numbers Leading To Fractional Or Mixed Number Answers

Multiplying Fractions And/or Mixed Numbers

Comparing The Size Of A Product Of Fractions To One Of The Fractions Based On Their Relative Sizes

Finding The Area Of A Rectangle With Fractional Side Lengths By Tiling

Interpreting The Product '(a/b) × Q' As 'a' Parts Of A Partition Of 'q' Into 'b' Equal Parts

Multiplying Two Or More Fractions Or Mixed Numbers

Solving Real-world Problems Involving Multiplication Of Fractions And Mixed Numbers

Understanding Fractions

Irrational And Rational Numbers

Operations With Irrational Numbers

Adding And Subtracting Irrational Numbers

Adding And/or Subtracting Radicals

Explaining/demonstrating Why The Sum Or Difference Of A Rational And Irrational Number Is Irrational

Multiplying And Dividing Irrational Numbers

Explaining Why The Product Or Quotient Of A Rational And Irrational Number Is Irrational

Multiplying And/or Dividing Radicals

Solving Problems Involving Mixed Operations On Radicals

Simplifying Multi-operation Expressions Involving Radicals (including Denominator Rationalisation)

Operations With Rational Numbers

Adding And Subtracting Rational Numbers

Explaining/demonstrating Why The Sum Or Difference Of Two Rational Numbers Is Rational

Multiplying And Dividing Rational Numbers

Explaining/demonstrating Why The Product Or Quotient Of Two Rational Numbers Is Rational

Properties Of Irrational Numbers

Rational & Irrational Numbers Operations

Matrices

Basic Matrix Operations

Add, Subtract, Multiply Matrices

Adding And Subtracting Matrices

Adding And/or Subtracting Matrices Of Appropriate Dimensions

Matrix Multiplication With Vectors

Multiplying Matrices By Scalars

Multiplying Matrices

Multiplying A Vector (column Matrix) By A Matrix To Produce Another Vector

Multiplying Matrices By Scalars

Multiplying Two Matrices Of Appropriate Dimensions

Understanding That Matrix Multiplication Is Associative And Distributive

Understanding That Matrix Multiplication Is Associative And Distributive But Not Commutative

Understanding The Role Of The Identity Matrix In Matrix Multiplication

Matrix Applications

2x2 Matrix Transformations & Determinant Area

Data Manipulation Using Matrices

Solving Problems Involving Mixed Operations

Solving Problems Involving A Mix Of Addition, Subtraction And/or Multiplication Of Matrices

Understanding And Applying Determinants

Finding The Inverse Of A Matrix (if It Exists)

Understanding And Using Matrices

Representing And Manipulating Data Through Matrices

Matrix Concepts

Understanding Role Of Zero, Identity Matrices & Determinants

Understanding And Applying Determinants

Finding The Inverse Of A Matrix (if It Exists)

Understanding And Using Matrices

Representing And Manipulating Data Through Matrices

Matrix Operations

Add, Subtract, Multiply Matrices

Adding And Subtracting Matrices

Adding And/or Subtracting Matrices Of Appropriate Dimensions

Matrix Multiplication With Vectors

Multiplying Matrices By Scalars

Multiplying Matrices

Multiplying A Vector (column Matrix) By A Matrix To Produce Another Vector

Multiplying Matrices By Scalars

Multiplying Two Matrices Of Appropriate Dimensions

Understanding That Matrix Multiplication Is Associative And Distributive

Understanding That Matrix Multiplication Is Associative And Distributive But Not Commutative

Understanding The Role Of The Identity Matrix In Matrix Multiplication

Non-commutative Matrix Multiplication

Matrix Properties

2x2 Matrix Transformations & Determinant Area

Matrix Multiplication With Vectors

Non-commutative Matrix Multiplication

Understanding Role Of Zero, Identity Matrices & Determinants

Measurement And Dimensional Analysis

Working With Units

Defining Quantities For Descriptive Modeling

Interpreting Units & Scales In Problem Solving

Selecting Accuracy Level For Quantity Reporting

Number Concepts

Comparing Numbers

Comparing Two Two-digit Numbers Using >, =, And <

Counting And Cardinality

Comparing Numbers

Equal To

More Than/less Than

Ordering Numbers

Counting

Counting Backward From 10

Counting Forward 1-20

One-to-one Correspondence

Skip Counting By 2s And 5s (introduction)

Number Recognition

Identifying Numbers 0-10

Identifying Numbers 11-20

Number Words

Counting And Place Value

Counting To 120 By Ones And Tens

Reading And Writing Numbers Up To 120

Representing A Number With A Written Numeral

Understanding Place Value For Two-digit Numbers

Understanding Tens And Ones

Factors And Multiples

Finding Factors

Finding Factor Pairs

Prime And Composite Numbers

Multiples

Determining Multiples

Relationship Between Factors And Multiples

Place Value

Comparing Numbers

Ordering Three-digit Numbers

Using Symbols (>, =, <) With Three-digit Numbers

Number Patterns

Even And Odd Numbers

Identifying Patterns On Number Lines

Skip Counting

Three-digit Numbers

Models And Expanded Form

Number Names

Reading And Writing Numbers

Understanding Hundreds, Tens, And Ones

Whole Numbers

Comparing And Rounding

Comparing Numbers

Comparing Numbers Above 1000

Rounding To Any Place

Rounding To Nearest 10, 100, Or 1000

Factors And Multiples

Understanding Factors And Multiples

Determining If A Number Is A Prime Or Composite Number

Number Properties

Integer Operations

Operations Properties

Associative Property

Commutative Property

Distributive Property

Rational Number Operations

Patterns

Analyzing Patterns

Explaining Patterns Using Properties

Generating Number Patterns

Generating Shape Patterns

Identifying And Extending Patterns

Place Value

Working With Units

Converting Between Measurement Units Within One System Of Units

Expressing Measurements In A Larger Unit In Terms Of A Smaller Unit

Expressing Measurements In A Smaller Unit In Terms Of A Larger Unit

Solving Multi-step Real-world Problems Involving Conversion Of Units Of Length

Solving Multi-step Real-world Problems Involving Conversion Of Units Of Mass

Solving Multi-step Real-world Problems Involving Conversion Of Units Of Volume

Number Patterns

Extending Patterns

Identifying Patterns

Number Properties

Decimal Operations

Decimal Operation Algorithms

Multi-digit Decimal Operations

Factors And Multiples

Distributive Property Applications

Greatest Common Factor And Least Common Multiple

Operation Properties

Associative Property

Commutative Property

Distributive Property

Numerical Expressions

Laws Of Exponents

Understanding And Applying The Laws Of Exponents To Numerical Expressions (integral Exponents)

Understanding And Applying Laws Of Exponents (product Law, Quotient Law And Power Law) To Numerical Expressions For Exponents >0.

Understanding And Using Zero And Negative Exponents, Applying Law Of Exponents To Numerical Expressions Where Exponent Is Zero Or Negative.

Understanding And Applying The Laws Of Exponents To Numerical Expressions (rational Exponents)

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

Understanding That The Definition Of Rational Exponents Follows From Extending Understanding Of Integer Exponents

Measurement Applications

Working With Units

Defining Quantities For Descriptive Modeling

Interpreting Units & Scales In Problem Solving

Selecting Accuracy Level For Quantity Reporting

Solving Mathematical And Real-world Problems Involving All Forms Of Rational Numbers

Evaluating The Reasonableness Of Answers Using Mental Computation And Estimation Strategies

Solving Mathematical And Real-world Problems Involving All Forms Of Rational Numbers

Solving Mathematical Problems Involving All Forms Of Rational Numbers

Solving Real-world Problems Involving All Forms Of Rational Numbers

Understanding And Applying The Laws Of Exponents To Numerical Expressions (integral Exponents)

Operations And Algebraic Thinking

Addition Concepts

Adding Within 10

Adding Within 5

Addition Stories

Addition And Subtraction

Mental Math Strategies

Finding 10 Or 100 More/less

Multi-digit Addition

Estimation

Using Place Value Strategies

Using Properties Of Operations

Using The Standard Algorithm

Multi-digit Subtraction

Estimation

Using Place Value Strategies

Using Properties Of Operations

Using The Standard Algorithm

Word Problems

Comparison Problems

Multi-step Problems

One-step Problems

Two-step Problems

Addition Strategies

Algebraic Expressions

Framing Algebraic Expressions For Mathematical And Real-world Problems

Expressing Operations Involving Both Numbers And Letters That Stand For Numbers

Algebraic Thinking

Expressing A Number As A Sum Of Two Addends

Expressions With Variables

Using Letters For Unknown Quantities

Finding Missing Numbers In Equations

Generating Patterns

Following Given Rules

Understanding The Equal Sign

Introduction To Multiplication

Equal Groups

Rectangular Arrays

Writing Equations For Arrays

Mental Computation

Finding 10 More/less

Finding 100 More/less

Mental Strategies For Addition

Mental Strategies For Subtraction

Operations On Integers

Adding And Subtracting Integers

Adding And/or Subtracting Two Or More Integers (including Interpreting Sums/differences In Real-world Contexts)

Applying Properties Of Operations As Strategies To Add And Subtract Integers

Calculating The Distance Between Two Integers As The Absolute Value Of Their Difference (including Interpreting Differences In Real-world Contexts)

Describing Situations In Which Opposite Quantities Combine To Make Zero

Understanding The Concept Of Additive Inverses In The Context Of Integers

Understanding The Representation Of P + Q On A Number Line Where P And Q Are Integers

Applying Operations On Integers To Solve Mathematical And Real-world Problems

Solving Problems Involving Multiple Operations On Integers

Integer Operations

Multiplying And Dividing Integers

Applying Prior Understanding Of Properties Of Division To Divide Integers (including Interpreting Quotients In Real-world Contexts)

Applying Prior Understanding Of Properties Of Multiplication To Multiply Integers (including Interpreting Products In Real-world Contexts)

Applying Prior Understanding Of Properties Of Operations To Multiply And/or Divide Integers (including Interpreting Products Or Quotient In Real-world Contexts)

Applying Properties Of Operations As Strategies To Multiply And Divide Integers

Operations On Rational Numbers

Adding And Subtracting Rational Numbers

Adding And/or Subtracting Two Or More Rational Numbers (including Interpreting Sums/differences In Real-world Contexts)

Applying Properties Of Operations As Strategies To Add And Subtract Rational Numbers

Calculating The Distance Between Two Rational Numbers As The Absolute Value Of Their Difference (including Interpreting Differences In Real-world Contexts)

Understanding The Concept Of Additive Inverses In The Context Of Rational Numbers

Understanding The Representation Of P + Q On A Number Line Where P And Q Are Rational Numbers

Applying Operations On Rational Numbers To Solve Mathematical And Real-world Problems

Evaluating Expressions Involving A Mix Of Addition, Subtraction, Multiplication And/or Division Of Rational Numbers

Solving Mathematical/real-world Problems Involving Multiple Operations On Rational Numbers

Solving Problems Involving Multiple Operations On Rational Numbers

Multiplying And Dividing Rational Numbers

Applying Prior Understanding Of Properties Of Division To Divide Two Rational Numbers (including Interpreting Quotients In Real-world Contexts)

Applying Prior Understanding Of Properties Of Multiplication To Multiply Rational Numbers (including Interpreting Products In Real-world Contexts)

Applying Properties Of Operations As Strategies To Multiply And Divide Rational Numbers

Converting A Rational Number To A Decimal Number Using Division And Vice Versa

Understanding Patterns In The Decimal Form Of A Rational Number (either Terminates In Zeroes Or Eventually Repeats)

Place Value

Number Composition

Teen Numbers

Tens And Ones

Quantities And Measurement

Numerical Expressions

Understanding And Applying The Laws Of Exponents To Numerical Expressions (integral Exponents)

Understanding And Applying Laws Of Exponents (product Law, Quotient Law And Power Law) To Numerical Expressions For Exponents >0.

Understanding And Using Zero And Negative Exponents, Applying Law Of Exponents To Numerical Expressions Where Exponent Is Zero Or Negative.

Working With Units

Defining Quantities For Descriptive Modeling

Interpreting Units & Scales In Problem Solving

Selecting Accuracy Level For Quantity Reporting

Radicals & Exponents

Rewriting Radicals & Rational Exponents

Understanding Rational Exponents & Radicals

Understanding And Applying The Laws Of Exponents To Numerical Expressions (rational Exponents)

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

Understanding That The Definition Of Rational Exponents Follows From Extending Understanding Of Integer Exponents

Rational Numbers

Operations With Rational Numbers

Adding/subtracting Rational Numbers

Adding & Subtracting Rational Numbers

Adding Rational Numbers

Additive Inverse

Subtracting Rational Numbers

Addition And Subtraction With Rational Numbers

Multiplication And Division With Rational Numbers

Multiplying/dividing Rational Numbers

Converting Rational Numbers To Decimals (and Vice Versa)

Dividing Rational Numbers

Multiplying & Dividing Rational Numbers

Multiplying Rational Numbers

Order Of Operations

Solving Multi-step Problems With Rational Numbers

Properties Of Rational Numbers

Absolute Value

Comparing Rational Numbers

Properties Of Operations

Understanding Rational Numbers

Comparing And Ordering Rational Numbers

Representing Rational Numbers On Number Lines

Understanding Absolute Value Of Rational Numbers

Real Numbers

Exponents And Radicals

Rewriting Radicals & Rational Exponents

Understanding Rational Exponents & Radicals

Understanding And Applying The Laws Of Exponents

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

Understanding And Applying Laws Of Exponents To Numerical Expressions

Understanding That The Definition Of Rational Exponents Follows From Extending Understanding Of Integer Exponents

Understanding Irrational Numbers

Writing A Radical In Its Simplest Form

Irrational Numbers

Number Properties

Operation Properties

Associative Property

Commutative Property

Distributive Property

Operations With Rational Numbers

Adding And Subtracting Rational Numbers

Explaining/demonstrating Why The Sum Or Difference Of Two Rational Numbers Is Rational

Multiplying And Dividing Rational Numbers

Explaining/demonstrating Why The Product Or Quotient Of Two Rational Numbers Is Rational

Radicals & Exponents

Operations On Irrational Numbers

Adding And Subtracting Irrational Numbers

Adding And/or Subtracting Radicals

Explaining/demonstrating Why The Sum Or Difference Of A Rational And Irrational Number Is Irrational

Multiplying And Dividing Irrational Numbers

Explaining Why The Product Or Quotient Of A Rational And Irrational Number Is Irrational

Multiplying And/or Dividing Radicals

Solving Problems Involving Mixed Operations On Radicals

Simplifying Multi-operation Expressions Involving Radicals (including Denominator Rationalisation)

Rewriting Radicals & Rational Exponents

Understanding Rational Exponents & Radicals

Rational Numbers

Operations On Rational Numbers

Adding And Subtracting Rational Numbers

Explaining/demonstrating Why The Sum Or Difference Of Two Rational Numbers Is Rational

Explaining/demonstrating Why The Product Or Quotient Of Two Rational Numbers Is Rational

Explaining/demonstrating Why The Sum Or Difference Of Two Rational Numbers Is Rational

Multiplying And Dividing Rational Numbers

Explaining/demonstrating Why The Product Or Quotient Of Two Rational Numbers Is Rational

Understanding Irrational Numbers

Scientific Notation

Applying Operations On Numbers Expressed Using Scientific Notation To Solve Mathematical And Real-world Problems

Performing Addition And/or Subtraction With Numbers Expressed In The Scientific Notation

Performing Multiple Operations With Numbers Expressed In The Scientific Notation

Performing Multiple Operations With Numbers Expressed In The Scientific Notation And Solving Real-world Problems.

Performing Multiplication And/or Division With Numbers Expressed In The Scientific Notation

Estimating Quantities And Units Using Scientific Notation

Choosing Units Of Appropriate Size For Measuring Very Large Or Very Small Quantities

Estimating Very Large Or Very Small Quantities Using Scientific Notation

Estimating/writing Quantities In Scientific Notation

Operations & Interpretation Of Scientific Notation

Understanding And Writing Numbers In Scientific Notation

Converting Scientific Notation To Standard Form And Vice Versa

Writing Very Large Or Very Small Quantities Using Scientific Notation

Vectors

Understanding Vectors

Understanding And Representing Vector Quantities

Understanding, Representing And Using Vectors

Vector Concepts

Understanding And Representing Vector Quantities

Understanding, Representing And Using Vectors

Vector Operations

Working With Units

Ratios And Proportional Relationships

Statistics And Probability

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8th Grade

Scientific Notation Operations - Addition, Subtraction, Multiplication & Division

Passage

Scientific Notation Operations - Addition, Subtraction, Multiplication & Division

8th Grade

Math

Understand and apply mathematical operations in scientific notation, including addition, subtraction, multiplication, and division. Develop the proficiency to efficiently handle problems involving very large and very small numbers, enhancing your problem-solving skills.

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1. 2021 survey of 800+ teachers conducted by Wayground

2. Journal of Education and e-Learning Research (Source)

3. International Online Journal of Education and Teaching (Source)

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