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Math

Algebra

Algebraic Expressions

Equation Of A Straight Line

Connecting Proportional Relationships And The Equation Of A Straight Line

Comparing Proportional Relationships Represented Graphically

Graphing And/or Comparing Proportional Relationships

Graphing Proportional Relationships

Slope Intercept Form

Understanding And Using Slopes

Solving Problems Involving Slopes (including Interpreting Unit Rates)

Using Similar Triangles To Understand Why The Slope Of A Straight Line Remains Constant

Writing Equation Of Straight Line

Writing The Equation Of A Straight Line

Deriving And Using The Equation Y = Mx + B For A Line With Y-intercept B

Deriving And Using The Equation Y = Mx + B Or Y = Mx

Deriving And Using The Equation Y = Mx For A Line Passing Through Origin

Writing An Equation Of A Straight Line Using A Slope And A General Point

Writing An Equation Of A Straight Line Using Two Points

Writing An Equation Of A Straight Line When The Line Is Represented Graphically

Equations

Equations And Inequalities

One-variable Equations

Representing Real-world Situations

Solving One-step Equations

Understanding Solution Methods

One-variable Inequalities

Representing Real-world Constraints

Solving Simple Inequalities

Writing And Graphing Inequalities

Exponents

Integer Exponents

Simplifying Exponents

Inequalities

Linear Inequalities

One-variable Linear Inequalities

Representing Solutions Of Linear Inequalities In One Variable On A Number Line

Representing Solutions Of Absolute Value Inequalities On Number Lines

Solving/interpreting Linear Inequalities In One Variable

Solving And/or Interpreting Absolute Value Inequalities

Two-variable Linear Inequalities

Framing/writing Linear Inequalities In Two Variables

Framing Linear Inequalities In Two Variables

Graphing Linear Inequalities

Representing Solutions Of Linear Inequalities In Two Variables On A Graph

Graphing The Solution Set To A System Of Linear Inequalities In Two Variables As The Intersection Of The Half-planes

Representing Solutions Of Inequalities Of The Form Px + Qy ≤ R Or Px + Qy < R On Graphs

Representing Solutions Of Inequalities On Graphs

Representing Solutions Of Linear Inequalities In Two Variables On Graphs

Solutions In Equation Modeling

Solving/interpreting Linear Inequalities In Two Variables

Solving Real-world Problems Involving Multi-step Linear Inequalities In Two Variables

Non-linear Inequalities

One-variable Non-linear Inequalities

Solving Multi-step Problems Using Non-linear Inequalities In One Variable

Solving Quadratic Inequalities In One Variable (algebraically Or Graphically)

Solving Multi-step Problems Using Non-linear Inequalities In One Variable

Solving Quadratic Inequalities In One Variable (algebraically Or Graphically)

Linear Equations (one Variable)

Applications Of Equations

Solving Multi-step Problems Using Linear Equations In One Variable

Generating And Understanding Linear Equations In One Variable With Infinitely Many Solutions

Generating And Understanding Linear Equations In One Variable With No Solution

Solving Linear Equations In One Variable With Variables On Both Sides Of The Equation

Solving Problems Involving Multi-step Linear Equations In One Variable

Solving Problems With Equations Of The Form P(x + Q) = R, Where P, Q And R Are Rational Numbers

Understanding Linear Equations In One Variable

Framing Linear Equations In One Variable (for Mathematical And Real-life Problems)

Multi-step Equations

Identify Equations With Infinite/no Solution

Solving Multi-step Equations

Two Step Equations

Functions

Advanced Functions

Advanced Function Analysis

Applying And Analysing Functions

Graphing Functions

Functions With Special Properties

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Understanding Sequences As Recursive Functions

Sequence Functions

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Equation Of A Line

Graphing The Equation Of A Straight Line

Graphing A Horizontal Line And/or Vertical Line

Graphing An Equation Of A Straight Line Represented In Different Forms

Identifying Axes Intercepts When A Line Is Represented Graphically

Writing The Equation Of A Straight Line

Writing An Equation Of A Straight Line Using A Slope And A General Point

Writing An Equation Of A Straight Line Using Two Points

Writing An Equation Of A Straight Line When The Line Is Represented Graphically

Exponential And Logarithmic Functions

Applications

Applying And Analysing Exponential And Logarithmic Functions

Applying The Laws Of Exponents To Interpret Expressions For Exponential Functions

Expressing The Solution Of Exponential Models (ab^(ct) = D) Where The Base Is B As Logarithms Using Technology

Observing That A Quantity Increasing As An Exponential Function Eventually Exceeds A Quantity Increasing As A Polynomial Function

Solving Real-world Problems Involving Exponential And/or Logarithmic Functions (including Modelling)

Understanding And Using The Inverse Relationship Between Exponential And Logarithmic Functions To Solve Problems

Comparing Function Types

Comparing Exponential & Polynomial Growth

Identifying Linear Vs Exponential Models

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

Exponential Functions

Graphing Exponential And Logarithmic Functions

Graphing Exponential Functions (including Growth/decay), Showing Intercepts And End Behavior

Performing Multiple Transformations On Different Exponential/logarithmic Functions (including Writing The Final Function)

Rewriting Exponential Functions To Reveal Properties

Interpreting Exponential Functions

Understanding Exponential And Logarithmic Functions

Identifying And Evaluating Exponential Functions

Proving That Exponential Functions Grow Or Decay By Equal Factors Over Equal Intervals

Recognising Situations And Solving Problems In Which A Quantity Grows Or Decays By A Constant Percent Rate

Writing And Interpreting Exponential Functions

Constructing An Exponential Function (including Geometric Sequences) From A Description

Constructing An Exponential Function (including Geometric Sequences) From A Graph

Constructing An Exponential Function (including Geometric Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters In An Exponential Function In Terms Of A Context

Function Relationships

Constructing Linear & Exponential Functions

Interpreting Parameters In Linear/exponential Functions

Understanding Inverse Of Exponents & Logarithms

Logarithmic Functions

Evaluating Logarithms In Exponential Models

Graphing Symbolic Functions

Graphing Exponential, Logarithmic & Trigonometric Functions

Graphing Logarithmic Functions, Showing Intercepts And End Behavior

Understanding Exponential And Logarithmic Functions

Applying The Laws Of Logarithms To Simplify/evaluate Expressions

Function Concepts

Functions (general)

Analyzing Functions

Analyzing & Sketching Graphs Of Functions

Comparing Properties Of Functions

Comparing Properties Of Two Functions That Are Represented Either Algebraically, Graphically, In Tables And/or Using Verbal Statements

Identifying Whether A Given Relation Is A Function

Writing And Interpreting Functions

Calculating/estimating And Interpreting The Average Rate Of Change (including Using The Initial Value Of The Function)

Understanding Functions

Graphing Functions

Graphing A Function Using Ordered Pairs (including Relating A Domain Of A Function To Its Graph)

Understanding Functions & Their Graphs

Understanding Functions

Classifying Equations/functions As Showing Direct Variation, Inverse Variation Or Neither

Understanding That A Function Is A Mapping From One Set Of Inputs (called The Domain) To Another Set Of Outputs (called The Range)

Functions (linear)

Linear Function Concepts

Interpreting Linear & Non-linear Functions

Modeling & Interpreting Linear Functions

Understanding Linear Functions

Distinguishing Between Linear And Non-linear Functions

Working With Linear Functions

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Description/equation

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Graph

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Linear Functions

Graphing Linear Functions

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

Understanding Linear Functions

Recognising Situations In Which One Quantity Changes At A Constant Rate With Respect To Another Quantity

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Description/equation

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Graph

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters Of A Linear Function In Terms Of A Context

Quadratic Functions

Applying And Analysing Quadratic Functions

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation/completing Square To Find/show Zeroes, Extreme Values And Symmetry On Graphs Of Quadratic Functions

Graphing Symbolic Quadratic Functions

Graphing Linear & Quadratic Functions

Graphing Quadratic Functions

Graphing Quadratic Functions (including Showing Intercepts, Maxima Or Minima)

Transformations On Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Interpreting Quadratic Graphs Via Factoring

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Specific Functions

Advanced Functions

Graphing Complex Functions

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Graphing Functions

Graphing Various Function Types

Identifying Effects Of Transformations On Graphs

Identifying Function Families

Identifying/finding Turning Points

Recursive Functions

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Understanding Sequences As Recursive Functions

Exponential And Logarithmic Functions

Applications Of Exponential And Logarithmic Functions

Applying And Analysing Exponential And Logarithmic Functions

Applying The Laws Of Exponents To Interpret Expressions For Exponential Functions

Comparing Exponential And Polynomial Growth Rates

Expressing Solutions Of Exponential Models Using Logarithms

Solving Real-world Problems With Exponential/logarithmic Functions

Using The Inverse Relationship Between Exponential And Logarithmic Functions

Understanding Exponential And Logarithmic Functions

Applying The Laws Of Logarithms

Identifying And Evaluating Exponential Functions

Proving Properties Of Exponential Growth/decay

Recognising Situations Involving Constant Percent Rates

Writing And Interpreting Exponential Functions

Constructing Exponential Functions From Various Representations

Interpreting Parameters In Exponential Contexts

Exponential Models

Comparing Exponential & Polynomial Growth

Constructing Linear & Exponential Functions

Identifying Linear Vs Exponential Models

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

Interpreting Parameters In Linear/exponential Functions

Rewriting Exponential Functions To Reveal Properties

Interpreting Exponential Functions

Logarithmic Functions

Evaluating Logarithms In Exponential Models

Graphing Exponential And Logarithmic Functions

Graphing Exponential Functions (including Growth/decay)

Graphing Logarithmic Functions

Performing Multiple Transformations On Functions

Understanding Inverse Of Exponents & Logarithms

Linear Functions

Graphing Linear Functions

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

Understanding Linear Functions

Recognising Situations In Which One Quantity Changes At A Constant Rate With Respect To Another Quantity

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function From Different Representations

Interpreting The Parameters Of A Linear Function In Terms Of A Context

Quadratic Functions

Expressions In Equivalent Forms

Quadratic Equations

Factoring Quadratics

Max/min Of Quadratic Functions

Transforming Exponential Functions

Graphing And Analyzing Quadratics

Graphing Symbolic Quadratic Functions

Graphing Linear & Quadratic Functions

Graphing Quadratic Functions

Graphing Quadratic Functions (including Showing Intercepts, Maxima Or Minima)

Transformations On Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Interpreting Quadratic Graphs Via Factoring

Working With Quadratic Functions

Applying And Analysing Quadratic Functions

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation/completing Square To Find/show Zeroes, Extreme Values And Symmetry On Graphs Of Quadratic Functions

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Trigonometric Functions

Applications Of Trigonometric Functions

Applying And Analysing Trigonometric Functions

Applying The Unit Circle To Explain Symmetry And Periodicity

Applying Trigonometric Identities And Formulas

Evaluating And Interpreting Trigonometric Equation Solutions

Solving Real-world Problems With Trigonometric Functions

Using Inverse Functions To Solve Trigonometric Equations

Understanding Trigonometric Functions

Extension Of Trig Functions Via Unit Circle

Understanding Radian Measure Of An Angle

Understanding Trigonometric Functions

Understanding And Using The Unit Circle To Extend Trigonometric Functions To All Real Numbers

Unit Circle: Symmetry & Periodicity In Trig Functions

Using Special Triangles & Unit Circle In Trigonometry

Working With Trigonometric Functions

Graphing Trigonometric Functions

Graphing The Sine And Cosine Functions (including Transformations)

Modeling Periodic Phenomena With Trig Functions

Proving & Applying Trig Addition/subtraction

Proving & Using Pythagorean Trigonometric Identity

Solving Trigonometric Equations With Inverse Functions

Understanding Inverse Of Restricted Trigonometric Functions

Trigonometric Functions

Graphing Trig Functions

Graphing Trigonometric Functions

Graphing The Sine And Cosine Functions (including Transformations)

Solving Trig Equations

Evaluating And Interpreting The Solutions To Trigonometric Equations In Real-world Contexts Using Technology

Solving Real-world Problems Involving Trigonometric Functions (including Frequencies And Modelling)

Using Inverse Functions To Solve Trigonometric Equations

Using Inverse Functions To Solve Trigonometric Equations Using Technology And/or Intrepret The Solutions

Trigonometric Applications

Modeling Periodic Phenomena With Trig Functions

Solving Trigonometric Equations With Inverse Functions

Understanding Inverse Of Restricted Trigonometric Functions

Trigonometric Basics

Extension Of Trig Functions Via Unit Circle

Understanding Radian Measure Of An Angle

Unit Circle: Symmetry & Periodicity In Trig Functions

Using Special Triangles & Unit Circle In Trigonometry

Trigonometric Identities

Applying And Analysing Trigonometric Functions

Proving & Applying Trig Addition/subtraction

Proving & Using Pythagorean Trigonometric Identity

Understanding Trig Functions

Understanding Trigonometric Functions

Understanding And Using The Unit Circle To Extend Trigonometric Functions To All Real Numbers (both Degrees And Radians)

Types Of Functions

Advanced Functions

Applying And Analysing Functions

Graphing Symbolic Functions & Key Features

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Graphing Functions

Understanding Sequences As Recursive Functions

Exponential And Logarithmic Functions

Function Sequence Relationships

Functions (sequence/series)

Arithmetic & Geometric Sequences: Recursive & Explicit

Linear Functions

Graphing Linear Functions

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

Understanding Linear Functions

Recognising Situations In Which One Quantity Changes At A Constant Rate With Respect To Another Quantity

Writing And Interpreting Linear Functions

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Description/equation

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Graph

Identifying/constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Interpreting The Parameters Of A Linear Function In Terms Of A Context

Quadratic Functions

Applying And Analysing Quadratic Functions

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation/completing Square To Find/show Zeroes, Extreme Values And Symmetry On Graphs Of Quadratic Functions

Graphing Symbolic Quadratic Functions

Graphing Linear & Quadratic Functions

Graphing Quadratic Functions

Graphing Quadratic Functions (including Showing Intercepts, Maxima Or Minima)

Transformations On Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Interpreting Quadratic Graphs Via Factoring

Understanding Quadratic Functions

Identifying Characteristics Of Quadratic Functions

Writing And Interpreting Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

Trigonometric Functions

Geometry

Angles

Angle Measurement

Understanding And Measuring Angles

Understanding That An Angle That Turns Through 'n' One-degree Angles Has An Angle Measure Of 'n' Degrees

Angle Relationships

Solving Equations For Unknown Angles

Solving Problems Involving Angles And Equations

Applying Facts About Complementary Angles To Solve Problems

Applying Facts About Supplementary Angles To Solve Problems

Applying Facts About Two Or More Types Of Angles (vertically Opposite, Complementary, Supplementary, Adjacent) To Solve Problems

Applying Facts About Vertically Opposite Angles To Solve Problems

Understanding Triangle Angles & Similarity

Understanding And Measuring Angles

Understanding That An Angle That Turns Through 'n' One-degree Angles Has An Angle Measure Of 'n' Degrees

Drawing Angles

Acute, Obtuse, And Right Angles

Naming Angles Using Points

Problem Solving With Angles

Unknown Angles

Understanding Angles

Additive Property Of Angles

Angle Measurement

Area

Circles

Applying The Understanding Of The Area Of A Circle To Solve Problems

Deriving The Relationship Between The Circumference And Area Of A Circle

Recalling And Using The Formulae For The Area Of A Circle To Solve Problems

Circle Area & Circumference Formulas Usage

Irregular Shapes

Measuring And Estimating Area Of Miscellaneous Shapes

Calculating And Comparing Areas Of Similar Polygons

Calculating Areas Of Irregular Polygons

Polygons

Area Of Irregular Figures

Area Of Quadrilaterals

Area Of Triangles

Area And Volume

Area

Measuring And Estimating Area Of Miscellaneous Shapes

Calculating Areas Of Irregular Polygons

Volume

Basic Geometry

Expressing Properties With Equations

Solving Geometry Problems With Line Slopes

Fundamental Concepts

Proving Theorems: Lines & Angles

Understanding Basic Geometry Definitions

Understanding And Measuring Angles

Understanding That An Angle That Turns Through 'n' One-degree Angles Has An Angle Measure Of 'n' Degrees

Geometric Elements

Drawing And Identifying Geometric Elements

Drawing And Understanding Skew Lines And Planes

Drawing And Identifying Pairs Of Lines

Drawing And Identifying Parallel And/or Perpendicular Lines

Geometric Properties

Proving And Using Geometric Properties

Using The Angle Bisector Theorem To Solve Problems

Using The Perpendicular Bisector Theorem To Solve Problems

Geometric Terminology

Naming Geometric Elements

Naming Points, Line Segments, Rays, Lines And Planes

Understanding Key Terms

Knowing Precise Definitions Of Line Segments, Perpendicular Lines And Parallel Lines

Geometry Terminology

Naming Geometric Elements

Naming Points, Line Segments, Rays, Lines And Planes

Understanding Key Terms

Knowing Precise Definitions Of Line Segments, Perpendicular Lines And Parallel Lines

Circles And Conic Sections

Composing Shapes

Building With Shapes

Combining Shapes

Congruence And Similarity

Applications

Applying Congruency And/or Similarity To Solve Problems

Use Congruency Criteria To Solve Problems

Use Similarity Criteria To Solve Problems

Congruence

Applying Congruency To Solve Problems

Use Congruency Criteria To Solve Problems

Congruence Of Triangles Via Rigid Motions

Transforming Figures & Determining Congruence

Triangle Congruence Via Rigid Motions

Understanding Congruency

Establishing The Conditions Necessary For Two Triangles To Be Congruent

Reasoning How Two Figures Are Congruent Using Transformations

Similarity

Applying Similarity To Solve Problems

Use Similarity Criteria To Solve Problems

Establishing Aa Criterion For Similar Triangles

Identifying Similarity In Triangles Using Transformations

Triangle Congruence & Similarity Problem Solving

Understanding Similarity

Describing A Sequence Of Transformations To Demonstrate Similarity Between Two Figures

Establishing The Conditions Necessary For Two Triangles To Be Similar

Identifying Similar Figures

Mathematical Practices

Math Puzzles And Logic

Mathematical Communication

Mathematical Reasoning

Modeling And Tools

Appropriate Tool Selection

Mathematical Models

Technology Use In Mathematics

Problem Solving

Reasoning And Proof

Logical Reasoning

Mathematical Arguments

Pattern Recognition

Mathematics Connections

Digital Tools

Math In Art

Math In Daily Life

Measurement

Unit Conversions

Applying Unit Rates To Conversions

Converting Within Measurement Systems

Solving Real-world Measurement Problems

Working With Units

Choosing Appropriate Units

Converting Between Related Units

Multiple-step Conversions

Measurement And Data

Data

Measurement Concepts

Money

Time

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

Ratio Concepts

Ratio Applications

Calculating Percentages

Measurement Conversions

Solving Rate Problems

Understanding Ratios

Calculating Unit Rates

Comparing Ratios

Representing Ratios

Ratio And Proportion

Solving Ratio Problems

Applying Proportional Relationships To Solve Multi-step Problems

Applying Proportional Relationships To Solve Multi-step Problems Involving Percentages And/or Ratios

Calculating Unit Rates With Fraction Ratios

Solving Multistep Ratio & Percent Problems

Understanding Proportional Relationships

Recognising And Representing Proportional Relationships Between Quantities

Representing Proportional Relationships

Identifying Proportional Relationships

Identifying Unit Rates (tables, Graphs, Equations Etc.)

Representing Proportion Relationships Using Equations

Representing Proportion Relationships Using Graphs

Understanding And Applying Equivalent Ratios

Unit Rates

Understanding Ratio Notation, Rate Language And Unit Rates

Calculating Unit Rates Associated With Ratios Of Fractions

Statistics And Probability

Basic Statistical Concepts

Understanding Statistical Variability (qualitative)

Recognising A Statistical Question

Basic Statistics

Statistical Questions

Understanding Statistical Variability (qualitative)

Recognising A Statistical Question

Basic Statistics And Visual Representations

Bivariate Statistics

Scatter Plots

Calculate & Interpret Correlation Coefficient

Correlation Vs Causation Distinction

Interpreting Frequencies & Trends In Data

Interpreting Slope & Intercept In Data Context

Scatter Plot Representation & Variable Relation

Assessing Function Fit Via Residual Analysis

Fit & Use Functions To Solve Data Problems

Fit Linear Function For Scatter Plot

Understanding And Applying Scatter Plots

Analyzing Residuals To Assess Model Fit

Distinguishing Between Correlation And Causation

Finding And Interpreting Correlation Coefficients

Fitting Lines And Functions To Data

Interpolating And Extrapolating With Linear Models

Using Fitted Functions To Solve Contextual Problems

Two-way Tables

Identifying And Interpreting Patterns Of Association

Calculating And Interpreting Relative Frequencies

Describing Possible Associations In Data

Interpreting Two-way Tables For Categorical Variables

Investigating Patterns In Scatter Plots

Bivariate Data

Linear Models

Applying The Fitted Straight Line To Identify Relationships And Solve Problems (including Interpreting Slopes And Intercepts)

Modeling & Assessing Linear Relationships

Solving Problems Using Linear Model Equations

Scatter Plots

Interpreting Scatter Plots & Data Patterns

Understanding And Applying Scatter Plots

Drawing Scatter Plots

Fitting A Straight Line And Assessing Its Fit (informally)

Interpreting Scatter Plots

Scatter Plots And Correlation

Calculate & Interpret Correlation Coefficient

Correlation Vs Causation Distinction

Interpreting Frequencies & Trends In Data

Interpreting Slope & Intercept In Data Context

Scatter Plot Representation & Variable Relation

Assessing Function Fit Via Residual Analysis

Fit & Use Functions To Solve Data Problems

Fit Linear Function For Scatter Plot

Understanding And Applying Scatter Plots

Two-way Tables

Identifying And Interpreting Patterns Of Association

Interpreting Associations In Bivariate Categorical Data

Data

Data Analysis

Interpreting Data

Data Representation

Organising And Representing Data

Representing Data Using Box-and-whisker Plots

Representing Data Using Circle Graphs (pie Charts)

Representing Data Using Dot Plots

Representing Data Using Histograms

Data Visualization

Organising And Representing Data

Representing Data Using Box-and-whisker Plots

Representing Data Using Dot Plots

Representing Data Using Histograms

Data Analysis

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Understanding Fractions - Unit Rates - Mathematical Problem Solving

7th Grade

Math

Develop proficiency in fraction manipulation by applying concepts to real-world scenarios, with a focus on calculating unit rates. Enhance the ability to identify and work with numerators and denominators to tackle complex problems effectively.

7th Grade - 8th Grade

Unit Rate Calculations - Challenge Problems - Mathematics

Presentation

Unit Rate Calculations - Challenge Problems - Mathematics

7th Grade - 8th Grade

Math

Engage with unit rate calculations through word problems that enhance skills in identifying and solving complex scenarios involving rates. Focus on developing proficiency in understanding and applying rates effectively.

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