Or Comparing Proportional Relationships

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

Solving

Framing

Graphing Linear Inequalities

Representing Solutions Of Linear Inequalities In Two Variables On A Graph

Solutions In Equation Modeling

Solving

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

Solving Quadratic Inequalities In One Variable (algebraically Or Graphically)

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

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

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

No Solution

Two Step Equations

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Series)

Or Vertical Line

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

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

Identifying Constant Percent Growth

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

Graphing Exponential Functions (including Growth

Performing Multiple Transformations On Different Exponential

Interpreting Exponential 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

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

Exponential Functions

Graphing Exponential, Logarithmic & Trigonometric Functions

Applying The Laws Of Logarithms To Simplify

Or Using Verbal Statements

Calculating

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

Classifying Equations

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

Distinguishing Between Linear And Non-linear Functions

Identifying

Constructing A Linear Function (including Arithmetic Sequences) From A Description

Constructing A Linear Function (including Arithmetic Sequences) From A Graph

Constructing A Linear Function (including Arithmetic Sequences) From A Set Of Input-output Pairs

Completing Square To Find

Graphing Symbolic Functions & Key Features

Graphing Functions

Functions (sequence

Understanding Sequences As Recursive Functions

Applying And Analysing Exponential And Logarithmic Functions

Understanding Exponential And Logarithmic Functions

Writing And Interpreting Exponential Functions

Comparing Exponential & Polynomial Growth

Constructing Linear & Exponential Functions

Identifying Linear Vs Exponential Models

Interpreting Parameters In Linear

Rewriting Exponential Functions To Reveal Properties

Evaluating Logarithms In Exponential Models

Graphing Exponential And Logarithmic Functions

Understanding Inverse Of Exponents & Logarithms

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

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

Identifying

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

Quadratic Equations

Graphing Symbolic Quadratic Functions

Graphing Quadratic Functions

Rewriting Quadratic Functions To Reveal Properties

Applying And Analysing Quadratic Functions

Understanding Quadratic Functions

Writing And Interpreting Quadratic Functions

Applying And Analysing Trigonometric Functions

Extension Of Trig Functions Via Unit Circle

Understanding Radian Measure Of An Angle

Understanding Trigonometric Functions

Unit Circle: Symmetry & Periodicity In Trig Functions

Using Special Triangles & Unit Circle In Trigonometry

Graphing Trigonometric Functions

Modeling Periodic Phenomena With Trig Functions

Proving & Applying Trig Addition

Proving & Using Pythagorean Trigonometric Identity

Solving Trigonometric Equations With Inverse Functions

Understanding Inverse Of Restricted Trigonometric Functions

Graphing The Sine And Cosine Functions (including Transformations)

Or Intrepret The Solutions

Subtraction

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

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Series)

Graphing Linear Functions And Showing Intercepts

Transformations On Absolute Value Linear Functions

Transformations On Linear Functions

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

Identifying

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

Solving Real-world Problems Involving Quadratic Functions

Using The Process Of Factorisation

Graphing Linear & Quadratic Functions

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

Transformations On Quadratic Functions

Interpreting Quadratic Graphs Via Factoring

Identifying Characteristics Of Quadratic Functions

Writing A Quadratic Function Under Specific Conditions

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

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

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

Calculating And Comparing Areas Of Similar Polygons

Calculating Areas Of Irregular Polygons

Calculating Areas Of Irregular Polygons

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

Drawing And Understanding Skew Lines And Planes

Drawing And Identifying Parallel And

Using The Angle Bisector Theorem To Solve Problems

Using The Perpendicular Bisector Theorem To Solve Problems

Naming Points, Line Segments, Rays, Lines And Planes

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

Naming Points, Line Segments, Rays, Lines And Planes

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

Or Similarity To Solve Problems

Use Congruency Criteria To Solve Problems

Establishing The Conditions Necessary For Two Triangles To Be Congruent

Reasoning How Two Figures Are Congruent Using Transformations

Use Similarity Criteria To Solve Problems

Describing A Sequence Of Transformations To Demonstrate Similarity Between Two Figures

Establishing The Conditions Necessary For Two Triangles To Be Similar

Identifying Similar Figures

Applying Conjugates To Find Quotients

Finding The Conjugate Of A Complex Number

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

Using Different Properties (commutative, Associative) To Add And

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

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

Finding The Modulus And

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

Using Different Properties (commutative, Associative) To Add And

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

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

Finding The Modulus And

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

Applying Conjugates To Find Quotients

Finding The Conjugate Of A Complex Number

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

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

Dividing Decimal Numbers Using Place Value Strategies

Dividing Decimal Numbers Using Properties Of Operations

Estimating Products And Quotients Using Rounding

Multiplying And

Multiplying Decimal Numbers Using Place Value Strategies

Multiplying Decimal Numbers Using Properties Of Operations

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

Understanding Irrational Numbers

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

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

Adding And

Solving Word Problems Involving Addition And

Or Mixed Numbers

Or Mixed Numbers

Adding And

Explaining

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

Multiplying And

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

Explaining

Explaining

Adding And

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

Solving Problems Involving A Mix Of Addition, Subtraction And

Finding The Inverse Of A Matrix (if It Exists)

Representing And Manipulating Data Through Matrices

Finding The Inverse Of A Matrix (if It Exists)

Representing And Manipulating Data Through Matrices

Adding And

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

Equal To

More Than

Ordering Numbers

Counting Backward From 10

Counting Forward 1-20

One-to-one Correspondence

Skip Counting By 2s And 5s (introduction)

Identifying Numbers 0-10

Identifying Numbers 11-20

Number Words

Finding Factor Pairs

Prime And Composite Numbers

Determining Multiples

Relationship Between Factors And Multiples

Ordering Three-digit Numbers

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

Even And Odd Numbers

Identifying Patterns On Number Lines

Skip Counting

Models And Expanded Form

Number Names

Reading And Writing Numbers

Understanding Hundreds, Tens, And Ones

Comparing Numbers

Comparing Numbers Above 1000

Rounding To Any Place

Rounding To Nearest 10, 100, Or 1000

Understanding Factors And Multiples

Integer Operations

Operations Properties

Rational Number Operations

Analyzing Patterns

Explaining Patterns Using Properties

Generating Number Patterns

Generating Shape Patterns

Identifying And Extending Patterns

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

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.

Simplifying Expressions Involving Rational Exponents Using The Laws Of Exponents

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

Defining Quantities For Descriptive Modeling

Interpreting Units & Scales In Problem Solving

Selecting Accuracy Level For Quantity Reporting

Finding 10 Or 100 More

Estimation

Using Place Value Strategies

Using Properties Of Operations

Using The Standard Algorithm

Estimation

Using Place Value Strategies