Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

Writing Expressions In Different Forms To Demonstrate How The Quantities Are Related

Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

Writing Expressions In Different Forms To Demonstrate How The Quantities Are Related

Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

Writing Expressions In Different Forms To Demonstrate How The Quantities Are Related

Applying Properties Of Operations To Add And/or Subtract Linear Expressions

Applying Properties Of Operations To Expand And/or Factor Linear Expressions

Adding And/or Subtracting Rational Algebraic Expressions

Knowing That Rational Algebraic Expressions Are Closed Under The Operations Of Addition, Subtraction, Multiplication And Division

Multiplying Two Or More Rational Algebraic Expressions

Rewriting Rational Algebraic Expressions By Cancelling Out Common Non-zero Factors

Writing A(x)/b(x) In The Form Of Q(x) + R(x)/b(x), With The Degree Of R(x) Less Than The Degree Of B(x) Using Either Inspection Or Technology

Adding And/or Subtracting Rational Algebraic Expressions

Knowing That Rational Algebraic Expressions Are Closed Under The Operations Of Addition, Subtraction, Multiplication And Division

Multiplying Two Or More Rational Algebraic Expressions

Rewriting Rational Algebraic Expressions By Cancelling Out Common Non-zero Factors

Writing A(x)/b(x) In The Form Of Q(x) + R(x)/b(x), With The Degree Of R(x) Less Than The Degree Of B(x) Using Either Inspection Or Technology

Applying Properties Of Operations To Simplify Algebraic Expressions Involving Exponents And/or Radicals

Writing Expressions In Different Forms To Demonstrate How The Quantities Are Related

Solving Multi-step Problems Involving Absolute Value Linear Equations In One Variable

Graphing Multi-variable Equations

Solving Linear Equation Systems (exact & Approximate)

Solving Pairs Of Linear Equations In Two Variables

Solving System Of Equations

Understanding And Solving Linear Equations In Three Variables

Understanding Pairs Of Linear Equations In Two Variables

Solving Linear Equations And Inequalities

Solving Multi-step Problems Involving Absolute Value Linear Equations In One Variable

Solving Multi-step Problems Using Linear Equations In One Variable

Understanding And Solving Linear Equations In Three Variables

Graphing Multi-variable Equations

Solving Linear Equation Systems (exact & Approximate)

Solving Pairs Of Linear Equations In Two Variables

Understanding Pairs Of Linear Equations In Two Variables

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

Solving/interpreting Linear Inequalities In One Variable

Framing/writing Linear Inequalities In Two Variables

Graphing Linear Inequalities

Representing Solutions Of Linear Inequalities In Two Variables On A Graph

Solutions In Equation Modeling

Solving/interpreting Linear Inequalities In Two Variables

Inverse Matrix To Solve Equations

Matrix Representation Of Linear Equations

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

Framing Non-linear Equations

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

Solving Radical Equations

Steps In Solving Non-linear Equations

Understanding Multi-step Problems Involving Non-linear Equations In One Variable

Completing The Square & Deriving Quadratic Formula

Quadratic Equations

Solving Multi-step Problems Using Quadratic Equations In One Variable

Solving Quadratic Equations

Understanding Quadratic Equations In One Variable

Explaining And Justifying Each Step In Solving A Non-linear Equation

Solving Exponential Equations In One Variable (including Unlike Bases)

Solving Logarithmic Equations In One Variable

Solving Radical Equations In One Variable (including Extraneous Solutions)

Solving Rational Equations In One Variable (including Extraneous Solutions)

Framing Non-linear Equations In One Variable

Representing Constraints By Linear Or Non-linear Equations In One Variable

Completing The Square & Deriving Quadratic Formula

Solving Quadratic Equations

Recognising When A Quadratic Equation Has Complex Solutions Using The Discriminant

Writing A Quadratic Equation In The Standard Form (ax^2 + Bx + C = 0)

Solving Equations With Matrices

Solving A System Consisting Of A Linear Equation And A Quadratic Equation In Two Variables Algebraically

Solving A System Consisting Of A Linear Equation And A Quadratic Equation In Two Variables Graphically

Framing Non-linear Equations In Two Or More Variables To Represent Relationships Between Quantities (including Graphing)

Rearranging And Using Formulae To Highlight A Quantity Of Interest

Representing A System Of Linear Equations As A Single Matrix Equation

Representing Constraints By Linear Or Non-linear Equations In Two Or More Variables

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

Solving/interpreting Linear Inequalities In One Variable

Framing/writing Linear Inequalities In Two Variables

Graphing Linear Inequalities

Representing Solutions Of Linear Inequalities In Two Variables On A Graph

Solutions In Equation Modeling

Solving/interpreting Linear Inequalities In Two Variables

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

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

Two Step Equations

Graphing Polynomial Functions & Identifying Zeros

Graphing Rational Functions With Zeros & Asymptotes

Graphing Root, Piecewise, Step & Absolute Value Functions

Arithmetic & Geometric Sequences: Recursive & Explicit

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

Identifying Constant Percent Growth/decay

Proving Growth Patterns In Linear & Exponential Functions

Recognizing Constant Rate Of Change

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

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

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

Graphing Exponential, Logarithmic & Trigonometric Functions

Applying The Laws Of Logarithms To Simplify/evaluate Expressions

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

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

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)

Distinguishing Between Linear And Non-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

Graphing Symbolic Functions & Key Features

Graphing Functions

Functions (sequence/series)

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/exponential Functions

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/constructing A Linear Function From Different Representations

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/subtraction

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)

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

Arithmetic & Geometric Sequences: Recursive & Explicit

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/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

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 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/or Perpendicular Lines

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

Use Congruency Criteria To Solve Problems

Use Similarity Criteria 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/or Subtract Complex Numbers

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

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

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

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

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

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

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

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/or Dividing Decimal Numbers Using The Standard Algorithm

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/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

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

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

Adding And/or Subtracting Radicals

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

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

Multiplying And/or Dividing Radicals

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

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

Adding And/or Subtracting Matrices Of Appropriate Dimensions

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/or Multiplication Of Matrices

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/or Subtracting Matrices Of Appropriate Dimensions

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

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

Identifying Proportional Relationships

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

Representing Proportion Relationships Using Equations

Representing Proportion Relationships Using Graphs

Calculating Unit Rates Associated With Ratios Of Fractions

Recognising A Statistical Question

Assessing Function Fit Via Residual Analysis

Fit & Use Functions To Solve Data Problems

Fit Linear Function For Scatter Plot

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

Calculating And Interpreting Relative Frequencies

Describing Possible Associations In Data

Interpreting Two-way Tables For Categorical Variables

Investigating Patterns In Scatter Plots

Drawing Scatter Plots

Fitting A Straight Line And Assessing Its Fit (informally)

Interpreting Scatter Plots

Assessing Function Fit Via Residual Analysis

Fit & Use Functions To Solve Data Problems

Fit Linear Function For Scatter Plot

Representing Data Using Box-and-whisker Plots

Representing Data Using Circle Graphs (pie Charts)

Representing Data Using Dot Plots

Representing Data Using Histograms

Representing Data Using Box-and-whisker Plots

Representing Data Using Dot Plots

Representing Data Using Histograms