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Math

Algebra

Algebraic Expressions

Analyzing Expressions

Interpreting Expressions

Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Rewriting Expressions Using Structure

Writing, Reading, And Evaluating Algebraic Expressions

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

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

Interpreting And Manipulating Expressions

Interpreting Expressions

Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Rewriting Expressions Using Structure

Writing, Reading, And Evaluating Algebraic Expressions

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

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

Interpreting And Rewriting Expressions

Interpreting Expressions

Intepreting Complicated Expressions

Interpreting Terms, Factors, Coefficients

Rewriting Expressions Using Structure

Writing, Reading, And Evaluating Algebraic Expressions

Interpreting Parts Of An Algebraic Expression In Terms Of A Context

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

Manipulating Expressions

Applying Properties Of Operations

Factoring Expressions

Generating Equivalent Expressions

Simplifying Algebraic Expressions

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

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

Simplifying Expressions

Operations With Rational Expressions

Operations On Rational Algebraic 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

Operations With Rational Expressions

Rational Expressions

Operations On Rational Algebraic 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

Operations With Rational Expressions

Simplifying Rational Expressions

Simplifying Expressions

Simplifying Algebraic Expressions

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

Simplifying Rational Expressions

Simplifying Algebraic Expressions

Understanding Expressions

Evaluating Expressions

Identifying Parts Of Expressions

Solving Multi-step Problems With Rational Numbers

Translating Verbal Descriptions To Expressions

Understanding Expressions & Quantity Relations

Writing And Evaluating Expressions

Writing, Reading, And Evaluating Algebraic Expressions

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

Writing, Reading, And Evaluating Algebraic Expressions

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

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

Linear Equations

Absolute Value Equations

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

Solving Absolute Value Equations With Extraneous Solutions

Solving Equations Where Absolute Value Expressions Are On One Side Of The The Equation

Multi-variable Linear Equations

Graphing Multi-variable Equations

Solving Linear Equation Systems (exact & Approximate)

Solving Pairs Of Linear Equations In Two Variables

Solving System Of Equations

System Of Equations Word Problems

Understanding Solutions To Linear Equations In Two Variables

Understanding And Solving Linear Equations In Three Variables

Solving A System Of Linear Equations In Three Variables Algebraically

Solving Real-world Problems Involving Multi-step Linear Equations In Three Variables

Understanding Pairs Of Linear Equations In Two Variables

Writing A Linear Equation In Two Variables In The Standard Form (ax + By + C = 0)

One-variable Linear Equations

Solving Linear Equations And Inequalities

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

Solving Absolute Value Equations With Extraneous Solutions

Solving Equations Where Absolute Value Expressions Are On One Side Of The The Equation

Solving Multi-step Problems Using Linear Equations In One Variable

Solving Linear Equations In One Variable, Where Coefficients Are Represented By Letters

Solving Linear Equations And Inequalities

Three-variable Linear Equations

Understanding And Solving Linear Equations In Three Variables

Solving A System Of Linear Equations In Three Variables Algebraically

Solving Real-world Problems Involving Multi-step Linear Equations In Three Variables

Two-variable Linear Equations

Graphing Multi-variable Equations

Solving Linear Equation Systems (exact & Approximate)

Solving Pairs Of Linear Equations In Two Variables

Solving Systems Of Linear Equations Using Elimination, Substitution, And Graphing

Solving Systems With No Solution Or Infinitely Many Solutions

Using The Inverse Of A Matrix To Solve Systems Of Linear Equations

Understanding Pairs Of Linear Equations In Two Variables

Writing A Linear Equation In Two Variables In The Standard Form (ax + By + C = 0)

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 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

Matrix Equations

Solving Equations With Matrices

Inverse Matrix To Solve Equations

Matrix Representation Of Linear Equations

Non-linear Equations

Multi-variable Non-linear Equations

Non-linear Inequalities

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

Solving Quadratic Inequalities In One Variable (algebraically Or Graphically)

Other Non-linear Equations

Framing Non-linear Equations

Solving Multi-step Problems Using Non-linear 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)

Solving Radical Equations

Steps In Solving Non-linear Equations

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

Framing Non-linear Equations In One Variable

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

Quadratic Equations

Completing The Square & Deriving Quadratic Formula

Quadratic Equations

Factoring Quadratics

Max/min Of Quadratic Functions

Transforming Exponential Functions

Solving Multi-step Problems Using Quadratic Equations In One Variable

Solving Quadratic Equations

Completing The Square & Deriving Quadratic Formula

Solving Quadratic Equations

Understanding Quadratic Equations In One Variable

Recognising When A Quadratic Equation Has Complex Solutions Using The Discriminant

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

Systems With Non-linear Equations

Other Non-linear Equations

Framing Non-linear Equations

Solving Multi-step Problems Using Non-linear 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)

Solving Radical Equations

Steps In Solving Non-linear Equations

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

Framing Non-linear Equations In One Variable

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

Quadratic Equations

Solving Multi-step Problems Using Quadratic Equations In One Variable

Solving Quadratic Equations

Completing The Square & Deriving Quadratic Formula

Solving Quadratic Equations

Understanding Quadratic Equations In One Variable

Recognising When A Quadratic Equation Has Complex Solutions Using The Discriminant

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

Systems Of Equations

Matrix Methods

Solving Equations With Matrices

Inverse Matrix To Solve Equations

Matrix Representation Of Linear Equations

Multi-variable Non-linear Equations

Systems With Non-linear 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

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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Mathematical Skills - Real-World Applications - Understanding Fractions

6th Grade - 8th Grade

Math

Investigate the significance and applications of fractions in everyday scenarios. Aim to develop skills for applying fractions effectively in areas such as cooking and finance, enhancing practical understanding and computational proficiency.

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1. 2021 survey of 800+ teachers conducted by Wayground

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