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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

Linear Equations (two Variables)

Systems Of Linear Equations

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 Pairs Of Linear Equations In Two Variables

Linear Inequalities (one Variable)

Applications Of Inequalities

Solving/interpreting Linear Inequalities In One Variable

Solving And/or Interpreting Compound Inequalities

Solving And/or Interpreting Inequalities (px + Q ≤ R Or Px + Q ≥ R Forms)

Solving Real-world Problems Involving Multi-step Linear Inequalities In One Variable

Solving Inequalities

Framing/solving Inequalities

One And Two Step Inequalities

Framing/writing Linear Inequalities In One Variable

Framing Compound Inequalities In The Context Of Different Problems

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

Solving/interpreting Linear Inequalities In One Variable

Understanding And Representing Inequalities

Framing/writing Linear Inequalities In One Variable

Framing Compound Inequalities In The Context Of Different Problems

Framing Inequalities (px + Q ≤ R Or Px + Q ≥ R Forms) In The Context Of Different Problems

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

Representing Solutions Of Compound Inequalities On Number Lines

Representing Solutions Of Inequalities (px + Q ≤ R Or Px + Q ≥ R Forms) On Number Lines

Linear Inequalities (two Variables)

Understanding Linear Inequalities In Two Variables

Using Substitution To Determine Whether A Given Pair Of Numbers Makes An Inequality True

Numerical Expressions

Exponents

Evaluating Expressions With Whole Number Exponents

Writing Expressions With Whole Number Exponents

Order Of Operations

Evaluating Numerical Expressions With Multiple Operations

Interpreting Numerical Expressions

Using Parentheses, Brackets, And Braces

Problem Solving

Evaluating The Reasonableness Of Answers

Using Mental Computation And Estimation Strategies

Polynomials

Advanced Polynomial Operations

Applying The Remainder Theorem

Dividing Polynomials

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 Inspection/technology/long Division

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 The Long Division Algorithm

Factorising Polynomials

Factorising Polynomials By Finding The Gcf Or Gcd Or Hcf

Factorising Polynomials By Grouping

Factorising Polynomials That Are Of The Form Or Reducible To The Form Ax^2 + Bx + C

Using Algebraic Identities To Factorise Polynomials And/or Solve Mathematical Problems

Graphing Polynomial Zeros

Using Polynomial Identities

Algebraic Identities

Applying Algebraic Identities To Solve Problems

Using Algebraic Identities To Solve Mathematical Problems

Using Polynomial Identities

Basic Polynomial Operations

Adding And Subtracting Polynomials

Adding Two Or More Polynomials

Subtracting Polynomials

Adding, Subtracting And Multiplying Polynomials

Multiplying Polynomials

Multiplying Two Or More Monomials

Multiplying Two Or More Polynomials

Binomial Theorem

Applying Binomial Theorem

Understanding And Applying The Binomial Theorem

Determining The Coefficients Of The Binomial Expansion By Pascal’s Triangle

Stating The Binomial Theorem (n Is A Positive Integer) For The Expansion Of (x + Y)^n

Stating/using The Binomial Theorem (n Is A Positive Integer) For The Expansion Of (x + Y)^n

Using The Binomial Theorem To Solve Problems

Factoring Polynomials

Factorising Polynomials

Factorising Polynomials By Finding The Gcf Or Gcd Or Hcf

Factorising Polynomials By Grouping

Factorising Polynomials That Are Of The Form Or Reducible To The Form Ax^2 + Bx + C

Using Algebraic Identities To Factorise Polynomials And/or Solve Mathematical Problems

Operations With Polynomials

Adding And Subtracting Polynomials

Adding Two Or More Polynomials

Subtracting Polynomials

Adding, Subtracting And Multiplying Polynomials

Dividing Polynomials

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 Inspection/technology/long Division

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 The Long Division Algorithm

Multiplying Polynomials

Multiplying Two Or More Monomials

Multiplying Two Or More Polynomials

Polynomial Applications

Applying Algebraic Identities To Solve Problems

Using Algebraic Identities To Solve Mathematical Problems

Applying Binomial Theorem

Expressions In Equivalent Forms

Quadratic Equations

Factoring Quadratics

Max/min Of Quadratic Functions

Transforming Exponential Functions

Graphing Polynomial Zeros

Understanding And Applying The Binomial Theorem

Determining The Coefficients Of The Binomial Expansion By Pascal’s Triangle

Stating The Binomial Theorem (n Is A Positive Integer) For The Expansion Of (x + Y)^n

Using The Binomial Theorem To Solve Problems

Understanding Zeroes And Factors Of Polynomials

Identifying Zeroes Of Polynomials (degree > 2) When Suitable Factorisations Are Available

Stating And Applying The Factor Theorem In Reasoning With Polynomials

Stating And Applying The Remainder Theorem In Reasoning With Polynomials

Using Zeroes Of Polynomials To Sketch Their Graphs And/or Write The Polynomials

Polynomial Operations

Adding And Subtracting Polynomials

Adding Two Or More Polynomials

Subtracting Polynomials

Adding, Subtracting And Multiplying Polynomials

Dividing Polynomials

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 Inspection/technology/long Division

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 The Long Division Algorithm

Multiplying Polynomials

Multiplying Two Or More Monomials

Multiplying Two Or More Polynomials

Polynomial Theorems

Applying The Remainder Theorem

Understanding Zeroes And Factors Of Polynomials

Identifying Zeroes Of Polynomials (degree > 2) When Suitable Factorisations Are Available

Stating And Applying The Factor Theorem In Reasoning With Polynomials

Stating And Applying The Remainder Theorem In Reasoning With Polynomials

Using Zeroes Of Polynomials To Sketch Their Graphs And/or Write The Polynomials

Polynomial Theorems And Applications

Applying The Remainder Theorem

Graphing Polynomial Zeros

Understanding Zeroes And Factors Of Polynomials

Identifying Zeroes Of Polynomials (degree > 2) When Suitable Factorisations Are Available

Stating And Applying The Factor Theorem In Reasoning With Polynomials

Stating And Applying The Remainder Theorem In Reasoning With Polynomials

Using Zeroes Of Polynomials To Sketch Their Graphs And/or Write The Polynomials

Polynomial Theorems And Identities

Applying Algebraic Identities To Solve Problems

Using Algebraic Identities To Solve Mathematical Problems

Applying The Remainder Theorem

Understanding Zeroes And Factors Of Polynomials

Identifying Zeroes Of Polynomials (degree > 2) When Suitable Factorisations Are Available

Stating And Applying The Factor Theorem In Reasoning With Polynomials

Stating And Applying The Remainder Theorem In Reasoning With Polynomials

Using Zeroes Of Polynomials To Sketch Their Graphs And/or Write The Polynomials

Using Polynomial Identities

The Binomial Theorem

Applying Binomial Theorem

Understanding And Applying The Binomial Theorem

Determining The Coefficients Of The Binomial Expansion By Pascal’s Triangle

Stating The Binomial Theorem (n Is A Positive Integer) For The Expansion Of (x + Y)^n

Stating/using The Binomial Theorem (n Is A Positive Integer) For The Expansion Of (x + Y)^n

Using The Binomial Theorem To Solve Problems

Roots

Applying Roots

Solving Problems Involving Cube Roots Of Positive/negative Numbers

Solving Problems Involving Square Roots Of Positive Numbers

Evaluating Roots

Evaluating Cube Roots Of Perfect Cubes

Evaluating Square Roots Of Perfect Squares

Square And Cube Roots

Using Symbols For Solutions To Equations

Using The Cube Root Symbol For Solutions To Equations Of The Form X^3 = P

Using The Square Root Symbol For Solutions To Equations Of The Form X^2 = P

Roots And Radicals

Applications Of Roots

Applying Roots

Solving Problems Involving Nth Roots

Graphing Polynomial Zeros

Applying Roots

Solving Problems Involving Nth Roots

Evaluating Roots

Evaluating Expressions Involving Cube Roots Of Positive/negative Numbers

Evaluating Expressions Involving Nth Roots

Evaluating Expressions Involving Square Roots Of Positive Numbers

Evaluating Nth Roots

Using Symbols For Solutions To Equations

Using The Cube Root Symbol For Solutions To Equations Of The Form X^3 = P

Using The Nth Root Symbol For Solutions To Equations Of The Form X^n = P

Using The Square Root Symbol For Solutions To Equations Of The Form X^2 = P

Understanding Roots

Applying Roots

Solving Problems Involving Nth Roots

Evaluating Roots

Evaluating Expressions Involving Cube Roots Of Positive/negative Numbers

Evaluating Expressions Involving Nth Roots

Evaluating Expressions Involving Square Roots Of Positive Numbers

Evaluating Nth Roots

Square And Cube Roots

Using Symbols For Solutions To Equations

Using The Cube Root Symbol For Solutions To Equations Of The Form X^3 = P

Using The Nth Root Symbol For Solutions To Equations Of The Form X^n = P

Using The Square Root Symbol For Solutions To Equations Of The Form X^2 = P

Sequences And Series

Sequences

Applications Of Sequences

Understanding And Applying Sequences

Using Arithmetic Sequences To Model Situations

Using Geometric Sequences To Model Situations

Identifying And Writing Sequences

Identifying And Writing Rules For A Sequence When Given Some Terms Of The Sequence (including Arithmetic And Geometric Sequences)

Writing Terms Of A Sequence Recursively (including Arithmetic And Geometric Sequences)

Writing Terms Of A Sequence When Given The General Formula (including Arithmetic And Geometric Sequences)

Understanding And Applying Sequences

Using Arithmetic Sequences To Model Situations

Using Geometric Sequences To Model Situations

Series

Sum Of Finite Geometric Series Formula

Understanding And Applying Arithmetic Series

Applying The Formula For The Sum Of A Finite Arithmetic Series To Solve Problems

Understanding And Applying Geometric Series

Applying The Formula For The Sum Of A Finite Geometric Series To Solve Problems

Applying The Formula For The Sum Of An Infinite Geometric Series To Solve Problems

Variable Relationships

Independent And Dependent Variables

Representing Relationships In Graphs

Representing Relationships In Tables

Writing Equations To Express Relationships

Patterns And Relationships

Extending Patterns

Identifying Numerical Patterns

Relating Patterns To Variables

Functions

Geometry

Mathematical Practices

Mathematics Connections

Measurement

Measurement And Data

Number System

Ratios And Proportional Relationships

Statistics And Probability

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Applications Of Roots

Applications Of Roots Passages

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Linear System Solutions - Problem Solving Applications - Algebra

9th Grade - 12th Grade

Math

Study the application of solving linear systems in real-world scenarios to enhance algebraic problem-solving proficiency. Develop the ability to efficiently determine unique and infinite solutions through mastery of key techniques.

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1. 2021 survey of 800+ teachers conducted by Wayground

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

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

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