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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

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Problem-Solving Skills - Multi-Step Equations - Algebra

7th Grade

Math

Focus on mastering strategies for solving multi-step equations and identify common misconceptions. Develop proficiency in isolating variables and balancing equations with engaging methods. Emphasize understanding key concepts and refining skills necessary for accurate and efficient problem-solving.

8th Grade

Equations and Their Solutions - Understanding Solution Types - Algebraic Problem Solving

Passage

Equations and Their Solutions - Understanding Solution Types - Algebraic Problem Solving

8th Grade

Math

Investigating the techniques to determine the number of solutions for algebraic equations and systems enables learners to improve their problem-solving skills and gain a deeper understanding of different types of solutions. This process fosters a comprehensive grasp of algebraic concepts and methods.

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1. 2021 survey of 800+ teachers conducted by Wayground

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

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