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Math

Algebra

Algebraic Expressions

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 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

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

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

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

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

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

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

Basic Geometry

Geometric Elements

Drawing And Identifying Geometric Elements

Drawing And Identifying Pairs Of Lines

Drawing And Identifying Parallel And/or Perpendicular 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

Congruency And Similarity

Congruence

Understanding Congruence Of 2d Figures

Understanding Congruency

Identifying Congruent Figures

Reasoning How Two Figures Are Congruent Using Transformations

Similar Figures

Understanding Similarity

Establishing The Conditions Necessary For Two Triangles To Be Similar

Identifying Similar Figures

Similarity

Understanding Similarity In 2d Figures

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

Constructions

Geometric Construction

Constructing Geometric Shapes & Triangles

Coordinate Geometry

Mathematical Practices

Math Puzzles And Logic

Mathematical Communication

Modeling And Tools

Appropriate Tool Selection

Mathematical Models

Technology Use In Mathematics

Problem Solving

Reasoning And Proof

Logical Reasoning

Mathematical Arguments

Pattern Recognition

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

Number System

Absolute Value And Operations

Number Properties

Decimal Operations

Decimal Operation Algorithms

Multi-digit Decimal Operations

Factors And Multiples

Distributive Property Applications

Greatest Common Factor And Least Common Multiple

Operation Properties

Associative Property

Commutative Property

Distributive Property

Numerical Expressions

Solving Mathematical And Real-world Problems Involving All Forms Of Rational Numbers

Evaluating The Reasonableness Of Answers Using Mental Computation And Estimation Strategies

Solving Mathematical And Real-world Problems Involving All Forms Of Rational Numbers

Solving Mathematical Problems Involving All Forms Of Rational Numbers

Solving Real-world Problems Involving All Forms Of Rational Numbers

Understanding And Applying The Laws Of Exponents To Numerical Expressions (integral Exponents)

Operations On Integers

Adding And Subtracting Integers

Adding And/or Subtracting Two Or More Integers (including Interpreting Sums/differences In Real-world Contexts)

Applying Properties Of Operations As Strategies To Add And Subtract Integers

Calculating The Distance Between Two Integers As The Absolute Value Of Their Difference (including Interpreting Differences In Real-world Contexts)

Describing Situations In Which Opposite Quantities Combine To Make Zero

Understanding The Concept Of Additive Inverses In The Context Of Integers

Understanding The Representation Of P + Q On A Number Line Where P And Q Are Integers

Applying Operations On Integers To Solve Mathematical And Real-world Problems

Solving Problems Involving Multiple Operations On Integers

Integer Operations

Multiplying And Dividing Integers

Applying Prior Understanding Of Properties Of Division To Divide Integers (including Interpreting Quotients In Real-world Contexts)

Applying Prior Understanding Of Properties Of Multiplication To Multiply Integers (including Interpreting Products In Real-world Contexts)

Applying Prior Understanding Of Properties Of Operations To Multiply And/or Divide Integers (including Interpreting Products Or Quotient In Real-world Contexts)

Applying Properties Of Operations As Strategies To Multiply And Divide Integers

Operations On Rational Numbers

Adding And Subtracting Rational Numbers

Adding And/or Subtracting Two Or More Rational Numbers (including Interpreting Sums/differences In Real-world Contexts)

Applying Properties Of Operations As Strategies To Add And Subtract Rational Numbers

Calculating The Distance Between Two Rational Numbers As The Absolute Value Of Their Difference (including Interpreting Differences In Real-world Contexts)

Understanding The Concept Of Additive Inverses In The Context Of Rational Numbers

Understanding The Representation Of P + Q On A Number Line Where P And Q Are Rational Numbers

Applying Operations On Rational Numbers To Solve Mathematical And Real-world Problems

Evaluating Expressions Involving A Mix Of Addition, Subtraction, Multiplication And/or Division Of Rational Numbers

Solving Mathematical/real-world Problems Involving Multiple Operations On Rational Numbers

Solving Problems Involving Multiple Operations On Rational Numbers

Multiplying And Dividing Rational Numbers

Applying Prior Understanding Of Properties Of Division To Divide Two Rational Numbers (including Interpreting Quotients In Real-world Contexts)

Applying Prior Understanding Of Properties Of Multiplication To Multiply Rational Numbers (including Interpreting Products In Real-world Contexts)

Applying Properties Of Operations As Strategies To Multiply And Divide Rational Numbers

Converting A Rational Number To A Decimal Number Using Division And Vice Versa

Understanding Patterns In The Decimal Form Of A Rational Number (either Terminates In Zeroes Or Eventually Repeats)

Rational Numbers

Operations With Rational Numbers

Adding/subtracting Rational Numbers

Adding & Subtracting Rational Numbers

Adding Rational Numbers

Additive Inverse

Subtracting Rational Numbers

Addition And Subtraction With Rational Numbers

Multiplication And Division With Rational Numbers

Multiplying/dividing Rational Numbers

Converting Rational Numbers To Decimals (and Vice Versa)

Dividing Rational Numbers

Multiplying & Dividing Rational Numbers

Multiplying Rational Numbers

Order Of Operations

Solving Multi-step Problems With Rational Numbers

Properties Of Rational Numbers

Absolute Value

Comparing Rational Numbers

Properties Of Operations

Understanding Rational Numbers

Comparing And Ordering Rational Numbers

Representing Rational Numbers On Number Lines

Understanding Absolute Value Of Rational Numbers

Real Numbers

Scientific Notation

Applying Operations On Numbers Expressed Using Scientific Notation To Solve Mathematical And Real-world Problems

Performing Addition And/or Subtraction With Numbers Expressed In The Scientific Notation

Performing Multiple Operations With Numbers Expressed In The Scientific Notation

Performing Multiple Operations With Numbers Expressed In The Scientific Notation And Solving Real-world Problems.

Performing Multiplication And/or Division With Numbers Expressed In The Scientific Notation

Estimating Quantities And Units Using Scientific Notation

Choosing Units Of Appropriate Size For Measuring Very Large Or Very Small Quantities

Estimating Very Large Or Very Small Quantities Using Scientific Notation

Estimating/writing Quantities In Scientific Notation

Operations & Interpretation Of Scientific Notation

Understanding And Writing Numbers In Scientific Notation

Converting Scientific Notation To Standard Form And Vice Versa

Writing Very Large Or Very Small Quantities Using Scientific Notation

Working With Units

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

Unit Rates

Understanding Ratio Notation, Rate Language And Unit Rates

Calculating Unit Rates Associated With Ratios Of Fractions

Statistics And Probability

Basic Statistics

Statistical Questions

Understanding Statistical Variability (qualitative)

Recognising A Statistical Question

Basic Statistics And Visual Representations

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

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 Displays

Interpreting Data

Analyzing Data Displays

Drawing Conclusions From Data

Representing Data

Creating Box Plots

Creating Dot Plots

Creating Histograms

Frequency Distributions

Describing Distributions

Describing And Understanding Distributions

Comparing Two Or More Distributions In Terms Of Their Shapes

Comparing Two Or More Distributions In Terms Of Their Shapes, Centre And Spread

Describing Any Overall Pattern And Any Striking Deviations From The Overall Pattern With Reference To Context

Relating The Choice Of Measures Of Central Tendency To The Shape Of The Data Distribution And The Context

Relating The Choice Of Measures Of Variability To The Shape Of The Data Distribution And The Context

Measures Of Variability

Estimating Measures Of Variability

Calculating Interquartile Range And Mean Absolute Deviation

Probability

Sampling And Population

Comparing Populations

Assessing Overlap Of Two Data Distributions

Comparing Data Variability & Center Measures

Drawing Inferences From Random Sample Data

Drawing Comparative Inferences About Two Populations Using Measures Of Central Tendency

Using The Measures Of Central Tendency Of Random Samples To Draw Comparative Inferences About Two Populations

Drawing Comparative Inferences About Two Populations Using Measures Of Variability

Using The Measures Of Variability Of Random Samples To Draw Comparative Inferences About Two Populations

Estimating Differences Between Populations Using Samples

Assessing The Degree Of Visual Overlap Of Two Numerical Data Distributions With Similar Variabilities

Estimating The Difference Between The Measures Of Central Tendency Of Random Samples

Expressing The Difference Between The Measures Of Central Tendency As A Multiple Of The Measures Of Variability

Random Sampling

Understanding Statistics & Representative Sampling

Using Random Sampling To Draw Inferences

Generating Multiple Samples Of The Same Size To Gauge Variation In Predictions

Understanding Representative Samples And The Idea That Examining A Sample Can Lead To Useful Information About The Population

Using Data From A Random Sample To Draw Inferences About A Population

Using Data From A Sample Survey To Estimate A Population Mean Or Proportion

Using Random Sampling To Draw Inferences

Generating Multiple Samples Of The Same Size To Gauge Variation In Predictions

Understanding Representative Samples And The Idea That Examining A Sample Can Lead To Useful Information About The Population

Using Data From A Sample Survey To Estimate A Population Mean Or Proportion

Statistical Variability

Understanding Data

Describing Data Distributions

Measures Of Center And Variation

Recognizing Statistical Questions

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Middle School

Math

Ratios And Proportional Relationships

Ratio Concepts

Middle School Ratio Concepts Passages

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[Ratio Simplification and Application - Understanding Part-to-Part and Part-to-Whole Ratios - Ratio and Proportion Concepts]

6th Grade

Math

Explore the principles of simplifying ratios and applying them in real-world contexts. Achieve proficiency in interpreting ratio relationships and calculating differences effectively, focusing on mastering the concepts and techniques needed to analyze and solve problems using ratios.

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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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