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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

Exponents

Integer 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

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

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)

Solving 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

Linear Inequalities (two Variables)

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

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 Relationships

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

Irregular Shapes

Measuring And Estimating Area Of Miscellaneous Shapes

Calculating Areas Of Irregular Polygons

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

Circle Terminology

Defining Key Terms Related To Circles

Defining Lines And Line Segments Associated With Circles (radius, Diameter, Chord, Secant And Tangent)

Congruency And Similarity

Congruence

Understanding Congruence Of 2d Figures

Understanding Congruency

Identifying Congruent Figures

Reasoning How Two Figures Are Congruent Using Transformations

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

Coordinate Geometry

Distance In The Coordinate Plane

Applying Coordinates To Different Geometrical Scenarios

Applying The Distance Formula

Using Coordinates To Compute Perimeters Of Polygons

Finding Distance Using Pythagorean Theorem

Parallel Lines

Angles Formed By Parallel Lines

Applying The Properties Of Angles Created When Parallel Lines Are Cut By A Transversal

Applying Angle Relationships Between Parallel Lines To Find Angle Measures In Mathematical Scenarios

Understanding And Using Angles Created When Parallel Lines Are Cut By A Transversal

Understanding And Using Co-interior Angles

Understanding And Using Corresponding Angles

Understanding And Using Interior And Exterior Angles

Perimeter

Circumference

Applying The Understanding Of The Circumference Of A Circle To Solve Problems

Describing An Informal Argument For The Formula For The Circumference Of A Circle

Quadrilaterals

Understanding Quadrilaterals

Scale Drawings And Models

Shapes

Cross-sections Of 3d Shapes

Reasoning With Three-dimensional Shapes And Their Attributes

Describing The Two-dimensional Figures That Result From Slicing Cones

Describing The Two-dimensional Figures That Result From Slicing Cylinders

Describing The Two-dimensional Figures That Result From Slicing Right Rectangular Prisms

Describing The Two-dimensional Figures That Result From Slicing Right Rectangular Pyramids

Surface Area

Surface Area Of 3d Figures

Solving Mathematical And Real-world Problems Involving Surface Area Of Cubes And Cuboids

Solving Mathematical And/or Real-world Problems Involving Surface Area Of Cubes And Cuboids

Transformations

Geometric Transformations

Properties Of Transformations

Representing And Comparing Transformations

Comparing Transformations That Preserve Distance And Angle To Those That Do Not

Describing Transformations As Functions That Take Points In The Plane As Inputs And Give Other Points As Outputs

Triangles

Pythagorean Theorem

Applying Pythagorean Theorem In 2d & 3d

Applying The Pythagorean Theorem

Applying The Pythagorean Theorem (and/or Its Converse) To Different Geometric Problems

Applying The Pythagorean Theorem To Determine Unknown Side Lengths In Right Triangles (both Two-dimensions And Three-dimensions)

Proof Of Pythagorean Theorem & Its Converse

Triangle Properties

Applying Properties Of Triangles

Applying The Angle Sum Property Of Triangles

Applying The Exterior Angle Property Of Triangles

Volume

Volume Of 3d Figures

Measuring And Estimating Volume Of Cones

Solving Mathematical And/or Real-world Problems Involving Volume Of Cones

Measuring And Estimating Volume Of Cylinders

Solving Mathematical And/or Real-world Problems Involving Volume Of Cylinders

Measuring And Estimating Volume Of Miscellaneous Shapes

Applying The Formulae For The Volumes Of Cones, Cylinders And Spheres To Real-world Problems Involving Composite Solids

Measuring And Estimating Volume Of Pyramids

Solving Problems Involving Volume Of Pyramids

Measuring And Estimating Volume Of Spheres

Solving Mathematical And/or Real-world Problems Involving Volume Of Spheres

Volume Formulas For Cones, Cylinders, Spheres

Mathematical Practices

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

Number System

Absolute Value And Operations

Numerical Expressions

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

Operations On Rational Numbers

Adding And Subtracting Rational Numbers

Multiplying And Dividing 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)

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

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 Visualization

Organising And Representing Data

Representing Data Using Box-and-whisker Plots

Representing Data Using Dot Plots

Representing Data Using Histograms

Frequency Distributions

Describing Distributions

Describing And Understanding Distributions

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

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

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8th Grade

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8th Grade Volume Passages

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Volume Calculation Skills - Geometric Shapes - Mathematics Quiz

8th Grade - 12th Grade

Math

Learn to effectively calculate the volume of cylinders, cones, and spheres. Enhance your ability to tackle geometry problems by mastering formula application and improving spatial understanding.

8th Grade

Calculating Volumes - Cones, Spheres, & Cylinders - Geometry

Passage

Calculating Volumes - Cones, Spheres, & Cylinders - Geometry

8th Grade

Math

Develop proficiency in calculating the volumes of cones, spheres, and cylinders while deepening your understanding of geometric formulas. Strengthen problem-solving abilities through the exploration of these essential mathematical concepts.

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