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Mr. Clarkson's Math

  • Home
    • About Mr. C
    • Curriculum Vitae
  • MS Math
    • Class Syllabus and Dates
    • Sixth Grade Math
      • My Math Bio (or Yo, this is me!)
      • Multiplication and Division Practice
      • Sixth Module 1
        • 6th-M1TAL1-Ratios
        • 6th-M1TAL2 Ratios
        • 6th-M1TAL3 Equivalent Ratios
        • 6th-M1TAL4 Equivalent Ratios
        • 6th-M1TAL5: Solving Problems by Finding Equivalent Ratios
        • 6th-M1TAL6: Solving Problems by Finding Equivalent Ratios
        • 6th-M1TAL7: Associated Ratios and the Value of a Ratio
        • 6th-M1TAL8: Equivalent Ratios Defined Through the Value of a Ratio
        • 6th-M1TBL9: Tables of Equivalent Ratios
        • 6th-M1TBL10: The Structure of Ratio Tables—Additive and Multiplicative
        • 6th-M1TBL11: Comparing Ratios Using Ratio Tables
        • 6th-M1TBL12: From Ratio Tables to Double Number Line Diagrams
        • 6th-M1TBL13: From Ratio Tables to Equations Using the Value of a Ratio
        • 6th-M1TBL14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
        • 6th-M1TBL15: A Synthesis of Representations of Equivalent Ratio Collections
        • 6th-M1TBL16: From Ratios to Rates
        • 6th-M1TBL17: From Rates to Ratios
        • 6th-M1TBL18: Finding a Rate by Dividing Two Quantities
        • 6th-M1TBL19: Comparison Shopping—Unit Price and Related Measurement Conversions
        • 6th-M1TBL20: Comparison Shopping—Unit Price and Related Measurement Conversions
        • 6th-M1TBL21: Getting the Job Done—Speed, Work, and Measurement Units
        • 6th-M1TBL22: Getting the Job Done—Speed, Work, and Measurement Units
        • 6th-M1TBL23: Problem Solving Using Rates, Unit Rates, and Conversions
        • 6th-M1TBL24: Percent and Rates per 100
        • 6th-M1TBL25: A Fraction as a Percent
        • 6th-M1TDL26: Percent of a Quantity
        • 6th-M1TBL27: Solving Percent Problems
        • 6th-M1TBL28: Solving Percent Problems
        • 6th-M1TBL29: Solving Percent Problems
      • Sixth Module 2
        • 6th-M2TaL1: Interpreting Division of a Fraction by a Whole Number—Visual Models
        • 6th-M2TaL2: Interpreting Division of a Whole Number by a Fraction—Visual Models
        • 6th-M2TaL3: Interpreting and Computing Division of a Fraction by a Fraction—More Models
        • 6th-M2TaL4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
        • 6th-M2TaL5: Creating Division Stories
        • 6th-M2TaL6: More Division Stories
        • 6th-M2TaL7: The Relationship Between Visual Fraction Models and Equations
        • 6th-m2tal8: Dividing Fractions and Mixed Numbers
        • 6th-m2tal9: Sums and Differences of Decimals
        • 6th-m2tal10 The Distributive Property and the Products of Decimals
        • 6th-m2tal11 : Fraction Multiplication and the Products of Decimals
        • 6th-m2tal12: Estimating Digits in a Quotient
        • 6th-m2tal13: Dividing Multi-Digit Numbers Using the Algorithm
        • 6th-m2tal14: The Division Algorithm — Converting Decimal Division
        • 6th-m2tal15: The Division Algorithm—Converting Decimal Division
        • 6th-m2tal16: Even and Odd Numbers
        • 6th-m2tal17: Divisibility Tests for 3 and 9
        • 6th-m2tal18: Least Common Multiple and Greatest Common Factor
        • 6th-m2tal19: The Euclidean Algorithm
      • Sixth Module 3
        • 6th-m3tal1: Positive and Negative Numbers on the Number Line—Opposite Direction and Value
        • 6th-m3tal2: Real-World Positive and Negative Numbers and Zero
        • 6th-m3tal3: Real-World Positive and Negative Numbers and Zero
        • 6th-m3tal4: The Opposite of a Number
        • 6th-m3tal5: The Opposite of a Number’s Opposite
        • 6th-m3tal6: Rational Numbers on the Number Line
        • 6th-m3tal7: Ordering Integers and Other Rational Numbers
        • 6th-m3tal8: Ordering Integers and Other Rational Numbers
        • 6th-m3tal9: Comparing Integers and Other Rational Numbers
        • 6th-m3tal10: Writing and Interpreting Inequality Statements Involving Rational Numbers
        • 6th-m3tal11: Absolute Value—Magnitude and Distance
        • 6th-m3tal12: The Relationship Between Absolute Value and Order
        • 6th-m3tal13: Statements of Order in the Real World
        • 6th-m3tal14: Ordered Pairs
        • 6th-m3tal15: Locating Ordered Pairs on the Coordinate Plane
        • 6th-m3tal16: Symmetry in the Coordinate Plane
        • 6th-m3tal17: Drawing the Coordinate Plane and Points on the Plane
        • 6th-m3tal18: Distance on the Coordinate Plane
        • 6th-m3tal19: Problem Solving and the Coordinate Plane
      • Sixth Module 4
        • 6th-m4ABC Relationships of Operations Calendar
        • 6th-m4DEF Expanding, Factoring, and Distributing Expressions Calendar
        • 6th-m4tal1: The Relationship of Addition and Subtraction
        • 6th-m4tal2: The Relationship of Multiplication and Division
        • 6th-m4tal3: The Relationship of Multiplication and Addition
        • 6th-m4tal4: The Relationship of Division and Subtraction
        • 6th-m4tal5: Exponents
        • 6th-m4tal6: The Order of Operations
        • 6th-m4tal7: Replacing Letters with Numbers
        • 6th-m4tal8: Replacing Numbers with Letters
        • 6th-m4tal9: Writing Addition and Subtraction Expressions
        • 6th-m4tal10: Writing and Expanding Multiplication Expressions
        • 6th-m4tal11: Factoring Expressions
        • 6th-m4tal12: Distributing Expressions
        • 6th-m4tal13: Writing Division Expressions
        • 6th-m4tal14: Writing Division Expressions
        • 6th-m4tal15: Read Expressions in Which Letters Stand for Numbers
        • 6th-m4tal16: Write Expressions in Which Letters Stand for Numbers
        • 6th-m4tal17: Write Expressions in Which Letters Stand for Numbers
        • 6th-m4tal18: Writing and Evaluating Expressions—Addition and Subtraction
        • 6th-m4tal19: Substituting to Evaluate Addition and Subtraction Expressions
        • 6th-m4tal20: Writing and Evaluating Expressions—Multiplication and Division
        • 6th-m4tal21: Writing and Evaluating Expressions—Multiplication and Addition
        • 6th-m4tal22: Writing and Evaluating Expressions—Exponents
        • 6th-m4tal23: True and False Number Sentences
        • 6th-m4tal24: True and False Number Sentences
        • 6th-m4tal25: Finding Solutions to Make Equations True
        • 6th-m4tal26: One-Step Equations—Addition and Subtraction
        • 6th-m4tal27: One-Step Equations—Multiplication and Division
        • 6th-m4tal28: Two-Step Problems—All Operations
        • 6th-m4tal29: Multi-Step Problems—All Operations
        • 6th-m4tal30: One-Step Problems in the Real World
        • 6th-m4tal31: Problems in Mathematical Terms
        • 6th-m4tal32: Multi-Step Problems in the Real World
        • 6th-m4tal33: From Equations to Inequalities
        • 6th-m4tal34: Writing and Graphing Inequalities in Real-World Problems
    • Eighth Grade Math
      • My Math Bio (or Yo, this is me!)
      • Eighth Module 1
        • 8th-1.1 Exponential Notation
        • 8th-1.2 Multiplication of Numbers in Exponential Form
        • 8th-1.3: Numbers in Exponential Form Raised to a Power
        • 8th-1.4: Numbers Raised to the Zeroth Power
        • 8th-1.5: Negative Exponents and the Laws of Exponents
        • 8th-1.6: Proofs of Laws of Exponents
        • 8th-1.7: Magnitude
        • 8th-1.8: Estimating Quantities
        • 8th-1. 9: Scientific Notation
        • 8th-1.10: Operations with Numbers in Scientific Notation
        • 8th-1.11: Efficacy of Scientific Notation
        • 8th-1.12: Choice of Unit
        • 8th-1.13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology
      • Eighth Module 2
        • 8th.2.1 Why Move Things Around?
        • 8th.2.2 Definition of Translation and Three Basic Properties
        • 8th.2.3 Translating Lines
        • 8th.2.4 Definition of Reflection and Basic Properties
        • 8th-2.5 Definition of Rotation and Basic Properties
        • 8th-2.6 Rotations of 180 Degrees
        • 8th-2.7 Sequencing Translations
        • 8th-2.8 Sequencing Reflections and Translations
        • 8th-2.9 Sequencing Rotations
        • 8th-2.10 Sequences of Rigid Motions
        • 8th-2.11 Definition of Congruence and Some Basic Properties
        • 8th-2.12 Angles Associated with Parallel Lines
        • 8th-2.13 Angle Sum of a Triangle
        • 8th-2.14 More on the Angles of a Triangle
        • 8th-2.15 Informal Proof of the Pythagorean Theorem
        • 8th-2.16 Applications of the Pythagorean Theorem
      • Eighth Module 3
        • 8th-3.1 What Lies Behind “Same Shape”?
        • 8th-3.2 Properties of Dilations
        • 8th-3.3 Examples of Dilations
        • 8th-3.4 Fundamental Theorem of Similarity (FTS)
        • 8th-3.5 First Consequences of FTS
        • 8th-3.6 Dilations on the Coordinate Plane
        • 8th-3.7 Informal Proofs of Properties of Dilations (optional)
        • 8th-3.8 Similarity
        • 8th-3.9 Basic Properties of Similarity
        • 8th-3.10 Informal Proof of AA Criterion for Similarity
        • 8th-3.11 More About Similar Triangles
        • 8th-3.12 Modeling Using Similarity
        • 8th-3.13 Proof of the Pythagorean Theorem
        • 8th-3.14 The Converse of the Pythagorean Theorem
      • Eighth Module 4
        • 8th-4.1 Writing Equations Using Symbols
        • 8th-4.2 Linear and Nonlinear Equations in x
        • 8th-4.3 Linear Expressions in x
        • 8th-4.4 Solving a Linear Equation
        • 8th-4.5: Writing and Solving Linear Equations
        • 8th-4.6 Solutions of a Linear Equation
        • 8th-4.7 Classification of Solutions
        • 8th-4.8 Linear Equations in Disguise
        • 8th-4.9 An Application of Linear Equations
      • Eighth Module 5
        • 8th M5 Examples of Functions from Geometry
        • 8th-5.1: The Concept of a Function
        • 8th-5.2: Formal Definition of a Function
        • 8th-5.3: Linear Functions and Proportionality
        • 8th-5.4: More Examples of Functions
        • 8th-5.5: Graphs of Functions and Equations
        • 8th-5.6: Graphs of Linear Functions and Rate of Change
        • 8th-5.7: Comparing Linear Functions and Graphs
        • 8th-5.8: Graphs of Simple Nonlinear Functions
        • 8th-5.9: Examples of Functions from Geometry
        • 8th-5.10: Volumes of Familiar Solids—Cones and Cylinders
        • 8th-5.11: Volume of a Sphere
      • Eighth Module 6
        • 8th M6 AB Linear Functions and Bivariate Data
        • 8th – 6.1: Modeling Linear Relationships
        • 8th – 6.2: Formal Definition of a Function
        • 8th – 6.3: Linear Functions and Proportionality
        • 8th – 6.4: More Examples of Functions
        • 8th – 6.5: Graphs of Functions and Equations
        • 8th – 6.6: Graphs of Linear Functions and Rate of Change
        • 8th – 6.7: Comparing Linear Functions and Graphs
        • 8th – 6.8: Graphs of Simple Nonlinear Functions
  • HS Math
    • Class Syllabus and Dates
    • Algebra 1
    • Geometry
      • My Math Bio (or Yo, this is me!)
      • Geometry Module 1
        • Geometry – 1.1: Basic Constructions
        • Geometry 1.2: Construct an Equilateral Triangle
        • Geometry – 1.3: Copy and Bisect an Angle
        • Geometry – 1.4: Construct a Perpendicular Bisector
        • Geometry – 1.5: Points of Concurrencies
        • Geometry – 1.6: Solve for Unknown Angles—Angles and Lines at a Point
        • Geometry – 1.7: Solve for Unknown Angles—Transversals
        • Geometry – 1.8: Solve for Unknown Angles—Angles in a Triangle
        • Geometry – 1.9: Unknown Angle Proofs—Writing Proofs
        • Geometry – 1.10: Unknown Angle Proofs—Proofs with Constructions
        • Geometry – 1.11: Unknown Angle Proofs—Proofs of Known Facts
        • Geometry – 1.12: Transformations—The Next Level
        • Geometry – 1.13: Rotations
        • Geometry – 1.14: Reflections
        • Geometry – 1.15: Rotations, Reflections, and Symmetry
        • Geometry – 1.16: Translations
        • Geometry – 1.17: Characterize Points on a Perpendicular Bisector
        • Geometry – 1.18: Looking More Carefully at Parallel Lines
        • Geometry – 1.19: Construct and Apply a Sequence of Rigid Motions
        • Geometry – 1.20: Applications of Congruence in Terms of Rigid Motions
        • Geometry – 1.21: Correspondence and Transformations
        • Geometry – 1.22: Congruence Criteria for Triangles—SAS
        • Geometry 1.22a Khan Academy
        • Geometry – 1.23: Base Angles of Isosceles Triangles
        • Geometry – 1.24: Congruence Criteria for Triangles—ASA and SSS
        • Geometry – 1.25: Congruence Criteria for Triangles—AAS and HL
        • Geometry – 1.26: Triangle Congruency Proofs
        • Geometry – 1.27: Triangle Congruency Proofs
        • Geometry – 1.28: Properties of Parallelograms
        • Geometry – 1.29: Special Lines in Triangles
        • Geometry – 1.30: Special Lines in Triangles
        • Geometry – 1.31: Construct a Square and a Nine-Point Circle
        • Geometry – 1.32: Construct a Nine-Point Circle
        • Geometry – 1.33: Review of the Assumptions
        • Geometry – 1.34: Review of the Assumptions
      • Geometry Module 2
        • 1: Scale Drawings
        • 2: Making Scale Drawings Using the Ratio Method
        • 3: Making Scale Drawings Using the Parallel Method
        • 4: Comparing the Ratio Method with the Parallel Method
        • 5: Scale Factors
        • 6: Dilations as Transformations of the Plane
        • 7: How Do Dilations Map Segments?
        • 8: How Do Dilations Map Lines, Rays, and Circles?
        • 9: How Do Dilations Map Angles?
        • 10: Dividing the King’s Foot into 12 Equal Pieces
        • 11: Dilations from Different Centers
        • 12 : What Are Similarity Transformations, and Why Do We Need Them?
        • 13 : Properties of Similarity Transformations
        • 14 : Similarity
        • 15 : The Angle – Angle (AA) Criterion for Two Triangles to B e Similar
        • 16 : Between – Figure and Within – Figure Ratios
        • 17 : The Side – Angle – Side (SAS) and Side – Side – Side (SSS) Criteria for Two Triangles to B e Similar
        • 18 : Similarity and the Angle Bisector Theorem
        • 19 : Families of Parallel Lines and the Circumference of the Earth
        • 20 : How Far Away I s the Moon?
      • Geometry Module 3
        • 1: What Is Area?
        • 2: Properties of Area
        • 3: The Scaling Principle for Area
        • 4: Proving the Area of a Disk
        • 5: Three-Dimensional Space
        • 6: General Prisms and Cylinders and Their Cross-Sections
        • 7: General Pyramids and Cones and Their Cross-Sections
        • 8: Definition and Properties of Volume
        • 9: Scaling Principle for Volumes
        • 10: The Volume of Prisms and Cylinders and Cavalieri’s Principle
        • 11: The Volume Formula of a Pyramid and Cone
        • 12: The Volume Formula of a Sphere
        • 13: How Do 3D Printers Work?
      • Geometry Module 4
        • 1: Searching a Region in the Plane
        • 2: Finding Systems of Inequalities That Describe Triangular and Rectangular Regions
        • 3: Lines That Pass Through Regions
        • 4: Designing a Search Robot to Find a Beacon
        • 5: Criterion for Perpendicularity
        • 6: Segments That Meet at Right Angles
        • 7: Equations for Lines Using Normal Segments
        • 8: Parallel and Perpendicular Lines
        • 9: Perimeter and Area of Triangles in the Cartesian Plane
        • 10: Perimeter and Area of Polygonal Regions in the Cartesian Plane
        • 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities
        • 12: Dividing Segments Proportionately
        • 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means
      • Square Root Triangle Generator
    • Algebra 2
      • My Math Bio (or Yo, this is me!)
      • Algebra II Calendar
      • AL2 Weekly Project Response
      • A2 Module 1
        • Algebra 2.1.A.1: Successive Differences in Polynomials
        • Algebra 2.1.A.2: The Multiplication of Polynomials
        • Algebra 2.1.A.3: The Division of Polynomials
        • Algebra 2.1.A.4: Comparing Methods—Long Division, Again?
        • Algebra 2.1.A.5: Putting It All Together
        • Algebra 2.1.A.6: Dividing by x-a and by x+a
        • Algebra 2.1.A.7: Mental Math
        • Algebra 2.1.A.8: The Power of Algebra—Finding Primes
        • Algebra 2.1.A.9: Radicals and Conjugates
        • Algebra 2.1.A.10: The Power of Algebra—Finding Pythagorean Triples
        • Algebra 2.1.A.11: The Special Role of Zero in Factoring
        • Algebra 2.1.B.12: Overcoming Obstacles in Factoring
        • Algebra 2.1.B.13: Mastering Factoring
        • Algebra 2.1.B.14: Graphing Factored Polynomials
        • Algebra 2.1.B.15: Structure in Graphs of Polynomial Functions
        • Algebra 2.1.B.16: Modeling with Polynomials—An Introduction
        • Algebra 2.1.B.17: Modeling with Polynomials—An Introduction
        • Algebra 2.1.B.18: Overcoming a Second Obstacle in Factoring—What If There Is a Remainder?
        • Algebra 2.1.B.19: The Remainder Theorem
        • Algebra 2.1.B.20: Using Remainder Theorem to Plot a Polynomial
        • Algebra 2.1.B.21: Digital Regression and Interpolation
        • Algebra 2.1.C.22: Equivalent Rational Expressions
        • Algebra 2.1.C.23: Comparing Rational Expressions
        • Algebra 2.1.C.24: Multiplying and Dividing Rational Expressions
        • Algebra 2.1.C.25: Adding and Subtracting Rational Expressions
        • Algebra 2.1.C.26: Solving Rational Equations
        • Algebra 2.1.C.27: Word Problems Leading to Rational Equations
        • Algebra 2.1.C.28: A Focus on Square Roots
        • Algebra 2.1.C.29: Solving Radical Equations
        • Algebra 2.1.C.30: Linear Systems in Three Variables
        • Algebra 2.1.C.31: Systems of Equations
        • Algebra 2.1.C.32: Graphing Systems of Equations
        • Algebra 2.1.C.33: The Definition of a Parabola
        • Algebra 2.1.C.34: Are All Parabolas Congruent?
        • Algebra 2.1.C.35: Are All Parabolas Similar?
        • Algebra 2.1.D.36: Overcoming a Third Obstacle to Factoring—What If There Are No Real Number Solutions?
        • Algebra 2.1.D.37: A Surprising Boost from Geometry
        • Algebra 2.1.D.38: Complex Numbers as Solutions to Equations
        • Algebra 2.1.D.39: Factoring Extended to the Complex Realm
        • Algebra 2.1.D.40: Obstacles Resolved—A Surprising Result
      • A2 Module 2
        • 1: Ferris Wheels—Tracking the Height of a Passenger Car
        • 2: The Height and Co-Height Functions of a Ferris Wheel
        • 3: The Motion of the Moon, Sun, and Stars—Motivating Mathematics
        • 4: From Circle-ometry to Trigonometry
        • 5: Extending the Domain of Sine and Cosine to All Real Numbers
        • 6: Why Call It Tangent?
        • 7: Secant and the Co-Functions
        • 8: Graphing the Sine and Cosine Functions
        • 9: Awkward! Who Chose the Number 360, Anyway?
        • 10: Basic Trigonometric Identities from Graphs
        • 11: Transforming the Graph of the Sine Function
        • 12: Ferris Wheels—Using Trigonometric Functions to Model Cyclical Behavior
        • 13: Tides, Sound Waves, and Stock Markets
        • 14: Graphing the Tangent Function
        • 15: What Is a Trigonometric Identity?
        • 16: Proving Trigonometric Identities
        • 17: Trigonometric Identity Proofs
      • A2 Module 3
        • 1: Integer Exponents
        • 2: Base 10 and Scientific Notation
        • 3: Rational Exponents—What are 2^(1/2) and 2^(1/3)?
        • 4: Properties of Exponents and Radicals
        • 5: Irrational Exponents—What are 2^(√2) and 2^π?
        • 6: Euler’s Number
        • 7: Bacteria and Exponential Growth
        • 8: The “What Power” Function
        • 9: Logarithms—How Many Digits Do You Need?
        • 10: Building Logarithmic Tables
        • 11: The Most Important Property of Logarithms
        • 12: Properties of Logarithms
        • 13: Changing the Base
        • 14: Solving Logarithmic Equations
        • 15: Why Were Logarithms Developed?
        • 16: Rational and Irrational Numbers
        • 17: Graphing the Logarithm Function
        • 18: Graphs of Exponential Functions and Logarithmic Functions
        • 19: The Inverse Relationship Between Logarithmic and Exponential Functions
        • 20: Transformations of the Graphs of Logarithmic and Exponential Functions
        • Lesson 21: The Graph of the Natural Logarithm Function
        • Lesson 22: Choosing a Model
        • 23: Bean Counting
        • 24: Solving Exponential Equations
        • 25: Geometric Sequences and Exponential Growth and Decay
        • 26: Percent Rate of Change
        • 27: Modeling with Exponential Functions
        • 28: Newton’s Law of Cooling, Revisited
        • 29: The Mathematics Behind a Structured Savings Plan
        • 30: Buying a Car
        • 31: Credit Cards
        • 32: Buying a House
        • 33: The Million Dollar Problem
      • Quadratic Equation Factorization Chart
    • Advanced Mathematics
      • My Math Bio (or Yo, this is me!)
  • Resources
    • Basic Math Practice
    • Personal Finance
      • Personal Finance Introduction
      • Personal Finance Prospectus
      • Descriptions and Responsibilities
      • Check Register
      • Account Registrer
      • Random Bill Amount
    • Desmos Calculator
    • Sketchometry
    • Seventh Grade Math
      • My Math Bio (or Yo, this is me!)
      • Seventh Grade Math Calendar
      • Seventh Module 1
        • 7th-1.1: An Experience in Relationships as Measuring Rate
        • 7th-1.2: Proportional Relationships
        • 7th-1.3 Identifying Proportional and Non-Proportional Relationships in Tables
        • 7th-1.4: Identifying Proportional and Non-Proportional Relationships in Tables
        • 7th-1.5: Identifying Proportional and Non-Proportional Relationships in Graphs
        • 7th-1.6: Identifying Proportional and Non-Proportional Relationships in Graphs
        • 7th-1.7: Unit Rate as the Constant of Proportionality
        • 7th-1.8 Representing Proportional Relationships with Equations
        • 7th-1.9: Representing Proportional Relationships with Equations
        • 7th-1.10: Interpreting Graphs of Proportional Relationships
        • 7th-1.11: Ratios of Fractions and Their Unit Rates
        • 7th-1.12: Ratios of Fractions and Their Unit Rates
        • 7th-1.13: Finding Equivalent Ratios Given the Total Quantity
        • 7th-1.14: Multi-Step Ratio Problems
        • 7th-1.15: Equations of Graphs of Proportional Relationships Involving Fractions
        • 7th-1.16: Relating Scale Drawings to Ratios and Rates
        • 7th-1.17: The Unit Rate as the Scale Factor
        • 7th-1.18: Computing Actual Lengths from a Scale Drawing
        • 7th-1.19: Computing Actual Areas from a Scale Drawing
        • 7th-1.20: An Exercise in Creating a Scale Drawing
        • 7th-1.21: An Exercise in Changing Scales
        • 7th-1.22: An Exercise in Changing Scales
  • Home
    • About Mr. C
    • Curriculum Vitae
  • MS Math
    • Class Syllabus and Dates
    • Sixth Grade Math
      • My Math Bio (or Yo, this is me!)
      • Multiplication and Division Practice
      • Sixth Module 1
        • 6th-M1TAL1-Ratios
        • 6th-M1TAL2 Ratios
        • 6th-M1TAL3 Equivalent Ratios
        • 6th-M1TAL4 Equivalent Ratios
        • 6th-M1TAL5: Solving Problems by Finding Equivalent Ratios
        • 6th-M1TAL6: Solving Problems by Finding Equivalent Ratios
        • 6th-M1TAL7: Associated Ratios and the Value of a Ratio
        • 6th-M1TAL8: Equivalent Ratios Defined Through the Value of a Ratio
        • 6th-M1TBL9: Tables of Equivalent Ratios
        • 6th-M1TBL10: The Structure of Ratio Tables—Additive and Multiplicative
        • 6th-M1TBL11: Comparing Ratios Using Ratio Tables
        • 6th-M1TBL12: From Ratio Tables to Double Number Line Diagrams
        • 6th-M1TBL13: From Ratio Tables to Equations Using the Value of a Ratio
        • 6th-M1TBL14: From Ratio Tables, Equations, and Double Number Line Diagrams to Plots on the Coordinate Plane
        • 6th-M1TBL15: A Synthesis of Representations of Equivalent Ratio Collections
        • 6th-M1TBL16: From Ratios to Rates
        • 6th-M1TBL17: From Rates to Ratios
        • 6th-M1TBL18: Finding a Rate by Dividing Two Quantities
        • 6th-M1TBL19: Comparison Shopping—Unit Price and Related Measurement Conversions
        • 6th-M1TBL20: Comparison Shopping—Unit Price and Related Measurement Conversions
        • 6th-M1TBL21: Getting the Job Done—Speed, Work, and Measurement Units
        • 6th-M1TBL22: Getting the Job Done—Speed, Work, and Measurement Units
        • 6th-M1TBL23: Problem Solving Using Rates, Unit Rates, and Conversions
        • 6th-M1TBL24: Percent and Rates per 100
        • 6th-M1TBL25: A Fraction as a Percent
        • 6th-M1TDL26: Percent of a Quantity
        • 6th-M1TBL27: Solving Percent Problems
        • 6th-M1TBL28: Solving Percent Problems
        • 6th-M1TBL29: Solving Percent Problems
      • Sixth Module 2
        • 6th-M2TaL1: Interpreting Division of a Fraction by a Whole Number—Visual Models
        • 6th-M2TaL2: Interpreting Division of a Whole Number by a Fraction—Visual Models
        • 6th-M2TaL3: Interpreting and Computing Division of a Fraction by a Fraction—More Models
        • 6th-M2TaL4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
        • 6th-M2TaL5: Creating Division Stories
        • 6th-M2TaL6: More Division Stories
        • 6th-M2TaL7: The Relationship Between Visual Fraction Models and Equations
        • 6th-m2tal8: Dividing Fractions and Mixed Numbers
        • 6th-m2tal9: Sums and Differences of Decimals
        • 6th-m2tal10 The Distributive Property and the Products of Decimals
        • 6th-m2tal11 : Fraction Multiplication and the Products of Decimals
        • 6th-m2tal12: Estimating Digits in a Quotient
        • 6th-m2tal13: Dividing Multi-Digit Numbers Using the Algorithm
        • 6th-m2tal14: The Division Algorithm — Converting Decimal Division
        • 6th-m2tal15: The Division Algorithm—Converting Decimal Division
        • 6th-m2tal16: Even and Odd Numbers
        • 6th-m2tal17: Divisibility Tests for 3 and 9
        • 6th-m2tal18: Least Common Multiple and Greatest Common Factor
        • 6th-m2tal19: The Euclidean Algorithm
      • Sixth Module 3
        • 6th-m3tal1: Positive and Negative Numbers on the Number Line—Opposite Direction and Value
        • 6th-m3tal2: Real-World Positive and Negative Numbers and Zero
        • 6th-m3tal3: Real-World Positive and Negative Numbers and Zero
        • 6th-m3tal4: The Opposite of a Number
        • 6th-m3tal5: The Opposite of a Number’s Opposite
        • 6th-m3tal6: Rational Numbers on the Number Line
        • 6th-m3tal7: Ordering Integers and Other Rational Numbers
        • 6th-m3tal8: Ordering Integers and Other Rational Numbers
        • 6th-m3tal9: Comparing Integers and Other Rational Numbers
        • 6th-m3tal10: Writing and Interpreting Inequality Statements Involving Rational Numbers
        • 6th-m3tal11: Absolute Value—Magnitude and Distance
        • 6th-m3tal12: The Relationship Between Absolute Value and Order
        • 6th-m3tal13: Statements of Order in the Real World
        • 6th-m3tal14: Ordered Pairs
        • 6th-m3tal15: Locating Ordered Pairs on the Coordinate Plane
        • 6th-m3tal16: Symmetry in the Coordinate Plane
        • 6th-m3tal17: Drawing the Coordinate Plane and Points on the Plane
        • 6th-m3tal18: Distance on the Coordinate Plane
        • 6th-m3tal19: Problem Solving and the Coordinate Plane
      • Sixth Module 4
        • 6th-m4ABC Relationships of Operations Calendar
        • 6th-m4DEF Expanding, Factoring, and Distributing Expressions Calendar
        • 6th-m4tal1: The Relationship of Addition and Subtraction
        • 6th-m4tal2: The Relationship of Multiplication and Division
        • 6th-m4tal3: The Relationship of Multiplication and Addition
        • 6th-m4tal4: The Relationship of Division and Subtraction
        • 6th-m4tal5: Exponents
        • 6th-m4tal6: The Order of Operations
        • 6th-m4tal7: Replacing Letters with Numbers
        • 6th-m4tal8: Replacing Numbers with Letters
        • 6th-m4tal9: Writing Addition and Subtraction Expressions
        • 6th-m4tal10: Writing and Expanding Multiplication Expressions
        • 6th-m4tal11: Factoring Expressions
        • 6th-m4tal12: Distributing Expressions
        • 6th-m4tal13: Writing Division Expressions
        • 6th-m4tal14: Writing Division Expressions
        • 6th-m4tal15: Read Expressions in Which Letters Stand for Numbers
        • 6th-m4tal16: Write Expressions in Which Letters Stand for Numbers
        • 6th-m4tal17: Write Expressions in Which Letters Stand for Numbers
        • 6th-m4tal18: Writing and Evaluating Expressions—Addition and Subtraction
        • 6th-m4tal19: Substituting to Evaluate Addition and Subtraction Expressions
        • 6th-m4tal20: Writing and Evaluating Expressions—Multiplication and Division
        • 6th-m4tal21: Writing and Evaluating Expressions—Multiplication and Addition
        • 6th-m4tal22: Writing and Evaluating Expressions—Exponents
        • 6th-m4tal23: True and False Number Sentences
        • 6th-m4tal24: True and False Number Sentences
        • 6th-m4tal25: Finding Solutions to Make Equations True
        • 6th-m4tal26: One-Step Equations—Addition and Subtraction
        • 6th-m4tal27: One-Step Equations—Multiplication and Division
        • 6th-m4tal28: Two-Step Problems—All Operations
        • 6th-m4tal29: Multi-Step Problems—All Operations
        • 6th-m4tal30: One-Step Problems in the Real World
        • 6th-m4tal31: Problems in Mathematical Terms
        • 6th-m4tal32: Multi-Step Problems in the Real World
        • 6th-m4tal33: From Equations to Inequalities
        • 6th-m4tal34: Writing and Graphing Inequalities in Real-World Problems
    • Eighth Grade Math
      • My Math Bio (or Yo, this is me!)
      • Eighth Module 1
        • 8th-1.1 Exponential Notation
        • 8th-1.2 Multiplication of Numbers in Exponential Form
        • 8th-1.3: Numbers in Exponential Form Raised to a Power
        • 8th-1.4: Numbers Raised to the Zeroth Power
        • 8th-1.5: Negative Exponents and the Laws of Exponents
        • 8th-1.6: Proofs of Laws of Exponents
        • 8th-1.7: Magnitude
        • 8th-1.8: Estimating Quantities
        • 8th-1. 9: Scientific Notation
        • 8th-1.10: Operations with Numbers in Scientific Notation
        • 8th-1.11: Efficacy of Scientific Notation
        • 8th-1.12: Choice of Unit
        • 8th-1.13: Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology
      • Eighth Module 2
        • 8th.2.1 Why Move Things Around?
        • 8th.2.2 Definition of Translation and Three Basic Properties
        • 8th.2.3 Translating Lines
        • 8th.2.4 Definition of Reflection and Basic Properties
        • 8th-2.5 Definition of Rotation and Basic Properties
        • 8th-2.6 Rotations of 180 Degrees
        • 8th-2.7 Sequencing Translations
        • 8th-2.8 Sequencing Reflections and Translations
        • 8th-2.9 Sequencing Rotations
        • 8th-2.10 Sequences of Rigid Motions
        • 8th-2.11 Definition of Congruence and Some Basic Properties
        • 8th-2.12 Angles Associated with Parallel Lines
        • 8th-2.13 Angle Sum of a Triangle
        • 8th-2.14 More on the Angles of a Triangle
        • 8th-2.15 Informal Proof of the Pythagorean Theorem
        • 8th-2.16 Applications of the Pythagorean Theorem
      • Eighth Module 3
        • 8th-3.1 What Lies Behind “Same Shape”?
        • 8th-3.2 Properties of Dilations
        • 8th-3.3 Examples of Dilations
        • 8th-3.4 Fundamental Theorem of Similarity (FTS)
        • 8th-3.5 First Consequences of FTS
        • 8th-3.6 Dilations on the Coordinate Plane
        • 8th-3.7 Informal Proofs of Properties of Dilations (optional)
        • 8th-3.8 Similarity
        • 8th-3.9 Basic Properties of Similarity
        • 8th-3.10 Informal Proof of AA Criterion for Similarity
        • 8th-3.11 More About Similar Triangles
        • 8th-3.12 Modeling Using Similarity
        • 8th-3.13 Proof of the Pythagorean Theorem
        • 8th-3.14 The Converse of the Pythagorean Theorem
      • Eighth Module 4
        • 8th-4.1 Writing Equations Using Symbols
        • 8th-4.2 Linear and Nonlinear Equations in x
        • 8th-4.3 Linear Expressions in x
        • 8th-4.4 Solving a Linear Equation
        • 8th-4.5: Writing and Solving Linear Equations
        • 8th-4.6 Solutions of a Linear Equation
        • 8th-4.7 Classification of Solutions
        • 8th-4.8 Linear Equations in Disguise
        • 8th-4.9 An Application of Linear Equations
      • Eighth Module 5
        • 8th M5 Examples of Functions from Geometry
        • 8th-5.1: The Concept of a Function
        • 8th-5.2: Formal Definition of a Function
        • 8th-5.3: Linear Functions and Proportionality
        • 8th-5.4: More Examples of Functions
        • 8th-5.5: Graphs of Functions and Equations
        • 8th-5.6: Graphs of Linear Functions and Rate of Change
        • 8th-5.7: Comparing Linear Functions and Graphs
        • 8th-5.8: Graphs of Simple Nonlinear Functions
        • 8th-5.9: Examples of Functions from Geometry
        • 8th-5.10: Volumes of Familiar Solids—Cones and Cylinders
        • 8th-5.11: Volume of a Sphere
      • Eighth Module 6
        • 8th M6 AB Linear Functions and Bivariate Data
        • 8th – 6.1: Modeling Linear Relationships
        • 8th – 6.2: Formal Definition of a Function
        • 8th – 6.3: Linear Functions and Proportionality
        • 8th – 6.4: More Examples of Functions
        • 8th – 6.5: Graphs of Functions and Equations
        • 8th – 6.6: Graphs of Linear Functions and Rate of Change
        • 8th – 6.7: Comparing Linear Functions and Graphs
        • 8th – 6.8: Graphs of Simple Nonlinear Functions
  • HS Math
    • Class Syllabus and Dates
    • Algebra 1
    • Geometry
      • My Math Bio (or Yo, this is me!)
      • Geometry Module 1
        • Geometry – 1.1: Basic Constructions
        • Geometry 1.2: Construct an Equilateral Triangle
        • Geometry – 1.3: Copy and Bisect an Angle
        • Geometry – 1.4: Construct a Perpendicular Bisector
        • Geometry – 1.5: Points of Concurrencies
        • Geometry – 1.6: Solve for Unknown Angles—Angles and Lines at a Point
        • Geometry – 1.7: Solve for Unknown Angles—Transversals
        • Geometry – 1.8: Solve for Unknown Angles—Angles in a Triangle
        • Geometry – 1.9: Unknown Angle Proofs—Writing Proofs
        • Geometry – 1.10: Unknown Angle Proofs—Proofs with Constructions
        • Geometry – 1.11: Unknown Angle Proofs—Proofs of Known Facts
        • Geometry – 1.12: Transformations—The Next Level
        • Geometry – 1.13: Rotations
        • Geometry – 1.14: Reflections
        • Geometry – 1.15: Rotations, Reflections, and Symmetry
        • Geometry – 1.16: Translations
        • Geometry – 1.17: Characterize Points on a Perpendicular Bisector
        • Geometry – 1.18: Looking More Carefully at Parallel Lines
        • Geometry – 1.19: Construct and Apply a Sequence of Rigid Motions
        • Geometry – 1.20: Applications of Congruence in Terms of Rigid Motions
        • Geometry – 1.21: Correspondence and Transformations
        • Geometry – 1.22: Congruence Criteria for Triangles—SAS
        • Geometry 1.22a Khan Academy
        • Geometry – 1.23: Base Angles of Isosceles Triangles
        • Geometry – 1.24: Congruence Criteria for Triangles—ASA and SSS
        • Geometry – 1.25: Congruence Criteria for Triangles—AAS and HL
        • Geometry – 1.26: Triangle Congruency Proofs
        • Geometry – 1.27: Triangle Congruency Proofs
        • Geometry – 1.28: Properties of Parallelograms
        • Geometry – 1.29: Special Lines in Triangles
        • Geometry – 1.30: Special Lines in Triangles
        • Geometry – 1.31: Construct a Square and a Nine-Point Circle
        • Geometry – 1.32: Construct a Nine-Point Circle
        • Geometry – 1.33: Review of the Assumptions
        • Geometry – 1.34: Review of the Assumptions
      • Geometry Module 2
        • 1: Scale Drawings
        • 2: Making Scale Drawings Using the Ratio Method
        • 3: Making Scale Drawings Using the Parallel Method
        • 4: Comparing the Ratio Method with the Parallel Method
        • 5: Scale Factors
        • 6: Dilations as Transformations of the Plane
        • 7: How Do Dilations Map Segments?
        • 8: How Do Dilations Map Lines, Rays, and Circles?
        • 9: How Do Dilations Map Angles?
        • 10: Dividing the King’s Foot into 12 Equal Pieces
        • 11: Dilations from Different Centers
        • 12 : What Are Similarity Transformations, and Why Do We Need Them?
        • 13 : Properties of Similarity Transformations
        • 14 : Similarity
        • 15 : The Angle – Angle (AA) Criterion for Two Triangles to B e Similar
        • 16 : Between – Figure and Within – Figure Ratios
        • 17 : The Side – Angle – Side (SAS) and Side – Side – Side (SSS) Criteria for Two Triangles to B e Similar
        • 18 : Similarity and the Angle Bisector Theorem
        • 19 : Families of Parallel Lines and the Circumference of the Earth
        • 20 : How Far Away I s the Moon?
      • Geometry Module 3
        • 1: What Is Area?
        • 2: Properties of Area
        • 3: The Scaling Principle for Area
        • 4: Proving the Area of a Disk
        • 5: Three-Dimensional Space
        • 6: General Prisms and Cylinders and Their Cross-Sections
        • 7: General Pyramids and Cones and Their Cross-Sections
        • 8: Definition and Properties of Volume
        • 9: Scaling Principle for Volumes
        • 10: The Volume of Prisms and Cylinders and Cavalieri’s Principle
        • 11: The Volume Formula of a Pyramid and Cone
        • 12: The Volume Formula of a Sphere
        • 13: How Do 3D Printers Work?
      • Geometry Module 4
        • 1: Searching a Region in the Plane
        • 2: Finding Systems of Inequalities That Describe Triangular and Rectangular Regions
        • 3: Lines That Pass Through Regions
        • 4: Designing a Search Robot to Find a Beacon
        • 5: Criterion for Perpendicularity
        • 6: Segments That Meet at Right Angles
        • 7: Equations for Lines Using Normal Segments
        • 8: Parallel and Perpendicular Lines
        • 9: Perimeter and Area of Triangles in the Cartesian Plane
        • 10: Perimeter and Area of Polygonal Regions in the Cartesian Plane
        • 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities
        • 12: Dividing Segments Proportionately
        • 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means
      • Square Root Triangle Generator
    • Algebra 2
      • My Math Bio (or Yo, this is me!)
      • Algebra II Calendar
      • AL2 Weekly Project Response
      • A2 Module 1
        • Algebra 2.1.A.1: Successive Differences in Polynomials
        • Algebra 2.1.A.2: The Multiplication of Polynomials
        • Algebra 2.1.A.3: The Division of Polynomials
        • Algebra 2.1.A.4: Comparing Methods—Long Division, Again?
        • Algebra 2.1.A.5: Putting It All Together
        • Algebra 2.1.A.6: Dividing by x-a and by x+a
        • Algebra 2.1.A.7: Mental Math
        • Algebra 2.1.A.8: The Power of Algebra—Finding Primes
        • Algebra 2.1.A.9: Radicals and Conjugates
        • Algebra 2.1.A.10: The Power of Algebra—Finding Pythagorean Triples
        • Algebra 2.1.A.11: The Special Role of Zero in Factoring
        • Algebra 2.1.B.12: Overcoming Obstacles in Factoring
        • Algebra 2.1.B.13: Mastering Factoring
        • Algebra 2.1.B.14: Graphing Factored Polynomials
        • Algebra 2.1.B.15: Structure in Graphs of Polynomial Functions
        • Algebra 2.1.B.16: Modeling with Polynomials—An Introduction
        • Algebra 2.1.B.17: Modeling with Polynomials—An Introduction
        • Algebra 2.1.B.18: Overcoming a Second Obstacle in Factoring—What If There Is a Remainder?
        • Algebra 2.1.B.19: The Remainder Theorem
        • Algebra 2.1.B.20: Using Remainder Theorem to Plot a Polynomial
        • Algebra 2.1.B.21: Digital Regression and Interpolation
        • Algebra 2.1.C.22: Equivalent Rational Expressions
        • Algebra 2.1.C.23: Comparing Rational Expressions
        • Algebra 2.1.C.24: Multiplying and Dividing Rational Expressions
        • Algebra 2.1.C.25: Adding and Subtracting Rational Expressions
        • Algebra 2.1.C.26: Solving Rational Equations
        • Algebra 2.1.C.27: Word Problems Leading to Rational Equations
        • Algebra 2.1.C.28: A Focus on Square Roots
        • Algebra 2.1.C.29: Solving Radical Equations
        • Algebra 2.1.C.30: Linear Systems in Three Variables
        • Algebra 2.1.C.31: Systems of Equations
        • Algebra 2.1.C.32: Graphing Systems of Equations
        • Algebra 2.1.C.33: The Definition of a Parabola
        • Algebra 2.1.C.34: Are All Parabolas Congruent?
        • Algebra 2.1.C.35: Are All Parabolas Similar?
        • Algebra 2.1.D.36: Overcoming a Third Obstacle to Factoring—What If There Are No Real Number Solutions?
        • Algebra 2.1.D.37: A Surprising Boost from Geometry
        • Algebra 2.1.D.38: Complex Numbers as Solutions to Equations
        • Algebra 2.1.D.39: Factoring Extended to the Complex Realm
        • Algebra 2.1.D.40: Obstacles Resolved—A Surprising Result
      • A2 Module 2
        • 1: Ferris Wheels—Tracking the Height of a Passenger Car
        • 2: The Height and Co-Height Functions of a Ferris Wheel
        • 3: The Motion of the Moon, Sun, and Stars—Motivating Mathematics
        • 4: From Circle-ometry to Trigonometry
        • 5: Extending the Domain of Sine and Cosine to All Real Numbers
        • 6: Why Call It Tangent?
        • 7: Secant and the Co-Functions
        • 8: Graphing the Sine and Cosine Functions
        • 9: Awkward! Who Chose the Number 360, Anyway?
        • 10: Basic Trigonometric Identities from Graphs
        • 11: Transforming the Graph of the Sine Function
        • 12: Ferris Wheels—Using Trigonometric Functions to Model Cyclical Behavior
        • 13: Tides, Sound Waves, and Stock Markets
        • 14: Graphing the Tangent Function
        • 15: What Is a Trigonometric Identity?
        • 16: Proving Trigonometric Identities
        • 17: Trigonometric Identity Proofs
      • A2 Module 3
        • 1: Integer Exponents
        • 2: Base 10 and Scientific Notation
        • 3: Rational Exponents—What are 2^(1/2) and 2^(1/3)?
        • 4: Properties of Exponents and Radicals
        • 5: Irrational Exponents—What are 2^(√2) and 2^π?
        • 6: Euler’s Number
        • 7: Bacteria and Exponential Growth
        • 8: The “What Power” Function
        • 9: Logarithms—How Many Digits Do You Need?
        • 10: Building Logarithmic Tables
        • 11: The Most Important Property of Logarithms
        • 12: Properties of Logarithms
        • 13: Changing the Base
        • 14: Solving Logarithmic Equations
        • 15: Why Were Logarithms Developed?
        • 16: Rational and Irrational Numbers
        • 17: Graphing the Logarithm Function
        • 18: Graphs of Exponential Functions and Logarithmic Functions
        • 19: The Inverse Relationship Between Logarithmic and Exponential Functions
        • 20: Transformations of the Graphs of Logarithmic and Exponential Functions
        • Lesson 21: The Graph of the Natural Logarithm Function
        • Lesson 22: Choosing a Model
        • 23: Bean Counting
        • 24: Solving Exponential Equations
        • 25: Geometric Sequences and Exponential Growth and Decay
        • 26: Percent Rate of Change
        • 27: Modeling with Exponential Functions
        • 28: Newton’s Law of Cooling, Revisited
        • 29: The Mathematics Behind a Structured Savings Plan
        • 30: Buying a Car
        • 31: Credit Cards
        • 32: Buying a House
        • 33: The Million Dollar Problem
      • Quadratic Equation Factorization Chart
    • Advanced Mathematics
      • My Math Bio (or Yo, this is me!)
  • Resources
    • Basic Math Practice
    • Personal Finance
      • Personal Finance Introduction
      • Personal Finance Prospectus
      • Descriptions and Responsibilities
      • Check Register
      • Account Registrer
      • Random Bill Amount
    • Desmos Calculator
    • Sketchometry
    • Seventh Grade Math
      • My Math Bio (or Yo, this is me!)
      • Seventh Grade Math Calendar
      • Seventh Module 1
        • 7th-1.1: An Experience in Relationships as Measuring Rate
        • 7th-1.2: Proportional Relationships
        • 7th-1.3 Identifying Proportional and Non-Proportional Relationships in Tables
        • 7th-1.4: Identifying Proportional and Non-Proportional Relationships in Tables
        • 7th-1.5: Identifying Proportional and Non-Proportional Relationships in Graphs
        • 7th-1.6: Identifying Proportional and Non-Proportional Relationships in Graphs
        • 7th-1.7: Unit Rate as the Constant of Proportionality
        • 7th-1.8 Representing Proportional Relationships with Equations
        • 7th-1.9: Representing Proportional Relationships with Equations
        • 7th-1.10: Interpreting Graphs of Proportional Relationships
        • 7th-1.11: Ratios of Fractions and Their Unit Rates
        • 7th-1.12: Ratios of Fractions and Their Unit Rates
        • 7th-1.13: Finding Equivalent Ratios Given the Total Quantity
        • 7th-1.14: Multi-Step Ratio Problems
        • 7th-1.15: Equations of Graphs of Proportional Relationships Involving Fractions
        • 7th-1.16: Relating Scale Drawings to Ratios and Rates
        • 7th-1.17: The Unit Rate as the Scale Factor
        • 7th-1.18: Computing Actual Lengths from a Scale Drawing
        • 7th-1.19: Computing Actual Areas from a Scale Drawing
        • 7th-1.20: An Exercise in Creating a Scale Drawing
        • 7th-1.21: An Exercise in Changing Scales
        • 7th-1.22: An Exercise in Changing Scales

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