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Mr. Clarkson's Math
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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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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
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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
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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
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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
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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
Scope and Sequence
Class Calendars
Year at a Glance (YAG)
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Seventh Grade Calendar
Seventh Grade YAG
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Eighth Grade Calendar
Eighth Grade YAG
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Geometry Calendar
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Algebra II YAG
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