Mr. Wadge's Math Shack
  • Welcome
  • Grade 12 Courses
    • Calculus 12 >
      • Projects
      • Ch 0: PreCalculus Review >
        • 0.0 One-Day Review
        • 0.1 PreCalculus Review (part 1)
        • 0.2 PreCalculus Review (part 2)
        • 0.3 PreCalculus Review (part 3)
        • 0.4 PreCalculus Review (part 4)
        • 0.5 PreCalculus Review (part 5)
      • Ch 1 Limits and Rates of Change >
        • 1.1 & 1.2 Tangent Problem / Limit of a Function
        • 1.3 One-Sided Limits
        • 1.3 (part 2) Intermediate Value Theorem
        • 5.1 Vertical Asymptotes
        • 5.2 Horizontal Asymptotes
        • 1.4 Using Limits to Find Tangents
        • 1.5 Velocity and Other Rates of Change
        • 1.8 Review Exercises / 1.9 Chapter Test
      • Ch 2 Derivatives >
        • 2.1 Derivatives
        • 2.2 The Power Rule
        • 2.3 The Sum and Difference Rules
        • 2.4 The Product Rule
        • 2.5 The Quotient Rule
        • 2.6 The Chain Rule
        • 2.7 Implicit Differentiation
        • 2.8 Higher Derivatives
        • 2.9 Review Exercises / 2.10 Chapter Test
      • Ch 3 Applications of Derivatives >
        • 3.1 Velocity
        • 3.2 Acceleration
        • 3.3 Rates of Change in the Natural Sciences
        • 3.5 Related Rates
        • 3.6 Newton's Method
        • BONUS: Local Linear Approximation
        • 3.7 Review Exercises / 3.8 Chapter Test
      • Ch 4 Extreme Values >
        • 4.1 Increasing and Decreasing Functions (part 1 of 2)
        • 4.1 Increasing and Decreasing Functions (part 2 of 2)
        • 4.2 Maximum and Minimum Values
        • 4.0 Existence Theorems
        • 4.3 The First Derivative Test
        • 4.4 Applied Maximum and Minimum Problems (part 1 of 2)
        • 4.4 Applied Maximum and Minimum Problems (part 2 of 2)
        • 4.6 Review Exercises / 4.7 Chapter Test
      • Ch 5 Curve Sketching >
        • 5.0 Review
        • 5.3 Concavity and Points of Inflection
        • 5.4 The Second Derivative Test
        • 5.5 A Procedure For Curve Sketching (part 1 of 2)
        • 5.5 A Procedure For Curve Sketching (part 2 of 2)
        • 5.6 Slant Asymptotes
        • 5.7 Review Exercises / 5.8 Chapter Test
      • Ch 6 Trigonometry Review >
        • 6.0 Review (part 1)
        • 6.0 Review (part 2)
        • 6.0 Review (part 3)
      • Ch 7 Derivatives of Trigonometric Functions >
        • 7.1 Limits of Trigonometric Functions
        • 7.2 Derivatives of the Sine and Cosine Functions (part 1 of 2)
        • 7.2 Derivatives of the Sine and Cosine Functions (part 2 of 2)
        • 7.3 Derivatives of Other Trigonometric Functions
        • 7.4 Applications
        • 7.5 Inverse Trigonometric Functions (part 1 of 2)
        • 7.5 Inverse Trigonometric Functions (part 2 of 2)
        • 7.6 Derivatives of the Inverse Trigonometric Functions
        • 7.7 Review Exercises / 7.8 Chapter Test
      • Ch 8 Exponential and Logarithmic Functions >
        • 8.1 Exponential Functions
        • 8.2 Derivatives of Exponential Functions
        • 8.0 Review of Logarithms
        • 8.3 Logarithmic Functions
        • 8.4 Derivatives of Logarithmic Functions
        • 8.6 Logarithmic Differentiation
        • BONUS: Indeterminate Forms and L'Hôpital's Rule
        • 8.7 Review Exercises / 8.8 Chapter Test
      • Ch 9 Area Under Curves >
        • 9.1 Riemann Sums
        • 9.2 The Trapezoidal Rule
        • 9.3 Sigma Notation
        • 9.4 Limit of Riemann Sums
      • Ch 10 Integration >
        • 10.1 Antiderivatives
        • 10.2 The Fundamental Theorem of Calculus
        • 10.3 The Substitution Rule
        • 10.4 Integration by Parts
      • Ch 11 Applications of Integrals >
        • 11.1 The Average Value Theorem
        • 11.2 Volume of Rotational Solids
        • 11.3 Volume of Rotational Solids (part 2)
        • 11.4 Volume of Rotational Solids (part 3)
        • 11.5 Differential Equations
        • 11.6 Slope Fields
      • Ch 12 Cumulative Review >
        • 12.1 Cumulative Review for Chapters 1 – 3
        • 12.2 Cumulative Review for Chapters 4 – 7
        • 12.3 Cumulative Review for Chapters 8 – 9
    • PreCalculus 12 >
      • Term Project Options
      • Review of Grade 11
      • Chapter 1: Sequence and Series >
        • 1.1 Arithmetic Sequences
        • 1.2 Arithmetic Series
        • 1.3 Geometric Sequences
        • 1.4 Geometric Series
        • 1.5 Infinite Geometric Series
        • 1.6 Chapter Review
      • Ch2: Transformations (First Half) >
        • 2.1 Functions and Relations (review)
        • 2.2 Arithmetic Combinations of Functions
        • 2.3 Composite Functions
        • 2.5 Inverse Functions (Part 1 of 2)
        • 2.5 Inverse Functions (Part 2 of 2)
        • 2.7 Chapter Review
      • Ch2: Transformations (Second Half) >
        • 2.4 Transformations of Graphs (Part 1 of 2)
        • 2.4 Transformations of Graphs (Part 2 of 2)
        • 2.6 Combined Transformations
        • 2.7 Chapter Review
      • Ch3: Polynomials >
        • 3.1 Polynomials
        • 3.2 Graphing Polynomial Functions
        • 3.3 Division of Polynomials
        • 3.4 The Remainder and Factor Theorems
        • 3.5 Polynomial Applications
        • 3.6 Chapter Review
      • Ch4: Radicals & Rational Functions >
        • 4.1 Radicals
        • 4.2 Graphing and Solving Radical Equations
        • 4.3 Rational Functions
        • 4.4 Graphing Rational Functions
        • 4.5 Chapter Review
      • Ch5: Logarithms >
        • 5.1 Exponents
        • 5.2 Logarithmic Functions and their Graphs (Part 1 of 2)
        • 5.2 Logarithmic Functions and their Graphs (Part 2 of 2)
        • 5.3 Properties of Logarithms
        • 5.4 Exponential and Logarithmic Equations
        • 5.5 Applications of Exponential and Logarithmic Functions
        • 5.6 Chapter Review
      • Ch6: Trigonometry (Pt. 1) >
        • 6.1 Angles and their Measure
        • 6.2 Trigonometric Functions of Acute Angles
        • 6.3 Trigonometric Function - General & Special Angles
        • 6.4 Graphing Basic Trigonometric Functions (part 1 of 3)
        • 6.4 Graphing Basic Trigonometric Functions (part 2 of 3)
        • 6.4 Graphing Basic Trigonometric Functions (part 3 of 3)
        • 6.5 Application of Periodic Functions
        • 6.6 Chapter Review
      • Ch7: Trigonometry (Pt. 2) >
        • 7.1 Trigonometric Identities and Equations
        • 7.2 Verifying Trigonometric Identities
        • 7.3 Trigonometric Equations (part 1 of 2)
        • 7.3 Trigonometric Equations (part 2 of 2)
        • 7.4 Sum and Difference Identities (part 1 of 2)
        • 7.4 Sum and Difference Identities (part 2 of 2)
        • 7.5 Double Angle Identities
        • 7.6 Chapter Review
      • Old Curriculum Material >
        • 7.1 Fundamental Counting Principle (part 1 of 2)
        • 7.1 Fundamental Counting Principle (part 2 of 2)
        • 7.2 Permutations
        • 7.3 Combinations
        • 7.4 Binomial Theorem
        • 7.5 Pathway Problems
        • 7.6 Chapter Review
      • Final Exam
    • Foundations 12 >
      • Ch 1: Logical Reasoning and Set Theory >
        • 1.1 Connecting Words "And", "Or", "Not"
        • 1.2 Set Theory (Part 1 of 2)
        • 1.2 Set Theory (Part 2 of 2)
        • 1.3 Venn Diagrams - Part One
        • 1.4 Venn Diagrams - Part Two
        • 1.5 Conditional Statements
        • 1.6 Chapter Review
      • Ch 2: Permutations and Combinations >
        • 2.1 The Fundamental Counting Principle (part 1 of 2)
        • 2.1 The Fundamental Counting Principle (part 2 of 2)
        • 2.2 Factorial Notation and Permutations (part 1 of 2)
        • 2.2 Factorial Notation and Permutations (part 2 of 2)
        • 2.3 Permutations with Restrictions
        • 2.4 Permutations with Repetitions
        • 2.5 Combinations - Part 1
        • 2.6 Combinations - Part 2
        • 2.7 Problem Solving with Permutations and Combinations
        • 2.8 Chapter Review
      • Ch 3: Probability >
        • 3.1 Probability Terminology and Notation
        • 3.2 Odds and Probability
        • 3.3 Mutually Exclusive Events and the Event "A ∪ B"
        • 3.4 Independent / Dependent Events and the Event "A ∩ B"
        • 3.5 Solving Problems Using Tables and Diagrams
        • 3.6 Probability Involving Permutations and Combinations
        • 3.7 Chapter Review
      • Ch 4: Exponential and Logarithmic Functions >
        • 4.1 Review and Preview (part 1 of 2)
        • 4.1 Review and Preview (part 2 of 2)
        • 4.2 Analyzing Exponential Functions (part 1 of 2)
        • 4.2 Analyzing Exponential Functions (part 2 of 2)
        • 4.3 Analyzing Logarithmic Functions (part 1 of 2)
        • 4.3 Analyzing Logarithmic Functions (part 2 of 2)
        • 4.4 Interpreting Graphs of Exponential and Logarithmic Functions
        • 4.5 Modelling Data Using Exponential and Logarithmic Functions
        • 4.6 Chapter Review
      • Ch 5: Polynomial and Sinusoidal Functions >
        • 5.1 Polynomial Functions of Degree Zero, One, and Two
        • 5.2 Polynomial Functions of Degree Three
        • 5.3 Modelling Data Using Polynomial Functions
        • 5.4 Angular Measure - Degrees and Radians (part 1 of 2)
        • 5.4 Angular Measure - Degrees and Radians (part 2 of 2)
        • 5.5 Amplitude and Period
        • 5.6 Horizontal & Vertical Shifts
        • 5.7 Modelling Data Using Sinusoidal Functions
        • 5.8 Chapter Review
      • Ch 6: Financial Mathematics >
        • 6.1 Simple Interest andCompound Interest
        • 6.2 Investments Using Compound Interest
        • 6.3 Basic Loans Using Compound Interest (part 1 of 2)
        • 6.3 Basic Loans Using Compound Interest (part 2 of 2)
        • 6.4 Mortgages
        • 6.5 Buying, Renting, and Leasing
        • 6.6 Investment Portfolios
        • 6.7 Chapter Review
  • Grade 11 Classes
    • PreCalculus 11 >
      • Review (what you should already know)
      • Ch1: Factoring and the Quadratic Function >
        • 1.1 Factoring
        • 1.2 Factoring (More Complicated Types)
        • 1.3 Properties of Quadratic Functions
        • 1.4 The Standard Form of a Quadratic Function
        • 1.5 Chapter Review
      • Ch2: Quadratic Transformations >
        • 2.1 Finding the Equation of a Parabola
        • 2.2 General Form to Standard Form
        • 2.3 Vertex of a Parabola
        • 2.4 Applications of Quadratic Functions
        • 2.5 Chapter Review
      • Ch3: Quadratic Equations >
        • 3.1 Solving Quadratic Equations by Factoring
        • 3.2 Completing the Square and Square Root Property
        • 3.3 The Quadratic Formula
        • 3.4 Graphing Calculator and the Discriminant
        • 3.5 Applications of Quadratic Equations
        • 3.6 Chapter Review
      • Ch4: Systems of Equations >
        • 4.1 Graphing Non-Linear Systems of Equations
        • 4.2 Solving Non-Linear Systems Algebraically
        • 4.3 Graphing Linear Inequalities in Two Variables
        • 4.4 Graphing Non-Linear Inequalities
        • 4.5 Applications of Inequalities
        • 4.6 Chapter Review
      • Ch5: Radicals >
        • 5.1 Radical Operations (Part 1 of 2)
        • 5.1 Radical Operations (Part 2 of 2)
        • 5.2 Simplifying Radicals
        • 5.3 Adding and Subtracting Radical Expressions
        • 5.4 Multiplying and Dividing Radical Expressions (Part 1 of 2)
        • 5.4 Multiplying and Dividing Radical Expressions (Part 2 of 2)
        • 5.5 Radical Equations
        • 5.6 Chapter Review
      • Ch6: Rational Functions >
        • 6.1 Properties of Rational Expressions
        • 6.2 Multiplication and Division of Rational Expressions
        • 6.3 Sums and Differences of Rational Expressions
        • 6.4 Mixed Operations
        • 6.5 Rational Equations
        • 6.6 Graphing Rational Functions
        • 6.7 Applications of Rational Equations
        • 6.8 Chapter Review
      • Ch7: Trigonometry >
        • 7.1 Angles and their Measure
        • 7.2 The Three Trigonometric Functions
        • 7.3 Special Angles
        • 7.4 & 7.5 Oblique Triangles / Law of Sines (Part 1)
        • 7.5 Law of Sines (Part 2)
        • 7.6 Law of Cosines
        • 7.7 Chapter Review
      • Ch8: Finance >
        • 8.1 Investments and Loans
        • 8.2 Effective Interest Rates and Annuities
        • 8.3 Stocks and Bonds
        • 8.4 Instalment Loans
        • 8.5 Canadian Mortgages
        • 8.6 Chapter Review
      • Final Exam Review
      • Old Curriculum Material >
        • 1.1 Absolute Value
        • 4.3 Absolute Value Functions
        • 4.4 Solving Absolute Value Equations
        • 4.5 Rational Functions
        • 4.6 Reciprocal Functions (Part 1 of 2)
        • 4.6 Reciprocal Functions (Part 2 of 2)
        • 4.7 Chapter Review
    • Foundations 11 >
      • Ch 1: Rates and Scale Factor >
        • 1.1 Ratios and Rates
        • 1.2 Visualizing Rates
        • 1.3 Similar Figures
        • 1.4 Perimeter, Area and Surface Area of Similar Figures
        • 1.5 Volume of Similar Figures
        • 1.6 Chapter Review
      • Ch 2: Geometry >
        • 2.1 Geometry
        • 2.2 Proofs
        • 2.3 Polygons
        • 2.4 Compass and Straightedge Construction
        • 2.5 Chapter Review
      • Ch 3: Non-Right Angle Triangles >
        • 3.1 Review of Sine, Cosine and Tangent for Right Triangles
        • 3.2 Law of Sines (Part 1 of 2)
        • 3.2 Law of Sines (Part 2 of 2)
        • 3.3 Law of Cosines
        • 3.4 Applied Problems
        • 3.5 Chapter Review
      • Ch 4: Analyze Puzzles and Games >
        • 4.1 Patterns
        • 4.2 Inductive Reasoning
        • 4.3 Deductive Reasoning
        • 4.4 Puzzles and Games of Strategy
        • 4.5 Chapter Review
      • Ch 5: Statistics >
        • 5.1 Mean, Median and Mode
        • 5.2 Standard Deviation
        • 5.3 The Normal Distribution (Part 1 of 2)
        • 5.3 The Normal Distribution (Part 2 of 2)
        • 5.4 Confidence Interval for Means
        • 5.5 Chapter Review
      • Ch 6: Linear Systems >
        • 6.1 Review: Graphing a Linear Equation (Part 1 of 2)
        • 6.1 Review: Graphing a Linear Equation (Part 2 of 2)
        • 6.2 Linear Inequalities
        • 6.3 Linear Programming
        • 6.4 Application of Linear Programming
        • 6.5 Chapter Review
      • Ch 7: Quadratic Functions >
        • 7.1 Quadratic Functions (Part 1 of 3)
        • 7.1 Quadratic Functions (Part 2 of 3)
        • 7.1 Quadratic Functions (Part 3 of 3)
        • 7.2 General Form of a Quadratic Function
        • 7.5 Application of Quadratic Functions & Equations (part 1 of 2)
        • 7.0 Graphing Non-Linear Systems of Equations (Part 1 of 2)
        • 7.0 Graphing Non-Linear Systems of Equations (Part 2 of 2)
        • 7.6 Chapter Review
      • Ch8: Math Research Project
      • Old Curriculum Material >
        • 7.3 Quadratic Equations
        • 7.4 Solving Quadratic Equations (part 1 of 2)
        • 7.4 Solving Quadratic Equations (part 2 of 2)
        • 7.5 Application of Quadratic Functions & Equations (part 2 of 2)
    • Workplace 11 >
      • Ch 1: Slope and Rate of Change >
        • 1.1 Ratios and Proportions
        • 1.2 Rates / Solving Problems with Proportions
        • 1.3 Slope
        • 1.4 Angle of Elevation
        • 1.5 Pitch, Grade, and Drop
        • 1.6 Calculating Slope on a Coordinate Plane
        • 1.7 Calculating Slope from Ordered Pairs
        • 1.8 Rate of Change
        • 1.9 Interpolation and Extrapolation
      • Ch 2: Graphs and Statistics >
        • 2.1 Broken Line Graphs
        • 2.2 Bar Graphs
        • 2.3 Pictographs
        • 2.4 Histograms
        • 2.5 Review of Percents / Circle Graphs ​(part 1 of 2)
        • 2.5 Making Circle Graphs (part 2 of 2)
        • 2.6 Graphs and Technology
        • 2.7 Other Types of Graphs
        • 2.8 Misleading Graphs
        • 2.9 Mean, Median, Mode, and Range
        • 2.10 Standard Deviation
      • Ch 3: Scale Factor and Representations >
        • 3.1 Scale Factor
        • 3.2 Scale Diagrams
        • 3.3 One-Point Perspective
        • 3.4 Two-Point Perspective
        • 3.5 Exploded Views and Component Parts
        • 3.6 Orthographic Drawings
        • 3.7 Isometric Drawings
        • 3.8 Oblique Drawings
      • Ch 4: Financial Literacy >
        • 4.1 Financial Institutions
        • 4.2 Bank Accounts
        • 4.3 Bank Statements
        • 4.4 Simple Interest
        • 4.5 Compound Interest
        • 4.6 Compounding Periods
        • 4.7 Credit
        • 4.8 Loans
        • 4.9 Mortgages
        • 4.10 Mortgage Payments
        • 4.11 Investments
  • Grade 8, 9, 10 Classes
    • Foundations & PreCalculus 10 >
      • Problem Sets
      • Review (what you should already know)
      • Ch 1: Measuring Systems, Surface Area, and Volume >
        • 1.1 Metric Systems
        • 1.2 Imperial Systems
        • 1.3 Converting Metric and Imperial Systems
        • 1.4 Surface Area and Volume of Prisms (part 1 of 2)
        • 1.4 Surface Area and Volume of Prisms (part 2 of 2)
        • 1.5 Surface Area and Volume of Pyramids
        • 1.6 Surface Area and Volume of Cylinders, Cones, and Spheres
        • 1.7 Chapter Review
      • Ch 2: Radicals >
        • 2.1 Number Systems
        • 2.2 Greatest Common Factor and Least Common Multiple (part 1 of 2)
        • 2.2 Greatest Common Factor and Least Common Multiple (part 2 of 2)
        • 2.3 Squares and Square Roots
        • 2.4 Rational And Irrational Numbers
        • 2.5 Simplifying Radicals
        • 2.6 Exponential Notation (part 1 of 3)
        • 2.6 Exponential Notation (part 2 of 3)
        • 2.6 Exponential Notation (part 3 of 3)
        • 2.7 Chapter Review
      • Ch 3: Polynomials >
        • 3.1 Classifying Polynomials (part 1 of 2)
        • 3.1 Classifying Polynomials (part 2 of 2)
        • 3.2 Multiplying Polynomials
        • 3.3 Removing Common Factors
        • 3.4 Factoring x^2 + bx + c (part 1 of 2)
        • 3.4 Factoring x^2 + bx + c (part 2 of 2)
        • 3.5 Factoring ax^2 + bx + c
        • 3.6 Special Factors
        • Algebra Tiles
        • 3.7 Chapter Review
      • Ch 4: Relations and Functions >
        • 4.1 Relations
        • 4.2 Functions
        • 4.3 Linear Equations
        • 4.4 Non-Linear Equations
        • 4.5 Graphing with a Calculator
        • 4.6 Chapter Review
      • Ch 5: Linear Functions >
        • 5.1 Slope
        • 5.2 Rate of Change
        • 5.3 Graphing Linear Functions
        • 5.4 Parallel and Perpendicular Lines
        • 5.5 Applications of Linear Relations
        • 5.6 Chapter Review
      • Ch 6: Linear Equations >
        • 6.0 Rewriting Equations
        • 6.1 Different Forms of Linear Equations (part 1 of 2)
        • 6.1 Different Forms of Linear Equations (part 2 of 2)
        • 6.2 Special Cases of Linear Equations
        • 6.3 Equations of Parallel and Perpendicular Lines
        • 6.4 Linear Applications and Modelling
        • 6.5 Function Notation
        • 6.6 Chapter Review
      • Ch 7: Solving Linear Systems >
        • 7.1 Solving Linear Systems by Graphing
        • 7.2 Solving Linear Systems by Addition
        • 7.3 Solving Linear Systems by Substitution
        • 7.4 Problem Solving with Two Variables
        • 7.5 Chapter Review
      • Ch 8: Trigonometry >
        • 8.1 Sine, Cosine, and Tangent for Right Triangles (part 1 of 2)
        • 8.1 Sine, Cosine, and Tangent for Right Triangles (part 2 of 2)
        • 8.2 Relationships Between Sine, Cosine, and Tangent
        • 8.3 Special Angles
        • 8.4 Applications of Trigonometry
        • 8.5 Compound Trigonometry Applications
        • 8.6 Chapter Review
    • Math 9 >
      • Ch 1: Square Roots, Powers, and Exponent Laws >
        • 1.1 Square Roots
        • 1.2 Square Roots of Big & Small Numbers
        • 1.3 Estimating Square Roots
        • 1.4 Powers
        • 1.5 Order of Operations
        • 1.6 Exponent Rules
        • 1.7 Power Rules
        • 1.8 Review
      • Ch 2: Finance >
        • 2.1 Salary and Wages
        • 2.2 Commission
        • 2.3 Tips and Piecework
        • 2.4 Deductions
        • 2.5 Simple Interest
        • 2.6 Budgeting
      • Ch 3: Rational Numbers >
        • 3.1 Rational Numbers
        • 3.2 Operations with Integers
        • 3.3 Operations with Decimals
        • 3.4 Dividing Decimals
        • 3.5 Multiplying and Dividing Fractions
        • 3.6 Adding Fractions
        • 3.7 Subtracting Fractions
        • 3.8 Adding and Subtracting Negative Rational Numbers
        • 3.9 Order of Operations with Rational Numbers
        • 3.10 Review
      • Ch 4: Polynomials >
        • 4.1 Defining Polynomials
        • 4.2 Simplifying Polynomials
        • 4.3 Adding & Subtracting Polynomials
        • 4.4 Multiplying Polynomials
        • 4.5 Dividing Polynomials
        • 4.6 Order of Operations with Polynomials
      • Ch 5: Linear Equations >
        • 5.1 One-Step Equations
        • 5.2 Two-Step Equations
        • 5.3 Using the Distributive Property
        • 5.4 Combining Like Terms
        • 5.5 Variables on Both Sides of an Equation
        • 5.6 Clearing Fractions
        • 5.7 Solving ANY Linear Equation
        • 5.8 Writing Algebraic Equations
      • Ch 6: Proportional Reasoning >
        • 6.1 Congruent Triangles
        • 6.2 Similar Triangles (Part 1 of 2)
        • 6.2 Similar Triangles (Part 2 of 2)
        • 6.3 Similar Polygons
        • 6.4 Scale Factor
        • 6.5 Scale Diagrams
        • 6.6 Unit Conversions
      • Ch 7: Statistics >
        • 7.1 Statistics
      • Ch 8: Linear Relations >
        • 8.1 Patterns (part 1 of 2)
        • 8.1 Patterns (part 2 of 2)
        • 8.2 Modeling Real-Life Situations
        • 8.3 Cartesian Plane
        • 8.4 Graphing a Table of Values
        • 8.5 Interpolation and Extrapolation
    • Math 8 >
      • Ch 1: Integers >
        • 1.1 Multiplying Integers
        • 1.2 Dividing Integers
        • 1.3 Adding Integers
        • 1.4 Subtracting Integers
        • Practice
      • Ch 2: Fractions >
        • 2.1 Basic Fraction Skills
        • 2.2 More Fraction Skills
        • 2.3 Multiplying Fractions
        • 2.4 Multiplying Mixed Fractions
        • 2.5 Dividing Fractions
        • 2.6 Dividing Mixed Fractions
        • 2.7 Adding and Subtracting Fractions
        • 2.8 Adding Mixed Fractions
        • 2.9 Subtracting Mixed Fractions
        • 2.10 Order of Operations with Fractions
        • Practice
      • Ch 3: Percent, Proportions, Ratio, and Rate >
        • 3.1 Converting Fractions, Decimals, & Percents
        • 3.2 Solving Proportions
        • 3.3 Percents
        • 3.4 Common Percent Problems
        • 3.5 Ratios
        • 3.6 Rates
        • 3.7 Proportion Problems
        • Handouts
      • Ch 4: Square Roots and the Pythagorean Theorem >
        • 4.1 Perfect Squares and Square Roots
        • 4.2 Estimating Square Roots
        • 4.3 Cube and Cube Roots
        • 4.4 The Pythagorean Theorem
        • 4.5 The Pythagorean Theorem (continued)
        • 4.6 Applications of the Pythagorean Theorem
        • Practice
      • Ch 5: Probability and Statistics >
        • 5.1 Probability
        • 5.2 Probability with Cards
        • 5.3 Tree Diagrams
        • 5.4 Independent and Dependent Events
        • 5.5 Dependent Events
        • 5.6 Measures of Central Tendency
      • Ch 6: Linear Equations and Relations >
        • 6.1 Algebraic Expressions
        • 6.2 Solving One-Step Equations
        • 6.3 Solving Two-Step Equations
        • 6.4 The Distributive Property
        • 6.5 The Cartesian Plane
        • 6.6 Linear Relations
        • 6.7 Linear Models
      • Ch 7: Geometry >
        • 7.1 Area Review
        • 7.2 Area of Composite Shapes
        • 7.3 Volume of Prisms
        • 7.4 Volume of Composite Shapes
        • 7.5 Surface Area of Prisms
        • 7.6 Surface Area of Cylinders
        • 7.7 Surface Area of Composite Shapes
  • (Retired) Blog
  • Marks
  • Contact Mr. Wadge

Student of the Week

7/3/2014

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This week's Student of the Week is Nour MG.

The amazing thing about Nour is she seems to get exponentially smarter every year! In grade 9 (when I first taught her) she was already a strong student. But every year since then she has made incredible strides until now - in grade 12 - I'd have to say she is one of the strongest math students in the school!

What's really impressive about Nour is the SPEED at which she figures things out. Sometimes she'll ask for help and I'll be about 1/4 of the way through my explanation: "Okay, I get it now" she'll say. And away she'll go. If I try to keep explaining it to her, she gives me a look like "Please stop talking. I want to forge ahead on my work now". hahaha She's very polite about it but she doesn't like to be interrupted when she's in her groove.

Nour is one of my CS students this year and - once again - SPEED is her secret weapon. To be fair, there are two CS's at the same time (the amazing Samantha G is also there) but, still, I can not believe how fast these girls work. I'll give them some task (make a poster and colour it, etc) and think "that should keep them busy for a few days" and 20 minutes later they are back. "All done". HOW?!??! And they do such a good work. Much, much appreciated!

One of the cutest things about Nour is when she makes a mistake (not very often) on a test or quiz and then I hand it back to her. She gets so perturbed... but in a good way. She'll be laughing and making fun of herself. "How could I be so dumb? It's so ANNOYING!!". It's great because she really cares about her mark, she wants to do well, and she works really hard. But when she makes a mistake, though she is annoyed, she never lets it impact her happy disposition (at least, not in front of me). 

It's been a pleasure teaching you for the past four years, Nour. It was truly very, very easy. I hope you take more math courses at university because I know you will be successful in them. In fact, I know that you will be successful in WHATEVER you put your mind to in the future. You are smart enough and personable enough to do whatever you want. Chase your dreams - I know you will reach them!
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Student of the Week

21/2/2014

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This week's Student of the Week is Sophia K!

The first thing that must be said about Sophia is that she has the absolute BEST first name!! It's even spelled correctly! Way to go, Sophia's parents! Way to go parents-of-Sophias everywhere!!

One thing I am very thankful for is that fact that Sophia has a spare block during Block F. Now why would that be? Because, Sophia often uses that time to come to a SECOND PreCalculus 12 class! That means I get to see Sophia not once, but twice, in a single DAY! 
This is a good thing because Sophia is a fantastic person! She's always so soft-spoken and polite. Every time I go to help her with her work she thanks me... EVERY time!! How great is that?!? Add to that, Sophia's great sense of humour and her willingness to work hard, and she is basically a dream student.

One of the things I love most about Sophia is her commitment to completion; this girl keeps working and working until she gets everything done. Have you ever seen Sophia get frustrated? It's actually pretty cute. With most students, when they are ranting away about math ("this is too hard? How are we supposed to do this?" etc) I get this feeling that, unless I say something (quick!), the student is going to give up completely. But with Sophia, even when she is telling me how hard something is, I have absolutely no doubt that she is going to keep trying and trying and trying... In other words, it doesn't scare me at all when she is complaining about her math troubles (sorry Sophia!).

Thanks, Sophia, for being such a great student, and a wonderful person. I am very thankful that I got to teach you four straight years. I know that, with your great determination and ultra-charming personality, that you will be successful in the future. And I know that i will miss you...

Good luck!
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Student of the Week

1/2/2014

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This week's Student of the Week is Jenny O!

Jenny is known to miss Math class from time to time  :(
But I'm always a little happier when she DOES show up.  :)

Jenny is blessed with a giant, beautiful smile. And she has always been very generous with sharing it with me. How can you not feel a little bit better about things in the world after seeing that grin of hers? It's THAT powerful!

Jenny and I have had a good many talks together over the years. Some have been light and funny and others have been more serious. No matter the tone, I always enjoy talking with Jenny. She is a very thoughtful and engaged conversationalist. She really considers what I have to say and offers her own well-expressed opinions. 

Jenny always has the final word on whether some of my more adventurous clothing decisions (scarves, denim shirt, camouflage tie, etc) are truly fashionable or just faux pas. This girl has style! Ten other people could tell me I look ridiculous but if Jenny gives her seal of approval... that's good enough for me!

Dear Jenny, I know that Math has been difficult at times (there MAY be a correlation between difficulty level and number of absences, by the way). I admire you very much for continuing all the way to PreCalculus 12. It would have been easier to stop after grade 11 but you never did. I'm so proud of you for that!  

Thank you for all the great chats we have had together these past four years. Thanks for your perseverance, your patience and for believing in yourself. I believe in you too, Jenny! I know that you will do amazing, creative, and worthwhile things in this world and I look forward to seeing what they will be!

Go get 'em J.O.!!
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Student of the Week

25/1/2014

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This week's Student of the Week is Dolores C!

I remember when she first arrived in my class in grade 9. I was a little intimidated by Dolores. "Whoa! This is one powerful, opinionated, determined girl!". I did not want to get on her bad side... I had the impression that she could make my life difficult.

Four years later and I now see these same traits - powerful, opinionated, determined - as Dolores's greatest attributes. I love how Dolores thinks issues through on her own, forms her own opinions and isn't scared to defend her position. I love how she is hungry for different ways of looking at life. I love her confidence and her kindness and her inquisitiveness. 

I have learned so much from Dolores. She has explained such things as:
  1. the difference between "Serbian" and "Serb"
  2. why Novak Djokovic is more than just a tennis player; he's a cultural symbol
  3. why new fathers should always wear more than one shirt
  4. the soothing powers of "chorba"
  5. various intricacies of the Serbian language, culture and geography

I would love to be able to see twenty years in the future and see what Dolores is up to at such time. With her incredible work ethic, charismatic personality, and well-earned self-confidence, she truly has countless avenues open to her. And I KNOW that she will be successful with whatever path she travels down.

Thank you Dolores for all the good talks we have shared together, the big laughs we have enjoyed together, and the (math) struggles we have conquered together. You have always treated me with respect, affection, and thoughtfulness and I love you for it!

I will think of you always when I look in the far back left corner of my classroom. Henceforth, I will refer to it always as "Dolores's Corner"...
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Student of the Week

14/12/2013

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This week's Student of the Week is Stefan A!

Stefan is another one of the students (well, to be more accurate, another one of the boys) in grade 12 that has, over his time at KG, sometimes run afoul of the rules of the school. I know there are some teachers who have had "run-ins" with Stefan, and I have to believe them when they relate these stories to me...

BUT THEY ARE HARD TO BELIEVE!!!

In the four years I have taught him, I honestly have never had to discipline Stefan in any way. Nothing! Not a single word. Maybe (MAYBE!!) I asked him to lower his voice on a couple of occasions but, c'mon, I've asked every ONE of you to lower your voices at least once.

So way to go Stefan! And thank-you very much!

Here's some other things about Stefan that I will not soon forget:
  1. the tremendous determination and hard-work that he has displayed in math class. Every year, he has worked harder and harder. He has developed into a very dedicated and serious student. Well done, Sir!
  2. the equal amount of hard-work that he displayed on the basketball court. Too bad there was no team this year S.A.! But it gave you more time to work on Math!! :)
  3. the time someone claimed that Stefan and I looked like father and son. Although silly, I can KIND OF see what they are talking about. Slim, dark-haired, wickedly handsome (ok. ok. The last one only applies to "my son").
  4. the couple of weeks when Stefan's abs became a KG sensation. I know that I should not admit to remembering this, but it was QUITE the sensation. Some people were literally in a tizzy over it / them (I will not mention any names here)

It's been fun, Stefan! Keep up your tremendous efforts. Thanks for always being so friendly and polite to me. You may not actually be my son, but I'm pretty darn proud of you anyway!!
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Student of the Week

26/10/2013

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This week's Student of the Week is Mursal N. (another 5-time Wadge math student). And, once again, I need a photo of this lovely human being. I would be most obliged if someone would send one to [email protected] (Thanks again Moe!)

Mursal has always been a quiet, gentle presence in my class. I remember, even in grade 8, being struck by her poise and her maturity. She always carries herself with great dignity. She is the sort of student who - I fear - must look at me sometimes and think: "why is my math teacher WAY more immature than I am? Why doesn't this guy grow up?". Not that I get the sense she is judging me - Mursal is way too kind for that - but this girl exudes nothing but class.

I am so pleased that Mursal took on the challenge of tackling Pre-Calculus 12 this year. And I was SOOOO excited and proud when I marked her first test of the year. She did AMAZING!! She's working hard and it's paying off! Go Mursal! You can do it!!

Thanks for believing in yourself, for working hard, and for being so fantastic Mursal! And thanks for being in my class for five straight years. It's been a pleasure getting to know you over that time.

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Student of the Week

5/10/2013

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Four incredible facts about this photo:
  1. that's MY cat!!! It's the amazing and wonderful Chloe!! What a magnificent animal!! So cute! So sweet! Yeah Chloe!!
  2. This photo was taken in my house!!! Yes, MY house!! Scary, right?? No need to worry. This lovely student is friends with my daughter. They were hanging out (with Chloe, apparently)  last summer.
  3. Speaking of my daughter, this photo includes her, looking hilariously grumpy (and with an apparent squished head). Sadly, she insisted that I crop her out of the photo. Boooooo! (Oh well, she'll never know if you ask me to see the photo at school)
  4. The other living being in this photo is the fantastically special Blaga!!!!


And today is the fantastically special Blaga's birthday! I am hoping that she has a great, great day. She deserves it. She is a kind and thoughtful person. Each and every class, as she is leaving, she always says "goodbye" to me. Every day! Even on days when I'm grumpy or angry or irritable. She always says goodbye. It's a small gesture but it has become a very special part of my day. What will I do next year when entire days pass by with no "goodbyes" from Blaga? I don't like to think of such things (maybe a photo posted by my door with her waving at me?). I will really, really miss her...

I remember last year when Blaga's class had a TOC when I was away. When I returned I found out that the TOC and Sophia K had gotten in a "little" argument (something about a cell phone, right SK?). And I remember how angry Blaga was about it. I think she may have even given the TOC a piece of her mind. While I don't condone berating VSB teaching staff, I do remember being touched my Blaga's loyalty to her friend. I believe, in the four years that I have taught Blaga, that this was the only time I have ever seen her angry. She is truly a gentle soul. And - obviously - a good person to count as one of your friends.

Have a great birthday Blaga! I will ALWAYS remember the date of your birthday (for obvious reasons). And, every October 5, I will think back to that kind and generous girl who I got to teach in grade 9, 10, 11, and 12. Lucky me!!

Thanks for being so awesome, Blaga!!
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Student(s) of the week!

27/9/2013

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It's Ayla!... It's Shali!... It's Shayla!!!!

The plan was for Shali to be this week's S.O.W. But how could I NOT include Ayla with her? Yeah, yeah, yeah... I know... Ayla's not even taking math this year but c'mon - these two make an incredible pair.

I loved having Shali and Ayla in my class together the last few years. It was wonderful to see how hard they worked together, supported each other, laughed with (and at) each other. These two get along incredibly well. There is something special about seeing two people who are the very best of friends... people like Shali and Ayla.

Of course, Ayla is also an incredible athlete! She was kind enough to invite me out to one of her gymnastic competitions a couple years ago... WOW!! So talented!! I admire her for all the time and effort that she puts into her sport. Such commitment!!

Shali is another one of my extra-special "taught 5 times" students. In those five years, she has arrived each day with a warm smile, a kind word, and a willingness to work her hardest. She is the kind of student who makes my job fun and easy and rewarding.

Thanks to both of you - Shali and Ayla - for being such unique and special individuals. But thanks even more for inspiring me with your beautiful friendship. It's a truly wonderful thing to behold!

Friendship is the hardest thing in the world to explain. It's not something you learn in school. But if you haven't learned the meaning of friendship, you really haven't learned anything.
                -Muhammad Ali
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Student of the Week #3

20/9/2013

5 Comments

 
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This week's student of the week is a big one - it's Daniel G (all 7 feet of him... or however tall he is)! I've seen this guy grow - A LOT!! - over the past five years, both in height and as a student. I think he may have sat in the back right corner in each of the five years I've taught him. While this may have been a strategy in grade 8 to avoid detection, he now works away in the same back corner, diligently getting his math done.

Daniel is one of the (many) kids in the Class of 2014 who mystify me when I hear from other teachers that he can be a bit... uh... challenging. I honestly can not think of a single time that Daniel has caused a problem in my class (besides his unwillingness to pay for his workbook). In fact, one of the things I will always remember about Daniel is his gentle nature and friendliness. I will miss his giant smile and warm welcome ("Greetings Friends") next year.

One last thing about Daniel. Whenever my daughter tells me that she is going downtown and I ask: "who are you meeting down there?" and she answers: "[whoever] and [whoever] and Daniel G" I breathe a sigh of relief. With this guy by her side I can sleep peacefully knowing that she is safe and sound.

Thanks for protecting my daughter Daniel. And thanks for being a great guy. Everyone loves a gentle giant... and that describes you perfectly!! 
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Student of the Week #2

15/9/2013

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Here's this week's Student of the Week. It's Galena B!! 

The G.B. teaching (non-Flip) method is named after Galena. Why? Because she HATES the Flipped Classroom method. But - in my 5 wonderful years of teaching Galena - I have never seen
anything else that Galena hates. She is a ray of sunshine in my classroom. Always kind. Always smiling. Always serious about her work. 

I remember when my daughter was going to come visit KG for the first time and I had this thought: "Sophia and Galena are kind of similar. I bet they'd get along great". So when Sophia arrived in my class I directed her to the back table where Galena would be sitting.

Galena arrived, class started... and I never saw them even look at each other (never mind saying a single word). Kind of awkward... or at least I thought. Turns out they connected (somehow) and have now spent quality time baking cookies, eating sushi, and doing (uh...) other stuff.

I have no idea what Galena's plans are for next year, after grade 12, but I do know two things with all certainty:

  1. She will be successful with whatever she sets her mind to doing
  2. I will miss her very much


Thank you Galena for being such a special student. I would have considered myself lucky to have taught you a single time. To teach you five times?!?!? I've been truly blessed...

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Student of the Week - First Ever!!!

10/9/2013

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Here's something new. It's my first ever Student of the Week. And here's something else: I never even asked the student for permission (hope he doesn't mind...)

Anyway, this is Moe G. and you gotta love this guy. Well, NOW you gotta love this guy. Grade 8 was a different story. I remember one time I had to go downstairs to get something in the middle of Moe's grade 8 class. This was probably the second week of school; you know, the time of year when grade 8's are supposed to still be quiet and respectful and a little fearful.

Well, I'm coming back from the office and I can hear Moe SCREAMING... and I'm still on the second floor. And you KNOW how much I hate screaming (#1 on Mr. Wadge's "Big Nose" list). I ran up the stairs in record time and took that guy outside the classroom. We had a short "discussion". I believe he experienced the fear that I mentioned earlier!

And now it's five years of math later. Moe has become one of my most dedicated, hard-working students. I am really proud of him for always trying to do his best, for getting involved with all the theatre productions (the guy is an amazing actor!) and for always being in such a friendly, light-hearted mood. I will really miss him next year. But now he can live forever on this incredible blog of mine!!

You are awesome Moe! Thanks for being in my class for the past 5 years! I won't forget you (blog or no blog)...
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    P. Wadge

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