Academic Mathematics Strands and Subgroups in the Grade 9 Course

  • Number Sense and Algebra
              - Operating with Exponents
              - Understanding Characteristics of Linear Relations
  • Linear Relations
              - Using Data Management to Investigate Relationship
              - Using Data Management to Investigate Relationship
              - Connecting Various Representations of Linear Relations
  • Analytic Geometry
              - Relationship Between the Equation of a Relation and the Shape of Its Graph
              - Investigating the Properties of Slope
              - Using the Properties of Linear Relations to Solve Problems
  • Measurement and Geometry
              - Investigating the Optimal Values of Measurements
              - Solving Problems Involving Perimeter, Area, Surface Area, and Volume
              - Investigating and Applying Geometric Relationships

Table of Contents by Nelson

Chapter 1: Rational Numbers

1.1: Interpreting Rational Numbers
1.2: Comparing and Ordering Rational Numbers
1.3: Adding and Subtracting Rational Numbers
1.4: Multiplying and Dividing Rational Numbers
1.5: Order of Operations with Rational Numbers
1.6: Calculating with Rational Numbers
1.7: Solve Problems Using Guess and Test


2.1: Modelling Squares and Cubes
2.2: Expressing a Number as a Power
2.3: Expressing a Number in Many Ways
2.4: Multiplying and Dividing Powers
2.5: Combining Powers
2.6: Communicate about Calculations with Powers
2.7: Calculating Square Roots
2.8: Estimating Square Roots


3.1: Enlargements and Reductions
3.2: Determining Similarity
3.3: Scale Factors
3.4: Drawing a Similar Polygon
3.5: Solving Problems Involving Similar Shapes
3.6: Communicate about Similarity


4.1: Exploring Cube Structures
4.2: Composite Objects and Their Components
4.3: Area of Overlap
4.4: Calculating the Surface Area of Composite Objects
4.5: Solve Problems Using Logical Reasoning


5.1: Describing Relations Algebraically
5.2: Graphing Linear Relations
5.3: Interpreting the Solution of a Linear Equation
5.4: Solving Linear Equations Using Inverse Operations
5.5: Equation-Solving Strategies
5.6: Solve Problems Using Diagrams
5.7: Graphing Linear Inequalities
5.8: Exploring Operations with Inequalities
5.9: Solving a Linear Inequality


6.1: Modelling with Polynomials
6.2: Exploring Models for Polynomials
6.3: Gathering Like Terms
6.4: Adding Polynomials
6.5: Subtracting Polynomials
6.6: Solve Problems Using an Organized List
6.7: Multiplying or Dividing a Polynomial by a Monomial


7.1: Recognizing Probability Situations
7.2: Using Probabilities to Make Decisions
7.3: Communicate about Probability
7.4: Using a Probability to Reach Alternative Conclusions


8.1: Line Symmetry
8.2: Rotation Symmetry
8.3: Symmetry in Art
8.4: Symmetry on the Coordinate Plane
8.5: Solve Problems Using Diagrams


9.1: Relating the Central Angle to an Inscribed Angle
9.2: Comparing Inscribed Angles
9.3: Chord Properties
9.4: Applying Chord Properties
9.5: Tangent Properties
9.6: Solve Problems by Using a Model


10.1: Collecting Data: Asking Appropriate Questions
10.2: Collecting Data: Bias, Sensitivity, and Method
10.3: Selecting a Sample or Population
10.4: Communicating about Collected Data

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Table of Contents by McGraw Hill

Chapter 1: Mathematical Processes

1.1: Focus on Problem Solving
1.2: Focus on Communicating
1.3: Focus on Connecting
1.4: Focus on Representing
1.5: Focus on Selecting Tools and Computational Strategies
1.6: Focus on Reasoning and Proving
1.7: Focus on Reflecting

CHAPTER 2: Relations

2.1: Hypotheses and Sources of Data
2.2: Sampling Principles
2.3: Use Scatter Plots to Analyse Data
2.4: Trends, Interpolation, and Extrapolation
2.5: Linear and Non-Linear Relations
2.6: Distance-Time Graphs

CHAPTER 3: Polynomials

3.1: Build Algebraic Models Using Concrete Materials
3.2: Work With Exponents
3.3: Discover the Exponent Laws
3.4: Communicate With Algebra
Use Technology
Virtual Algebra Tiles With
The Geometer’s Sketchpad®
3.5: Collect Like Terms
3.6: Add and Subtract Polynomials
3.7: The Distributive Property

CHAPTER 4: Equations

4.1: Solve Simple Equations
4.2: Solve Multi-Step Equations
4.3: Solve Equations Involving Fractions
4.4: Modelling With Formulas
4.5: Modelling With Algebra

CHAPTER 5: Modelling With Graphs

5.1: Direct Variation
5.2: Partial Variation
5.3: Slope
5.4: Slope as a Rate of Change
5.5: First Differences
5.6: Connecting Variation, Slope, and First Differences

CHAPTER 6: Analyse Linear Relations

6.1: The Equation of a Line in Slope y-Intercept Form: y = mx + b
6.2: The Equation of a Line in Standard Form: Ax + By + C = 0
6.3: Graph a Line Using Intercepts
Use Technology
Use The Geometer’s Sketchpad®
to Explore Parallel and Perpendicular Lines
6.4: Parallel and Perpendicular Lines
6.5: Find an Equation for a Line Given the Slope and a Point
6.6: Find an Equation for a Line Given Two Points
6.7: Linear Systems

CHAPTER 7: Geometric Relationships

7.1: Angle Relationships in Triangles
7.2: Angle Relationships in Quadrilaterals
7.3: Angle Relationships in Polygons
7.4: Midpoints and Medians in Triangles
7.5: Midpoints and Diagonals in Quadrilaterals

CHAPTER 8: Measurement Relationships

8.1: Apply the Pythagorean Theorem
8.2: Perimeter and Area of Composite Figures
8.3: Surface Area and Volume of Prisms and Pyramids
8.4: Surface Area of a Cone
8.5: Volume of a Cone
8.6: Surface Area of a Sphere
8.7: Volume of a Sphere

CHAPTER 9: Optimizing Measurements

9.1 Investigate Measurement Concepts
9.2 Perimeter and Area Relationships of a Rectangle
9.3 Minimize the Surface Area of a Square-Based Prism
9.4 Maximize the Volume of a Square-Based Prism
9.5 Maximize the Volume of a Cylinder
9.6 Minimize the Surface Area of a Cylinder

Strictly Ontario Curriculum

Mathematical Processes