## Applied Mathematics Strands and Subgroups in the Grade 9 Course

• Number Sense and Algebra
- Solving Problems Involving Proportional Reasoning
- Simplifying Expressions and Solving Equations
• Linear Relations
- Using Data Management to Investigate Relationships
- Determining Characteristics of Linear Relations
- Investigating Constant Rate of Change
- Connecting Various Representations of Linear Relations and Solving Problems Using the Representation
• Analytic Geometry
- Investigating the Optimal Values of Measurements of Rectangles
- Solving Problems Involving Perimeter, Area, and Volume
- Investigating and Applying Geometric Relationships

### Chapter 1: Ratios, Rates, and Proportions

1.1: Equivalent Ratios
1.2: Proportional Thinking
1.3: Unit Rates
1.4: Proportions
1.5: Ratios as Percents

### CHAPTER 2: One- and Two-Dimensional Measurement

2.1: Pythagorean Theorem
2.2: Perimeter of Composite Shapes
2.3: Area of Composite Shapes
2.4: Perimeter and Area Relationships

### CHAPTER 3: Data Relationships

3.1: Interpreting Scatter Plots
3.2: Constructing Scatter Plots
3.3: Drawing Lines and Curves of Best Fit
3.4: Designing Experiments

### CHAPTER 4: Characteristics of Linear Relations

4.1: Graphs of Linear Relations
4.2: Rate of Change
4.3: Direct Variation
4.4: Partial Variation
4.5: Connecting Variation, Rate of Change, and First Differences

### CHAPTER 5: Linear Relations

5.1: Describing Linear Relations
5.2: Connecting Graphs to Events
5.3: Representing Linear Growing Patterns
5.4: Analysing Linear Models
5.5: Point of Intersection of Two Linear Relations

### CHAPTER 6: Three-Dimensional Measurement

6.1: Volume of Prisms and Cylinders
6.2: Volume of Pyramids and Cones
6.3: Volume of Spheres

### CHAPTER 7: Algebraic Modelling

7.1: Geometric Representations of x, x2, and x3
7.2: Substituting and Evaluating
7.4: Multiplying a Polynomial by a Monomial
7.5: Solving Equations
7.6: Solving More Complex Equations

### CHAPTER 8: Geometric Relationships

8.1: Classifying and Estimating Angles
8.2: Angle Relationships of Triangles
8.3: Angles of Quadrilaterals and Other Polygons
8.4: Angles of Parallel Lines

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### Chapter 1: Numbers and Operations

1.1:Integers and Rational Numbers
1.2: Number forms: Percents, Fractions, Decimals
1.3: Natural Number Exponents
1.4: Squaring and Square Rooting
1.5: Order of Operations
1.6: Ratios and Unit Rates

### CHAPTER 2: Algebra

2.1: Substitution and Evaluating for variables in the 1st degree and 3rd degree
2.2: Simplify Expressions (3rd degree of 1 variable)
2.3: Simplify Expressions (3rd degree, 1 variable multiplication of monomials with polynomials)

### CHAPTER 3: Equations

3.1: Solve Simple Equations
3.2: Solve Equations with Brackets
3.3: Proportion Problems
3.4: Percentage Problems

### CHAPTER 4: Angle Geometry

4.1: Pythagoras and Applications
4.2: Properties of Relationships of Interior and Exterior Angles of a Triangles, Quads, and Polys
4.3: Angles Formed by Parallel Lines with Transversal Lines

### CHAPTER 5: Relationships

5.1: Construct Scatter Plots and Lines of Best Fits
5.2: Interpret the meaning of points on a scatter plot
5.3: Relationships between two variables
5.4: Make Inferences in Data and Explain Differences in Data and Outliers
5.6: Describe Trends and Relationships in Data
5.7: Describe a Situation Given a Graph

### CHAPTER 6: Linear Relationships

6.1: Co-ordinate Plane
6.2: Defining Linear through graphs, tables, first differences and Eqn
6.3: Compare Properties of Direct and Partial Variation (Initial Values)
6.4: Properties of Linear Relations: Rate of Change and Constant
6.5: Calculating Rates of Change
6.6: Representations of Constant of Change (50 +5p)
6.7: Determine Values for Linear Relations Using a Table of Values, an Equation, a Graph
6.8: Express a Linear Relation as an Equation in Two Variables (Rate of Change + Initial Value)
6.9: Solve by Graphing and Applications
6.10: Describe Effects on a Linear Graph by Changing Conditions of the Question

### CHAPTER 7: Measurement of Plane and Solid Figures

7.1: Areas and Perimeters of 2D Composite Figures
7.2: Determine Maximum Area of rectangle for Fixed Perimeter and Applications
7.3: Determine Minimum Perimeter of rectangle Given Fixed Area and Applications
7.4: Develop Formulas For Volume of Pyramid, Cone, Sphere (Relate Vcone to 1/3 VPrism
7.5: Applications of Volumes of Prisms, Pyramids, Cylinders, Cones and Spheres

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