# Principles Of Mathematics – Grade 9

This course enables students to develop an understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships, which they will then generalize as equations of lines, and will determine the connections between different representations of a linear relation. They will also explore relationships that emerge from the measurement of three-dimensional figures and two-dimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

From: $500.00

### Overall Curriculum Expectations

By the end of this course, students will be:

**Number Sense and Algebra**

**By the end of this course the student will:**

- Demonstrate an understanding of the exponent rules of multiplication and division and apply them to simplify expressions.
- Manipulate numerical and polynomial expressions and solve first-degree equations.

**Linear Relations**

By the end of this course the student will:

- Apply data-management techniques to investigate relationships between two variables.
- Demonstrate an understanding of the characteristics of a linear relation.
- Connect various representations of a linear relation.

**Analytic Geometry**

By the end of this course the student will:

- Determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity.
- Determine, through investigation, the properties of the slope and y-intercept of a linear relation.
- Solve problems involving linear relations.

**Measurement and Geometry**

By the end of this course the student will:

- Determine, through investigation, the optimal values of various measurements.
- Solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures.
- Verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.

### Course Details

Course Code | ENG1D |

Course Type | Academic |

Format | Online School Course |

Prerequisite | None |

Tuition Fee | 650 – 1300 |

Department | Mathematics |

Course Title | Principles of Mathematics |

Grade | Grade 9 |

Credit Value | 1.0 |

### Outline of Course Content

Unit | Title | Time |

1 | Mathematical Processes | 10 hours |

2 | Relations | 12 hours |

3 | Polynomials | 14 hours |

4 | Equations | 10 hours |

5 | Modelling With Graphs | 12 hours |

5 | Analyse Linear Relations | 14 hours |

5 | Geometric Relationships | 11 hours |

5 | Measurement Relationships | 14 hours |

5 | Optimizing Measurements | 11 hours |

Final Examination | 2 hours | |

Total | 110 hours |

### Course Details

Course Code | ENG1D |

Course Type | Academic |

Format | Online School Course |

Prerequisite | None |

Tuition Fee | 650 – 1300 |

Department | Mathematics |

Course Title | Principles of Mathematics |

Grade | Grade 9 |

Credit Value | 1.0 |

### Overall Curriculum Expectations

By the end of this course, students will be:

**Number Sense and Algebra**

**By the end of this course the student will:**

- Demonstrate an understanding of the exponent rules of multiplication and division and apply them to simplify expressions.
- Manipulate numerical and polynomial expressions and solve first-degree equations.

**Linear Relations**

By the end of this course the student will:

- Apply data-management techniques to investigate relationships between two variables.
- Demonstrate an understanding of the characteristics of a linear relation.
- Connect various representations of a linear relation.

**Analytic Geometry**

By the end of this course the student will:

- Determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity.
- Determine, through investigation, the properties of the slope and y-intercept of a linear relation.
- Solve problems involving linear relations.

**Measurement and Geometry**

By the end of this course the student will:

- Determine, through investigation, the optimal values of various measurements.
- Solve problems involving the measurements of two-dimensional shapes and the surface areas and volumes of three-dimensional figures.
- Verify, through investigation facilitated by dynamic geometry software, geometric properties and relationships involving two-dimensional shapes, and apply the results to solving problems.

### Outline of Course Content

Unit | Title | Time |

1 | Mathematical Processes | 10 hours |

2 | Relations | 12 hours |

3 | Polynomials | 14 hours |

4 | Equations | 10 hours |

5 | Modelling With Graphs | 12 hours |

5 | Analyse Linear Relations | 14 hours |

5 | Geometric Relationships | 11 hours |

5 | Measurement Relationships | 14 hours |

5 | Optimizing Measurements | 11 hours |

Final Examination | 2 hours | |

Total | 110 hours |