# Summer Math Programs

## Online and In-Person Options

Students entering Grades 6-8 will work together at Pickering College through hands-on and fun-filled leadership activities to promote community and collaboration among peers of all levels of math. Students will leave with new friends, new ideas, and a new perspective on mathematics. To further develop their leadership skills, they will create and lead an activity for younger campers.

For students entering Grades 9-11, our Math Bridge courses are online summer courses designed to give students extra confidence as they enter the next year of mathematics. These courses will review the material covered in their previous math year and preview important concepts in the grade to come. By revisiting important ideas and exploring upcoming material, students will deepen their understanding of key mathematical concepts and feel secure in their ability to be successful. Experienced online teachers will work with students in interactive live lessons once a week, and provide feedback on weekly independent work.

Space is limited. Minimum numbers must be reached to run programs.

For more information please email auxiliaryprograms@pickeringcollege.on.ca

## Explore Our Programs

## Course Descriptions & Registration

- Grade 8 Reach Ahead Math Program
- Grade 9 Math Bridge
- Grade 10 Math Bridge
- Grade 11 Math Bridge
- Grade 12 Advanced Functions (MHF4U)

## Grade 8 Reach Ahead Math Program

### Course name:

Summer Grade 8 Reach Ahead Math Program (students who are working to complete the Grade 8 self-study summer 2022 in hopes of earning a place in the reach ahead Grade 9 mathematics class in September)

### Prerequisite:

Grade 7 math

### Course dates:

Week of June 27, 2022 - Week of August 22, 2022

### Lessons:

Mondays, 6:00 p.m. - 7:00 p.m.

### Curriculum:

https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics/grades/g8-math/strands

### Summary:

This summer, Pickering College will be offering a course that is designed to support students who are working through Grade 8 mathematics independently so they feel supported and prepared to reach ahead to take Grade 9 mathematics in September. An experienced online teacher will work with students in interactive live lessons once a week to supplement what they are learning through the independent Mathspace program with review and extensions as needed. Students will also be able to ask questions about concepts that they find challenging, and the teacher will be able to monitor the student’s progress through Mathspace offering encouragement and support as needed. By revisiting important ideas and exploring upcoming material, students will deepen their understanding of key mathematical concepts and feel secure in their ability to be successful.

## Grade 9 Math Bridge

### Course name:

Math Bridge Course (Mathematics Preparation Course for students entering Grade 9, non-credit)

### Prerequisite:

Grade 8 math

### Course dates:

Week of June 27, 2022 - Week of August 22, 2022

### Lessons:

Mondays from 7:00 p.m. - 8:00 p.m.

### Curriculum:

https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics/grades/g8-math/strands

### Summary:

This summer course is designed to give students extra confidence as they enter the next year of mathematics. The course will review the learning of the previous math year, and preview important concepts in the grade to come. By revisiting important ideas and exploring upcoming material, students will deepen their understanding of key mathematical concepts and feel secure in their ability to be successful. Experienced online teachers will work with students in interactive live lessons once a week, and provide feedback on weekly independent work.

### Outline of course content:

#### Number Sense and Algebra

- Scientific notation, fractions, percentages, square numbers, proportions, decimals and integers
- Patterns, algebraic notation, terms, integers, decimals, coding, data points, modelling
- Operating with exponents
- Manipulating expressions and solving equations

#### Linear Relations and Data Analysis

- Data relationship, analysis, variables and probability
- Using data management to investigate relationships
- Understanding characteristics of linear relations
- Connecting various representations of linear relations

#### Analytic Geometry

- Investigating the 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

- Angles, triangles, Pythagorean Theory, intersecting and parallel lines, units used in technology
- Investigating the optimal values of measurements
- Solving problems involving perimeter, area, surface area, and volume
- Investigating and applying geometric relationships

## Grade 10 Math Bridge

### Course name:

Math Bridge Course (Mathematics Preparation Course for students entering Grade 10, non-credit)

### Prerequisite:

Grade 9 math

### Course dates:

Week of June 27, 2022 - Week of August 22, 2022

### Lessons:

Tuesdays from 6:00 p.m. - 7:00 p.m.

### Curriculum:

http://www.edu.gov.on.ca/eng/curriculum/secondary/math910curr.pdf

### Summary:

This summer course is designed to give students extra confidence as they enter the next year of mathematics. The course will review the learning of the previous math year, and preview important concepts in the grade to come. By revisiting important ideas and exploring upcoming material, students will deepen their understanding of key mathematical concepts and feel secure in their ability to be successful. Experienced online teachers will work with students in interactive live lessons once a week, and provide feedback on weekly independent work.

### Outline of course content:

#### Number Sense and Algebra

- Operating with exponents
- Manipulating expressions and solving equations

#### Linear Relations

- Using data management to investigate relationships
- Understanding characteristics of linear relations
- Connecting various representations of linear relations

#### Analytic Geometry

- Investigating the relationship between the equation of a relation and the shape of its graph
- Investigating the properties of slope
- Using linear systems to solve problems
- Solving problems involving properties of line segments
- Using analytic geometry to verify geometric properties

#### Measurement and Geometry

- Investigating the optimal values of measurements
- Solving problems involving perimeter, area, surface area, and volume
- Investigating and applying geometric relationships

## Grade 11 Math Bridge

### Course name:

Math Bridge Course (Mathematics Preparation Course for students entering Grade 11, non-credit)

Prerequisite:

Grade 10 math

### Course dates:

Week of June 27, 2022 - Week of August 22, 2022

### Lessons:

Tuesdays from 7:00 p.m. - 8:00 p.m.

### Curriculum:

http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

### Summary:

This summer course is designed to give students extra confidence as they enter the next year of mathematics. The course will review the learning of the previous math year, and preview important concepts in the grade to come. By revisiting important ideas and exploring upcoming material, students will deepen their understanding of key mathematical concepts and feel secure in their ability to be successful. Experienced online teachers will work with students in interactive live lessons once a week, and provide feedback on weekly independent work.

### Outline of course content:

#### Number Sense and Algebra

- Operating with exponents
- Manipulating expressions and solving equations

#### Quadratic Relations of the Form y = ax2 + bx + c

- Investigating the basic properties of quadratic relations
- Relating the graph of y = x2 and its transformations
- Solving quadratic equations
- Solving problems involving quadratic relations

#### Linear Relations

- Using data management to investigate relationships
- Understanding characteristics of linear relations
- Connecting various representations of linear relations

#### Analytic Geometry

- Investigating the relationship between the equation of a relation and the shape of its graph
- Investigating the properties of slope
- Using linear systems to solve problems
- Solving problems involving properties of line segments
- Using analytic geometry to verify geometric properties

#### Measurement, Geometry and Trigonometry

- Solving problems involving perimeter, area, surface area, and volume
- Investigating and applying geometric relationships
- Investigating similarity and solving problems involving similar triangles
- Solving problems involving the trigonometry of right triangles
- Solving problems involving the trigonometry of acute triangles

## Grade 12 Advanced Functions (MHF4U)

### Course name:

Advanced Functions, Grade 12, University Preparation

### Course code:

MHF4U

### Prerequisite:

MCR3U Functions, Grade 11 University Preparation or MCT4C Mathematics for College Technology, Grade 12 College Preparation

### Course dates:

Week of June 27, 2022 - Week of August 22, 2022

This credit will total 110 hours of synchronous and asynchronous work

### Lessons:

Tuesdays, 7:00 p.m. - 8:00 p.m. (lesson), and Thursdays from 7:00 p.m. - 8:00 p.m. (tutorial)

### Curriculum:

http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

### Summary:

This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to a variety of university programs.

### Units:

- Unit 1: Exponential and Logarithmic Functions
- Unit 2: Rational Functions and Combinations
- Unit 3a: Trigonometric Functions
- Unit 3b: Independent Online Learning on Trigonometric Functions
- Unit 4a: Polynomial Functions
- Unit 4b: Polynomial Equations and Combinations
- Unit 5: Sinusoidal Functions and Combinations
- Unit 6: Course Review, Final Assessment Activities

Overall curriculum expectations:

### Exponential and Logarithmic Functions

- Demonstrate an understanding of the relationship between exponential expressions and logarithmic expressions, evaluate logarithms, and apply the laws of logarithms to simplify numeric expressions
- Identify and describe some key features of the graphs of logarithmic functions, make connections between the numeric, graphical, and algebraic representations of logarithmic functions, and solve related problems graphically
- Solve exponential and simple logarithmic equations in one variable algebraically, including those arising from real-world applications

### Trigonometric Functions

- Demonstrate an understanding of the meaning and application of radian measure
- Make connections between trigonometric ratios and the graphical and algebraic representations of the corresponding trigonometric functions and between trigonometric functions and their reciprocals, and use these connections to solve problems
- Solve problems involving trigonometric equations and prove trigonometric identities

### Polynomial and Rational Functions

- Identify and describe some key features of polynomial functions, and make connections between the numeric, graphical, and algebraic representations of polynomial functions
- Identify and describe some key features of the graphs of rational functions, and represent rational functions graphically
- Solve problems involving polynomial and simple rational equations graphically and algebraically
- Demonstrate an understanding of solving polynomial and simple rational inequalities
- Demonstrate an understanding of average and instantaneous rate of change, and determine, numerically and graphically, and interpret the average rate of change of a function over a given interval and the instantaneous rate of change of a function at a given point

### Combining Functions

- Determine functions that result from the addition, subtraction, multiplication, and division of two functions and from the composition of two functions, describe some properties of the resulting functions, and solve related problems
- Compare the characteristics of functions, and solve problems by modelling and reasoning with functions, including problems with solutions that are not accessible by standard algebraic techniques