# Mathematics & IT

Mathematics Faculty

Steven Prokopchuk

Harold Wardrop

Mario DeSandoli

Kate Coull

Fiona Dalrymple

Dan Norman

Jordan Warner

Phil Smith

Mathematical literacy is a primary goal of the school curriculum. Competence in mathematics underpins the successful study of many academic disciplines at Brentwood. Becoming numerate involves developing the ability to explore, conjecture, reason logically, and use a variety of mathematical methods to solve problems. It also involves the development of self-confidence and the ability to use quantitative and spatial information in problem solving and decision making.

The Brentwood mathematics curriculum emphasizes the development of numeracy skills and concepts as well as their practical application in higher education and the workplace. The curriculum emphasizes probability and statistics, reasoning and communication, measurement, and problem solving. Technology is used to collect and analyze data and bring a context to our explorations. Complementing these real world applications, we also investigate the creative and aesthetic aspects of mathematics by exploring the connections between mathematics, art, and design.

At Brentwood we believe that learning requires the active participation of the student; that people learn in a variety of ways and at different rates, and that learning is both an individual and a group process.

# Mario DeSandoli

### B.Ed. (University of Victoria), Mathematics, Hope Assistant Houseparent

Mario DeSandoli joined us from Dwight School Canada in Shawnigan Lake where he spent five years. Born and raised in the small town of 100 Mile House in the Cariboo region of B.C., Mario attended UVIC and graduated with a Bachelor of Education in 2002. He has a rich personal history having climbed Mt. Kilimanjaro, volunteered in refugee camps in Sierra Leone for a year, taken a school service trip to Tanzania and taken a meditation course where he went 12 days without human interaction (or talking or eye contact or reading or writing or anything else)! He loves getting students excited about their studies and enjoys trying to convince them that other subject areas would not even exist if it were not for mathematics. He and his wife, Marianna, are the Hope Assistant Houseparents and live on campus with their three young children - Luca, Massimo and Floriana.

## Harold Wardrop

### B.Sc. (UBC) Head of Mathematics. Mathematics, Robotics

Head of the Mathematics Department, Harold Wardrop is the product of a military upbringing. His childhood was divided between Ontario and Europe. He eventually settled in British Columbia where he earned a B.Sc. (Mathematics) at the University of British Columbia. At Simon Fraser University, he completed his professional teaching certification, a post-baccalaureate diploma in education, and met his lovely wife, Sharon. After eight years of teaching mathematics in Surrey, he joined the Brentwood faculty in 2002. In addition to his teaching, Mr. Wardrop has also developed and co-authored textbooks for Grades 10, 11, and 12, all of which are currently used across Western Canada and the Territories. In 2011 he received a National Prime Minister's Award for teaching excellence. Integrating his enthusiasm for teaching with his inner geek, Mr. Wardrop started a Brentwood robotics program in 2012. Although he claims he no longer needs friends, since he can build his own, he still very much enjoys many outdoor adventures accompanied by his wife and two children. His favourite number is three.

## Kate Coull

### B.Sc. (Guelph), B.Ed. (Queen’s) University Counselling, Mathematics

After growing up in Peterborough, Ontario and receiving her B.Sc (University of Guelph) and B.Ed (Queen’s University), Kate Coull taught mathematics and calculus for three years in Ontario before making the decision to move to New Zealand in 1987. What was initially to be a two year teaching experience in New Zealand followed by world travel, Kate met her Kiwi husband, David, within days of setting foot on NZ soil and ended up staying there for 10 years. During that time Kate taught senior mathematics and Calculus and helped produce a new form 5 Math textbook along with a team of 3 other math teachers. During this time, Kate and David welcomed the birth of their son, Ben, a Brentwood lifer and grad 2010. On a family holiday to the Island, Kate first visited Brentwood in 1991, initiating the desire to one day teach at our school. Returning to Canada in 1997, Kate taught for eight years at Queen Margaret’s School where she was Head of the Mathematics/Science Department and Director of Residence. In 2005 Kate joined Aspengrove School, an independent school on Vancouver Island, and helped initiate many new programs at the school in addition to teaching math, AP Calculus and running the University Counselling and Outdoor Education programs. Passionate about math, Kate also enjoys running, hiking, kayaking, and spending time with her family in Mill Bay.

## Steven Prokopchuk

### B.Sc., B.Ed. (Alberta) Senior Math Teacher

Steven is originally from Edmonton and has lived in Vancouver, rural Quebec, Scotland, and most recently, Washington state. He has B.Sc and B.Ed degrees from the University of Alberta and is currently completing his Masters of Mathematics Teaching (MMT) from the University of Waterloo. Steven has experience in the public school system and more recently was the Upper School Mathematics Department Head at Sedbergh School in Montebello, Quebec (2006-2010). Since 2010, he has been Mathematics Department Chair at The Bear Creek School in Redmond, Washington, where he coached the school's math team to several state titles. Steven enjoys hiking, biking, camping, and cross-country skiing.

## Dan Norman

### B.Ed. (Ottawa), B.Sc. (Western) Mathematics, Outdoor Pursuits

Dan Norman was born and raised in Toronto, but quickly left. He studied mathematics at the University of Western Ontario and education at the University of Ottawa. During this time, he trained and competed in the sport of whitewater canoe slalom, first qualifying for the Canadian national team in 1988. In 1992, he represented Canada at the Barcelona Olympics. His involvement in competitive kayaking brought him to British Columbia and his interest in the outdoors became a cornerstone of his personal and professional life. Since 2001, in addition to mathematics, Mr. Norman has taught the Outdoor Pursuits programme at Brentwood College since 2001. His passion for the West Coast environment drives him to take students to beautiful places all over Vancouver Island. His preferred modes of transportation are human-powered and include sea kayaks, canoes, and hiking boots. Mr. Norman likes very few things more than goofing around in paddle powered boats – canoes, kayaks, and paddleboards. His current challenges include developing and delivering outdoor and experiential education at Brentwood and finding ways to teach math outside the classroom. In his leisure, he and his family spend as much time as possible in remote wilderness locations, and work hard to minimize their footprint on this beautiful island they call home.

## Jordan Warner

### B.Sc., B.Ed. (University of Manitoba), Mathematics, Basketball, Volleyball

Growing up in Roblin, Manitoba, Jordan Warner played a variety of sports in his youth, with his main focus on hockey and baseball. After graduating from high school as one of the top scholar/athletes in Manitoba, he obtained both his Bachelor of Science (Math and Physics) and Bachelor of Education with distinction from the University of Manitoba. It was during this time that he met his future wife. After a summer of teaching kindergarten in Thailand, Mr. Warner and his wife came to Brentwood to teach mathematics and coach basketball. A former assistant houseparent of Rogers House, Mr. Warner currently lives with his wife in Alexandra House.

## Phil Smith

### B.Ed. (UVic), Assistant Houseparent - Allard, M.A Mathematics (Waterloo), Mathematics, Rugby

A keen rugby man, Phil was raised in Victoria and graduated with a B.Ed from the University of Victoria. Urged by his rugby coaches to quit playing (they recognized talent), he started refereeing instead, and progressed to several international tournaments and fixtures. Around 10 years ago he up and left for Wellington, New Zealand, where he continued to referee, though he quickly became distracted by his future wife Maraina, with whom he now has two children. Teaching has kept him busy too; he has embraced his inner geek and loves math and technology. In 2014 he was awarded a Teacher Fellowship through the Royal Society of New Zealand to investigate Maori health and education, and in 2015 he completed a Masters of Mathematics for Teachers at the University of Waterloo. The lure of Brentwood and the opportunity for his children to connect with their Canadian roots has brought Phil back to Canada, and he is excited to be here!

## Mathematics 9

Coursework begins with a study of exponents and the laws governing order of operations with respect to rational numbers, bases and their exponents. A problem solving context is used to derive patterns and relationships to introduce and explore linear equations and the algebra that is used to solve them. Polynomials are also explored with students, concretely, pictorially and symbolically. Students model, record and explain their approach to solving problems involving addition and subtraction of polynomial expressions. Graphing of linear relationships and extrapolating and interpolating from graphs introduces students to some of the concepts involved in critically analyzing and intelligently displaying data. Students move through the course to then conduct a study of statistics within a social context and brings them to an understanding of statistical bias in the collection, analysis and display of data. A study of 2D and 3D shapes requires students to solve problems and justify solution strategies involving circles, tangents, polygons and the surface area of objects. A unit on transformations involves students in drawing scale diagrams of 2D shapes and gaining an appreciation of line and rotational symmetry. Technology is incorporated into the curriculum through such means as data collection and GPS devices which provide information students can discuss, display and analyze within the classroom.

## Foundations of Mathematics & Pre-Calculus 10

Foundations of Mathematics and Pre-Calculus 10 is a course designed to build on concepts introduced in Mathematics 9 in addition to preparing students for the complex concepts developed in Pre-Calculus 11 and 12. The core curriculum consists of algebra, geometry, trigonometry, number operations and data analysis. Major emphasis is placed on symbolic manipulation, sophisticated generalisation of mathematical concepts, and the development of formal mathematics.The following mathematical processes are emphasized throughout the year: Communication, Problem Solving, Connections, Reasoning, Mental Mathematics, Technology and Estimation, Visualization

## Pre-Calculus 11

Pre-Calculus 11 is a course designed, along with Pre-Calculus 12, to give students who are interested in pursuing future studies that require calculus, the necessary foundation of algebraic skills. Students begin by representing and analyzing situations that involve expressions, equations and inequalities. Quadratic, polynomial and rational functions are represented and analyzed. Students solve coordinate geometry problems involving points, lines and line segments and apply the geometric properties of circles to solve problems. The following mathematical processes are emphasized throughout the year: Communication, Problem Solving, Connections, Reasoning, Mental Mathematics, Technology and Estimation Visualization.

## Foundations of Mathematics 12

This course focuses on problem solving and analysis, trying, where possible, to set the mathematics within a real world context. Students will typically take this to fulfill their Math 11 graduation requirement and as a terminal math course. Critical thinking in a mathematical setting is the primary goal of the course.

Topics include; analyzing puzzles and games that involve numerical and logical reasoning, using problem-solving strategies. Solving problems that involve compound interest in financial decision making. Collecting primary or secondary data (statistical or informational) related to the topic. Assessing the accuracy, reliability and relevance of the primary or secondary data collected by:

- identifying examples of bias and points of view
- identifying and describing the data collection methods
- determining if the data is relevant
- determining if the data is consistent with information obtained from other sources on the same topic.

## Pre-Calculus 12

Students generate and analyze exponential patterns. They solve exponential, logarithmic and trigonometric equations and identities. Graphing calculators are used to represent and analyze exponential and logarithmic functions. In the transformations unit students perform, analyze and create transformations of functions and relations that are described by equations or graphs. The topics of chance and uncertainty are introduced in the statistics unit where students ultimately solve problems using probability theory including permutations and combinations.

Pre-Calculus 12 is a course designed to give students who are interested in pursuing future studies that require calculus, the necessary foundation of algebraic skills. The core curriculum consists of working extensively with functions: polynomial, radical, trigonometric, exponential, logarithmic, and rational. Graphing calculators are used throughout the course as an exploration tool and links are made between the similarities and differences from one function to the next. Function notation, operations and transformations are applied throughout the course.

The following mathematical processes are emphasized throughout the year: [C] Communication [PS] Problem Solving [CN] Connections [R] Reasoning [ME] Mental Mathematics [T] Technology and Estimation [V] Visualization

## Calculus 12

Students will quickly realize that calculus is an exciting field of mathematics unlike any math course they have previously studied. They will learn the power of calculus as the mathematics that enables scientists, engineers, economists, and many others to model real-life, dynamic situations.

Calculus 12 is a course designed to give students an appreciation for, and an understanding of, the concepts included in most first year university calculus courses. Although this is not a preparation course for the AP Calculus exam, upon completion of this course students will have covered the majority of the topics in our AP curriculum.

## AP Calculus AB 12

Students will embark upon a mathematical journey unlike any that they have previously experienced. They will learn the power of calculus as the mathematics that enables scientists, engineers, economists, and many others to model real-life, dynamic situations.

All students must possess a graphing calculator for use in this course, a course recommended for all students who will be required to take a calculus course (first year mathematics) at university. This is essentially a first year university course that will cover the following topics:

Functions and Historical perspective: A review of functions (this will be complemented by the Math 12 curriculum). Historical perspective. Origins of the calculus approach. Contributions by famous mathematicians.

Continuity and Limit Theory: Secants and tangents. Limiting position/limiting value/instantaneous value. Limit notation. One-sided and two sided limits. Continuous functions, discontinuities. Horizontal and vertical asymptotes, limits at infinity. Computation of limits.

The Derivative: Differentiation from first principles. Derivative notation: Techniques of differentiation: Power Rule, Product Rule, Quotient Rule (plus Reciprocal Rule). Higher derivative. The Chain Rule. Implicit differentiation.

Curve Analysis: Conditions for increasing, decreasing, concave up, concave down functions. Definition of point of inflection, critical point. Relative and absolute maxima/minima. First derivative test and second derivative test for classification of maxima/minima. Analysis of the properties of functions through: symmetry, intercepts, intervals of increase/decrease, infinite tendencies, asymptotes (horizontal, vertical, and oblique), concavity, points of inflection, periodicity.

Applications of the Derivative: Applied maximum and minimum problems. Related rates. Kinematics — motion along a line. Rolle's Theorem. Mean Value Theorem.

Specific Functions: Inverse functions. Continuity/differentiability of inverse functions. Logarithmic and exponential functions (review of log laws). Derivatives of exponential and logarithmic functions. Derivatives of trigonometric functions. Derivatives of inverse trigonometric functions. L'Hopital's rule for indeterminate forms.

Integration: Analysis of the area problem. The indefinite integral. Integration formulae. Integral curves. Differential equations. Integration by substitution. The definite integral. The Fundamental Theorem of Calculus. Average value of a function. Slope fields.

Areas & Volumes: Area under a curve. Area between two curves. Reversal of variables/axes. Volumes of rotation computed by slicing (disks and washers) and cylindrical shells.

Techniques for Integration: Integration by parts, trigonometric integrals, cyclic integrals, partial fractions. Enrichment: trigonometric substitution.

# Coding 11: Python

Learn the basics of one of the world's most popular programming languages which is used by software engineers, analysts, data scientists, and machine learning engineers alike. Python is a general-purpose, versatile and modern programming language. It's great as a first language because it is concise and easy to read. It is used for everything from web development to software development and scientific applications. In this course students will use Python for applications such as: controlling a Nao robot and using the GPIO pins on a Rasperry Pi computer to interface with electronic components like LEDs, Sensors, Lasers, and Relays. This is very much a hands-on, project-based course where, upon completion of this course, students should have the confidence and knowhow to move into any aspect of programming that they desire.

# Advanced Topics in Math 12

Advanced Topics in Mathematics course is intended for our top scholars who have already completed PreCalculus 12 and wish to continue studying mathematics at high school. Completion of calculus is also an asset but not necessary as it can be taken concurrently. Students will explore topics that they would not typically see until university, providing them with an exposure to mathematics that is relevant to post-secondary pursuits in mathematics, engineering, computer science, or any science program. The main focus will be an introduction to Linear Algebra where students will learn topics such as: systems of equations, matrices, determinants, and vectors. This course will also include calculus topics from AP Calculus BC such as parametric, polar, and vector functions, and series (i.e. those that are not in AP Calculus AB).

# AP Statistics 12

The course introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. There are four themes in the AP Statistics course: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students use technology, investigations, problem solving, and writing as they build conceptual understanding.

## Applied Coding Explorations 11

Students will explore concepts such as Top Down Design, basic coding structure, event driven applications and user interface design while learning the Javascript language. Javascript is widely used in mobile app development and large scale interactive web applications (Facebook, Netflix, eBay) and is now rapidly moving into the desktop application environment. No prior coding knowledge is required, the language constructs are introduced through a graphical block environment which allows students to gradually migrate to hand typed code. Students may also have the opportunity to delve into physical computing.

## AP Computer Science Principles 12

In AP Computer Science Principles, students will develop computational thinking vital for success across all disciplines, such as using computational tools to analyze and study data and working with large data sets to analyze, visualize, and draw conclusions from trends. The course is unique in its focus on fostering student creativity. Students are encouraged to apply creative processes when developing computational artifacts and to think creatively while using computer software and other technology to explore questions that interest them. They will also develop effective communication and collaboration skills, working individually and collaboratively to solve problems, and discussing and writing about the importance of these problems and the impacts to their community, society, and the world.

Different from AP Computer Science A which is taught in Java, this course does not have a designated programming language. The programming languages that are most appropriate for the students will be selected and used in the course.