Course Syllabus

 

St. George's School

 Foundations of Mathematics and Pre-Calculus 10

COURSE OUTLINE 2022-2023 for Students

 

 

 

Mathematical content throughout the school is taught through the lens of ‘curricular competencies”.

Mathematics is more than a sequence of calculations that lead to the correct solution to a problem. It is a state of mind and an intellectual art. It is a discipline that goes beyond its immediate, apparent, and obvious applications. It confirms, expands and diversifies the meaning of what it is to be human, and its language is accessible to people of all cultures and backgrounds. Mathematics has been with us ever since we began using language, and the requirement for mathematics was, and is, inescapable ever since we civilized.

 

It is a way of analytical thinking whose benefits extrapolate well beyond the boundaries of a classroom. Our world out there is crying out for thinkers; people who can critically analyze, deductively reason, substantiate their thoughts and come up with creative and innovative solutions to problems whose consequences greatly affect the world we live in.

 

The study of mathematics can encourage the development of such thinkers. The way in which you will be taught (and the way in which you will be challenged to learn) is for you to understand what it is you are learning... for you to struggle, negotiate, and overcome.... emerging as a more resilient , more well-thought-out, more communicative thinking individual. It is with this hope that we look forward to our experience with you in the classroom this year. We are optimistic that you are up to the challenge. 

 

 

 

 

 

 

The British Columbia curriculum is centred on the following five Big Ideas:

 

  1. Algebra allows us to generalize relationships through abstract thinking.
  2. The meanings of, and connections between, each operation extend to powers and polynomials.
  3. Constant rate of change is an essential attribute of linear relations and has meaning in different representations and contexts.
  4. Trigonometry involves using proportional reasoning to solve indirect measurement problems.
  5. Representing and analyzing situations allows us to notice and wonder about relationships.

At St. George’s School, mathematical content will be taught with an emphasis on four curricular competencies:

 

i. Reasoning and Modelling                    iii. Communicating and Representing

ii. Understanding and Solving               iv. Connecting and Reflecting

In addition to the content-based learning outcomes, these curricular competencies will be emphasized, embraced, valued, supported and encouraged throughout, and will be built into assessment where appropriate and relevant.  In addition, separate assignments focusing specifically on curricular competencies should be expected.  The curricular competencies together will account for 40% of the final course mark.

 

 

Curricular Competency Breakdown

 

Reasoning and Modelling

  • Develop thinking strategies to solve puzzles and play games
  • Explore, analyze, and apply mathematical ideas using reason, technology, and other tools
  • Estimate reasonably and demonstrate fluent, flexible, and strategic thinking about number
  • Model with mathematics in situational contexts
  • Think creatively and with curiosity and wonder when exploring problems

 

Understanding and Solving

  • Develop, demonstrate, and apply mathematical understanding through play, story, inquiry, and problem solving
  • Visualize to explore and illustrate mathematical concepts and relationships
  • Apply flexible and strategic approaches to solve problems
  • Solve problems with persistence and a positive disposition
  • Engage in problem-solving experiences connected with place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

 

Communicating and Representing

  • Explain and justify mathematical ideas and decisions in many ways
  • Represent mathematical ideas in concrete, pictorial, and symbolic forms
  • Use mathematical vocabulary and language to contribute to discussions in the classroom
  • Take risks when offering ideas in classroom discourse

 

Connecting and Reflecting

  • Reflect on mathematical thinking
  • Connect mathematical concepts with each other, other areas, and personal interests
  • Use mistakes as opportunities to advance learning
  • Incorporate First Peoples worldviews, perspectives, knowledge, and practices to make connections with mathematical concepts

 

Mathematical Content Topics

 

                                                                                                                                   

TERM 1

 

Trigonometry                                   [Ministry: Primary Trigonometric Ratios]

 

Factors and Products                      [Ministry: Prime Factorization; Multiplication of Polynomial Expressions; Polynomial Factoring]             

 

 

TERM 2

 

Exponents                                         [Ministry: Operations on Powers with Integral Exponents]

 

Relations and Functions                 [Ministry: Functions and Relations: Connecting data, graphs, and situations]

 

Linear Functions                              [Ministry: Linear Functions: slope and equations of lines]        

 

                       

TERM  3

 

Systems of Linear Equations         [Ministry: Systems of Linear Equations]

 

Arithmetic Sequences                    [Ministry: Arithmetic Sequences]

 

Financial Literacy                             [Ministry: Financial Literacy: gross and net pay]

 

 

 

 

 

 

 

Primary Text: Foundations and Pre-Calculus Mathematics 10 (Pearson)

Supplementary Text(s): Canvas (incl. MATHPOWER 11 & McGraw-Hill Ryerson Pre-Calculus 11)

 

 

 

Trigonometry (Pearson)

  • sine, cosine, and tangent ratios
  • right-triangle problems: determining missing sides and/or angles using trigonometric ratios and the Pythagorean theorem
  • contexts involving direct and indirect measurement

 

Factors and Products (Pearson)

  • expressing prime factorization of a number using powers
  • identifying the factors of a number
  • includes greatest common factor (GCF) and least common multiple (LCM)
  • strategies include using factor trees and factor pairs
  • applying the distributive property between two polynomials, including trinomials
  • connecting the product of binomials with an area model
  • greatest common factor of a polynomial
  • simpler cases involving trinomials y = x2 + bx + c and difference of squares

 

Exponents (Pearson)

  • positive and negative exponents
  • exponent laws
  • evaluation using order of operations
  • numerical and variable bases

 

 

Relations and Functions (Pearson)

  • communicating domain and range in both situational and non-situational contexts
  • connecting graphs and context
  • understanding the meaning of a function
  • identifying whether a relation is a function
  • using function notation

 

Linear Functions (Pearson)

  • slope: positive, negative, zero, and undefined
  • types of equations of lines (point-slope, slope intercept, and general)
  • equations of parallel and perpendicular lines
  • equations of horizontal and vertical lines
  • connections between representations: graphs, tables, equations

 

Systems of Linear Equations (Pearson)

  • solving graphically
  • solving algebraically by inspection, substitution, elimination
  • connecting ordered pair with meaning of an algebraic solution
  • solving problems in situational contexts

 

Arithmetic Sequences (Canvas)

  • applying formal language (common difference, first term, general term) to increasing and decreasing linear patterns
  • connecting to linear relations
  • extension: exploring arithmetic series

 

Financial Literacy (Canvas)

  • types of income
  • income tax and other deductions

 

Unit 1: Trigonometry (Chapter 2 Pearson)                                                                                                                     

 

  1. i) sine, cosine, and tangent ratios; ii) right-triangle problems: determining missing sides and/or angles using trigonometric ratios and the Pythagorean theorem; iii) contexts involving direct and indirect measurement

 

[10-M1]         Understand the properties of the three primary trigonometric ratios; solve right triangles; apply the Pythagorean Theorem; problem-solve.

 

 

Specific Outcome(s)

Curriculum Focus

Primary reference

The Tangent Ratio

10-M1

·       Develop the tangent ratio and relate it to the angle of inclination of a line segment.

2.1

Using the Tangent Ratio to Calculate Lengths

10-M1

·       Apply the tangent ratio to calculate lengths.

2.2

[Optional] Math Lab: Measuring an Inaccessible Height

10-M1

·       Determine a height which cannot be measured directly.

2.3

The Sine and Cosine Ratios

10-M1

·       Develop and apply the sine and cosine ratios to determine angle measures.

2.4

Using the Sine and Cosine Ratios to Calculate Lengths

10-M1

·       Use the sine and cosine ratios to determine lengths indirectly.

2.5

Applying the Trigonometric Ratios

10-M1

·       Use a primary trigonometric ratio to solve a problem modelled by a right triangle.

2.6

Solving Problems Involving More than One Right Triangle

10-M1

·       Use trigonometry to solve problems modelled by more than one right triangle.

2.7

 

                                

 

Unit 2: Factors and Products (Chapter 3 Pearson)                                                                                                                   

 

  1. i) expressing prime factorization of a number using powers; ii) identifying the factors of a number; iii) includes greatest common factor (GCF) and least common multiple (LCM); iv) strategies include using factor trees and factor pairs; v) applying the distributive property between two polynomials, including trinomials; vi) connecting the product of binomials with an area model; vii) greatest common factor of a polynomial; viii) simpler cases involving trinomials y = x2 + bx + c and difference of squares

 

[10-AN1]        Demonstrate a thorough understanding of prime factorization, LCM, GCF, and common factors of polynomials.

[10-AN2]        Demonstrate an understanding of polynomial multiplication and factoring in multiple ways (visually, algebraically, etc.).

 

Optional Enrichment: (3.2) Perfect Squares, Perfect Cubes, and Their Roots; (3.6) Polynomials of the Form ax2 + bx + c

 

Specific Outcome(s)

Curriculum Focus

Primary Reference

Factors and Multiples of Whole Numbers

10-AN1

·       Determine prime factors, GCF, and LCM.

3.1

Common Factors of a Polynomial

10-AN1

·       Model and record factoring a polynomial.

3.3

[Optional] Math Lab: Modelling Trinomials as Binomial Products

10-AN2

·       Explore factoring polynomials with algebra tiles.

3.4

Polynomials of the Form ax2 + bx + c

10-AN2

·       Use models and algebraic strategies to multiply binomials and to factor trinomials.

3.5

Multiplying Polynomials

10-AN2

·       Extend the strategies for multiplying binomials to multiplying polynomials.

3.7

Factoring Special Polynomials

10-AN2

·       Investigate some special factoring patterns.

3.8

 

 

Unit 3: Exponents (Chapter 4 Pearson – adapted from “Roots and Powers”)                       

 

  1. i) positive and negative exponents
  2. ii) exponent laws

iii) evaluation using order of operations

  1. iv) numerical and variable bases

 

[10-AN3]        Demonstrate an understanding of powers with integral (positive and negative) exponents;

                                    apply various exponent laws and incorporate both integral exponents and order of operations.

 

Note: Sections 4.1, 4.2, 4.3, and 4.4 of the primary text are now covered in Pre-Calculus 11.

 

Recommended Enrichment: (4.4) Fractional Exponents and Radicals

 

Specific Outcome(s)

Curriculum Focus

Primary reference

[Optional/Recommended] Fractional Exponents and Radicals

N/A

·       Relate rational exponents and radicals.

4.4

Negative Exponents and Reciprocals

10-AN3

·       Relate negative exponents to reciprocals.

4.5

Applying Exponent Laws

10-AN3

·       Apply the exponent laws to simplify expressions.

4.6

 

 

 

Unit 4: Relations and Functions (Chapter 5 Pearson)                                                                          

 

  1. i) communicating domain and range in both situational and non-situational contexts; ii) connecting graphs and context

understanding the meaning of a function; iii) identifying whether a relation is a function; iv) using function notation

 

[10-RF1]         Explain relationships among data and graphs and represent relations in multiple ways.                                    

[10-RF2]         Understand and explain the properties of a function; state domain and range; utilize function notation.

[10-RF3]         Understand properties of linear relations, rate of change, and interpret their graphs.

 

 

Specific Outcome(s)

Curriculum Focus

Primary reference

Representing Relations

10-RF1

·       Represent relations in different ways.

5.1

Properties of Functions

10-RF2

·       Develop the concept of a function.

5.2

 

Interpreting and Sketching Graphs          

10-RF1, 10-RF2

·       Describe a possible situation for a given graph and sketch a possible graph for a given situation.

5.3

[Optional] Math Lab: Graphing Data         

10-RF1, 10-RF2

·       Graph data and investigate the domain and range when the data represents a function.

5.4

Graphs of Relations and Functions     

10-RF1, 10-RF2

·       Determine the properties of the graphs of relations and functions.

5.5

Properties of Linear Relations

10-RF2, 10-RF3

·       Identify and represent linear relations in different ways.

5.6

Interpreting Graphs of Linear Functions

10-RF2, 10-RF3

·       Use intercepts, rate of change, domain, and range to describe the graph of a linear function.

5.7

 

 

 

Unit 5: Linear Functions (Chapter 6 Pearson)                                                                                                                

 

  1. i) slope: positive, negative, zero, and undefined; ii) types of equations of lines (point-slope, slope intercept, and general); iii) equations of parallel and perpendicular lines; iv) equations of horizontal and vertical lines; v) connections between representations: graphs, tables, equations

 

[10-RF4]         Demonstrate an understanding of slope, interpret its meaning and graphical representation;

understand and utilize the relationship between parallel and perpendicular lines.

            [10-RF5]         Use graphs and/or points to determine equations of linear functions in different forms, and vice versa;

use various forms of linear functions to solve problems.

 

 

Specific Outcome(s)

Curriculum Focus

Primary Reference

Slope of a Line

10-RF4

·       Determine the slope of a line segment and a line

6.1

Slopes of Parallel and Perpendicular Lines

10-RF4

·       Understand conditions for perpendicularity and parallel

6.2

[Optional] Math Lab: Investigating Graphs of Linear Functions

10-RF4, 10-RF5

·       Investigate the relationship between the graph and the equation of a linear function.

6.3

Slope-Intercept Form of the Equation for a Linear Function

10-RF5

·       Relate the graph of a linear function to its equation in slope-intercept form.

6.4

Slope-Point Form of the Equation for a Linear Function

10-RF5

·       Relate the graph of a linear function to its equation in slope-point form.

6.5

General Form of the Equation for a Linear Relation

10-RF5

·       Relate the graph of a linear function to its equation in general form.

6.6

 

 

 

Unit 6: Systems of Linear Equations (Chapter 7 Pearson)                                                                                           

 

  1. i) solving graphically; ii) solving algebraically by inspection, substitution, elimination; iii) connecting ordered pair with meaning of an algebraic solution; iv) solving problems in situational contexts

 

[10-RF6]         Construct a system of linear equations to model a situation; determine whether a given ordered pair is a solution.

[10-RF7]         Solve problems involving systems of linear equations in two variables, both graphically and algebraically;

understand the properties of a system of linear equations and determine the nature of any solutions.

 

 

Specific Outcome(s)

Curriculum Focus

Primary Reference

Developing Systems of Linear Equations

10-RF6

·       Model a situation using a system of linear equations.

7.1

Solving a System of Linear Equations Graphically

10-RF7

·       Use the graphs of the equations of a linear system to estimate/determine its solution.

7.2

[Optional] Math Lab: Using Graphing Technology to Solve a System of Linear Equations

10-RF7

·       Determine and verify the solution of a linear system using graphing technology.

7.3

Using a Substitution Strategy to Solve a System of Linear Equations

10-RF7

·       Use the substitution of one variable to solve a linear system.

7.4

Using an Elimination Strategy to Solve a System of Linear Equations

10-RF7

·       Use the elimination of one variable to solve a linear system.

7.5

Properties of Systems of Linear Equations

10-RF7

·       Determine the number of solutions of different types of linear systems.

 

7.6

 

 

Unit 7: Arithmetic Sequences and Series (supplementary Canvas material)                                    

 

  1. i) applying formal language (common difference, first term, general term) to increasing and decreasing linear patterns
  2. ii) connecting to linear relations

            iii) extension: exploring arithmetic series

 

[10-RF8]         Understand and utilize arithmetic sequences and series to solve problems.

 

Note: Material for this section can be found on Canvas and is compiled using sections of various texts/supplementary worksheets.

 

 

Specific Outcome(s)

Curriculum Focus

Primary reference

Arithmetic Sequences

10-RF8

·       Derive rules for general nth term, determine the values of a, tn, d, or n, and solve problems

Canvas (1.1 Pre-Calculus 11)

Arithmetic Series

10-RF8

·       Derive the rule to find the sum of a series, determine the values to use in the formula, and solve problems

Canvas (1.2 Pre-Calculus 11)

 

 

 

 

 

 

 

 

 

 

 

 

                                                      

Unit 8: Financial Literacy (supplementary Canvas material)                                                               

 

  1. i) types of income
  2. ii) income tax and other deductions

 

[10-FL1]         Understand the different types of income or expenditure;

perform calculations to determine the effects of taxation, deductions, discounts and interest.

 

Note:  1) Material for this section can be found on Canvas and is compiled using sections of various texts/supplementary worksheets.

            2) Financial literacy may be embedded within the fabric of the course where relevant and appropriate – not merely these few classes.

 

 

Specific Outcome(s)

Curriculum Focus

Primary reference

Income and Expenditure

10-FL1

·       Types of income and expenditure

MP11 9.1 & 9.2

Taxes and Deductions

10-FL1

·       Taxation, deductions, discounts and interest

Canvas supplementary material

 

 

 

 

How your mark will be calculated:

Most regular assessments will be based upon the learning outcomes (content-specific).  These assessments might be tests, quizzes, assignments, or some special project.  This content component will account for 60% of your course mark.  You will also be assessed on various “mathematical habits of thinking” via the four curricular competencies in the form of additional rich assessments tasks, projects, additional test questions, etc.  It is here you will be asked to communicate and/or justify your work based on a particular curricular competency.  This will account for 40% of your course mark.  Your final grade in the course will be determined as follows: 85% (course mark) + 15% (final exam) = 100%.

Content LEARNING OUTCOMES and WEIGHTINGS (60% of course mark)

 

[10-M1]              Understand the properties of the three primary trigonometric ratios; solve right triangles;

apply the Pythagorean Theorem; problem-solve.                                                                                                                                   9%

 

[10-AN1]            Demonstrate a thorough understanding of prime factorization, LCM, GCF, and common factors of polynomials.                    3%

[10-AN2]            Demonstrate an understanding of polynomial multiplication and factoring in multiple ways (visually, algebraically, etc.).   7%

 

[10-AN3]            Demonstrate an understanding of powers with integral (positive and negative) exponents;

apply various exponent laws and incorporate both integral exponents and order of operations.                                     5%

 

[10-RF1]             Explain relationships among data and graphs and represent relations in multiple ways.                                                              2%

[10-RF2]             Understand and explain the properties of a function; state domain and range; utilize function notation.                                            4%

[10-RF3]             Understand properties of linear relations, rate of change, and interpret their graphs.                                                                                 3%

 

[10-RF4]             Demonstrate an understanding of slope, interpret its meaning and graphical representation;

understand and utilize the relationship between parallel and perpendicular lines.                                                                   4%

[10-RF5]             Use graphs and/or points to determine equations of linear functions in different forms, and vice versa;

use various forms of linear functions to solve problems.                                                                                                                      5%

 

[10-RF6]             Construct a system of linear equations to model a situation; determine whether a given ordered pair is a solution.                       2%

[10-RF7]             Solve problems involving systems of linear equations in two variables, both graphically and algebraically;

understand the properties of a system of linear equations and determine the nature of any solutions.                               7%

 

[10-RF8]             Understand and utilize arithmetic sequences and series to solve problems.                                                                                                         5%

 

[10-FL1]              Understand the different types of income or expenditure;

perform calculations to determine the effects of taxation, deductions, discounts and interest.                                     4%

 

 

CURRICULAR COMPETENCIES and WEIGHTINGS (40% of course mark)

 

[10-CC]                Reasoning and Analyzing; Understanding and Solving; Communicating and Representing; Connecting and Reflecting                           40%