Functions & Trigonometry – Course Objectives



There are four main objectives to this course:


1.   Develop problem solving skills and strategies: this course will aim to get students developing key habits of mind that are involved in basic problem solving skills and include:


o      Developing persistence

o      Developing an ability to listen with empathy and understanding

o      Developing an ability to think flexibly

o      Developing a strive for accuracy

o      Developing an ability to question and pose problems

o      Developing an ability to apply past knowledge to new situations

o      Developing an ability to think and communicate with clarity and precision

o      Developing an ability to create, imagine, and be innovative

o      Developing an ability to take responsible risks

o      Developing an ability to think interdependently

o      Developing an ability to remain open to continuous learning



2.   Develop fundamental algebra skills:


o      All students should become proficient with fundamental algebra skills including factoring, expanding, solving equations and inequalities, working with exponents and logarithms, numeracy skills and pattern recognition, graphing functions, etc. The student should be able to perform all fundamental algebra skills with and without technology,



3.   Develop fundamental technology skills with graphing calculators and other technologies (like GeoSketchPad, spreadsheets like EXCEL, PowerPoint Presentation, Equation Editor in WORD, etc..)



4.   Develop an understanding of the real world applications of mathematics



Functions & Trigonometry – Course Outline



This course will comprise of 8 units which are as follows:


  1. Modeling with Linear Functions
  2. Modeling with Quadratic Functions
  3. Modeling with Polynomial Functions
  4. Modeling with Exponential Functions
  5. Modeling with Series and Sequences
  6. Modeling with Triangle Trigonometry
  7. Modeling with Trigonometric Functions
  8. Modeling with Statistics and Probability


Each unit will last 3-5 weeks and each unit will have a unit test at the end of the unit.





Functions & Trigonometry – Student Assessment


There are 7 expectations that describe the mathematical processes that students need to learn and apply as they work to achieve the expectations of this course. These include expectations include:


  1. Problem Solving
  2. Reasoning and Proving
  3. Reflecting
  4. Selection of Tools and Strategies
  5. Connecting
  6. Representing
  7. Communicating



Student work will be selected to help students develop proficiency with these expectations and thus, one component of assessing student work will be the demonstration of the pertinent expectation(s)



The student mark will be determined according to the following breakdown:


Unit Portfolio Work


Unit Tests


Semester Exam





Instructional Strategy: Layered Curriculum



  1. We will work with three “layers” or “levels” as we design work, lessons, and assessments for this unit. The three layers are appropriately called:


    1. “C” layer which addresses the ideas of basic subject/skill knowledge and skill/concept mastery
    2. “B” layer in which we address application of skills and concepts and some manipulation of skills/concepts presented in the “C” layer. Features some problem solving and higher level thinking skills
    3. “A” layer which addresses critical thinking and analysis and combining/synthesis of skills from other areas of math (ie. Geometry)




  1. Student assessment categories and weighting will change for Semester II


    1. Tests will still count 30% of the semester mark (tests will also feature “layering”).
    2. The semester exam will still count 20% of the semester mark (semester exam will also feature “layering”)
    3. The student portfolio will now count 50% of the semester mark (which will also feature “layering”)




  1. The student portfolio will be complete and submitted at latest on the due date assigned. Portfolios will comprise of 4 items:


    1. Class notes
    2. Lesson Quizzes
    3. Lesson work
    4. Research or investigations or “concept extensions”




  1. Marks associated with the “layers”:


    1. Work done at the “C” level will score you a maximum of 75% on your portfolio/tests/exam. “C” level assignments are so-called because if that’s all you do, generally the highest mark you can expect for that portfolio is a C. They are nuts-and-bolts sort of assignments with an emphasis on a basic skill/concept mastery - which is consistent with the implications of a C grade anyway!


    1. Work done at the “B” level will score you a maximum of 85% on your portfolio/tests/exam. “B” level assignments are so-called because if you complete them (along with enough “C” level assignments), the highest mark you can expect for that portfolio is a “B”. They are application and/or extension types of assignments. Recall that “B” layer implies an ability to go beyond the basics and actually do “something” with the basics - which is consistent with the implications of a B grade anyway!


    1. Work done at the “A” level will score you a maximum of 95% on your portfolio/tests/exam. “A” level assignments are so-called because you need to complete one of them (along with enough “C” and “B” level assignments), to expect a mark of at least an “A” (and maybe an “A+”) for that portfolio. These assignments are generally challenging and open-ended - there’s more than one “right” answer, or perhaps none at all! Recall that “A” layer implies an outstanding ability to synthesis skills/concepts and evaluate issues critically - which is consistent with the implications of an A grade anyway!




  1. Implications for you as a student in Functions & Trig in semester I Ź BIG PICTURE is you work toward a level of skill mastery and concept understanding (or a mark if you prefer to be motivated by such) that is consistent with your skills, interest, ability, motivation, educational goals beyond high school math, etc, etc ….  Look at this “restructuring” as a student-teacher contract ….” I will guarantee you a mark of XX and this is how you go about getting it”  or look at it from a student ownership perspective …  “If this is the mark I want, then this is what I must do to earn it”




  1. Different brains learn differently - In this and other courses you will find out about learning styles. Your brain is unique; no one way of teaching is good for everybody. I will try and make sure that all learning styles are targeted. If I am not meeting your needs—tell me! So you will find that the “tasks” in the portfolio cater to a wide variety of learning styles.




  1. Work in groups!!! You will find it beneficial to exchange ideas and strategies with others. Word of caution … do not make group work simply a strategy for “creatively consulting comrades”  i.e. cheating, copying, or communing! See point #8.




  1. Teaching is one of the best ways to learn - This sounds like a contradiction. But think about it. How did I get so good? Partially, by explaining it over and over again to other people. This will work for you, too. If you can teach someone else, you know you understand it yourself.



  1. Student choice (within reason) is good - I am willing to give you all the power and options you can handle in order to help you learn. All portfolio marking schemes will be handed out ahead of time so you know what you’re shooting for. You will have a lot of choice in how you spend your time in class and how you are evaluated; how you decide to spend your time and what your goals are up to you.




  1. Most classes will begin with a homework quiz. I will then give a short lecture. All of these are optional. If you choose not to participate in these activities, I expect you to go to work on other assignments. All period, I will be circulating around the room, available for extra-help, and evaluating assignments as they are turned in. We will keep track of the assignment points you have collected on your Chapter Sheet, so you will know at all times what your Term Mark is.