Principles of Mathematics 10
Course Outline
Text: Mathematics 10: Addison-Wesley
General Objectives:
1. To develop skills in logical analysis and to present problem solutions in a clear and precise
manner.
2. To develop the mathematics necessary to function in society.
3. To develop the mathematics necessary to engage in life long learning.
4. To develop the mathematics necessary to pursue further formal study in
mathematically related areas.
IRP Objectives:
Problem Solving
It is expected that students will use a variety of methods to solve real-life, practical,
technical, and theoretical problems.
It is expected that students will:
• solve problems that involve a specific content area such as geometry, algebra, trigonometry,
statistics, probability
• solve problems that involve more than one content area
• solve problems that involve mathematics within other disciplines
• analyse problems and identify the significant elements
• develop specific skills in selecting and using an appropriate problem-solving strategy or
combination of strategies chosen from, but not restricted to, the following:
◊ guess and check
◊ look for a pattern
◊ make a systematic list
◊ make and use a drawing or model
◊ eliminate possibilities
◊ work backward
◊ simplify the original problem
◊ develop alternative original approaches
◊ analyse keywords
• demonstrate the ability to work individually and cooperatively to solve problems
• determine that their solutions are correct and reasonable
• clearly explain the solution to a problem and justify the processes used to solve it use
appropriate technology to assist in problem solving
1
Number (Number Concepts)
It is expected that students will:
• analyse the numerical data in a table for trends, patterns and interrelationships.
• explain and illustrate the structure and the interrelationship of the sets of numbers within
the real number system.
It is expected that students will:
• use words and algebraic expressions to describe the data and the interrelationships in a
table with rows that are not related recursively (not calculated from previous data)
• use words and algebraic expressions to describe the data and the interrelationships in a
table with rows that are related recursively (calculated from previous data)
• classify numbers as natural, whole, integer, rational or irrational, and show that these
number sets are "nested" within the real number system
Number (Number Operations)
It is expected that students will:
• use basic arithmetic operations on real numbers to solve problems.
• describe and apply arithmetic operations on tables to solve problems, using technology as
required.
• use exact values, arithmetic operations and algebraic operations on real numbers to solve
problems.
It is expected that students will:
• communicate a set of instructions used to solve an arithmetic problem
• perform arithmetic operations on irrational numbers, using appropriate decimal
approximations
• create and modify tables from both recursive and non recursive situations
• use and modify a spreadsheet template to model recursive situations
• perform operations on irrational numbers of monomial and binomial form, using exact
values
• explain and apply the exponent laws for powers of numbers and for variables with rational
exponents
Patterns and Relations (Patterns)
It is expected that students will generate and analyse number patterns.
It is expected that students will:
• generate number patterns exhibiting arithmetic growth use expressions to represent
general terms and sums for arithmetic growth, and apply these expressions to solve
problems
• relate arithmetic sequences to linear functions defined over the natural numbers
• generate number patterns exhibiting geometric growth
2
Patterns and Relations (Variables and Equations)
It is expected that students will generalize operations on polynomials to include
rational expressions.
It is expected that students will:
• factor polynomial expressions of the form ax2 + bx + c and a2x2 – b2x2
• find the product of polynomials
• divide a polynomial by a binomial and express the result in the forms:
P x
Rx
 Qx 
D x 
◊ D x
◊ P(x)= D(x)Q(x)+ R
• determine equivalent forms of simple rational expressions with polynomial numerators,
and denominators that are monomials, binomials or trinomials that can be factored
• determine the non permissible values for the variable in rational expressions
• perform the operations of addition, subtraction, multiplication, and division on rational
expressions
• find and verify the solutions of rational equations that reduce to linear form
Patterns and Relations (Relations and Functions)
It is expected that students will:
• examine the nature of relations with an emphasis on functions.
• represent data, using linear function models.
It is expected that students will:
• plot linear and nonlinear data, using appropriate scales
• represent data, using function models
• use a graphing tool to draw the graph of a function from its equation
• describe a function in terms of:
◊ ordered pairs a rule,
◊ in word or equation form
◊ a graph
• use function notation to evaluate and represent functions
• determine the domain and range of a relation from its graph
• determine the following characteristics of the graph of a linear function, given its equation:
◊ intercepts
◊ slope
◊ domain
◊ range
• use partial variation and arithmetic sequences as applications of linear functions
3
Shape and Space (Measurement)
It is expected that students will:
• demonstrate an understanding of scale factors, and their interrelationship with the
dimensions of similar shapes and objects.
• solve problems involving triangles, including those found in 3–D and 2–D applications.
It is expected that students will:
• calculate the volume and surface area of a sphere, using formulas that are provided
• determine the relationships among linear scale factors, areas, the surface areas and the
volumes of similar figures and objects
• solve problems involving two right triangles
• extend the concepts of sine and cosine for angles through to 180°
• apply the sine and cosine laws, excluding the ambiguous case, to solve problems
Shape and Space (3–D Objects and 2–D Shapes)
It is expected that students will solve coordinate geometry problems involving lines
and line segments.
It is expected that students will:
• solve problems involving distances between points in the coordinate plane
• solve problems involving midpoints of line segments
• solve problems involving rise, run and slope of line segments
• determine the equation of a line, given information that uniquely determines the line
• solve problems using slopes of:
◊ parallel lines
◊ perpendicular lines
Statistics and Probability (Data Analysis)
It is expected that students will implement and analyse sampling procedures, and draw
appropriate inferences from the data collected.
It is expected that students will:
• choose, justify and apply sampling techniques that will result in an appropriate, unbiased
sample from a given population
• defend or oppose inferences and generalizations about populations, based on data from
samples
4
Time line:
Unit
Number Sequences
Real Numbers
Polynomials
Rational Algebraic Expressions
Coordinate Geometry
Functions
Trigonometry
Statistics & Probability
Total
Time (h)
12
12
14
12
14
12
12
12
100
Evaluation:
Term
Assignments ……………………… .................................
Quizzes ................................................................................
Unit Tests ............................................................................
25 %
35 %
40 %
100 %
* Assignment mark will be based on daily assignments and a portfolio. The daily
assignments will be marked out of the number of questions assigned. The portfolio
will be marked on a performance scheme.
Course Mark
Term Work...........................................................................
Provincial Exam.................................................................
5
80 %
20 %
100 %
Portfolio Marking Scheme:
Student portfolios are due at the end of each unit and will be marked based upon the
performance scheme. In addition, selected daily assignments will be handed in and
marked on the performance scheme.
Any portfolio that is handed in and deemed unacceptable will not be graded.
◊ binder is unacceptable (broken, zippered, …)
◊ no dividers
◊ no table of contents
◊ unit quizzes are missing
◊ portfolio contains notes or other miscellaneous material
Student Expectations:
1. The student must come to class prepared and on time. This means that they have
their text book, pencils, erasers, paper, calculator, etc.
2. Be quiet and ready to start working when the bell rings to indicate the start of class.
In addition, to remain at work the bell sounds indicating the end of class or until you
are dismissed.
3. Evaluation is done on an ongoing basis and as such it is very important that students'
work be kept up to date. If you have any difficulties be sure to ask for help as early
as possible.
4. All missed tests, quizzes and assignments must be completed! Students who are
absent on the day of these events must make arrangements to write the missed
evaluation on their return to school. Failure to do this will result in a mark of ZERO.
Remember, the onus is on YOU to make up any and all missed work!
5. Late portfolio/assignments will not be accepted! However, the sequential nature of
mathematics requires that you make some attempt to complete the work.
6. Students should plan to spend at least one-half hour on homework each night in
addition to preparation for exams, or studying.
7. All garbage including used gum is to be placed in the garbage can at the front of the
room.
8. No food or drink is allowed inside the classroom.
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