Mr. Harwood's Principles of Math 11 Enriched Block B (1-2) for 2010/2011
Portable One - The Learning Hut
Problem Solving
Rather than being taught as a separate unit, problem solving will be integrated throughout the course. Problems relevant to each particular strand will be covered in each unit. Students will develop skills in selecting and using an appropriate problem solving strategy. Appropriate technologies including computers and graphic calculators will be used throughout the course to further students’ understanding and problem solving skills.
UNIT #1 -Systems of Equations
solving systems in two variables
by graphing and by algebraic techniques (substitution & elimination)
solving systems in three variables algebraically and by using technology [enrichment: by matrices]
solving non-linear systems using technology
UNIT #2 - Linear Inequalities
solving linear inequalities in one variable
graphing linear inequalities in two variables
solving systems of linear inequalities
UNIT #3 - Quadratic Functions
graphing quadratic functions using standard form
finding domain and range, vertex, axis of symmetry, intercepts, max/min values
changing to standard form by completing the square
UNIT #4 - Quadratic and Polynomial Equations
solving quadratic equations by graphing, factoring, completing the square, formula
complex roots
discriminant
remainder theorem
rational root theorem
factor theorem
solving polynomial equations by factoring and graphically
UNIT #5 - Functions:this unit will be tested in two parts
composition of functions
inverse functions
polynomial functions and inequalities
rational functions and inequalities
absolute value functions
radical functions
UNIT #6 - Geometry
geometric proofs
chord properties
angles in circles
tangent properties
cyclic quadrilaterals
arc length and sector area
angles and polygons
UNIT #7 - Coordinate Geometry and Trigonometry
connecting coordinate geometry and plane geometry
distances between points and lines
equation of a circle
intersections of lines and circles
review of trigonometric ratios
cosine law
sine law - ambiguous case
UNIT #8 (Time permitted) - Probability and Statistics
Due to the heavy emphasis in Math 12 on these topics, I will introduce a probability unit at this time and cover some of the foundational skills: basic probability, counting theorems, permutations, combinations to aid students in mastering the component in Math 12 that covers 25% of their course.
Assessment Grading will be done in three terms and not cumulatively: Please view the following link for Mr. Harwood's assessment guiding principles: AssessmentNotes
Homework is a key component of a work habits assessment. Homework is essential for developing a complete understanding of the mathematical concepts. Therefore, late homework will also be assessed.
Unit Tests and Assignments will determine a report card grade. [Most tests will have a rewrite available if the student studies to learn from their mistakes. At the completion of a rewrite, students must indicate to me which test they want to stand before I mark a rewrite. This demonstrates their confidence and understanding of how well they are doing. The last exam marked stands for that unit.]
Grades reported on each report card will represent this particular terms grade and a fresh start will be offered students at the start of each term.. The three terms will be averaged to give a class mark entering the final exam and used to determine the final grade.
Final Grade: Class Work 80% + Final Exam 20%
Skills needed: PRINCIPLES OF MATHEMATICS 11 - Intended Learning Outcomes
0. Problem Solving: It is expected that students will use a variety of methods to solve all forms of problems (real-life, practical, technical, theoretical).
It is expected that students will:
solve problems that involve one and more than one content area
solve problems that involve mathematics within other disciplines
analyse a problem 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 / eliminate possibilities / work backward / analyse key words / make and use a drawing or model / simplify the original problem / develop alternative original approaches
demonstrate the ability to work individually & co-operatively to solve problems
determine that their solutions are correct and reasonable, and clearly communicate the process used to solve the problem
use appropriate technology to assist in problem solving
I. Patterns and Relations (Relations and Functions I): It is expected that students will demonstrate an understanding of relation & function terminology and notation as part of using algebraic and graphical models to generalize patterns, make predictions, and solve problems.
It is expected that students will:
express a relation between 2 quantities in table, graph, or equation form
solve systems of linear equations by each of the following methods: graphing / substitution / addition and multiplication / using appropriate technology
determine if a linear system has no, one, or infinite solutions
solve applied problems using systems of linear equations
II. Patterns and Relations (Relations and Functions III): It is expected that students will apply knowledge of relations and functions as part of using algebraic and graphical models to generalize patterns, make predictions, and solve problems.
It is expected that students will:
express variations in the form of equations (direct, interval, joint, combined)
solve problems involving direct, interval , joint, and combined variation
transform equation of a parabola from general to standard form, & vice versa
analyse the equation of a parabola to determine the domain, range, intercepts, vertex , axis of symmetry , & max or min values
solve problems involving maximum or minimum values
III. Patterns and Relations (Relations and Functions II): It is expected that students will demonstrate an understanding of graphing techniques as part of using algebraic and graphical models to generalize patterns, make predictions, and solve problems.
It is expected that students will:
distinguish between functions and non-functions
use and interpret function notation
identify an appropriate graph for a given relation
graph relations or functions of the following types and analyse them to determine domain, range, symmetries, vertices, asymptotes, intercepts, and maximum or minimum values:
constant functions linear functions quadratic functions (parabola ) square root functions cubic functions exponential functions reciprocal functions absolute-value functions piecewise functions quadratic relations origin centred (circle, ellipse)
understand and demonstrate transformations in graphs resulting from the following changes in the defining equation: translation reflection dilation
determine the equation of a relation given its graph
create a model function given data or a description
graph quadratic inequalities in two variables
IV. Patterns and Relations (Variables and Equations I): It is expected that students will simplify and manipulate algebraic expressions as part of representing them in multiple ways.
It is expected that students will:
factor polynomials of up to three terms
factor the sum and difference of cubes
factor polynomials using combinations of techniques
add, subtract, multiply, and divide rational expressions with polynomial denominators
simplify algebraic complex fractions
V. Patterns and Relations (Variables and Equations II): It is expected that students will simplify and manipulate numeric and algebraic radical expressions as part of representing them in multiple ways.
It is expected that students will:
convert terminating & repeating decimals to rational form & vice versa
simplify numeric expressions involving radicals (+, -, x, ÷)
simplify algebraic expressions involving radicals (+, -, x, ÷)
rationalize the numerator or denominator of expressions containing radicals (including the use of conjugates)
extend their knowledge of exponent laws to include rational exponents and their radical equivalents
VI. Patterns and Relations (Variables and Equations III): It is expected that students will perform algebraic calculations and apply them to solve problems, using appropriate technology, as part of representing algebraic expressions in multiple ways.
It is expected that students will:
solve quadratic equations by: square root method factoring completing the square quadratic formula appropriate technology
solve rational equations and test for extraneous roots
solve radical equations and test for extraneous roots
solve equations containing rational exponents
solve exponential equations with related bases
use equations to solve a variety of problems
determine if solutions are reasonable within the context of the problem
VII. Shape and Space (3-D Objects & 2-D Shapes): It is expected that students will demonstrate an understanding of circle properties and their applications in solving applied & theoretical problems, as part of describing the characteristics of 3-D objects and 2-D shapes, and analysing the relationships among them.
It is expected that students will:
recall the properties of parallel lines, similar and congruent figures, polygons, angle relationships,
angle measurement, and basic compass and straightedge construction
demonstrate an understanding of the following properties of a circle:
perpendicular bisector of chord passes through the centre of the circle
the line joining midpoint of a chord to the centre is perpendicular to the chord
the line through the centre, perpendicular to a chord, bisects the chord
central angles containing equal chords or arcs are equal (the converse is also true)
inscribed angles containing the same or equal chords (on same side of chord) or arcs are equal
an inscribed angle equals half the central angle containing the same or equal chords (on same side of chord) or arcsare equal
an inscribed angle in a semi-circle measures 90°
opposite angles of a cyclic (inscribed) quadrilateral are supplementary
a tangent is perpendicular to the radius at the point of contact (converse true also)
tangents from an external point are equal
the angle between a chord & tangent equals the inscribed angle on the opposite side of the chord (the converse is also true)
demonstrate and clearly communicate deductive reasoning in the solution of applied problems
VIII. Shape and Space (Measurement I): It is expected that students will demonstrate an understanding of primary trigonometric functions as part of describing and comparing real-world phenomena using measurement.
It is expected that students will:
recall basic primary trigonometric ratios
determine the quadrant for +ve and -ve angles in standard position
identify coterminal angles
determine primary trig function values for angles in standard position
identify reference angles
evaluate primary trig functions for any angle given a variety of conditions
IX. Shape and Space (Measurement II): It is expected that students will solve trigonometric equations as part of describing and comparing real-world phenomena using measurement.
It is expected that students will:
solve trig equations involving the primary functions over a specific domain
examine appropriate interpretation of the calculator display when solving trigonometric equations
use the trigonometric definitions to deduce unknown trigonometric values from given values
X. Shape and Space (Measurement III): It is expected that students will use trigonometry to solve applied and theoretical problems, as part of describing and comparing real-world phenomena using measurement.
It is expected that students will:
use right triangle trigonometry to solve problems
use the formula: Area = 1/2 bc sin A to find the area of a triangle
solve triangles with the sine law & the cosine law
solve applied problems using trigonometric ratios, sine and cosine laws, and area formulae
XI. Statistics & Probability (Data Analysis) as time allows:
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