Course
Overview
Functions
and Relations, Grade 11, University Preparation, MCR3U
Prerequisite: Principles of Mathematics, Grade 10, Academic
Course Description
This
course introduces some financial applications of mathematics, extends students
experiences with functions and trigonometry, and introduces second-degree
relations. Many of the expectations of this course are based on direct
extensions of concepts introduced in Grades 9 and 10. Having previously
explored linear and quadratic relationships, students study polynomial and
rational functions, and investigate the relationship between functions and
their inverses. Students continue their study of trigonometry and discover new
properties and contexts to which it can be applied. Graphing and algebraic
skills are also consolidated and extended in this course. Identifying
connections between the algebraic and graphic representations of functions
continues to be an important skill.
Successful
completion of MCR3U Functions and Relations will prepare students for any of
the five Grade 12 University and College Preparation courses, and provides the
necessary foundation for mathematically rich university programs. In
particular, this course should be taken by students who are planning to study
engineering, computer science, pure mathematics, or the physical sciences at
the university level. This course shares a core set of expectations with the
Grade 11 Functions course, MCF3M, which is comprised of three strands:
Financial Applications of Sequences and Series, Trigonometric Functions, and
Tools for Operating and Communicating with Functions. Completion of either of
these two Grade 11 programs will prepare students for the Grade 12 courses
Advanced Functions and Introductory Calculus (MCB4U), Mathematics of Data
Management (MDM4U), Mathematics for College Technology (MCT4C), and College and
Apprenticeship Mathematics (MAP4C). In addition to this common core, the
Functions and Relations course contains some extension to the core plus a
fourth strand, Investigations of Loci and Conics, which provides students with
the knowledge and skills necessary for MGA4U, Geometry and Discrete
Mathematics.
In
addition to the Investigations of Loci and Conics strand and operations on
complex numbers, the MCR3U course differs from the MCF3M course in timing and
context. The pace of delivery in MCR3U will require students to consistently
demonstrate the ability to:
·
investigate
and construct mathematical concepts independently;
·
conjecture
and, through inquiry, test a hypothesis;
·
generate
multiple types of solutions to complex problems which may cross strands,
require the use of appropriate technology, and require abstract thinking (e.g.,
the consideration of cases);
·
expand
the depth of their inquiry in order to solve higher-order problems;
·
analyse
and design proofs from multiple perspectives.
Because
of the destination intended for students enrolled in MCR3U, the contextual
examples and activities should be drawn largely from the areas of engineering,
the physical sciences, computer science, and pure mathematics.
In
the Financial Applications of Sequences and Series strand, students will
acquire the tools required to make sound personal financial decisions. Students
will investigate and solve problems involving applications of sequences related
to compound interest, annuities, and financial decision-making. In the
Trigonometric Functions strand, students will investigate and apply properties
of the primary trigonometric functions and develop a competency in the
manipulation of these functions. This strand has been divided into two units:
Trigonometry (covering radian measure and the sine and cosine laws) and
Trigonometric Functions (with particular emphasis on the study of sinusoidal
functions). The Tools for Operating and Communicating with Functions strand
allows students to develop skills in operating with various algebraic
expressions and to develop facility in using function notation and in
communicating reasoning. This strand has also been divided into two units:
Exploring Functions: Connecting Algebra and Geometry and Function Notation,
Inverses, and Transformations. In the Investigations of Loci and Conics strand,
students will extend their inquiry of loci into a study of conics. Students
will become proficient in two- and three-dimensional modelling, which is
essential to achieving success in MGA4U, Geometry and Discrete Mathematics.
How This Course Supports
the Ontario Catholic School Graduate Expectations
This course
encourages the Catholic learner to develop his/her God-given gifts and
abilities to promote growth toward personal responsibility in preparation for a
chosen career path. Throughout this course, emphasis should be placed on moral,
ethical, and realistic decision-making in an effort to build responsible
citizenship. The classroom environment should instil a spirit of cooperation,
rather than competition amongst students, and should foster a collaborative
sense of community. This course provides many opportunities for students to
work effectively as interdependent team members and to acknowledge others for
their opinions.
Course Notes
This
course profile builds on previous mathematics course profiles written for
Grades 9 and 10. The Grade 11 course profiles produced by the Catholic and
Public systems represent a collaborative effort between the two writing teams.
While not as detailed as the Grade 9 and 10 profiles, each is designed to
complement and supplement the other. Due to the common core of learning
expectations between the MCR3U and MCF3M courses, a common unit breakdown has
been suggested, and four different sample units have been developed. Thus, the
MCR3U and MCF3M course profiles can also be used as complementary resources.
With appropriate adjustments to the complexity of problems and the need for
abstract thinking, activities from either profile can be used by a teacher of
either course. It should be noted that in this course, it is appropriate in
certain situations for mathematics itself to provide the context for new
concepts, while in MCF3M it would be more appropriate to provide other contexts
as well. The sample units provided in this (MCR3U) profile are Exploring
Functions: Connecting Algebra and Geometry and Trigonometric Functions, while
the sample units provided in the MCF3M profile are Function Notation, Inverses,
and Transformations and Financial Applications of Sequences and Series. In
addition to these four complete sample units, a less-detailed Unit Overview
chart offers a recommended clustering of expectations for each of the remaining
units, providing a starting point from which teachers can develop their own,
individualized units.
For
some students, mathematics is perceived to be a collection of isolated and
complex topics, each requiring skills that may soon be forgotten. The
mathematics teacher must address these perceptions by creating a context in
which students can learn and connect concepts and skills. Students must be
exposed to a variety of teaching, learning, and problem solving techniques to
best synthesize the information presented by the curriculum, and should be
provided applications and context to bring meaning to their learning.
The
activities in this profile are designed to both introduce and consolidate
skills necessary for success in this course. These activities can be used in
conjunction with or independently of one another. Alternate teaching strategies
and suggestions for technological tools are included to help teachers present
the lessons contained in the activities.
Because
this course has been designed to prepare students for further mathematical
studies at university, the specific nature of the learning activities should
reflect this destination. In particular, students in this course should
routinely be challenged with investigations and problems which require
sustained, independent effort. Students destined for university should have the
opportunity to develop and demonstrate a high level of complex problem-solving
ability.
Students with learning disabilities
will need specific guidance in order to benefit from the investigative approach
presented in this profile. Review of prerequisite skills and instructions in
the use of technology, and in particular graphing calculators, will be required
before any activities are begun. Clear and precise instructions with examples
will need to be provided.
Several
of the activities presented in this profile include extensions of the required
content, which can be used to meet the need to challenge gifted students. Other
accommodations may include allowing for student preferences in supplemental
learning, altering the pace of instruction, creating a flexible classroom
environment, and using specific instructional strategies. Creative approaches
to problem solving must be encouraged.
The
Achievement Chart for Mathematics is the basis of all assessment and evaluation
for this course. The Principles of Mathematics Academic (Grade 10) Public
Course Profile includes charts suggesting strategies that can be used for the
assessment and evaluation of all categories of the Achievement Chart (p. 11).
In addition, a chart outlining the component actions that are needed for
successful inquiry and problem solving in particular is also included in their
profile (p. 12). These charts provide an excellent base with which to begin the
implementation of these strategies, and for teachers of this course to extend,
depending on their degree of readiness. Another excellent resource is the Concerning
Assessment and Reflective Evaluation (CARE) package of materials, available
for free download at http://www.oame.on.ca. Among the resources included in
this package are generic rubrics for Communication and Thinking/Inquiry/Problem
Solving skills, along with suggested applications of these instruments.
Units: Titles and Time
|
* Unit 1 |
Exploring Functions: Connecting Algebra and Geometry |
18 hours |
|
Unit 2 |
Function Notation, Inverses, and Transformations |
18 hours |
|
Unit 3 |
Trigonometry |
13 hours |
|
* Unit 4 |
Trigonometric Functions |
19 hours |
|
Unit 5 |
Financial Applications of Sequences and Series |
23 hours |
|
Unit 6 |
Investigations of Loci and Conics |
13 hours |
|
Unit 7 |
Final Summative Assessment |
6 hours |
* These
units are fully developed in this Course Profile.
Unit Overviews
Unit 1: Exploring Functions:
Connecting Algebra and Geometry
Time: 18 hours
Ontario
Catholic School Graduate Expectations: CGE2b, CGE2c, CGE3c, CGE3e, CGE4a,
CGE4b, CGE4f, CGE5a, CGE5g, CGE7b, CGE7j.
Unit
Description
Students investigate quadratic
functions and related concepts from algebraic and geometric perspectives, in
order to deepen their understanding and prepare them for further explorations
of functions and relations. A winter recreation theme is loosely woven
throughout selected activities in the unit, providing a contextual framework
for students to solve problems, both with and without the use of graphing
technology. Students solve first-degree inequalities and graph their solutions
on number lines. Skills involving operations with polynomials and rational
expressions are consolidated, and then extended to the complex number system,
which is introduced in this unit. Students apply the method of completing the
square in order to solve maximum/minimum problems involving quadratic functions.
Algebraic and graphical methods are used to determine the roots of quadratic
equations. The exponent laws are applied to expressions which have powers
containing integer and rational exponents. Students discover the nature of
exponential functions and solve exponential equations.
Unit
Overview Chart
|
Activity |
Time |
Expectations |
Assessment |
Tasks |
|
1. A Range of Possibilities |
75 min |
OCV.01, OCV.03 OC1.01, OC1.02, OC3.04, OC3.05 |
Knowledge |
Solve and graph inequalities; Perform operations with polynomials |
|
2. Ski-Jumping to the Max! |
150 min |
OCV.01, OCV.03 OC1.03, OC1.05, OC3.01, OC3.05 |
Knowledge |
Complete the square; Investigate the graphs of quadratic functions |
|
3. Rooting Around the Parabola |
150 min |
OCV.01, OCV.03 OC1.04, OC1.05, OC3.02, OC3.05 |
Knowledge |
Determine real/complex roots of quadratic equations; Relate roots to x-intercepts of quadratic functions |
|
4. Complex Basics are Basically not Complex! |
150 min |
OCV.01, OCV.03 OC1.06, OC3.04, OC3.05 |
Knowledge |
Perform algebraic operations on complex numbers; Graph numbers on the complex plane |
|
5. Can We Please be Rational?! |
150 min |
OCV.01, OCV.03 OC1.07, OC3.01, OC3.03, OC3.04, OC3.05 |
Knowledge |
Perform algebraic operations on rational expressions; State restrictions on the variables |
|
6. Power Play |
75 min |
OCV.01, OCV.03 OC1.08, OC3.01, OC3.05 |
Inquiry |
Explore powers with rational exponents; Apply exponent laws to powers containing integer and rational exponents |
|
7. Its Snowing Cats and Dogs! |
150 min |
OCV.01, OCV.03 OC1.09, OC.3.03, OC3.05 |
Knowledge |
Explore exponential relations; Solve exponential equations |
|
8. Summative Assessment |
75 min |
All expectations within unit |
Knowledge |
Summative assessment |
Any
additional time can be allocated for remediation and consolidation of skills at
the discretion of the teacher, depending on the needs of the students.
Unit 2: Function Notation, Inverses, and
Transformations
Time: 18 hours
Unit
Description
Through
authentic models, students are introduced to the definition of a function and
the notations associated with it. Students use graphing technology and
paper-and-pencil tasks to investigate the properties of functions and their
inverses, and the transformations of functions. The investigations are used to
introduce and extend the use of function notation to inverses and
transformations. Students explore the domain and range of functions, inverses,
and transformations.
Unit
Overview Chart
|
Activity |
Time |
Expectations |
Assessment |
Tasks |
|
1. Wrap Around Follow-Up Skills |
150 min 75 min |
OCV.02, OCV.03 OC2.01, OC2.02, OC3.01, OC3.02, OC3.04 CGE2c, CGE3c, CGE4f, CGE5e, CGE5g |
Knowledge |
Investigate the concept of a function; Formalize the definition of the term function; Apply function notation |
|
2. Home on the Range Follow-Up Skills |
150 min 75 min |
OCV.02, OCV.03 OC2.02, OC2.03, OC3.03, OC3.05 CGE4f, CGE5a |
Knowledge |
Explore through the use of graphing technology the properties of various functions; Investigate domain and range |
|
3. Follow the Bouncing Ball |
105 min |
OCV.02, OCV.03 OC2.02, OC3.03, OC3.04, OC3.05 CGE2b, CGE3c, CGE5a |
Knowledge |
Develop a model with the use of graphing technology; Apply appropriate function notation with the model; Investigate properties of the function/model |
|
4. Lets Switch Seats! Follow-Up Skills |
105 min 75 min |
OCV.02, OCV.03 OC2.04, OC3.03, OC3.05 CGE3c, CGE4f |
Inquiry |
Investigate the properties of inverse functions; Discover algebraic approaches for finding the inverse of functions |
|
5. On the Move |
150 min |
OCV.02, OCV.03 OC2.06, OC2.07, OC2.08, OC3.02, OC3.04 CGE2c, CGE5a |
Knowledge |
Investigate the effect of transformations on mathematical functions; Apply appropriate function notation to transformations of functions |
|
6. Be my Valentine |
105 min |
OCV.02, OCV.03 OC2.06, OC2.07, OC2.08, OC3.01, OC3.05 CGE2b, CGE2f |
Knowledge |
Apply and analyse transformations of functions |
|
7. Consolidating and Connecting |
105 min |
OCV.02, OCV.03 OC1.03, OC2.02, OC2.06, OC2.07, OC3.02, OC3.03 CGE3c, CGE4f, CGE5a |
Knowledge |
Summative assessment |
Any
additional time can be allocated for remediation and consolidation of skills at
the discretion of the teacher, depending on the needs of the students.
Unit 3: Trigonometry
Time: 13 hours
Ontario
Catholic School Graduate Expectations: CGE2b, CGE2c, CGE3c, CGE3e, CGE4a,
CGE4b, CGE4f, CGE5a, CGE5g, CGE7b, CGE7j.
Unit
Description
Students
consolidate and extend concepts first introduced in Grade 10. Students use the
primary trigonometric ratios, the sine law, and the cosine law to model and
solve two- and three-dimensional problems involving acute, right, and oblique
triangles. Students investigate the relationship between degree and radian
measure, and explore the use of the unit circle and special triangles to
determine selected values of the primary trigonometric ratios. Methods of proof
are introduced and applied to verify trigonometric identities. Students develop
the skills to manipulate and solve trigonometric equations.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
TFV.02 TF2.01, TF2.02, TF2.03, TF2.07 |
Knowledge |
Define terms and concepts; Convert degrees to radians; Apply radian measure |
|
2 |
TFV.01, TF1.02, TF2.03 |
Knowledge |
Review the primary trigonometric ratios; Review the sine and cosine laws for acute triangles; Explore the sine and cosine laws for oblique triangles; Investigate the ambiguous case of the sine law |
|
3 |
TFV.02 TF2.03, TF2.04 |
Knowledge |
Investigate special triangles |
|
4 |
TFV.02 TF1.01, TF2.05 |
Knowledge |
Derive the unit circle; Use the Pythagorean theorem to prove identities; Discuss the use of proof |
|
5 |
TFV.02 TF2.03, TF2.06, TF2.07 |
Knowledge |
Solve linear and quadratic trigonometric equations |
|
6 |
All expectations within unit |
Knowledge |
Summative assessment |
Unit 4: Trigonometric Functions
Time: 19 hours
Unit
Description
Students
investigate the periodic nature and graphical properties of the primary
trigonometric functions. Using technology, students explore the effects of
simple transformations on their graphs and equations. Students apply these
concepts to model authentic problems.
Unit
Overview Chart
|
Activity |
Time |
Expectations |
Assessment |
Tasks |
|
1. Surfs Up! Lets Catch the Sine Wave |
75 min |
TFV.02, TFV.03 TF2.07, TF3.01 CGE3c |
Knowledge |
Derive y = sin x and y = cos x from the unit circle |
|
2. Transformations: More than Meets the Eye Follow-Up Skills Give Me a Sine Follow-Up Skills |
75 min 30 min 75 min 45 min |
TFV.02, TFV.03, OCV.02 TF2.07, TF3.01, TF3.02, TF3.03, TF3.04, TF3.05, OC2.06, OC2.07, OC2.08 CGE3c, CGE5a, CGE5e, CGE5f |
Knowledge |
Investigate the properties of various transformations of
y = sin x and |
|
3. Dont Go Off on a Tangent Follow-Up Skills |
75 min 30 min |
TFV.03 TF3.01, TF3.06 CGE3c, CGE 4b, CGE 4f |
Knowledge |
Investigate the properties of |
|
4a. Its a Spring Thing |
150 min |
TFV.03, TFV.04, OCV.02 TF3.02, TF3.03, TF3.04, TF3.05, TF4.01, TF4.02, OC2.06, OC2.08 CGE2c, CGE3c, CGE4b, CGE5a, CGE5g |
Knowledge |
Model the motion of a mass on a spring |
|
4b. Ferris Fair Follow-Up Skills |
150 min 75 min |
Model the height of a gondola on a Ferris wheel |
||
|
4c. Let the Sine Shine In Follow-Up Skills |
150 min 60 min |
Model an hours of daylight function |
||
|
5. Summative Assessment |
150 min |
All expectations within unit CGE2b, CGE3c, CGE3e |
Knowledge |
Apply concepts in familiar and unfamiliar contexts |
Unit 5: Financial Applications of
Sequences and Series
Time: 23 hours
Ontario
Catholic School Graduate Expectations: CGE2b, CGE2c, CGE3b, CGE3c, CGE3e,
CGE4a, CGE4f, CGE5a, CGE5c, CGE7b, CGE7c.
Unit
Description
Students
investigate arithmetic and geometric sequences and series. This knowledge
serves as the basis for applications of personal finance. Students develop the
formula for compound interest and solve problems related to compound interest
and annuities. As skills are developed, students use spreadsheets to
investigate the cost of borrowing when interest rates, compound periods,
lending terms, etc., are varied. The activities are designed to reflect the
type of decisions that students are likely to face in the future. Students
apply skills with linear and exponential functions.
Unit
Overview Chart
|
Activity |
Time |
Expectations |
Assessment |
Tasks |
|
1. Investigating Attributes of Sequences |
150 min |
FAV.01 FA1.01, FA1.02 |
Inquiry |
Investigate sequences |
|
2. Summing Up: Arithmetic Sequences and Series |
150 min |
FAV.01, FAV.02 FA1.04, FA1.05, FA2.04 |
Knowledge |
Develop formula for arithmetic sequences and series |
|
3. Compound Interest: Exploring Geometric Sequences |
150 min |
FAV.01, FAV.02 FA1.03, FA1.04, FA2.01, FA2.02, FA2.05 |
Knowledge |
Use a financial application to investigate geometric sequences; Develop the compound interest formula |
|
4. Applications: Finding the Amount and the Present Value of a Long Term Investment |
75 min |
FAV.02, FAV.03 FA2.02, FA3.01, FA3.02 |
Knowledge |
Extend knowledge of the compound interest formula and introduce financial applications of a graphing calculator |
|
5. Introduction to Geometric Series |
75 min |
FAV.01 FA1.05 |
Knowledge |
Develop the formula for the sum of a geometric series |
|
6. Applications: Finding the Amount and the Present Value of an Annuity. |
150 min |
FAV.02 FA2.02, FA2.03 FA3.05 |
Inquiry |
Apply geometric sequences and series to finding the amount and present value of an annuity |
|
7. What Happens When?: Changing the Time, Rate and Amount. |
150 min |
FAV.03 FA3.01 FA3.05 |
Knowledge |
Use financial applications of a graphing calculator to investigate the effect of changing conditions when borrowing and saving |
|
8. Mortgages: How They Work. |
150 min |
FAV.03 FA3.02, FA3.03, FA3.04 FA3.05 |
Communication |
Use technology to generate amortization tables |
|
9. Financial Decision Making: A Case Study |
300 min |
All expectations within unit |
Knowledge |
Summative assessment |
Any
additional time can be allocated for remediation and consolidation of skills at
the discretion of the teacher, depending on the needs of the students.
Unit 6: Investigations of Loci and Conics
Time: 13 hours
Ontario
Catholic School Graduate Expectations: CGE2b, CGE2c, CGE3c, CGE3e, CGE4a, CGE4b,
CGE4f, CGE5a, CGE5g, CGE7b, CGE7j.
Unit
Description
Students
investigate the concept of locus of points, using dynamic geometry software.
Conic sections are introduced as second-degree relations, containing some
examples that are not functions. Physical models (e.g., string models,
sketches) representing conic sections are constructed, which serve to
illustrate their geometric properties. By translating to standard position,
students identify conic sections by type, given their equations. Students determine
the intersection of lines and conics, and solve problems involving the
application of conics.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
LCV.01 LC1.01, LC1.02, LC1.03 |
Knowledge |
Construct geometric models of loci with and without dynamic geometry software |
|
2 |
LCV.01, LCV.02 LC1.02, LC1.04, LC1.05, LC2.05 |
Communication |
Construct geometric models of conic sections with and without dynamic geometry software |
|
3 |
LCV.02 LC2.01, LC2.03, LC2.04 |
Knowledge |
Identify geometric properties of conics in standard position |
|
4 |
LCV.02 LC2.02, LC2.03, LC2.04 |
Knowledge |
Translate conics to standard position; Identify geometric properties of generic conics |
|
5 |
LCV.02, LCV.03 LC2.04, LC3.03 |
Knowledge |
Determine points of intersection of lines and conics |
|
6 |
LCV.03 LC3.01, LC3.02 |
Inquiry |
Investigate applications of conics |
|
7 |
All expectations within unit |
Knowledge |
Summative assessment |
Unit 7: Final Summative
Assessment
Time: 6 hours
Ontario
Catholic School Graduate Expectations: CGE2b, CGE2c, CGE3c, CGE3e, CGE4a, CGE4b,
CGE4f, CGE5a, CGE5g, CGE7b, CGE7j.
Unit Description
Summative
assessment should be designed to provide the opportunity for students to
demonstrate comprehensive learning in each of the four achievement categories.
Some ideas are suggested in the chart that follows, however any of the various
assessment tools mentioned in the Assessment Strategies section could be
used. A short paper-and-pencil task would review key terms, skills, and
concepts. Investigations comparing the buying and leasing of a car yield a wide
variety of applications pertaining to both personal finance and the modelling
of functions. An assignment exploring trigonometric inverses (for example, the
arcsine function) would serve to review the concepts introduced in the
functions and trigonometry units. This topic also provides students with an
exposure to a subject further explored in Grade 12. An additional activity
linking the conics and trigonometry strands (using the unit circle and
parametric equations, perhaps) could also be designed. These topics are
suggested as one possible way to revisit the expectations in a new mathematical
context. Accordingly, students are to be assessed solely on the expectations of
this course, and not on the extension topics themselves. Due to the particular
emphasis of cumulative tests and examinations in university and college
programs, a formal examination should be play a prominent role in the final
summative assessment of the student.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
All strands |
Knowledge |
Review key concepts and terms |
|
2 |
· Financial Applications of Sequences and Series · Tools for Operating and Communicating with Functions |
Knowledge |
Examine financial commitments of owning a car: buying vs. leasing |
|
3 |
· Trigonometric Functions · Tools for Operating and Communicating with Functions |
Knowledge |
Explore trigonometric inverses |
|
4 |
· Trigonometric Functions · Investigations of Loci and Conics |
Knowledge |
Explore parametric equations |
|
5 |
All strands |
Knowledge |
Final examination |
Some Considerations for
Alternate Delivery Models
Because
of the similarity of the learning expectations of the MCR3U and MCF3M courses,
it is possible that some schools may run split classes, combining both courses
in the same room. While this situation should be avoided wherever possible,
timetabling issues may make it impossible to have separate classrooms for each
of these two courses. Therefore, in order to satisfy the needs of all students
in this situation, the following delivery model, patterned after the scope and
sequence of the MCF3M Course Profile, is proposed.
Note
that the Investigations of Loci and Conics unit is to be delivered largely as
an independent study, throughout the length of the course. Only students
enrolled in MCR3U would be required to complete this unit. The teacher should
provide instructional support where necessary. It is suggested during these
times that the teacher have MCF3M students otherwise engaged in activities
designed to consolidate skills in the three core strands.
As the
times for the remaining units have all been increased, it is expected that the
pace of the delivery of course will be appropriately altered. This will allow
MCR3U students time to expand the depth and scope of their inquiry and
problem-solving skills relating to relevant subject matter. The Financial
Applications of Sequences and Series unit can be delivered either before or
after the two trigonometry units, depending on the students needs.
Units: Titles and Time
|
* Unit 1 |
Exploring Functions: Connecting Algebra and Geometry |
20 hours |
|
Unit 2 |
Function Notation, Inverses, and Transformations |
20 hours |
|
Unit 3 |
Financial Applications of Sequences and Series |
25 hours |
|
* Unit 4 |
Trigonometry |
13 hours |
|
Unit 5 |
Trigonometric Functions |
22 hours |
|
Unit 6 |
Investigations of Loci and Conics |
v 0 |
|
Unit 7 |
Final Summative Assessment |
10 hours |
* These
units are fully developed in this Course Profile.
v Independent study unit that must be
completed by all MCR3U students.
Teaching/Learning
Strategies
In order
to address the wide range of expectations in this course, a variety of
teaching, learning, and assessment strategies and tools need to be used.
Teachers should assume a variety of roles (including guide, facilitator,
consultant, and instructor), and should employ a variety of strategies
including:
·
a
balance of whole-class, small group, mixed-ability structured group, and
individual instruction through student-centred and teacher-directed activities
(group work should be carefully structured along cooperative learning
principles to be effective);
·
the
use of rich contextual problems which engage students and provide them with
opportunities to demonstrate learning, and appreciate the need for new skills;
·
the
prompting, supporting, and challenging of individual students as well as the
class as a whole;
·
approaches
that will accommodate multiple learning styles (e.g., the provision of verbal
and written instructions, the inclusion of hands-on activities, etc.);
·
the
use of technological tools and software (e.g., graphing software, dynamic
geometry software, the Internet, spreadsheets, and multimedia) in activities,
demonstrations, and investigations to facilitate the exploration and understanding
of mathematical concepts;
·
the
use of learning/performance tasks that are designed to link several
expectations and give the students occasion to demonstrate their optimal levels
of achievement through the demonstration of skill acquisition, the
communication of results, the ability to pose extending questions following an
inquiry, and the determination of a solution to unfamiliar problems;
·
the
use of accommodations, remediation, and/or extension activities, where
necessary, to meet the needs of exceptional students;
·
the
provision of opportunities for students to practise and extend their skills and
knowledge outside of the classroom.
In addition to the contribution of
the teacher, students themselves should play an active role in their own
learning. In order to successfully complete the requirements of this course,
students are expected to:
·
develop
an increased responsibility for their own learning;
·
be
accountable for prerequisite skills;
·
participate
as active learners;
·
engage
in explorations using technology;
·
apply
individual and group learning skills;
·
describe
mathematical patterns that emerge verbally, algebraically, and visually in the
course of learning.
Assessment Strategies
An
effective assessment program in mathematics must include a balance of
diagnostic, formative and summative assessment instruments that incorporate the
categories of learning as defined in The Achievement Chart for Mathematics. One
approach is shown below:
|
|
Knowledge/
Understanding |
Thinking/Inquiry/
Problem Solving |
Communication |
Application |
|
final examinations |
3 |
3 |
3 |
3 |
|
journals |
3 |
|
3 |
3 |
|
observations |
|
3 |
3 |
3 |
|
oral presentations |
3 |
|
3 |
|
|
performance tasks |
3 |
3 |
3 |
3 |
|
portfolios |
3 |
3 |
3 |
3 |
|
quizzes |
3 |
|
|
|
|
reports/assignments |
3 |
|
3 |
3 |
|
student-teacher conferences |
3 |
|
3 |
|
|
unit tests |
3 |
3 |
3 |
3 |
Assessment
tools such as observational checklists, performance criteria, rubrics, The
Achievement Chart for Mathematics, marking schemes, rating scales, peer
evaluation, and self-evaluation can and should be used to assist in developing
objective and consistent evaluations of student achievement.
Assessment &
Evaluation of Student Achievement
Assessment, as defined in the document Ontario
Secondary Schools, Grades 9-12: Program and Diploma Requirements, 1999, is
the process of gathering information from a variety of sources (including
assignments, demonstrations, projects, performances, and tests) that accurately
reflects how well students are achieving the curriculum expectations (p. 31).
Assessment tools should be designed to allow students to demonstrate the full
extent of their learning across the four categories of knowledge and skills. As
teachers will use a variety of assessment tools, it is necessary to ensure that
a consistent standard is maintained. These tools should be developed with the
learning expectations of the course as the criteria for this standard. Thus, a
grade of 70-79% using an objective marking scheme should be equivalent to a
Level 3 performance, as defined by the Achievement Chart. Teachers may find it
more appropriate to use rubrics to assess Thinking/Inquiry/Problem Solving, and
Communication skills, but to use objective scales for Knowledge/Understanding,
and Application skills. High-quality assessment can measure individual and
group performance, and individual performance within a group.
The
students effective demonstration of communication skills is an essential
component of this course when evaluating achievement. Students are required to
display and convey their knowledge and understanding of concepts, share their
process of thought and inquiry, and justify their application of concepts in an
unfamiliar situation. In addition, their ability to communicate these
skills is also assessed.
It
should also be noted that teachers must continue to expand their understanding
of Application skills to include non-routine applications. This view requires a
shift from the specific application of concepts (i.e., familiar
situations), to the general application of concepts (i.e., unfamiliar
situations).
Assessment
strategies and tools must address a wide variety of teaching and learning styles
in addition to the criteria established by the learning expectations. Tests
consisting only of questions that ask students to perform algorithms and apply
their knowledge do not necessarily offer an opportunity for students to
demonstrate Level 4 performance.
Also, it is understood that students
will meet course expectations at a variety of performance levels. An effective
and well-balanced assessment program will provide students with several
opportunities to demonstrate growth and improvement over time, across all of
the knowledge and skill categories.
Evaluation, as defined by Ontario Secondary
Schools, Grades 9-12: Program and Diploma Requirements, 1999, is the
process of judging the quality of a students work on the basis of established
achievement criteria, and assigning a value to represent that quality (p. 31).
Whereas assessment is the collection of information about student performance
in a variety of methods, evaluation is the determination of a quantitative
value describing the students overall level of achievement. Effective
assessment, evaluation, and reporting require the teacher to do more than just
average marks. While averaging may be more useful in some Knowledge and
Application skill categories, it is not comprehensive enough for accurate
reporting in the Inquiry and Communication skill categories. The use of rubrics
is a suggested technique for these categories. As students can be expected to
improve their performances over time, particular emphasis should be placed on
their most recent and most consistent level of achievement.
Students who receive a final performance evaluation of Level 3 or better are well prepared for work in the university preparation courses Geometry and Discrete Mathematics (MGA4U), Advanced Functions and Introductory Calculus (MCB4U), and Mathematics of Data Management (MDM4U). Accordingly, in order to prepare students for the academic reality of most mathematically rich university programs, proper attention should be placed on the students effective preparation for a comprehensive final examination. While other rich, performance-based activities can and should be part of the Final Summative Assessment unit, a formal examination should play a significant role in this particular course.
Seventy
per cent of the grade will be based on assessments and evaluations conducted
throughout the course. Thirty per cent of the grade will be based on a final
evaluation in the form of an examination, performance, essay, and/or other
method of evaluation.
Accommodations
Teachers
should refer to the students Individual Education Plans (IEP) and consider
their particular learning characteristics to make any necessary accommodations.
Teachers should work in consultation with resource teachers, ESL/ELD teachers,
and parents or guardians to determine appropriate accommodations as they work
through the course in order to achieve the IEP expectations.
Accommodations
for ESL/ELD Students
·
Have
ESL students work in pairs, with peer tutors, with classmates that have the
same linguistic background, or with cooperative supportive groups, where they
are more likely to improve their use of English. Brainstorm in groups using the
students first language if their usage of English is limited.
·
Use
peer conferencing to reinforce instructions or information.
·
Provide
reference notes, outlines of critical information, models of charts, timelines
or diagrams.
·
Use
visuals to illustrate definitions for the students dictionary of terms.
·
Pair
written instructions with verbal instructions. Provide visual or auditory cues.
·
Simplify
instructions. Highlight key words or phrases.
·
Reinforce
main ideas by using the think/pair/share peer-assessment strategy.
·
Provide
opportunities for students to practice oral presentation skills.
·
Ask
an ESL/ELD teacher to review questions, assignments, or assessment instruments.
Accommodations
for Students with Learning Disabilities
·
Provide
extensive student-teacher conferencing.
·
Provide
a list of terms (possibly simplified) before an activity begins.
·
Modify
handouts in terms of the terminology and content used, as well as the size and
typeface of the selected font. Allow plenty of space for written responses.
·
Allow
assignments to be completed in alternate formats or using longer timelines.
·
Keep
manipulatives, grid paper, formula sheets, and other aids available for needs
that arise.
·
Provide
the students with oral pre-planning of activities.
·
Pair
students in order to provide appropriate support, for the identified student.
·
Contact
parents or guardians for support and suggestions.
Accommodations
for Gifted Students
·
Pose
open-ended questions that require higher-level thinking.
·
Accept
ideas and suggestions from students and expand on them.
·
Model
creative thinking strategies, (e.g., decision-making and evaluation of
problem-solving approaches).
·
Create
flexible instructional groups.
·
Encourage
independent investigations and projects.
·
Facilitate
original and independent problems and solutions.
·
Take
the time to explain the nature of errors.
·
Find
academic and community mentors for students.
Resources
This
course profile has been provided as a resource to aid the teacher in delivering
the curriculum. Through the discretionary use of other materials, the teacher
can enrich, remediate, or otherwise supplement their students education. The
following is a partial list of widely available resources.
Software (Ministry-Licensed)
Geometers
Sketchpad (dynamic
geometry)
Maple (word processor/programming)
Mastering
Calculus (concept
and skill development)
Math
Trek (concept and
skill development)
Virtual
Tiles (algebraic
concept and skill development)
Zap-a-Graph (graphing)
Internet sites
Note: The URLs for the websites have been
verified by the writer prior to publication. Given the frequency with which
these designations change, teachers should always verify the websites prior to
assigning them for student use.
Canadian
Education on the Web (http://www.oise.on.ca/~mpress/eduweb.html)
A compendium of Canadian education-related resources maintained by Marian Press
at the Ontario Institute for Studies in Education/University of Toronto.
Education
Network of Ontario (http://www.enoreo.on.ca/)
ENO is a computer communications network for everyone who works in elementary
and secondary education in
Hewlett-Packard
(http://www.hp.com/calculators/)
National
Council of Teachers of Mathematics (http://www.nctm.org)
Ontario
Association of Mathematics Educators (http://www.oame.on.ca)
Ontario
Curriculum Centre (http://www.curriculum.org)
A non-profit organization established to coordinate the sharing of teaching
materials across
Texas
Instruments (http://www.ti.com/calc/docs)
Print
Burz,
H.L.,
Concerning Assessment and Reflective
Evaluation (CARE) Package (download from
http://www.oame.on.ca)
MathMania: Adventures in Mathematics.
The
Mathematics Teacher.
ISSN 0025-5769
Connecting
Mathematics: Addenda Series, Grades 9-12. NCTM
O.S.S.T.F.
Quality Assessment.
Stiggins,
R. Classroom Assessment for Student Success.
Taggart,
G. (Ed.) Rubrics A Handbook for Construction and Use.
OSS
The
following list of resources will support many of the Ontario Secondary School
Policies as well as the Ontario Catholic Secondary School Graduate
Expectations.
·
Ministry
of Education Policy and Reference Documents
Choices
into Action: Guidance and Career Education Program Policy
Cooperative
Education: Policies and Procedures for Ontario Secondary Schools
Individual
Education Plans: Standards for Development, Program Planning, and Implementation,
2000
Mathematics,
Grades 9-10
Mathematics,
Grades 11-12
Ontario
Schools Code of Conduct
Ontario
Secondary Schools, Grades 9-12: Program and Diploma Requirements
Program
Planning and Assessment, Grades 9-12
Violence-Free
Schools Policy
The Ministry
of Education has also published several resource documents, brochures, and
policy/program memoranda in support of its
·
Publications
Concerning Faith Development
Blueprints (Catholic Curriculum Cooperative -
Catholicity
Across The Curriculum
(
Educating
the Soul (Institute
for Catholic Education)
This
Moment of Promise (
·
Career
Goals/Cooperative Education Programs
Youth
Employment Skills Program
·
Community
Partnerships
Refer to
local board policies (e.g., Relations with Business - Corporate Donations,
Sponsorships and Agreements).
Coded
Expectations, Functions and Relations, Grade 11,
University Preparation, MCR3U
Financial Applications of
Sequences and Series
Overall Expectations
FAV.01 · solve problems involving
arithmetic and geometric sequences and series;
FAV.02 · solve problems involving compound
interest and annuities;
FAV.03 · solve problems involving financial
decision making, using spreadsheets or other appropriate technology.
Specific Expectations
Solving
Problems Involving Arithmetic and Geometric Sequences and Series
FA1.01 write terms of a sequence, given
the formula for the nth term or given a recursion formula;
FA1.02 determine a formula for the nth
term of a given sequence (e.g., the nth term of the sequence
... is 
);
FA1.03 identify sequences as arithmetic
or geometric, or neither;
FA1.04 determine the value of any term in an
arithmetic or a geometric sequence, using the formula for the nth term
of the sequence;
FA1.05 determine the sum of the terms of
an arithmetic or a geometric series, using appropriate formulas and techniques.
Solving Problems
Involving Compound Interest and Annuities
FA2.01 derive the formulas for compound
interest and present value, the amount of an ordinary annuity, and the present
value of an ordinary annuity, using the formulas for the nth term of a
geometric sequence and the sum of the first n terms of a geometric
series;
FA2.02 solve problems involving compound
interest and present value;
FA2.03 solve problems involving the
amount and the present value of an ordinary annuity;
FA2.04 demonstrate an understanding of
the relationships between simple interest, arithmetic sequences, and linear
growth;
FA2.05 demonstrate an understanding of
the relationships between compound interest, geometric sequences, and
exponential growth.
Solving
Problems Involving Financial Decision Making
FA3.01 analyse the effects of changing
the conditions in long-term savings plans (e.g., altering the frequency of
deposits, the amount of deposit, the interest rate, the compounding period, or
a combination of these) (Sample problem: Compare the results of making
an annual deposit of $1000 to an RRSP, beginning at age 20, with the results of
making an annual deposit of $3000, beginning at age 50);
FA3.02 describe the manner in which
interest is calculated on a mortgage (i.e., compounded semi-annually but
calculated monthly) and compare this with the method of interest compounded
monthly and calculated monthly;
FA3.03 generate amortization tables for
mortgages, using spreadsheets or other appropriate software;
FA3.04 analyse the effects of changing
the conditions of a mortgage (e.g., the effect on the length of time needed to
pay off the mortgage of changing the payment frequency or the interest rate);
FA3.05 communicate the solutions to
problems and the findings of investigations with clarity and justification.
Trigonometric Functions
Overall Expectations
TFV.01 · solve problems involving the sine
law and the cosine law in oblique triangles;
TFV.02 · demonstrate an understanding of
the meaning and application of radian measure;
TFV.03 · determine, through investigation,
the relationships between the graphs and the equations of sinusoidal functions;
TFV.04 · solve problems involving models
of sinusoidal functions drawn from a variety of applications.
Specific Expectations
Solving
Problems Involving the Sine Law and the Cosine Law in Oblique Triangles
TF1.01 determine the sine, cosine, and
tangent of angles greater than 90°, using a suitable technique (e.g., related
angles, the unit circle), and determine two angles that correspond to a given
single trigonometric function value;
TF1.02 solve problems in two dimensions
and three dimensions involving right triangles and oblique triangles, using the
primary trigonometric ratios, the cosine law, and the sine law (including the
ambiguous case).
Understanding
the Meaning and Application of Radian Measure
TF2.01 define the term radian measure;
TF2.02 describe the relationship between
radian measure and degree measure;
TF2.03 represent, in applications,
radian measure in exact form as an expression involving π (e.g., 
) and
in approximate form as a real number (e.g., 1.05);
TF2.04 determine the exact values of the
sine, cosine, and tangent of the special angles 0, 
and their multiples less than or equal to 2π;
TF2.05 prove simple identities, using
the Pythagorean identity, sin2x + cos2x =
1, and the quotient relation, tan x = 
;
TF2.06 solve linear and quadratic
trigonometric equations (e.g., 6 cos2x sin x 4 =
0)
on the interval 0 £ x £ 2π;
TF2.07 demonstrate facility in the use
of radian measure in solving equations and in graphing.
Investigating
the Relationships Between the Graphs and the Equations of Sinusoidal Functions
TF3.01 sketch the graphs of y =
sin x and y = cos x, and describe their periodic
properties;
TF3.02 determine, through investigation,
using graphing calculators or graphing software, the effect of simple
transformations (e.g., translations, reflections, stretches) on the graphs and
equations of
y = sin x and y =
cos x;
TF3.03 determine the amplitude, period,
phase shift, domain, and range of sinusoidal functions whose equations are
given in the form y = a sin(kx + d) + c or y
= a cos(kx + d) + c;
TF3.04 sketch the graphs of simple
sinusoidal functions
[e.g., y = a sin x, y = cos kx, y =
sin(x + d), y = a cos kx + c];
TF3.05 write the equation of a
sinusoidal function, given its graph and given its properties;
TF3.06 sketch the graph of y =
tan x; identify the period, domain, and range of the function; and
explain the occurrence of asymptotes.
Solving
Problems Involving Models of Sinusoidal Functions
TF4.01 determine, through investigation, the
periodic properties of various models (e.g., the table of values, the graph,
the equation) of sinusoidal functions drawn from a variety of applications;
TF4.02 explain the relationship between the
properties of a sinusoidal function and the parameters of its equation, within
the context of an application, and over a restricted domain;
TF4.03 predict the effects on the
mathematical model of an application involving sinusoidal functions when the
conditions in the application are varied;
TF4.04 pose and solve problems related
to models of sinusoidal functions drawn from a variety of applications, and
communicate the solutions with clarity and justification, using appropriate
mathematical forms.
Tools for Operating and
Communicating with Functions
Overall Expectations
OCV.01 · demonstrate facility in
manipulating polynomials, rational expressions, and exponential expressions;
OCV.02 · demonstrate an understanding of
inverses and transformations of functions and facility in the use of function
notation;
OCV.03 · communicate mathematical
reasoning with precision and clarity throughout the course.
Specific Expectations
Manipulating
Polynomials, Rational Expressions, and Exponential Expressions
OC1.01 solve first-degree inequalities and
represent the solutions on number lines;
OC1.02 add, subtract, and multiply
polynomials;
OC1.03 determine the maximum or minimum
value of a quadratic function whose equation is given in the form y = ax
2+ bx + c, using the algebraic method of completing the
square;
OC1.04 identify the structure of the
complex number system and express complex numbers in the form
a + bi, where i2 = 1 (e.g., 4i, 3 2i);
OC1.05 determine the real or complex
roots of quadratic equations, using an appropriate method (e.g., factoring, the
quadratic formula, completing the square), and relate the roots to the x-intercepts
of the graph of the corresponding function;
OC1.06 add, subtract, multiply, and
divide complex numbers in rectangular form;
OC1.07 add, subtract, multiply, and
divide rational expressions, and state the restrictions on the variable values;
OC1.08 simplify and evaluate expressions
containing integer and rational exponents, using the laws of exponents;
OC1.09 solve exponential equations
(e.g., 4x = 8x+3, 22x
2x = 12).
Understanding
Inverses and Transformations and Using Function Notation
OC2.01 define the term function;
OC2.02 demonstrate facility in the use
of function notation for substituting into and evaluating functions;
OC2.03 determine, through investigation,
the properties of the functions defined by f(x) = 
[e.g., domain, range, relationship to f(x) = x2]
and f(x) = 
[e.g., domain, range, relationship to
f(x) = x.];
OC2.04 explain the relationship between a function
and its inverse (i.e., symmetry of their graphs in the line y = x;
the interchange of x and y in the equation of the function; the
interchanges of the domain and range), using examples drawn from linear and
quadratic functions, and from the functions f(x) = and f(x) = 
;
OC2.05 represent inverse functions,
using function notation, where appropriate;
OC2.06 represent transformations (e.g.,
translations, reflections, stretches) of the functions defined by
f(x) = x, f(x)
= x2, f(x) = , f(x) = sin x, and f(x)
= cos x, using function notation;
OC2.07 describe, by interpreting
function notation, the relationship between the graph of a function and its
image under one or more transformations;
OC2.08 state the domain and range of
transformations of the functions defined by
f(x) = x, f(x) = x2, f(x) = , f(x) = sin x, and f(x)
= cos x.
Communicating
Mathematical Reasoning
OC3.01 explain mathematical processes,
methods of solution, and concepts clearly to others;
OC3.02 present problems and their
solutions to a group, and answer questions about the problems and the
solutions;
OC3.03 communicate solutions to problems
and to findings of investigations clearly and concisely, orally and in writing,
using an effective integration of essay and mathematical forms;
OC3.04 demonstrate the correct use of
mathematical language, symbols, visuals (e.g., diagrams, graphs), and
conventions;
OC3.05 use graphing technology
effectively (e.g., use appropriate menus and algorithms; set the graph window
to display the appropriate section of a curve).
Investigations of Loci and
Conics
Overall Expectations
LCV.01 · represent loci, using various
models (e.g., a verbal description, a diagram, a dynamic model, an equation);
LCV.02 · determine the equation and the
key features of a conic;
LCV.03 · solve problems involving
applications of the conics.
Specific Expectations
Representing
Loci
LC1.01 construct a geometric model
(e.g., a diagram created by hand, a diagram created by using dynamic geometry
software) to represent a described locus of points; determine the properties of
the geometric model; and use the properties to interpret the locus (e.g., the
locus of points equidistant from two fixed points is the right bisector of the
line segment joining the two fixed points);
LC1.02 explain the process used in
constructing a geometric model of a described locus;
LC1.03 determine an equation to
represent a described locus [e.g., determine the equation of the locus of
points equidistant from (2, 7) and (5, 4)];
LC1.04 construct geometric models to
represent the locus definitions of the conics;
LC1.05 determine equations for conics
from their locus definitions, by hand for simple particular cases [e.g.,
determine the equation of the locus of points the sum of whose distances from
(3, 0) and (3, 0) is 10].
Determining
the Equation and the Key Features of a Conic
LC2.01 identify the standard forms for the
equations of parabolas, circles, ellipses, and hyperbolas having centres at (0,
0) and at (h, k);
LC2.02 identify the type of conic, given its
equation in the form ax2 + by2 + 2gx
+ 2fy + c = 0;
LC2.03 determine the key features (e.g.,
the centre or the vertex, the focus or foci, the asymptotes, the lengths of the
axes) of a conic whose equation is given in the form
ax2 + by2 + 2gx + 2fy + c
= 0, by hand in simple cases (e.g., x2 + 9y2
6x + 36y 36 = 0);
LC2.04 sketch the graph of a conic whose
equation is given in the form ax2 + by2 + 2gx
+ 2fy + c = 0;
LC2.05 illustrate the conics as
intersections of planes with cones, using concrete materials or technology.
Solving
Problems Involving Applications of the Conics
LC3.01 describe the importance, within
applications, of the focus of a parabola, an ellipse, or a hyperbola (e.g., all
incoming rays parallel to the axis of a parabolic antenna are reflected through
the focus; the planets move in elliptical orbits with the sun at one of the
foci);
LC3.02 pose and solve problems drawn
from a variety of applications involving conics, and communicate the solutions
with clarity and justification (Sample problem: A parabolic antenna is
320 m wide at a distance of 50 m above its vertex. Determine the distance above
the vertex of the focus of the antenna);
LC3.03 solve problems involving the
intersections of lines and conics.
The
graduate is expected to be:
A
Discerning Believer Formed in the Catholic Faith Community
who
CGE1a -illustrates
a basic understanding of the saving story of our Christian faith;
CGE1b -participates
in the sacramental life of the church and demonstrates an understanding
of the centrality of the Eucharist to our Catholic story;
CGE1c -actively
reflects on Gods Word as communicated through the Hebrew and Christian
scriptures;
CGE1d -develops
attitudes and values founded on Catholic social teaching and acts to
promote social responsibility, human solidarity and the common good;
CGE1e -speaks
the language of life... recognizing that life is an unearned gift and
that a person entrusted with life does not own it but that one is called to
protect and cherish it. (Witnesses to Faith)
CGE1f -seeks
intimacy with God and celebrates communion with God, others and creation
through prayer and worship;
CGE1g -understands
that ones purpose or call in life comes from God and strives to discern
and live out this call throughout lifes journey;
CGE1h -respects
the faith traditions, world religions and the life-journeys of all
people of good will;
CGE1i -integrates
faith with life;
CGE1j -recognizes
that sin, human weakness, conflict and forgiveness are part of the human
journey and that the cross, the ultimate sign of forgiveness is at the heart
of redemption. (Witnesses to Faith)
An
Effective Communicator who
CGE2a -listens
actively and critically to understand and learn in light of gospel values;
CGE2b -reads,
understands and uses written materials effectively;
CGE2c -presents
information and ideas clearly and honestly and with sensitivity to others;
CGE2d -writes
and speaks fluently one or both of
CGE2e -uses
and integrates the Catholic faith tradition, in the critical analysis of the
arts, media, technology and information systems to enhance the quality of life.
A
Reflective and Creative Thinker who
CGE3a -recognizes
there is more grace in our world than sin and that hope is essential in facing
all challenges;
CGE3b -creates,
adapts, evaluates new ideas in light of the common good;
CGE3c -thinks
reflectively and creatively to evaluate situations and solve problems;
CGE3d -makes
decisions in light of gospel values with an informed moral conscience;
CGE3e -adopts
a holistic approach to life by integrating learning from various subject areas
and experience;
CGE3f -examines,
evaluates and applies knowledge of interdependent systems (physical, political,
ethical, socio-economic and ecological) for the development of a just and
compassionate society.
A Self-Directed, Responsible, Life Long Learner
who
CGE4a -demonstrates
a confident and positive sense of self and respect for the dignity and welfare
of others;
CGE4b -demonstrates
flexibility and adaptability;
CGE4c -takes
initiative and demonstrates Christian leadership;
CGE4d -responds
to, manages and constructively influences change in a discerning manner;
CGE4e -sets
appropriate goals and priorities in school, work and personal life;
CGE4f -applies
effective communication, decision-making, problem-solving, time and resource
management skills;
CGE4g -examines
and reflects on ones personal values, abilities and aspirations influencing
lifes choices and opportunities;
CGE4h -participates
in leisure and fitness activities for a balanced and healthy lifestyle.
A
Collaborative Contributor who
CGE5a -works
effectively as an interdependent team member;
CGE5b -thinks
critically about the meaning and purpose of work;
CGE5c -develops
ones God-given potential and makes a meaningful contribution to society;
CGE5d -finds
meaning, dignity, fulfillment and vocation in work which contributes to the
common good;
CGE5e -respects
the rights, responsibilities and contributions of self and others;
CGE5f -exercises
Christian leadership in the achievement of individual and group goals;
CGE5g -achieves
excellence, originality, and integrity in ones own work and supports these
qualities in the work of others;
CGE5h -applies
skills for employability, self-employment and entrepreneurship relative to
Christian vocation.
A
Caring Family Member who
CGE6a -relates
to family members in a loving, compassionate and respectful manner;
CGE6b -recognizes
human intimacy and sexuality as God given gifts, to be used as the creator
intended;
CGE6c -values
and honours the important role of the family in society;
CGE6d -values
and nurtures opportunities for family prayer;
CGE6e -ministers
to the family, school, parish, and wider community through service.
A
Responsible Citizen who
CGE7a -acts
morally and legally as a person formed in Catholic traditions;
CGE7b -accepts
accountability for ones own actions;
CGE7c -seeks
and grants forgiveness;
CGE7d -promotes
the sacredness of life;
CGE7e -witnesses
Catholic social teaching by promoting equality, democracy, and solidarity for a
just, peaceful and compassionate society;
CGE7f -respects
and affirms the diversity and interdependence of the worlds peoples and
cultures;
CGE7g -respects
and understands the history, cultural heritage and pluralism of todays
contemporary society;
CGE7h -exercises
the rights and responsibilities of Canadian citizenship;
CGE7i -respects
the environment and uses resources wisely;
CGE7j -contributes
to the common good.
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