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Course Profile College and Apprenticeship Mathematics
(MAP4C), Grade 12, College Preparation, Combined
Course Overview
Prerequisite: Mathematics of
Personal Finance, Grade 11, College Preparation, or
Functions, Grade 11, University/College
Preparation,
(or Functions and Relations, Grade 11, University
Preparation)
This course equips students with the
mathematical knowledge and skills they will need in many college programs.
Students will use statistical methods to analyse problems; solve problems
involving the application of principles of geometry and measurement to the
design and construction of physical models; solve problems involving
trigonometry in triangles; and consolidate their skills in analysing and
interpreting mathematical models.
Students use statistical methods to analyse
problems and examine the various uses and misuses of statistics. Students use
principles of geometry and measurement to construct physical models as well as
models using technology. Students work with measurements in both the metric and
imperial systems. Applications of trigonometry in triangles are examined.
In the
classroom, the use of technology is recommended to allow students to
efficiently and effectively understand the concepts of the course. Appropriate
technology enables students to more easily visualize concepts and allows more
time for consolidation and practice. Furthermore, technology helps students
investigate and develop concepts to enhance understanding and make skill
development more meaningful.
This
course encourages the Catholic learner to promote growth towards her/his
personal responsibilities, faith, and moral and ethical decision making in
order to make better and more informed career choices. The classroom
environment should foster mutual and self-respect and individual
self-discipline, along with the practice of cooperative learning and the
ability to work in groups or as part of a team. Students develop an awareness
of theirs and others’ strengths, along with tolerance and compassion for the
weaknesses and inabilities of others. Collectively, these expectations are
significant to our goal of our students becoming well-rounded apprentices,
professionals, employees, or business leaders in society.
The
purpose of this course is to give students the skills to be su
The teacher should take an informal
survey of the desired destinations of students and gear the activities to best
suit students. Students may be interested in such careers as recreation,
tourism, health/sports management, law enforcement, construction, fashion
design, and interior design. Guest speakers may help students understand the
use and importance of math in their choice of careers by providing expertise in
their fields. If time permits, the teacher may have students research entrance
requirements, tuition costs, possible apprenticeship pay, and the time required
to complete college or apprenticeship programs.
Students
could keep a journal or portfolio of how concepts taught in the class are
applied in the everyday world. Many activities are based on problems in the
industrial or business fields. The portfolio contains activities or projects
that relate to fields students are interested in. Students or groups of
students could give presentations of the math related to their field of choice
as part of their summative assessment.
Technology should be used as a tool to help
students better learn the concepts and skills needed in their college or
apprenticeship programs and to solve rich problems that otherwise would be ina
In the
area of design, students are expected to be proficient in the different methods
of representing models and be comfortable moving from one model to another. The
models include: physical models, diagrams, and technological models. Knowledge
of an object’s shape and size through the interpretation of engineering or
technical drawings is a necessary skill. For these reasons, students benefit
from exposure to both drawings and computer-aided design (CAD), as well as the
process of converting one to the other.
The organization of this course allows students
to begin with a new look at a familiar concept. In Unit 1, students work with
two-variable data as studied in previous grades. However, most of the graphing
is done with technology, and the focus now will be on the appropriate
collection and analysis of the data, including an introduction to the
correlation coefficient. In Unit 2, students continue to see the importance of
appropriate collection and interpretation of data but from the perspective of
examining one variable data. Students are introduced to the various methods
used for analysing one variable and learn how to look critically at the a
The
expectations of the mathematical modelling strand have been woven throughout
the units to allow students to make connections and focus on certain models.
This also allows students to master key algebraic skills as needed throughout
the course rather than isolating them within one unit.
In Units 1 and 2, students may have
opportunities to survey students, friends, and family. Students must be
instructed to a
|
Unit 1 |
Collecting,
Analysing, and Evaluating Data Involving Two Variables |
21
hours |
|
Unit 2 |
Statistics:
Its Uses and Misuses |
25
hours |
|
* Unit
3 |
Design |
19
hours |
|
Unit 4 |
Trigonometry |
15
hours |
|
* Unit
5 |
Modelling |
18
hours |
|
Unit 6 |
Final
Summative Assessment |
12
hours |
* These
units are fully developed in this Course Profile.
Time: 21 hours
Unit
Description
Students
collect, analyse, and interpret two-variable data. Although some concepts are a
review of material from previous courses, the focus in this course is on the
importance of appropriate methods of data collection and the role collection
plays in the validity of conclusions. Students develop their algebraic skills
with linear equations as they analyse and explore two-variable data. Students
are introduced to examples of both linear and non-linear statistical models.
Unit
Overview Chart
|
Cluster |
Learning Expectations |
Assessment Categories |
Focus |
|
1 |
ASV.02,
MMV.01, AS2.02, AS2.06, MM1.01, MM1.03 |
Knowledge/
Understanding Communication |
Graph
given data, make predictions, and describe trends |
|
2 |
ASV.02,
MMV.01, MMV.02, MMV.03, AS2.06, MM1.02, MM1.03, MM1.04, MM2.05, MM3.04 |
Application Communication |
Given
an equation, graph, find the slope and intercepts, interpret rate of change
and intercept, and describe effect on graph of change in condition |
|
3 |
ASV.02,
ASV.04, MMV.02, AS2.01, AS2.02, AS2.03, AS4.01, MM2.04 |
Knowledge/
Understanding Application Thinking/Inquiry Communication |
Gather information,
and graph and construct lines of best fit, both manually and with the use of
technology (e.g., graphing calculator) |
|
4 |
ASV.02,
ASV.04, MMV.01, AS2.04, AS2.05, AS2.07, AS4.01, MM1.03 |
Knowledge/
Understanding Application Thinking/Inquiry Communication |
Find
and discuss correlation coefficient, make statements about population based
on sample, and discuss misuses of regression |
|
5 |
MMV.01, MMV.02, ASV.03, MM1.02, MM1.04,
MM1.05, MM2.05, AS3.03, AS3.04 |
Application Communication |
Analyse and solve linear systems, make and
communicate conclusions, and form extending questions |
Time: 25 hours
Unit
Description
In this
unit, students develop an understanding of how data collected from a variety of
sources can be used to make predictions and to present different viewpoints. A
variety of statistical techniques is developed to determine whether data is
reliable or contains bias. Data collected from sources related to appropriate
fields of study are used to reinforce concepts.
Ontario Catholic School Graduate Expectations: 2a, 2b, 2e, 3b, 3c, 3e, 3f, 4b, 4c, 4d, 4f, 5a, 5h, 7i.
Unit
Overview Chart
|
Cluster |
Learning Expectations |
Assessment Categories |
Focus |
|
1 |
ASV.01,
AS1.02, AS1.03, AS1.04 |
Communication Application |
Design
surveys, practise sampling techniques, and distinguish between a population
and a sample |
|
2 |
ASV.01,
ASV.03, MMV.01, AS1.01, AS1.04, AS1.05, AS1.09, AS3.01, AS3.04, MM1.03,
MM1.05 |
Knowledge/
Understanding Communication Application |
Determine
and use appropriate methods of data collection, select a sampling technique,
create graphs of the data, and form appropriate conclusions |
|
3 |
ASV.01,
ASV.03, MMV.01, MMV.02, AS1.07, AS1.08, AS3.01, AS3.02, AS3.04, MM1.05,
MM2.04 |
Knowledge/
Understanding Application Communication |
Collect
data, calculate various statistical measures, and analyse the results of the calculations,
including the significance of the data distribution |
|
4 |
ASV.01,
ASV.03, ASV.04, AS1.06, AS1.07, AS1.08, AS3.03, AS4.02 |
Thinking/Inquiry Application Communication |
Perform
calculations on given data to analyse sources of bias and significance and
properties of the distributions; formulate extending questions based on
analysis |
|
5 |
ASV.01,
ASV.04, AS4.01, AS4.02, AS4.03, AS1.09 |
Application Communication |
Look at
examples of statistics in the media and examine validity and possible sources
of bias |
Time: 19 hours
Unit
Description
Students
design and construct physical models to expand their knowledge of geometry and measurement.
Connections are made to the fields of construction, fashion design, and
machining. Students take a three-dimensional object and make a two-dimensional
representation of it. They expand their knowledge of measurement by using both
the metric and imperial systems.
Unit
Overview Chart
|
Cluster |
Learning Expectations |
Assessment Categories |
Focus |
|
1 |
AGV.01,
AGV.02, AG1.04, AG2.04, AG2.06 |
Thinking/Inquiry Knowledge/Understanding Application |
Explore
spatial awareness involving measurement in the design of a floor plan |
|
2 |
AGV.01,
AGV.02, AG1.01, AG1.02, AG1.04, AG2.03, AG2.05, AG2.06 |
Knowledge/Understanding Thinking/Inquiry Application |
Construct
a three-dimensional model based on a two-dimensional plan |
|
3 |
AGV.01,
AGV.02, AG1.01, AG1.03, AG2.01 |
Knowledge/Understanding Thinking/Inquiry Application |
Create
patterns of combined geometric shapes related to interior decorating. |
|
4 |
AGV.01,
AGV.02, AG1.02, AG2.04, AG2.05 |
Knowledge/Understanding Thinking/Inquiry Application |
Represent
a three-dimensional shape in an orthographic drawing. |
|
5 |
AGV.01,
AGV.02, AG1.02, AG2.02 |
Knowledge/Understanding Thinking/Inquiry Application |
Design
a physical model of a piece of equipment given constraints |
|
6 |
AGV.01,
AGV.02, AG1.01, AG1.02, AG1.03, AG1.04, AG2.01, AG2.02, AG2.06 |
Knowledge/Understanding Application Thinking/Inquiry Communication |
Summative
Assessment |
Time: 15
hours
Unit
Description
Students
use the primary trigonometric ratios to solve problems in right-angle triangles
and the sine and cosine laws to solve problems in obtuse triangles. Connections
are identified between various trigonometric applications and potential
postsecondary fields of study and/or related o
Unit
Overview Chart
|
Cluster |
Learning
Expectations |
Assessment
Categories |
Focus |
|
1 |
AGV.03, MMV.02, AG3.01, AG3.04, MM2.03 |
Knowledge/ Understanding Application |
Review the primary trigonometric ratios and
apply trigonometry in right triangles |
|
2 |
AGV.03,
AG3.02, AG3.04 |
Knowledge/
Understanding |
Explore
the signs of the primary trigonometric ratios in obtuse angles |
|
3 |
AGV.03,
MMV.02, AG3.03, AG3.04, MM2.03 |
Knowledge/
Understanding Thinking/Inquiry Application |
Investigate
side lengths and angle measures in oblique triangles using the sine and
cosine laws |
|
4 |
AGV.03,
AGV.02, MMV.02, AG3.03, AG3.04, AG2.01, AG2.02, AG2.04, AG2.06 |
Application Problem
Solving |
Apply
sine and cosine law to practical applications using measurements in both the
metric and imperial systems (e.g., finding the area of a triangular lot) |
|
5 |
AGV.03,
MMV.02, AG3.01, AG3.03, AG3.04, MM2.03 |
Thinking/Inquiry Application Communication |
Demonstrate
an understanding of various trigonometric applications related to future
programs and o |
Time: 18 hours
Unit
Description
Students examine and work with a variety of
mathematical models in various forms, e.g., tables, graphs, and formulas.
Students investigate linear, quadratic, and exponential models in a context
that allows students to develop an understanding of how models are used and
created. Connections are made to o
Unit
Overview Chart
|
Cluster |
Learning
Expectations |
Assessment
Categories |
Tasks |
|
1 |
MMV.01, MMV.03, MM1.01, MM1.03, MM3.04 |
Knowledge/ Understanding Communication |
Examine and make predictions from a variety
of models: linear, quadratic and exponential graphs and tables |
|
2 |
MMV.01, MMV.03, MM1.01, MM1.03, MM1.05, MM3.04 |
Application Communication |
Gather and graph light intensity data, and
work with exponential models |
|
3 |
MMV.01,
MMV.02, ASV.04, MM1.01, MM1.03, MM2.01, AS4.03 |
Thinking/Inquiry Communication |
Examine
CPI (Consumer Price Index) as an example of exponential growth; create and
analyse graphical and formulaic models and make predictions |
|
4 |
MMV.01,
MMV.03, MM1.01, MM1.03, MM1.04, MM3.04 |
Thinking/Inquiry Application |
Make
predictions, analyse quadratic graphs, and find roots graphically or by
examining table of values |
|
5 |
MMV.01,
MMV.03, MM3.04, MM1.03, MM1.04 |
Application Communication |
Graph
data on the stopping distances under various conditions, analyse the model,
and predict how the model would change if conditions change |
|
6 |
MMV.01,
MMV.02, MMV.03, MM2.06, MM2.07, MM3.04, MM1.05 |
Knowledge/
Understanding Application |
Create
graphs from a given quadratic equation for various applications, factor, find
roots, and make decisions |
|
7 |
MMV.03,
MM3.01, MM3.02, MM3.03 |
Thinking/Inquiry Application |
Plan a
trip to see various sports teams play in their hometowns while meeting budget
constraints |
|
8 |
MMV.01,
MMV.02, MMV.03, MM1.05, MM2.01, MM2.02, MM2.04, MM3.03, MM3.04 |
Application Thinking/Inquiry Communication |
Choose
appropriate models to create a formula to calculate cost of building a deck |
Time: 12 hours
Unit
Description
The
summative assessment should provide the opportunity for students to demonstrate
comprehensive learning in each of the four Achievement Chart categories and in
each of the strands. Some ideas are suggested in the chart that follows,
however, many of the assessment tools mentioned in the Assessment section could
be used. In addition to paper-and-pencil tasks, it is important to include
tasks which allow students to apply the technology used throughout the course.
Another aspect that could be incorporated is the use of a portfolio where
students gather activities, problems, or projects they have completed that
relate to their field of interest. Students could then do further research on
the math related to their field of choice and present this information to the
class.
Unit
Overview Chart
|
Cluster |
Learning Expectations |
Assessment Categories |
Focus |
|
1 |
All Strands |
Knowledge/
Understanding Application |
Review
key concepts and terms |
|
2 |
All Strands |
Knowledge/
Understanding Application Thinking/Inquiry/Problem
Solving Communication |
Students
design a product and complete research on it. Students then present their
product to the class using diagrams and models and provide a statistical
analysis of some aspect of the product (e.g., safety, how marketable it is,
optimal pricing, etc.) |
|
3 |
All Strands |
Knowledge/
Understanding Thinking/Inquiry Communication Application |
Final
Examination |
A wide range of teaching and learning
strategies should be used to address the expectations of this course and to
reach students enrolled in it.
Teachers should:
·
include
a balance of whole-class, pairings, small-group, and individual instruction;
·
provide
students with materials, technological tools, and software for use in
investigations;
·
make
connections between the concepts learned and potential careers and, as often as
possible, allow students the option to make connections to careers of their
choice;
·
make
appropriate and effective use of technology;
·
use
technology for classroom demonstrations as well as having students working
independently;
·
invite
guest speakers to speak about the use of mathematics in their jobs;
·
use
a variety of media resources (e.g., newspapers, Internet, magazines);
·
offer
a variety of instructional methods and tools (investigations, use of
technology, station-based activities, dialogues, discussion, use of visual
aids, manipulatives, etc.) to a
·
provide
practise and extension opportunities;
·
provide
regular, informal assessment, which provides the feedback that students need in
order to improve their achievement.
Students:
·
demonstrate
their knowledge and understanding using a variety of methods and mathematical/technological
tools;
·
develop
responsibility for their own learning and decision-making;
·
use
technology to investigate different concepts;
·
apply
individual and group learning skills;
·
make
decisions and support them with mathematical reasoning;
·
engage
in explorations involving the use of technology and the collection of data;
·
make
connections between the mathematics they are working with and their future.
Assessment
is a systematic process of collecting information or evidence about student
learning; evaluation is the judgement we make about the assessments of student
learning based on established criteria. Assessment tools should be designed to
allow students to demonstrate the full extent of their learning across the four
categories of the Achievement Chart.
As
teachers will use a variety of assessment tools, it is necessary to ensure that
a consistent standard is maintained. Thus, these tools should be developed with
the learning expectations of the course as the criteria for this standard. A
student demonstrating characteristics of Level 3 performance, as defined by the
Achievement Chart, should have a grade of 70-79%. Assessment strategies and
tools must address a wide variety of teaching and learning styles in addition
to the criteria established by the learning expectations. It is understood that
students will meet course expectations at a variety of performance levels. An
effective and well-balanced assessment program provides students with several
opportunities to demonstrate growth and improvement over time, across all of
the knowledge and skill categories.
It should be noted that:
·
Tests
that include only questions that ask students to perform algorithms and apply
their knowledge do not necessarily offer an opportunity for students to
demonstrate Level 4 performance. Use of open-ended performance tasks allows
students to explore all levels of achievement.
·
It
is often easier to pose questions with the expectation of Level 1 to 4
responses in the Thinking/Inquiry/Problem Solving and Communication categories
than the Knowledge/Understanding and Application categories.
·
Teachers
must continue to expand their own understanding of application skills to
include non-routine problems. This requires a shift from the specific application of concepts (i.e.,
familiar situations), to the general
application of concepts (i.e., unfamiliar situations).
·
Teachers
need to ask students to communicate their understanding of their knowledge,
their stages of thought in an inquiry, and their process of applying
mathematics to a problem, in order to assess performances in the other three
categories of the Achievement Chart. Then, they need to report on the
Communication category separately from those categories.
·
The
expectations of the course include a wide range of skills, all of which must be
addressed. Teachers must be careful to identify the critical skills required
for this course, with the belief that students should be encouraged to practise
those skills on their own time, persevering until those skills have been
mastered. To ensure that learning of these critical skills has happened, the
teacher keeps track of which students have and have not demonstrated the
required learning.
·
Assessment
strategies should reflect the style of the lessons taught. If the unit
primarily contains hands-on activities (e.g., using technology), then the
end-of-unit summative assessment should also utilize a performance task.
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, and/or other method of
evaluation suitable to the course content and administered towards the end of
the course.
Learning
skills are not included in the determination of the percentage grade. However,
learning skills need to be assessed and reported separately on students’ report
cards and should be tracked throughout the term. The following is a partial
list of suggested indicators of learning skills.
Organization
·
Preparedness
(materials for class)
·
Submitted
work (including timeliness)
Work
Habits
·
Completion
of homework
·
Use
of class time
Teamwork
·
Cooperation
in group setting
·
Contribution
in group setting
Initiative
·
Display
of leadership where appropriate
·
Participation
in class discussion
·
Responsibility
for own learning
Works
Independently
·
Commitment
to task
·
Effort
in solving problems individually
A goal
for each identified exceptional student should be that they become
self-advocates for their needs. These students will soon be on their own and
will need the skills and understanding to advocate for themselves. This may
mean making appropriate a
The following are suggestions for a
·
Provide
ongoing student-teacher conferencing.
·
Have
students work with appropriate partners to provide support.
·
Provide
a list of simplified terms or terms with diagrams and provide a breakdown of
the steps involved in the multitask activities and projects.
·
Use
mind mapping for review, consolidation of ideas, and interrelation of concepts.
·
Allow
alternate timelines for the completion of work and assignments, determined in
consultation with the student.
·
Allow
a variety of opportunities for students to demonstrate their understanding.
·
Provide
manipulatives, grid paper, formula sheets, technology, and other aids.
·
Provide
outline of notes and when a significant amount of writing is required, provide
photocopied materials and encourage highlighting of information.
·
Teachers
may wish to break down tasks or have students repeat instruction, e.g., TELL
students, SHOW students and then let students DO what is required.
·
When
oral presentations are required, allow students to tape or present to the teacher
individually for assessment.
·
Visual
clues and auditory clues during class or assessment may be required. Permit
students to have a
·
Students
work in pairs, with peer tutors, or with classmates who have the same
linguistic background.
·
Use
peer conferencing to reinforce instructions or information.
·
Provide
sets of reference notes, outlines, or critical information, as well as models
of charts, timelines, or diagrams.
·
Pair
written instructions with verbal instructions.
·
Use
visual aids to illustrate definition for the student’s dictionary of terms.
·
Simplify
instructions and highlight key words or phrases.
·
Provide
opportunities for students to practise oral presentation skills in a setting
where they will be su
·
Provide
visual or auditory cues.
Units
in this Course Profile make reference to the use of specific texts, magazines,
films, videos, and websites. The teachers need to consult their board policies
regarding use of any copyrighted materials. Before reproducing materials for
student use from printed publications, teachers need to ensure that their board
has a Cancopy licence and that this licence covers the resources they wish to
use. Before screening videos/films with their students, teachers need to ensure
that their board/school has obtained the appropriate public performance
videocassette licence from an authorized distributor, e.g., Audio Cine Films
Inc. The teachers are reminded that much of the material on the Internet is
protected by copyright. The copyright is usually owned by the person or
organization that created the work. Reproduction of any work or substantial
part of any work from the Internet is not allowed without the permission of the
owner.
This Course Profile has
been provided to aid the teacher so they may better deliver the curriculum. It
is recommended that the teacher a
· Any Ministry-licensed software (e.g., word processing or spreadsheet programs, Geometer’s Sketchpad, ZAP-A-GRAPH)
· AutoCAD, AutoCAD LITE (must be purchased from a distributor and is used in most schools in their design programs)
·
Fathom
These may
be obtained by a
·
Set
squares
·
T-squares
·
Micrometers,
scales, and measuring tapes
Airasian,
P.W. Classroom Assessment. New York:
McGraw-Hill, 1994.
Andrini,
B. Cooperative Learning and Mathematics:
A Multi-Structural Approach. California: Resources for Teachers, 1991.
Baker,
E. “Making Performance Assessment Work: The Road Ahead.” Educational Leadership 51, (1994): 6: pp. 58-62.
Brueningsen,
C., B. Bower, L. Antinone, and E. Brueningsen-Kerner. Real-World Math with the CBL System: Activities for the TI-83 and TI-83
Plus. Texas: Texas Instruments Incorporated, 1999.
ISBN 1-886309-28-0
Burz,
H.L. and K. Marshall. Performance-Based
Curriculum for Mathematics. California: Sage, 1996.
Bush,
W.S. and A.S. Greer, eds. Mathematics
Assessment – A Practical Handbook for Grades 9-12. Retson, VA: The National
Council of Teachers of Mathematics, 1999.
Giesecke,
F., A. Mitchell, H.C. Spencer, I.L. Hill, R.O. Loving, J.T. Dygdon, and J.E.
Novak. Principles of Engineering Graphics
2nd ed. Prentice Hall, 1994. ISBN 0-02-342820-1
Grout,
D., P. Resetarits, and J. James. AUTOCAD
Drafting. Glencoe/McGraw-Hill, 1995.
ISBN 0-02-677135- 7
Harms,
H. and N. Swernofsky. Technology
Interactions. Glencoe/McGraw-Hill, 1999.
ISBN 0-02-8387791-1
Hibbard,
K.M., et al. A Teacher’s Guide to Performance-Based Learning
and Assessment.
Alexandria, VA: Association for Supervision and Curriculum Department, 1996.
McArthur,
A., C. Etchells, and T. Shepard. Design
and Make It! Textiles Technology. London: Stanley Thornes, 1997. ISBN
0-748724710
National
Council of Teachers of Mathematics. Assessment
Standards for School Mathematics. Reston, VA: National Council of Teachers
of Mathematics, 1997.
Silver,
E.A., et al. Thinking Through Mathematics: Fostering Inquiry
and Communication in Mathematics Classrooms. New York: College Entrance Examination Board,
1990.
Stepien,
W. and S. Gallagher. “Problem-Based Learning: As Authentic As It Gets.” Educational Leadership 50, (1993): 7:
pp. 25-28.
The URLs for the websites were verified by the writers prior to publication. Given the frequency with which these designations change, teachers should always verify the websites prior to assigning them for student use.
CallCareers.com
Canada – http://www.callcareers.com
Canada’s
Biggest Job Site – Workopolis.com – http://www.globecareers.workopolis.com
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
(A computer communications network for everyone who works in elementary and
secondary education in Ontario. Members have private a
Hewlett-Packard
– http://www.hp.com/calculators/
Hospitality
Careers Online – http://www.hcareers.com
The
Learning Disabilities Association of Ontario – http://www.ldao.on.ca
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
Texas
Instruments – http://www.ti.com/calc/docs
Think3
Design – http://www.think3.com
(Provider of 3-D design software)
The following resources support many of the Ontario Secondary School policies, as well as the Ontario Catholic School Graduate Expectations.
Ministry
of Education Policy and Reference Documents
Choices Into Action: Guidance and
Career Education Program Policy 1999.
Cooperative Education: Policies and
Procedures for Ontario Secondary Schools 2000.
Individual Education Plans:
Standards for Development, Program Planning, and Implementation, 2000.
The Ontario Curriculum, Mathematics,
Grades 9-10, 1999.
The Ontario Curriculum, Mathematics,
Grades 11-12, 2000.
Ontario Schools Code of Conduct.
Ontario Secondary Schools, Grades 9-12, Program and Diploma Requirements
1999.
Program Planning and Assessment,
Grades 9-12 2000.
Violence-Free Schools Policy.
The Ministry of Education has also published several resource documents, brochures, and policy/program memoranda in support of its OSS policies. They are available online at the Ministry of Education website (http://www.edu.gov.on.ca/eng/document/document.html).
·
Publications Concerning Faith Development
Catholic
Curriculum Cooperative (Central Ontario Region). Blueprints.
Ontario
Catholic School Trustees’ Association. Catholicity
Across the Curriculum.
Institute
for Catholic Education. Educating the
Soul.
Institute
for Catholic Education. Ontario Catholic
Secondary School Graduate Expectations.
Ontario
Conference of Catholic Bishops. This Moment of Promise.
·
Career Goals/Co-operative Education Programs
Ontario Youth Apprenticeship Program
Youth Employment Skills Program
·
Community Partnerships
Refer
to local board policies (e.g., Relations with Business – Corporate Donations,
Sponsorships, and Agreements).
Coded
Expectations, College and Apprenticeship Mathematics, Grade 12, College
Preparation, MAP4C
ASV.01 · collect, analyse, and evaluate
data involving one variable;
ASV.02 · collect, analyse, and evaluate
data involving two variables;
ASV.03 · analyse significant problems or
issues, using statistics;
ASV.04 · evaluate the validity of the use
of statistics in the media.
Collecting,
Analysing, and Evaluating Data Involving One Variable
AS1.01 – determine appropriate methods for
collecting, storing, and retrieving, from primary or secondary sources, data
involving one variable;
AS1.02 – design questionnaires for
gathering data through surveys, giving consideration to possible sources of
bias;
AS1.03 – demonstrate an understanding of
the distinction between the terms population and sample;
AS1.04 – choose from and apply a variety
of sampling techniques (e.g., random, stratified);
AS1.05 – represent data in appropriate
graphical forms (e.g., histograms, bar graphs), using technology;
AS1.06 – identify and describe properties
of common distributions of data (e.g., normal, bimodal, exponential, skewed);
AS1.07 – calculate the mean, median, mode,
range, variance, and standard deviation of a data set, using standard
statistical notation and technology;
AS1.08 – describe the significance of
results drawn from analysed data (e.g., the shape of the distribution, the
mean, the standard deviation);
AS1.09 – make and justify statements about
a population on the basis of sample data.
Collecting,
Analysing, and Evaluating Data Involving Two Variables
AS2.01 – determine appropriate methods for
collecting, storing, and retrieving, from primary or secondary sources, data
involving two variables;
AS2.02 – construct a scatter plot to
represent data, using technology;
AS2.03 – determine an equation of a line
of best fit, using the regression capabilities of graphing technology;
AS2.04 – calculate and interpret the
correlation coefficient, using appropriate technology;
AS2.05 – describe possible misuses of
regression (e.g., use with too small a sample, use without considering the
effect of outliers, inappropriate extrapolation);
AS2.06 – describe the relationship between
two variables suggested by a scatter plot (e.g., no relationship, a positive
correlation, a negative correlation);
AS2.07 – make and justify statements about
a population on the basis of sample data.
Analysing
Problems
AS3.01 – collect, organize, and analyse
data to address problems or issues, and calculate relevant statistical
measures;
AS3.02 – formulate a summary conclusion to
a problem or an issue, by synthesizing interpretations of individual
statistical measures;
AS3.03 – formulate extending questions
related to the conclusion reached in the investigation of a problem or an
issue;
AS3.04 – communicate the process used and
the conclusions reached in the investigation of a problem or an issue, using
appropriate mathematical forms (e.g., oral and written explanations, tables,
graphs, formulas).
Evaluating
Validity
AS4.01 – explain the use and misuse in the
media of graphs and commonly used statistical terms (e.g., percentile),
and expressions (e.g., 19 times out of 20);
AS4.02 – assess the validity of
conclusions made on the basis of statistical studies, by analysing possible
sources of bias in the studies (e.g., sampling bias);
AS4.03 – explain the meaning, and the use
in the media, of indices based on surveys (e.g., the consumer price index).
AGV.01 · demonstrate an understanding of
the relationship between three-dimensional objects and their two-dimensional
representations;
AGV.02 · solve problems involving
measurement;
AGV.03 · solve problems involving
trigonometry in triangles.
Understanding
Two-Dimensional and Three-Dimensional Shapes
AG1.01 – identify, through observation and
measurement, the uses of geometric shapes and the reasons for those uses, in a
variety of applications (e.g., product design, architecture, fashion);
AG1.02 – represent three-dimensional
objects in a variety of ways (e.g., front, side, and top views; perspective
drawings; scale models), using concrete materials and design or drawing
software;
AG1.03 – create nets, plans, and patterns
from physical models related to a variety of applications (e.g., fashion
design, interior decorating, building construction), using design or drawing
software;
AG1.04 – design and construct physical
models of things (e.g., structures, equipment, furniture), satisfying given constraints
and using concrete materials, design software, or drawing software.
Solving
Problems Involving Measurement
AG2.01 – solve problems related to the
perimeter and area of plane figures, and the surface area and volume of prisms,
pyramids, cylinders, spheres, and cones, including problems involving
combinations of these objects;
AG2.02 – demonstrate a
AG2.03 – demonstrate an understanding of
the use of the imperial system in a variety of applications (e.g., bolt and
screw sizes; tool sizes; quantities of soil, water, or cement);
AG2.04 – demonstrate a working knowledge
of the measurement of length and area in the imperial system, in relation to
applications (e.g., design, construction);
AG2.05 – perform required conversions
between the imperial system and the metric system, as necessary within projects
and applications;
AG2.06 – use calculators effectively in
solving problems involving measurement, and judge the reasonableness of the
answers produced.
Solving
Problems Involving Trigonometry in Triangles
AG3.01 – solve problems involving
trigonometry in right triangles;
AG3.02 – demonstrate an understanding of
the signs of the sine, cosine, and tangent of obtuse angles;
AG3.03 – determine side lengths and angle measures in
oblique triangles, using the cosine law and the sine law, and solve related
problems;
AG3.04 – identify applications of
trigonometry in o
MMV.01 · interpret and analyse given
graphical models;
MMV.02 · interpret and analyse given
formulaic models;
MMV.03 · interpret and analyse data given
in a variety of forms.
Interpreting
and Analysing Given Graphical Models
MM1.01 – interpret a given linear,
quadratic, or exponential graph to answer questions, using language and units
appropriate to the context from which the graph was drawn;
MM1.02 – interpret the rate of change and
initial conditions (i.e., the slope and y-intercept) of a linear model
given within a context;
MM1.03 – make and justify a decision or
prediction and discuss trends based on a given graph;
MM1.04 – describe the effect on a given
graph of new information about the circumstances represented by the graph
(e.g., describe the effect of a significant change in population on a graph
representing the size of the population over time);
MM1.05 – communicate the results of an
analysis orally, in a written report, and graphically.
Interpreting
and Analysing Given Formulaic Models
MM2.01 – evaluate any variable in a given
formula drawn from an application by substituting into the formula and using
the appropriate order of operations on a scientific calculator;
MM2.02 – construct (e.g., combine or
modify) formulas to solve multi-step problems in particular situations (e.g.,
determine the amount of paint required to paint two coats on a large
cylindrical water tank);
MM2.03 – rearrange a formula to isolate
any variable in it (e.g., to determine the values of a variable in a formula,
using a spreadsheet);
MM2.04 – judge the reasonableness of
answers to problems;
MM2.05 – demonstrate mastery of key
algebraic skills, including the ability to solve linear equations, to solve
systems of linear equations, to graph a linear function from its equation, and
to determine the slope and intercepts of a linear function from its equation;
MM2.06 – factor expressions of the form ax2
+ bx + c;
MM2.07 – solve quadratic equations by
factoring.
Interpreting
and Analysing Data Given in a Variety of Forms
MM3.01 – retrieve information from various
sources (e.g., graphs, charts, spreadsheets, schedules);
MM3.02 – identify options that meet
certain criteria, using more than one chart, spreadsheet, or schedule (e.g.,
the schedules of connecting flights; the spreadsheets of mortgage- payment
plans);
MM3.03 – make informed decisions, using
data provided in chart, spreadsheet, or schedule format and taking into a
MM3.04 – enter data or a formula into a
graphing calculator and retrieve other forms of the model (e.g., enter data and
retrieve a scatter graph or a table of values; enter a formula and retrieve a
table of values or the graph of a function).
Ontario
Catholic School Graduate Expectations
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 God’s 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 one’s purpose or call in life comes from God and strives to discern
and live out this call throughout life’s 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 Canada’s official languages;
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 one’s personal values, abilities and aspirations influencing
life’s 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
one’s 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 one’s 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 -a
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 world’s peoples and
cultures;
CGE7g -respects
and understands the history, cultural heritage and pluralism of today’s
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.