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Course Profile Mathematics of Data Management (MDM4U),
Grade 12, University Preparation, Combined
Course Overview
Policy
Document: The
Ontario
Prerequisite: Functions and
Relations, Grade 11, University Preparation;
or
Functions, Grade 11, University/College Preparation
Course
Description
This
course broadens students’ understanding of mathematics as it relates to
managing information and focuses on a culminating project throughout the
course. Students will apply methods for organizing and analysing large amounts
of information; apply counting techniques, probability, and statistics in
modelling and solving problems; and carry out a culminating project that
integrates the expectations of the course and encourages perseverance and
independence. Su
Course Profile Design
The
course is comprised of four strands: Organization of Data for Analysis;
Counting and Probability; Statistics; and Integration of the Techniques of Data
Management. In Organization of Data for Analysis, students look at finding and
retrieving the data needed to answer significant questions. In addition,
students develop facility with the use of diagrams and matrices to model and
solve problems. In Counting and Probability, students have opportunities to
solve counting problems, use counting techniques to determine and interpret
theoretical probabilities, and design and carry out simulations to estimate
probabilities. In Statistics, students acquire the tools to analyse data
involving one variable and solve problems involving normal distribution.
Students describe the relationship between two variables and assess the
validity of statistics drawn from a variety of sources. In Integration of the
Techniques of Data Management, students complete a major project on a topic of
their choosing which requires them to integrate expectations of the course.
Students present their projects to the class and critique the projects of
others.
How
This Course Supports the Ontario Catholic School
This
course encourages the Catholic learner to develop his/her God-given gifts and
abilities and 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
The last strand is the
focal point of the Course Profile. The overall expectations of this strand are
that students will:
·
carry
out a culminating project on a topic or issue of significance that requires the
integration and application of the expectations of the course;
·
present
a project to an audience;
·
critique
the projects of others.
The course needs to be structured
with the expectations of this strand in mind. In this profile, the course is
organized into five units, some of which encompass expectations taken from different
strands.
In Unit
1: Posing Questions with Data, students are introduced to problems that require
the retrieval and/or manipulation of data from large bodies of information. In
particular, students will have the opportunity to:
·
view
some sample data sets and pose questions about those data sets;
·
given
a question, determine/locate the data needed to answer the question;
·
use
technology to search, effectively, for the data needed to answer particular
questions;
·
create
database or spreadsheet templates that facilitate the retrieval of data from
large bodies of information;
·
critique
the appropriateness of data sets which have been gathered to answer specific
questions.
In Unit 2, Data Analysis, students acquire the
tools to demonstrate an understanding of standard techniques for collecting
data; analyse data involving one variable using a variety of techniques; solve
problems involving the normal distribution; describe the relationship between
two variables by interpreting the correlation coefficient; and evaluate the
validity of statistics drawn from a variety of sources.
In
Unit 3: Counting and Probability, students solve introductory counting problems
using Venn diagrams, as well as the additive and multiplicative counting
principles; develop techniques for counting permutations and combinations;
determine theoretical probabilities using combinatorial techniques; construct
discrete probability distribution functions; and calculate expected values
within the context of an application. In addition, students determine
probabilities using the binomial distribution; design and carry out simulations
to estimate probabilities, and assess the validity of simulation results by
comparing them with the theoretical probabilities.
In
Unit 4: Additional Tools for Data Management, students solve problems involving
complex relationships with the aid of diagrams (e.g., network diagrams, tree
diagrams, cause-and-effect diagrams, timelines), and model situations and solve
problems using matrices.
In
Unit 5: Managing the Culminating Project, students prepare to su
The
Grade 12 course profiles represent a collaborative effort between the Public
and Catholic writing teams. While not as detailed as previous profiles, they
are designed to complement and supplement each other. In addition to two
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.
Note:
The activities in
this profile both introduce and consolidate skills necessary for su
Note:
Teachers will note
that some of the data sets provided here, and those that will be encountered on
available licenced software, will pertain to issues that can be sensitive or
troublesome to some students. Teachers will need to carefully consider the
selection of such items for student use, being sensitive to individual student
circumstances. The screen captures and graphics can be found within the
software program used in presenting the activities.
Because
this course has been designed to prepare students for entry into various
programs at university, the specific nature of the learning activities should
reflect this destination. In particular, students in this course should
routinely be challenged with problems and questions, which require
investigation, research, data collection, analysis, and reflection. Students must
engage in activities that require collaboration with other students and other
activities that need sustained, independent effort. Students must also have the
tools and the time to work on complex tasks to develop their problem-solving
skills.
Students
with learning disabilities need specific guidance 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
a
The
Achievement Chart for Mathematics is the basis of all assessment and evaluation
for this course. The Grade 10 Principles
of Mathematics Academic 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). A chart outlining the component actions that
are needed for su
Units: Titles and Time
|
* Unit
1 |
Posing
Questions With Data |
21
hours |
|
Unit 2 |
Data
Analysis |
23
hours |
|
Unit 3 |
Counting
and Probability |
20
hours |
|
Unit 4 |
Additional
Tools for Data Management |
20
hours |
|
** Unit
5 |
Managing
the Culminating Project |
26
hours |
* Unit 1
is fully developed by the Catholic Course Profile writing team.
** Unit 5
is fully developed by the Public Course Profile writing team.
Unit Overviews
Unit 1: Posing Questions With Data
Time: 21 hours
Unit
Description
Students learn to find, retrieve,
and organize credible data. They learn to pose significant questions through
the use of journals and critique the work of others. Some activities are
grouped to teach the expectations in an instructional activity followed by an
assessment activity.
Using Fathom, students locate and retrieve large data sets from a variety
of Internet sites, including Statistics Canada (E-STAT). Students answer
questions using the data sets and consider and explore other factors that could
influence the data. They use the analysis features of Fathom to analyse one- and two-variable data; analyses include
cause-and-effect and regression. Students present their findings in small-group
settings and critique the data analyses of others clearly, honestly, and with
sensitivity. Students complete the unit by posing a problem, finding and
analysing data, presenting their work on a poster, and critiquing the work of
others.
Unit
Overview Chart
|
Activity |
Expectations |
Assessment |
Tasks |
|
1.1 |
DMV.02,
DM2.02 CGE5a,
7e |
Communication Teamwork Inquiry |
A hook
to begin looking at and reading graphs and a beginning point to stimulate
ideas for the culminating project. |
|
1.2 |
ODV.01,
OD1.01, OD1.02 CGE2b,
3c, 3d, 7i |
Knowledge Works
Independently Teamwork |
Locate
and retrieve data to answer questions. |
|
1.3 |
ODV.01,
OD1.01, OD1.02, DMV.02, DM2.01, DM2.02, DM2.03 CGE5a,
5b, 5e |
Knowledge Communication Application Initiative Teamwork |
Use
E-STAT to locate and retrieve data to answer questions; present work and
critique the work of peers. |
|
1.4 |
ODV.01,
OD1.03, STV.01, ST1.04, STV.02, ST2.01, ST2.02, STV.03, ST3.02, STV.04,
ST4.01, ST4.02, ST4.03 CGE2b,
2c |
Knowledge Teamwork Works
Independently |
Use Fathom to retrieve identified data
sets and create a database for one- and two-variable analyses. |
|
1.5 |
ODV.01,
OD1.03, STV.01, ST1.04, DMV.01, DM1.02, DMV.02, DM2.03 CGE2b,
2c, 3d, 4e (could
include assessment of ST2.01, ST2.02, ST3.02, ST4.01, ST4.02) |
Knowledge Inquiry Application Communication |
Use Fathom to retrieve, organize, and
analyse data from secondary sources. |
|
1.6 |
ODV.01,
OD1.02, STV.01, ST1.04 CGE1d,
3e, 5a, 5e |
Knowledge |
Investigate
and critique the usefulness of different sites; search for other useful data
sites. |
|
1.7 |
ODV.01, OD1.01, OD1.02, OD1.03, DMV.01,
DM1.01, DM1.02, DM1.03, DMV.02 DM2.03 CGE3b, 3e, 4e, 4f |
Knowledge Inquiry Communication Application |
Pose a significant problem, use the Internet
to find data, organize and analyse the data, and produce a poster; critique
the work of peers. |
*
Integration with Unit 2 is discussed within the activity description. Any
additional time can be allocated for remediation and consolidation of skills at
the discretion of the teacher, depending on the needs of students.
Unit 2: Data Analysis
Time: 23 hours
Ontario
Catholic School Graduate Expectations: 2e, 3b, 3c, 3d,
5a
Unit
Description
Students
learn techniques for sampling data, including awareness of bias. They apply the
common techniques used for analysing one- and two-variable data and they learn
to evaluate and critique the use and misuse of statistics. Catholic students
integrate their Catholic faith tradition as reflective and creative thinkers
making decisions in light of gospel values.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
STV.01,
ST1.01, ST1.02, ST1.03 CGE2e,
3b, 5a |
Knowledge Communication Application |
Demonstrate
an understanding of standard techniques for collecting data and of different
types of bias |
|
2 |
STV.02,
ST2.01, ST2.02, ST2.03 CGE3c,
3d |
Knowledge Communication Application |
Compute
and interpret measures of one-variable statistics using a variety of
techniques. |
|
3 |
STV.03,
ST3.01, ST3.02, ST3.03 CGE3c,
3d |
Knowledge Inquiry Communication Application |
Solve
problems involving the normal distribution. |
|
4 |
STV.04,
ST4.01, ST4.02, ST4.03, ST4.04 CGE3c,
3d |
Knowledge Communication Application |
Describe
the relation between two variables by interpreting the correlation
coefficient. |
|
5 |
STV.05,
ST5.01, ST5.02, ST5.03 CGE2e,
3b, 3c, 3d |
Knowledge Inquiry Communication Application |
Evaluate
the validity of statistics drawn from a variety of sources. |
Unit 3: Counting and Probability
Time: 20 hours
Ontario
Catholic School Graduate Expectations: 3b, 3c, 3d, 5b
Unit
Description
Students
develop skills for counting and determining probabilities using Venn diagrams,
simulations, counting principles, factorial notation, permutations, and
combinations. They consider experimental and theoretical probability, calculate
expected values, and use the binomial distribution.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
CPV.01,
CP1.01, CP1.02, CP1.08 |
Knowledge Communication Application |
Solve
introductory counting problems using Venn diagrams together with the additive
and multiplicative counting principles. |
|
2 |
CPV.01,
CP1.03, CP1.04, CP1.05, CP1.06, CP1.08 |
Knowledge Inquiry Communication Application |
Solve
problems involving permutations and combinations. |
|
3 |
CPV.01,
CP1.07, CP1.08 |
Knowledge Communication Application |
Connect
Pascal’s Triangle with binomial expansions. |
|
4 |
CPV.02,
CP2.01, CP2.06, OD2.02 |
Knowledge Application Communication |
Use
counting techniques to solve simple probability problems. |
|
5 |
CPV.02,
CP2.02, CP2.03, CP2.04, CP2.06, CPV.03, CP3.02 |
Knowledge Inquiry Communication Application |
Determine
expected values and interpret them within the context of an application. |
|
6 |
CPV.02,
CP2.05, CP2.06 |
Knowledge Inquiry Communication Application |
Use the
binomial distribution model to determine probabilities. |
Unit 4: Additional Tools for Data Management
Time: 20 hours
Ontario
Catholic School Graduate Expectations: 3b, 3c, 3d, 5b
Unit
Description
Students
use matrices to organize and analyse data. Concepts and skills, understood and
practised using small data sets, can be applied to large data sets with the use
of technology.
Unit
Overview Chart
|
Cluster |
Expectations |
Assessment |
Focus |
|
1 |
ODV.02,
OD2.01, OD2.02 |
Knowledge Application Communication |
Investigate
situations that can be modelled using diagrams (e.g., tree diagrams, network
diagrams, cause-and-effect diagrams). |
|
2 |
ODV.02,
OD2.03 |
Application Inquiry |
Solve
network problems using introductory graph theory. |
|
3 |
ODV.03,
OD3.01 |
Communication Application |
Use
matrices as a tool for organizing data; develop the related terminology and
notation. |
|
4 |
ODV.03,
OD3.02 |
Knowledge Application |
Develop
proficiency with matrix operations, such as addition, scalar multiplication,
and matrix multiplication, with and without the use of technology. |
|
5 |
ODV.03, OD3.03 |
Application Inquiry |
Apply matrix tools to solve problems drawn
from a variety of applications. |
Unit 5: Managing the Culminating Project
Time: 26 hours
Ontario
Catholic School Graduate Expectations: 1d, 1i, 2a, 2b, 3c, 3b, 5a,
5g, 5e
Unit
Description
Students
prepare to su
Unit
Overview Chart
|
Activity |
Expectations |
Assessment |
Tasks |
|
5.1 |
DMV.01,
DM1.01, DM1.02, DM1.03 CGE1i |
Application Communication |
Sequenced
planning approach to the culminating project |
|
5.2 |
ODV.01,
OD1.01, OD1.03, STV.01, ST1.04, STV.02, ST2.01, ST2.02, ST2.03, STV.05,
ST5.03 CGE3c |
Knowledge Inquiry Communication Application |
Analyse
a set of data about family income in Canada and then pose and answer
questions about it. |
|
5.3 |
ODV.01,
OD1.02, CPV.03, CP3.01, CP3.02, STV.01, ST1.04, STV.04, ST4.01, ST4.02,
ST4.04 CGE1d,
2a |
Knowledge Inquiry Communication Application |
Analyse
data related to the spread of AIDS in Canada over 20 years and construct a
simulation to compare and contrast with the actual data. |
|
5.4 |
CPV.02,
CPV.03, CP2.01, CP2.02, CP2.04, CP2.05, CP2.06, CP3.01, CP3.02, CP3.03 CGE5a,
3b |
Inquiry Application |
Examine
selected games to compare experimental and theoretical probability. |
|
5.5 |
ODV.02,
OD2.01, OD2.02, OD2.03, ODV.03, OD3.01, OD3.02, OD3.03 CGE2b,
3b |
Application |
Introduction
to possible areas for further study by the use of famous ideas |
|
5.6 |
DMV.01,
DM1.03, DMV.02, DM2.01, DM2.02, DM2.03 CGE5e,
5g |
Communication Knowledge |
Feedback,
tools, and guidance in the preparation of presentations |
Teaching/Learning
Strategies
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 assume
a variety of roles (including guide, facilitator, consultant, and instructor)
and 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 to appreciate the need for new
skills;
·
the
prompting, supporting, and challenging of individual students, as well as the
class as a whole;
·
approaches
that a
·
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 students o
·
the
use of a
·
opportunities
for students to practise and extend their skills and knowledge outside of the
classroom.
Students themselves should
play an active role in their own learning. To su
·
develop
an increased responsibility for their own learning;
·
be
a
·
participate
as active learners;
·
engage
in explorations using technology;
·
apply
individual and group learning skills;
·
describe
verbally, algebraically, and visually the mathematical patterns that emerge.
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 a
Students’
effective demonstration of communication skills is an essential component 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.
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 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.
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.
Evaluation,
as defined by Ontario Secondary Schools,
Grades 9-12, Program and Diploma Requirements, 1999, is “the process of
judging the quality of a student’s work on the basis of established achievement
criteria, and assigning a value to represent that quality” (p. 31). Assessment
is the collection of information about student performance; evaluation is the
determination of a quantitative value describing the student’s overall level of
achievement. Effective assessment, evaluation, and reporting require the
teacher to do more than average marks. Averaging is not comprehensive enough
for a
Seventy
per cent of the grade will be based on assessments conducted throughout the
course. Thirty per cent of the grade will be based on a final evaluation which
would include a combination of a formal examination and a culminating
performance task (student project presentation and critiques). It would be
reasonable to weight the culminating performance task higher than the final
examination (e.g., culminating performance task twenty percent and the final
examination ten percent).
Assessment Strategies
An
effective assessment program includes a balance of diagnostic, formative, and
summative assessment instruments that incorporate the categories defined in the
Achievement Chart for Mathematics. The following are examples of strategies.
|
|
Knowledge/ Understanding |
Thinking/Inquiry/ Problem Solving |
Communication |
Application |
|
final
examinations |
4 |
4 |
4 |
4 |
|
journals |
4 |
|
4 |
4 |
|
observations |
|
4 |
4 |
4 |
|
oral
presentations |
4 |
|
4 |
|
|
performance
tasks |
4 |
4 |
4 |
4 |
|
portfolios |
4 |
4 |
4 |
4 |
|
quizzes |
4 |
|
|
|
|
reports/assignments |
4 |
|
4 |
4 |
|
student/teacher
conferences |
4 |
|
4 |
|
|
unit
tests |
4 |
4 |
4 |
4 |
Assessment tools, such as observational
checklists, performance criteria, rubrics, the Achievement Chart, marking
schemes, rating scales, peer evaluation, and self-evaluation, are used to
assist in developing objective and consistent evaluations of student
achievement.
Acc ommodations
Teachers refer to and contribute to
Individual Education Plans (IEPs) of students and consider their particular
learning characteristics to make necessary a
Specific Acc ommodations
·
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
students with oral pre-planning of activities.
·
Give
more time to complete written work (copying from the board proofreading).
·
Have
students produce work using a word-processing package on a computer.
·
Allow
students to read pertinent text into a recording device, such as an audio tape
recorder.
·
Give
several short assignments rather than one long one.
·
Use
oral presentation.
·
Provide
overhead copies before the class begins.
·
Describe
using diagrams, charts, and graphs. Reinforce verbally.
·
Have
interesting, relevant books and articles available that are at the appropriate
reading level.
·
Have
all responses given in a written format.
·
Do
not ask the student to respond to questions without forewarning.
Alternative Assessment
Techniques
·
Use
oral tests; give open-book tests or use of notes; give tests that elicit short
answers and multiple choice, true/false, matching tests; use short quizzes
instead of major tests.
·
Assign
fewer questions, especially in research projects if the student is unable to
indicate that he/she comprehends and has mastered task.
·
Tape
tests. Student listens and/or responds on tape.
·
Extend
time on tests.
·
Give
tasks that allow for a variety of responses, visual, oral, etc.
·
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 practise oral presentation skills.
Resources
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.
The
URLs for the websites were verified by the writers prior to publication. Given
the frequency with which these designations change, teachers should verify the
websites prior to assigning them for student use.
Fathom, TI-Interactive, graphing calculators (e.g., TI-83+)
Spreadsheet
software (e.g., Quattro Pro, Excel)
Internet
a
Statistics
Canada – www.statcan.ca or http://estat.statcan.ca
Environment
Canada – www.ec.gc.ca
School
library/resource centre for guides to help students in preparing essays,
bibliographies, etc.
Teachers
in other departments can also be used as resources.
OSS Considerations
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 published several resource documents, brochures, and
policy/program memoranda in support of its OSS policies, available online
(www.edu.gov.on.ca).
Coded
Expectations, Mathematics of Data Management, Grade 12,
University Preparation, MDM4U
Organization of Data for
Analysis
Overall Expectations
ODV.01 · organize data to facilitate
manipulation and retrieval;
ODV.02 · solve problems involving complex
relationships, with the aid of diagrams;
ODV.03 · model situations and solve
problems involving large amounts of information, using matrices.
Specific Expectations
Organizing
Data
OD1.01 – locate data to answer questions
of significance or personal interest, by searching well-organized databases;
OD1.02 – use the Internet effectively as a
source for databases;
OD1.03 – create database or spreadsheet
templates that facilitate the manipulation and retrieval of data from large
bodies of information that have a variety of characteristics (e.g., a compact
disc collection classified by artist, by date, by type of music).
Using
Diagrams to Solve Problems
OD2.01 – represent simple iterative
processes (e.g., the water cycle, a person’s daily routine, the creation of a
fractal design), using diagrams that involve branches and loops;
OD2.02 – represent complex tasks (e.g.,
searching a list by using algorithms; classifying organisms; calculating
dependent or independent outcomes in probability) or issues (e.g., the origin
of global warming), using diagrams (e.g., tree diagrams, network diagrams,
cause-and-effect diagrams, time lines);
OD2.03 – solve network problems (e.g.,
scheduling problems, optimum-path problems, critical-path problems), using
introductory graph theory.
Using
Matrices to Model and Solve Problems
OD3.01 – represent numerical data, using
matrices, and demonstrate an understanding of terminology and notation related
to matrices;
OD3.02 – demonstrate proficiency in matrix
operations, including addition, scalar multiplication, matrix multiplication,
the calculation of row sums, and the calculation of column sums, as necessary
to solve problems, with and without the aid of technology;
OD3.03 – solve problems drawn from a
variety of applications (e.g., inventory control, production costs, codes),
using matrix methods.
Counting and Probability
Overall Expectations
CPV.01 · solve counting problems and
clearly communicate the results;
CPV.02 · determine and interpret
theoretical probabilities, using combinatorial techniques;
CPV.03 · design and carry out simulations
to estimate probabilities.
Specific Expectations
Solving
Counting Problems
CP1.01 – use Venn diagrams as a tool for organizing
information in counting problems;
CP1.02 – solve introductory counting
problems involving the additive and multiplicative counting principles;
CP1.03 – express the answers to
permutation and combination problems, using standard combinatorial symbols,
[e.g., 
, P(n, r)];
CP1.04 – evaluate expressions involving
factorial notation, using appropriate methods (e.g., evaluating mentally, by
hand, by using a calculator);
CP1.05 – solve problems, using techniques
for counting permutations where some objects may be alike;
CP1.06 – solve problems, using techniques
for counting combinations;
CP1.07 – identify patterns in Pascal’s
triangle and relate the terms of Pascal’s triangle to values of 
, to the expansion of a binomial, and to the solution of
related problems (Sample problem: A girl’s school is 5 blocks west and 3
blocks south of her home. Assuming that she leaves home and walks only west or
south, how many different routes can she take to school?);
CP1.08 – communicate clearly, coherently,
and precisely the solutions to counting problems.
Determining
and Interpreting Theoretical Probabilities
CP2.01 – solve probability problems
involving combinations of simple events, using counting techniques [i.e., P(A
or B), P(A and B), and P(~A)];
CP2.02 – identify examples of discrete
random variables (e.g., the sums that are possible when two dice are rolled);
CP2.03 – construct a discrete probability
distribution function by calculating the probabilities of a discrete random
variable;
CP2.04 – calculate expected values and
interpret them within applications (e.g., lottery prizes, tests of the fairness
of games, estimates of wildlife populations) as averages over a large number of
trials;
CP2.05 – determine probabilities, using
the binomial distribution (Sample problem: A light-bulb manufacturer
estimates that 0.5% of the bulbs manufactured are defective. If a client places
an order for 100 bulbs, what is the probability that at least one bulb is
defective?);
CP2.06 – interpret probability statements,
including statements about odds, from a variety of sources.
Simulating
and Predicting
CP3.01 – identify the advantages of using
simulations in contexts;
CP3.02 – design and carry out simulations
to estimate probabilities in situations for which the calculation of the
theoretical probabilities is difficult or impossible (Sample problem: A
set of 6 baseball cards can be collected from cereal boxes. If the different
cards are evenly distributed throughout the boxes, carry out a simulation to
determine the probability of collecting one complete set in a purchase of 14
boxes);
CP3.03 – assess the validity of some
simulation results by comparing them with the theoretical probabilities, using
the probability concepts developed in the course (Sample problem: A
light-bulb manufacturer estimates that 0.5% of the bulbs manufactured are
defective. Carry out a simulation to estimate the probability that at least one
bulb is defective in an order of 100 bulbs).
Statistics
Overall Expectations
STV.01 · demonstrate an understanding of standard
techniques for collecting data;
STV.02 · analyse data involving one variable, using a
variety of techniques;
STV.03 · solve problems involving the
normal distribution;
STV.04 · describe the relationship between
two variables by interpreting the correlation coefficient;
STV.05 · evaluate the validity of
statistics drawn from a variety of sources.
Specific Expectations
Collecting
Data
ST1.01 – demonstrate an understanding of
the purpose and the use of a variety of sampling techniques (e.g., a simple
random sample, a systematic sample, a stratified sample);
ST1.02 – describe different types of bias
that may arise in surveys (e.g., response bias, measurement bias, non-response
bias, sampling bias);
ST1.03 – illustrate sampling bias and
variability by comparing the characteristics of a known population with the
characteristics of samples taken repeatedly from that population, using
different sampling techniques;
ST1.04 – organize and summarize data from
secondary sources (e.g., the Internet, computer databases), using technology
(e.g., spreadsheets, graphing calculators).
Analysing
Data Involving One Variable
ST2.01 – compute, using technology,
measures of one-variable statistics (i.e., the mean, median, mode, range,
interquartile range, variance, and standard deviation), and demonstrate an
understanding of the appropriate use of each measure;
ST2.02 – interpret one-variable statistics
to describe characteristics of a data set;
ST2.03 – describe the position of
individual observations within a data set, using z-scores and percentiles.
Solving
Problems Involving the Normal Distribution
ST3.01 – identify situations that give
rise to common distributions (e.g., bimodal, U-shaped, exponential, skewed,
normal);
ST3.02 – demonstrate an understanding of
the properties of the normal distribution (e.g., the mean, median, and mode are
equal; the curve is symmetric about the mean; 68% of the population are within
one standard deviation of the mean) and use these properties to solve problems;
ST3.03 – make probability statements about
normal distributions, on the basis of information drawn from a variety of
applications.
Describing
the Relationship Between Two Variables
ST4.01 – define the correlation
coefficient as a measure of the fit of a scatter graph to a linear model;
ST4.02 – calculate the correlation
coefficient for a set of data, using graphing calculators or statistical
software;
ST4.03 – demonstrate an understanding of
the distinction between cause-effect relationships and the mathematical
correlation between variables;
ST4.04 – describe possible misuses of
regression (e.g., use with too small a sample, use without considering the
effect of outliers, inappropriate extrapolation).
Evaluating
Validity
ST5.01 – explain examples of the use and misuse of
statistics in the media;
ST5.02 – assess the validity of conclusions made on
the basis of statistical studies, by analyzing possible sources of bias in the
studies (e.g., sampling bias) and by calculating and interpreting additional
statistics, where possible (e.g., measures of central tendency, the standard
deviation);
ST5.03 – explain the meaning and the use
in the media of indices based on surveys (e.g., the consumer price index, the
cost of living index).
Integration of the
Techniques of Data Management
Overall Expectations
DMV.01 · carry out a culminating project
on a topic or issue of significance that requires the integration and
application of the expectations of the course;
DMV.02 · present a project to an audience
and critique the projects of others.
Specific Expectations
Carrying
Out a Culminating Project
DM1.01 – pose a significant problem whose
solution would require the organization and analysis of a large amount of data;
DM1.02 – select and apply the tools of the
course (e.g., methods for organizing data, methods for calculating and
interpreting measures of probability and statistics, methods for data
collection) to design and carry out a study of the problem;
DM1.03 – compile a clear, well-organized,
and fully justified report of the investigation and its findings.
Presenting
and Critiquing Projects
DM2.01 – create a summary of a project to
present within a restricted length of time, using communications technology
effectively;
DM2.02 – answer questions about a project,
fully justifying mathematical reasoning;
DM2.03 – critique the mathematical work of
others in a constructive fashion.
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.