MDM4U – DATA MANAGEMENT, Grade 12 University MDM4U

COURSE OUTLINE Course Title: Mathematics of Data Management, Grade 12 University Preparation MDM4U Ministry Course Code: MDM4U Grade: 12 Course Ty … Read more
CAD300.00 each
  • Description
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Course Title: Mathematics of Data Management, Grade 12 University Preparation MDM4U

Ministry Course Code: MDM4U

Grade: 12

Course Type: University Preparation

Credit Value: 1.0

Prerequisite: Functions, Grade 11, University Preparation, or Functions and Applications, Grade 11, University/College Preparation MCR3U

Department: Mathematics

Course Developer: Academy of Royal International Education

Development Date: 2017

Course Revision Date: n/a

Ontario Ministry of Education Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)


This course broadens students’ understanding of mathematics as it relates to managing

data. Students will apply methods for organizing and analysing large amounts of

information; solve problems involving probability and statistics; and carry out a

culminating investigation that integrates statistical concepts and skills. Students will

also refine their use of the mathematical processes necessary for success in senior

mathematics. Students planning to enter university programs in business, the social

sciences, and the humanities will find this course of particular interest.


Data Management is broken down into the following units:

Unit Titles and Descriptions (in sequence delivered)


Unit 1: Statistics of One Variable

15 hours

Unit 2: Statistics of Two Variables

15 hours

Unit 3: Permutations and Organized Counting

16 hours

Unit 4: Combinations

15 hours

Unit 5: Probability

16 hours

Unit 6: Probability Distributions

15 hours

Unit 7: Normal Distribution

16 hours

Final Assessment: Final Examination

2 hours


110 hours


This course is entirely online and does not require a textbook.


Throughout the course, students will:

By the end of this course, students will:

Counting and Probability

1. solve problems involving the probability of an event or a combination of events for discrete sample spaces;

2. solve problems involving the application of permutations and combinations to determine the probability of an event.

Probability Distributions

1. demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications;

2. demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications.

Organization of Data for Analysis

1. demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data;

2. describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection, and collect and organize data to solve a problem.

Statistical Analysis

1. analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries;

2. analyse, interpret, and draw conclusions from two-variable data using numerical, graphical, and algebraic summaries;

3. demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

Culminating Data Management Investigation

1. design and carry out a culminating investigation* that requires the integration and application of the knowledge and skills related to the expectations of this course;

2. communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.


The Academy of Royal International Education follows seven mathematical

process expectations that describe a set of skills that support lifelong learning in mathematics and that students need to develop on an ongoing basis, as they work to achieve the expectations outlined within each course. Teaching and learning strategies used ensure that students are actively engaged to help students develop the following mathematical processes.

  • problem solving
  • reasoning and proving
  • reflecting
  • selecting tools and computational strategies
  • connecting
  • representing
  • communicating

Each course presents students with rich problem-solving experiences through a variety of approaches, including investigation. These experiences provide students with opportunities to develop and apply the mathematical processes. The mathematical processes are interconnected. Problem solving and communicating

have strong links to all the other processes. Problem solving provides students with the opportunity to make connections to their prior learning and to make decisions about the representations, tools, and computational strategies needed to solve the problem. Students justify their solutions, communicate them orally and in writing, and reflect on alternative solutions. By seeing how others solve a problem, students can begin to think about their own thinking (metacognition) and the thinking of others, and to consciously adjust their own strategies in order to make their solutions as efficient and accurate as possible. The mathematical processes cannot be separated from the knowledge and skills that students acquire throughout the course. Students who problem solve, communicate, reason, reflect, and so on, as they learn mathematics, will develop the knowledge, the understanding of concepts, and the skills required in the course in a more meaningful way.


  • Online lecture
  • Exemplars, demonstrations
  • Practice activities
  • Discussions
  • Video conferencing
  • Descriptive feedback
  • Homework
  • Self- assessment
  • Opinion sharing
  • Oral explanations
  • Reasoning, proving
  • Analysis
  • Independent research

We develop instructional strategies to help students achieve curriculum expectations and we incorporate techniques applicable to the various learning styles, abilities and interest levels that exist among students that best motivate students toward achieving their goals. Learning should be seen as a process in which students monitor and reflect on the development of their knowledge, understandings, and skills.

It is important for students to complete all assignments for the course by the end of the course.

We use asynchronous processes/technologies, such as online class/group and one-on-one chats, bulletin boards/forums, group and personal emails, telephone, and skype. Audio and video elements are incorporated into many courses. Document sharing is included.

Students will have online progress and grade reports, and an ‘account’ accessible 24/7 where they will see their grade remarks and other information pertinent to them. Tests are taken online, within a specific time frame, projects and other documents can be sent via email. Each course has a major cumulative project with written and presentation requirements and a final 2-hour proctored exam.

Each student is required to consistently maintain a Learning Log as a personal record that evidences their learning and skills development and Work Portfolio of their assignments assessments.


The Ontario Ministry of Education determines the nature of assessment and evaluation of student learning for Ontario credit courses. Our School’s assessment and evaluation policy conforms to the following outlined by the Ontario Ministry of Education in its document, Growing Success: Assessment, Evaluation and Reporting in Ontario Schools, 2010.

The Seven Fundamental Principles of Assessment and Evaluation

To ensure that assessment, evaluation, and reporting are valid and reliable, and that they lead to the improvement of learning for all students, teachers use practices and procedures that:

  • are fair, transparent, and equitable for all students;
  • support all students, including those with special education needs, those who are learning the language of instruction (English or French), and those who are First Nation, Métis, or Inuit;
  • are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
  • are communicated clearly to students and parents at the beginning of the school year or course and at other appropriate points throughout the school year or course;
  • are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
  • provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement;
  • develop students’ self-assessment skills to enable them to assess their own learning, set specific goals, and plan next steps for their learning.

From Growing Success:



All assessment and evaluation is based upon the Ministry of Education’s document Growing Success 2010 and Ontario Schools, K-12 2011. Assessment is based on a combination of class work, regular class tests and examinations. Examinations are written at the end of each course. The final evaluation for all courses comprises 30% of the total grade. The remaining 70% is for summative assessment and evaluations conducted throughout the course.

Assessment and evaluation is based on the provincial expectations and achievement levels outlined in provincial curriculum documents. A wide range of assessment and evaluation opportunities allows students to demonstrate their learning in a variety of ways. This information provides the basis for reporting student grades. Assessment and evaluation includes the following four categories:

  • knowledge and understanding
  • thinking
  • communication
  • application

Achievement Categories and Value:



Knowledge and Understanding






Teachers assess and evaluate student work with reference to established criteria for four levels of achievement that are standard across the province, rather than by comparison with work done by other students, or through the ranking of student performance, or with reference to performance standards developed by individual teachers for their own classrooms. There is no expectation that a certain number or percentage of students must be allocated to any one level of achievement.

Assessment is the process of gathering information from a variety of sources (including assignments, demonstrations, projects, performances, and tests) that accurately reflect how well a student is achieving the curriculum expectations in a subject or course. The primary purpose of assessment is to improve student learning. Assessment for the purpose of improving student learning is seen as both “assessment for learning” and “assessment as learning”. Information gathered through assessment helps teachers to determine students’ strengths and weaknesses in their achievement of the overall curriculum expectations in each course. This information also serves to guide teachers in adapting curriculum and instructional approaches to students’ needs and in assessing the overall effectiveness of programs and classroom practices.

As part of assessment for learning, teachers provide students with descriptive feedback that guides their efforts towards improvement. Descriptive feedback helps students learn by providing them with specific information about what they are doing well, what needs improvement, and what specific steps they can take to improve. Multiple opportunities for feedback and follow-up are provided during a student’s course to allow for improvement in learning prior to assessment of learning and evaluation.


Evaluation refers to the process of judging the quality of student work on the basis of established criteria, and assigning a value to represent that quality. In Ontario secondary schools, the value assigned will be in the form of a percentage grade. Although all curriculum expectations in a course are accounted for in instruction, student evaluations focus solely on a student’s achievement of the overall curriculum expectations in his or her course. Evidence of student achievement for evaluation is collected over the duration of a course and is based on observations, conversations, and student products. Evaluation is based on assessment of learning that provides evidence of student achievement at strategic times throughout each course, typically at the end of a module of study.

Student marks in The Academy of Royal International Education courses are based on his or her most consistent effort with special emphasis on his or her most recent work.
In determining a student’s final grade, teachers will consider:

  • All evidence collected through observations, conversations, and student products (tests, exams and assignments for evaluation);
  • The number of tests/exams or assignments that were not completed or submitted;
  • The evidence of achievement that is available for each overall expectation for a subject in a particular course;
  • The teacher will consider that some evidence carries greater weight than other evidence because some performance tasks are richer and reveal more about a student’s skills and knowledge than others;
  • A final grade is recorded for every course, and a credit is granted and recorded for every course in which the student’s grade is 50% or higher. The final grade for each course will be determined as follows:
    • Seventy percent of the grade will be based on evaluations conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
    • Thirty per cent of the grade will be based on a final evaluation in the form of a supervised final examination, performance, essay, and/or other method of evaluation suitable to the course content and administered towards the end of the course.


Final examinations are normally conducted via the Internet, and under the supervision of an authorized exam proctor. Students may also come into the school location in Markham and write a supervised examination.

Students must complete and submit all course requirements (such as tests, assignments, discussion forums, learning logs, independent study units, etc.) to their teacher prior to booking their final exam. Once a student has completed all course requirements, his or her teacher will contact the Principal and provide approval for the student to write his or her final examination. The final examination must be written within 21 days of completion of course requirements. Students must be supervised during the time they write their final examination. An exam supervisor is the person who will confirm students’ identity and supervise them while they write their final exam. All students are responsible for booking their own exam and selecting a location to write their exam from the list of Approved Examination Centres available from the Office.

Students must submit a request for examination supervision at least 5 business days prior to their desired examination date. International students should allow 5-8 business days for application processing. Please note that if a student does not write his or her exam on the scheduled date, an administration fee will apply to reschedule the examination. Final marks are released approximately 10 business days after the final examination is received from the exam supervisor.


A Summary Description of Achievement in each Percentage Grade Range and Corresponding Level of Achievement

Percentage Grade Range

Achievement Level

Summary Description


Level 4

A very high to outstanding level of achievement. Above provincial standards.


Level 3

A high level of achievement. At provincial standards.


Level 2

A moderate level of achievement. Below but approaching provincial standards.


Level 1

Passable level of achievement. Below provincial standards.

Below 50%

Level R

Insufficient achievement of curriculum expectations. No credit granted.


At the midterm point and final point in the course, students will receive report cards which communicate the student’s achievement. The teacher will indicate the percentage mark the student has attained as well as issue comments regarding areas of strength and areas requiring improvement. Also, learning skills are reported as a letter grade representing one of the four levels of accomplishment. The report cards will be sent to the student’s home address and, if the student is a part time student, a copy will be sent to the student’s home school.


Students are expected to maintain high standards of honesty and academic integrity which means avoiding any instance of fraud, plagiarism and cheating. To ensure academic integrity:

  • Students provide photo identification;
  • Course assignments include audio and video components;
  • Teachers Skype regularly with their students;
  • Students are encouraged and supported to develop original work;
  • Exams are proctored by adults in professional, trusted positions.

When a teacher has reasonable grounds to believe that a student has violated these standards, the school principal will review the incident and, if needed, enforce disciplinary procedures.


The Academy of Royal International Education provides a flexible, self-paced learning opportunity, which allows students to proceed through each course at their own speed. Students may submit any assignment from any unit while he or she is enrolled in this course. Assignments will not be accepted once the student’s enrolment period has ended. Students must complete and submit all course requirements prior to booking their final exam. Course requirements include but are not limited to: assignments, tests, and learning log.


The following Program Planning considerations, in alignment with the Ontario Ministry of Education will be available:


Students whose Individual Education Plan (IEP) indicates that accommodations and/or modifications are required will be given such considerations. Classroom teachers are the key educators of students with special education needs. They have a responsibility to help all students learn, and they work collaboratively with special education teachers, where appropriate, to achieve this goal. Learning for All: A Guide to Effective Assessment and Instruction for All Students, Kindergarten to Grade 12 (Draft 2011) describes a set of beliefs, based in research, that should guide program planning for students with special education needs in all disciplines. Teachers pay particular attention to these beliefs, which are as follows:

  • All students can succeed.
  • Each student has his or her own unique patterns of learning.
  • Successful instructional practices are founded on evidence-based research, tempered by experience.
  • Universal designed and differentiated instruction are effective and interconnected means of meeting the learning or productivity needs of any group of students.
  • Classroom teachers are the key educators for a student’s literacy and numeracy development.
  • Classroom teachers need the support of the larger community to create a learning environment that supports students with special education needs.
  • Fairness is not sameness.



All teachers share in the responsibility for developing and supporting the English language needs of students. The Academy of Royal International Education is committed to cultural and linguistic diversity in the ways it enhances learning.


Ontario’s education system will prepare students with the knowledge, skills, perspectives, and practices they need to be environmentally responsible citizens. Students will understand our fundamental connections to each other and to the world around us through our relationship to food, water, energy, air, and land, and our interaction with all living things. The education system will provide opportunities within the classroom and the community for students to engage in actions that deepen this understanding. -Acting Today, Shaping Tomorrow: A Policy Framework for Environmental Education in Ontario Schools, 2009, p. 6. In this course, students may investigate environmental issues relating to topics such as resource management, population growth and urban sprawl, and the impact of human activity on the natural environment. Students also analyse the environmental sustainability of current behaviours and practices, explore ways in which environmental stewardship can be improved, and make connections between local, national, and global environmental issues, practices, and processes.


Every student is entitled to learn in a safe, caring environment, free from violence and harassment. Research has shown that students learn and achieve better in such environments. A safe and supportive social environment in a school is founded on healthy relationships – the relationships between students, between students and adults, and between adults. Healthy relationships are based on respect, caring, empathy, trust, and dignity, and thrive in an environment in which diversity is honoured and accepted. Healthy relationships do not tolerate abusive, controlling, violent, bullying/harassing, or other inappropriate behaviours. To experience themselves as valued and connected members of an inclusive social environment, students need to be involved in healthy relationships with their peers, teachers, and other members of the school community. Several provincial policies and initiatives, including the Foundations for a Healthy School framework, the equity and inclusive education strategy, and the Safe Schools strategy, are designed to foster caring and safe learning environments in the context of healthy and inclusive schools. -Shaping a Culture of Respect in Our Schools: Promoting Safe and Healthy Relationships, 2008


The Ontario equity and inclusive education strategy focuses on respecting diversity, promoting inclusive education, and identifying and eliminating discriminatory biases, systemic barriers, and power dynamics that limit the ability of students to learn, grow, and contribute to society. Antidiscrimination education continues to be an important and integral component of the strategy. In an environment based on the principles of inclusive education, all students, parents, caregivers, and other members of the school community – regardless of ancestry, culture, ethnicity, sex, physical or intellectual ability, race, religion, gender identity, sexual orientation, socio-economic status, or other similar factors – are welcomed, included, treated fairly, and respected.


The Ministry supports initiatives that encourage the development of financial knowledge and skills in students. The document A Sound Investment: Financial Literacy Education in Ontario Schools, 2010 (p. 4) sets out the vision that Ontario students will have the skills and knowledge to take responsibility for managing their personal financial well-being with confidence, competence, and a compassionate awareness of the world around them. The Ministry’s resource document – The Ontario Curriculum, Grades 9–12: Financial Literacy Scope and Sequence of Expectations, 2011 assists teachers in incorporating financial literacy in the classroom. Education can play an important role in preparing young people to take their place as informed, engaged, and knowledgeable citizens in the global economy. Financial literacy education can provide the preparation Ontario students need to make informed decisions and choices in a complex and fast-changing financial world. Making informed decisions about economic and financial matters has become an increasingly complex undertaking in the modern world, students need to build knowledge and skills in a wide variety of areas.


Literacy is defined as the ability to use language and images in rich and varied forms to read, write, listen, view, represent, and think critically about ideas. It involves the capacity to access, manage, and evaluate information; to think imaginatively and analytically; and to communicate thoughts and ideas effectively. Literacy includes critical thinking and reasoning to solve problems and make decisions related to issues of fairness, equity, and social justice. Literacy connects individuals and communities and is an essential tool for personal growth and active participation in a cohesive, democratic society. Reach Every Student: Energizing Ontario Education, 2008, p. 6

Literacy instruction must be embedded across the curriculum. All teachers of all subjects … are teachers of literacy. -Think Literacy Success, Grades 7–12: The Report of the Expert Panel on Students at Risk in Ontario, 2003, p. 10. To develop literacy skills, explicit instruction is required in all subject areas. Literacy, mathematical literacy, and inquiry/research skills are critical to students’ success in all subjects of the curriculum and in all areas of their lives. Students who are taught these skills become critical thinkers who can move beyond superficial conclusions to a deeper understanding of the issues they are examining. They are able to engage in an inquiry process in which they explore complex and multifaceted issues, and questions for which there may be no clear-cut answers. Students who are critically literate are able, for example, to actively analyse media messages and determine potential motives and underlying messages. They are able to determine what biases might be contained in texts, media, and resource material and why that might be, how the content of these materials might be determined and by whom, and whose perspectives might have been left out and why.


Courses at The Academy of Royal International Education help students to develop literacy in using non-print forms, such as the Internet, CDs, DVDs, and videos, in order to access Canadian and world studies information, databases, demonstrations, and a variety of performances; articulate questions for inquiries; create and produce single-medium or multimedia presentations. Access to diverse information can build students’ knowledge to develop lifelong learners in our information and knowledge-based society. Our resources in our courses encourage students to read widely, teaching them to examine and read many forms of text for understanding and enjoyment, and helping them improve their research skills and effectively use information gathered through research.


Information and communications technology (ICT) provides a range of tools that can significantly extend and enrich teachers’ instructional strategies and support student learning. ICT tools include multimedia resources, databases, websites, digital cameras, and word-processing programs. The Academy of Royal International Education supports enhanced student learning through a diverse range of information and communications technology.


The Ontario Skills Passport (OSP) identifies the following Essential Skills:


Reading Text

The comprehension of text consisting of sentences and paragraphs.


The preparation of written materials for a variety of purposes.

Document Use

The use of labels, lists, signs, graphs, charts, tables, forms, and other similar materials

Computer Use

The use of any type of computerized technology.


Oral Communication

The use of speech for a variety of purposes.


Money Math

The use of mathematical skills in making financial transactions, such as handling cash, preparing bills, and making payments.

Scheduling or Budgeting and Accounting

Planning for the best use of time and money, as well as monitoring the use of time and money.

Measurement and Calculation

The measurement and calculation of quantities, areas, volumes, and/or distances.

Data Analysis

The collection and analysis of data in numerical form.

Numerical Estimation

The production of estimates in numerical terms.


Job Task Planning

The planning and organization of one's own work.

Decision Making

The making of any type of decision, using appropriate information.

Problem Solving

The identification and solving of problems.

Finding Information

The use of a variety of sources, including written text, people, computerized databases, and information systems. (See also Reading Text, Document Use, Computer Use, and Oral Communication above).

Critical Thinking


Making judgments by using criteria to evaluate ideas and information and the related consequences.

For further information on the Ontario Skills Passport, including the Essential Skills and work habits, visit



The goals of the Kindergarten to Grade 12 education and career/life planning program are to:

  • ensure that all students develop the knowledge and skills they need to make informed education and career/life choices;
  • provide classroom and school-wide opportunities for this learning;
  • engage parents and the broader community in the development, implementation, and evaluation of the program, to support students in their learning.

The framework of the program is a four-step inquiry process based on four questions linked to four areas of learning:

  • knowing yourself – Who am I?;
  • exploring opportunities – What are my opportunities?;
  • making decisions and setting goals – Who do I want to become?;
  • achieving goals and making transitions – What is my plan for achieving my goals?


Planned learning experiences in the community, including job shadowing and job twinning, field trips, work experience, and cooperative education, provide students with opportunities to see the relevance of their classroom learning in a work setting, make connections between school and work, and explore a career of interest as they plan their pathway through secondary school and on to their postsecondary destination. While The Academy of Royal International Education does not provide cooperative learning experiences, courses often encourage experiential learning. -Cooperative Education and Other Forms of Experiential Learning: Policies and Procedures for Ontario Secondary Schools, 2000.


As part of every course, students must be made aware that health and safety are everyone’s responsibility – at home, at school, and in the workplace. Teachers must model safe practices at all times and communicate safety requirements to students in accordance with school board and Ministry of Education policies and Ministry of Labour regulations.


Courses at The Academy of Royal International Education provide numerous opportunities for students to learn about ethical issues and to explore the role of ethics in both public and personal decision making. Ethical discussion and judgements are made in consideration of data, evidence and in alignment with the inquiry process.

Ethical consideration extends to academic integrity, such as plagiarism. Using accepted forms of documentation to acknowledge sources is a specific expectation within the inquiry and skill development strand for each course.


Grade 12