Grade 12 Mathematics of Data Management University MDM4U Course Outline

Basic Information

Department: Math

Course Developer: Canada Online School, Bill Zhou

Development Date: April 2018

Revision Date: June 2019

Credit value: 1.0

Credit Hours: 110

Ministry Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007

Prerequisite(s): MCR3U OR MCF3M

Course Description

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; apply counting techniques, probability, and statistics in modelling and solving problems; and carry out a data management investigation that integrates the expectations of the course and encourages perseverance and independence. Students planning to pursue university programs in business, the social sciences, or the humanities will find this course of particular interest.

Textbooks and other required resources

  • A non-programmable scientific calculator
  • An Internet connection and a device with basic web browsing capabilities (see System Requirements in Course Calendar
  • Tool for scanning or taking photos of handwritten work for uploading
  • Statistical Modeling tool such as Excel, Fathom, graphing calculator, or web-based tool

Overall Curriculum Expectations

A. Counting and Probability
A1 solve problems involving the probability of an event or a combination of events for discrete sample spaces;
A2 solve problems involving the application of permutations and combinations to determine the probability of an event.
B. Probability and Distributions
B1 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;
B2 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.
C. Organization of Data for Analysis
C1 demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data;
C2 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.
D. Statistical Analysis
D1 analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries;
D2 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.
D3 demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.
E. Culminating Data Management Investigation
E1 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;
E2 communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.



Course Units

Unit Title Expected Hours Final Grade Weighting
Counting 18 70% – Grades and the curriculum strands evaluated are cumulative across the entire term. Special consideration may be given to more recent evidence of achievement.
Probability 18
Probability Distributions 22
Organizing Data 7
One Variable Statistics 21
Two Variable Statistics 14
Data Management Investigation 10 30% – An exam which covers all course learning.
Total 110 100%

Teaching & Learning Strategies

Teaching and learning strategies assist both teachers and students in achieving specific learning objectives. A number of methods have been used to create an online learning environment that will engage students in a variety of ways and support their understanding of scientific concepts. These strategies may include:

  • Clearly communicated curriculum expectations for each unit
  • Clearly communicated learning goals and success criteria in language that can be understood by the student, sometimes co-constructed with the student
  • Text, image, or video-based lesson content and directed reading
  • Diagnostic assessments
  • Animations and simulations
  • Practice question sets and review notes
  • Reports and investigations
  • Presentations
  • Assignments, quizzes, and tests
  • Assessments FOR learning with teacher feedback
  • Reflections and self-assessments, leading to conferences when necessary


In order to apply their knowledge effectively and to continue to learn, students must have a solid conceptual foundation in mathematics. Successful classroom practices engage students in activities that require higher-order thinking, with an emphasis on problem solving. Learning experienced in the primary, junior, and intermediate divisions should have provided students with a good grounding in the investigative approach to learning new mathematical concepts, including inquiry models of problem solving, and this approach continues to be important in the senior mathematics program.

Visual and other representations, including graphical and algebraic representations, are also a valuable aid to teachers. By analysing students’ representations of mathematical concepts and listening carefully to their reasoning, teachers can gain useful insights into students’ thinking and provide supports to help enhance their thinking.

All learning, especially new learning, should be embedded in well-chosen contexts for learning – that is, contexts that are broad enough to allow students to investigate initial understandings, identify and develop relevant supporting skills, and gain experience with varied and interesting applications of the new knowledge. Such rich contexts for learning open the door for students to see the “big ideas” of mathematics – that is, the major underlying principles or relationships that will enable and encourage students to reason mathematically throughout their lives.


Assessment & Evaluation

Assessment & evaluation is based on the Ministry of Education’s Growing Success (click to access) guidelines and the course-specific guidelines in the curriculum documents. The primary purpose of assessment and evaluation is to improve student learning. Information gathered through assessment helps teachers to determine students’ strengths and weaknesses in their achievement of the curriculum expectations in each course.

Assessment is the process of gathering information from a variety of sources (including assignments, day-to-day observations, conversations or conferences, demonstrations, projects, performances, and tests) that accurately reflects how well a student is achieving the curriculum expectations in a course. As part of assessment, teachers provide students with descriptive feedback that guides their efforts towards improvement. 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.

There are seven fundamental principles that ensure best practices and procedures of assessment and evaluation by COS teachers. COS assessments and evaluations,

  • 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 course and at other 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.


Assessments have three categories based on the intent behind the assessment:

Assessment for learning (AfL): diagnostic or formative assessments used to determine what students already know in order to plan further instruction, or monitor progress towards achieving overall expectations so that teachers can provide timely feedback and plan next steps.

Assessment as learning (AaL): used by students to monitor their own progress, assess peers, reflect on learning, or set individual goals.

Assessment of learning (AoL): summative assessment used to evaluate and make judgements about students’ quality of learning at a given point in time. It can also be used to inform further instruction.

All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations. A student’s achievement of the overall expectations is evaluated on the basis of his or her achievement of related specific expectations. The overall expectations are broad in nature, and the specific expectations define the particular content or scope of the knowledge and skills referred to in the overall expectations. Teachers will use their professional judgement to determine which specific expectations should be used to evaluate achievement of the overall expectations, and which ones will be covered in instruction and assessment but not necessarily evaluated.

Evaluation is done through the four Achievement Categories:

Knowledge and Understanding. Subject-specific content acquired in each course (knowledge), and the comprehension of its meaning and significance (understanding).

Thinking and Investigation. The use of critical and creative thinking skills and inquiry, research, and problem-solving skills and/or processes.

Communication. The conveying of meaning through various forms.

Application. The use of knowledge and skills to make connections within and between various contexts.

Teachers will ensure that student work is assessed and/or evaluated in a balanced manner with respect to the four categories, and that achievement of particular expectations is considered within the appropriate categories.

To arrive at a percentage grade, evaluation of achievement is guided by the four levels of achievement:

Level 1:  50 – 59% – limited

Level 2:  60 – 69% – some

Level 3:  70 – 79% – considerable

Level 4:  80 – 100% – high degree

Each level corresponds to a particular qualifier describing performance in the Achievement Chart, which can be found in the curriculum document.

The four Achievement categories are assessed throughout the course in a balanced manner given the nature of the overall curriculum expectations. Each category approximately contributes to the 70% term weight as follows:

20% 15% 15% 20%


These percentages above are only approximations. The four categories are evaluated in every assessment of learning. Some assessments include all four categories, whereas others may focus on one or two categories only. The exact individual composition of an assessment is provided with the assessment itself as a marking guide or rubric, which generates a single grade for the assessment. The grades of all assessments are then aggregated for the final term grade before the final summative. Exact weights of each individual assessment as a proportion of the overall term grade are given in the table below.

Term Assessment/Evaluation Plan

Assessment/Evaluation Assessment Type Evidence Type Grade Weight
Diagnostic Assessment FOR observation, product 0
Unit 1     8
A1 Exercise FOR observation 0
A2 Exercise FOR observation 0
A3 Exercise FOR observation 0
A1-3 Assignment OF product 2
Assignment OF product, observation 2
Review FOR observation 0
Reflection AS, FOR conversation, observation 0
Test OR Assignment OF product 4
Unit 2     10
A1 Discussion FOR observation 0
A3 Assignment OF product 2
A4 Discussion FOR observation 0
Activity 4 Assignment OF product 3
A5 Exercise FOR observation 0
A6 Discussion FOR observation 0
Reflection AS, FOR conversation, observation 0
Test OR Assignment OF product 5
Unit 3     14
A1 Assignment OF product 2
A2 Exercise FOR observation 0
A3 Exercise FOR observation 0
A4 Assignment OF product 2
A5-7 Exercise FOR observation 0
A5-7 Assignment OF product 3
Reflection AS, FOR conversation, observation 0
Test OR Assignment OF product 7
Unit 4     2
A1 Discussion FOR observation 0
A2 Discussion FOR observation 0
A3 Discussion FOR observation 0
A4 Assignment OF product 1
A5 Assignment OF product 1
Reflection AS, FOR conversation, observation 0
Unit 5     13
A1 Exercise FOR observation 0
A2 Assignment OF product 2
A3 Exercise FOR observation 0
A4 Exercise FOR observation 0
A5 Exercise FOR observation 0
A6 Assignment FOR product 1
A6 Discussion FOR observation 0
A7 Exercise FOR observation 0
A8 Discussion For observation 0
Assignment OF product 4
Review FOR observation 0
Reflection AS, FOR conversation, observation 0
Test OR Assignment OF product 6
Unit 6     13
A1 Discussion FOR observation 0
A2 Discussion FOR observation 0
A3 Assignment OF product 2
A4 Assignment OF product 2
A5 Discussion FOR observation 0
A6 Discussion FOR observation 0
Assignment OF product, observation 3
Reflection AS, FOR conversation, observation 0
Test OR Assignment OF product 6
Term Discussion Contribution OF observation, product, conversation 10
Term Total     70
Culminating     30



Student achievement is communicated formally to students and parents by means of the COS Report Card. The report card provides a record of the student’s achievement of the curriculum expectations in every course, at the mid-point and final point of a course, in the form of a percentage grade. The percentage grade represents the quality of the student’s overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline.

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 per cent 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 an examination, performance, essay, and/or other method of evaluation suitable to the course content and administered towards the end of the course.


Program Planning Considerations

COS develops its programs with consideration for Ontario Ministry of Education policies and initiatives. Many areas of special consideration are embedded naturally within course content. These include but are not limited to the following:


  • English language learners: At the beginning of a course, students are expected to complete a diagnostic activity to identify their preparedness for the course. This process identifies whether ESL learners or former ESL learners have language-specific difficulties, or any other difficulties. If through the diagnostic activity the student is shown to have language difficulties, the teacher will take extra steps to help the student through conversation, defining a course dictionary, extended explanations, and/or other strategies as necessary. There are also images, sound, interactive activities, and universal mathematical notation to assist students’ comprehension.
  • Healthy Relationships: Every student is entitled to a safe environment based on mutual respect. Our courses use online discussions, case studies, role play, etc, to encourage cooperation and constructive comments. Students are asked to follow the code of conduct on the course calendar when engaging in any such processes.
  • Financial Literacy: Financial literacy may be defined as having the knowledge and skills needed to make responsible economic and financial decisions with competence and confidence. Since making financial decisions has become an increasingly complex task in the modern world, students need to have knowledge in various areas and a wide range of skills in order to make informed decisions about financial matters. Students need to be aware of risks that accompany various financial choices. They need to develop an understanding of world economic forces as well as ways in which they themselves can respond to those influences and make informed choices. In addition to acquiring knowledge in such specific areas as saving, spending, borrowing, and investing, students need to develop skills in problem solving, inquiry, decision making, critical thinking, and critical literacy related to financial and other issues. Relevant courses naturally embed financial literacy knowledge and skills in their content. Where relevant, this course provides examples of how the mathematical skills may be applied to financial situations.
  • Literacy, Mathematical Literacy, and Inquiry Skills: 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. Literacy involves a range of critical-thinking skills and is essential for learning across the curriculum. Literacy instruction takes different forms of emphasis in different subjects, but in all subjects, literacy needs to be explicitly taught. 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. Many of the activities and tasks that students undertake in the Canada Online School courses involve the literacy skills relating to oral, written, and visual communication. For example, they develop literacy skills by reading, interpreting, and analysing various texts. In addition, they develop the skills needed to construct, extract information from, and analyse various types information presented in a variety of media forms. In all Canada Online School courses, students are required to use appropriate and correct terminology, including that related to the concepts of disciplinary thinking, and are encouraged to use language with care and precision in order to communicate effectively. Inquiry and research are at the heart of learning in all subject areas at Canada Online School. Students are encouraged to develop their ability to ask questions and to explore a variety of possible answers to those questions. This math course emphasizes inquiry through statistical investigation and theoretical experiments. It also extensively uses mathematical notation.
  • Critical thinking, literacy, numeracy and inquiry: Literacy is more than reading and writing. Its definition is constantly evolving and by today’s standard increasingly needs more sophisticated skills. It is the entire set of skills that allow a person to critically comprehend, analyze, generate and process information in all its forms, and then communicate it meaningfully to others. Every subject is responsible for enhancing students’ literacy, including mathematical literacy (numeracy). Students learn to inquiry deeply and think critically at all times, use relevant terminology, and conduct their own research. They will form opinions backed by logical evidence, detect bias, uncover implied meanings, and take big picture perspectives. With numeracy, students learn to not only perform mathematical operations but also understand their significance, application, and hidden biases.
  • School library: A library provides access to resources and also allows students to develop skills in research. COS does not have a library in the conventional sense but we do provide information to students on how to access information they need, find useful texts or other media, and use electronic tools of research. Consult Additional Resources for free online libraries. The course occasionally links to 3rd party resources in lesson content where relevant.
  • Information and communications technology (ICT): By use the COS online learning platform, students will naturally develop transferable skills relating to ICT. Students will learn to use various electronic tools to communicate, cooperate, and conduct research. Students will also be made aware of pitfalls and potential abuse in using the Internet or other electronic tools.
  • Education and career/life planning: As online students progress through online courses, teachers are available to help the student prepare for employment in a number of diverse areas. With the help of teachers, students will learn to set and achieve goals and will gain experience in making meaningful decisions concerning career choices. The skills, knowledge and creativity that students acquire through this online course are essential for a wide range of careers. Students will learn about related careers at specific points in the lesson content.
  • Health and Safety: Because the school operates in an online environment, there are fewer physical health and safety risks for students, especially when doing lab experiments, which are generally virtual. However, student should be careful not to spend excessive amounts of time in front of the computer with breaks, and take steps to login from a secure environment to avoid electronic malware or losing access.
  • Ethics: Canada Online School courses provide varied opportunities for students to learn about ethical issues and to explore the role of ethics in both public and personal decision making. During the inquiry process, students may need to make ethical judgements when evaluating evidence and positions on various issues, and when drawing their own conclusions about issues, developments, and events. Teachers may need to help students in determining appropriate factors to consider when making such judgements. In addition, it is crucial that Canada Online School teachers provide support and supervision to students throughout the inquiry process, ensuring that students engaged in an inquiry are aware of potential ethical concerns and address them in acceptable ways. Teachers at Canada Online School will ensure that they thoroughly address the issue of plagiarism with students. In a digital world in which there is easy access to abundant information, it is very easy to copy the words of others and present them as one’s own. Students need to be reminded, even at the secondary level, of the ethical issues surrounding plagiarism, and the consequences of plagiarism should be clearly discussed before students engage in an inquiry. It is important to discuss not only dishonest plagiarism but also more negligent plagiarism instances. Students often struggle to find a balance between writing in their own voice and acknowledging the work of others in the field. Merely telling students not to plagiarize, and admonishing those who do, is not enough. The skill of writing in one’s own voice, while appropriately acknowledging the work of others, must be explicitly taught to all Canada Online School courses. Using accepted forms of documentation to acknowledge sources is a specific expectation within the inquiry and skill development strand for each course. In this math course, students may also learn about the ethics of statistical reporting.

Additional Resources

For additional resources, students can consult the following: