MDM4U – Data Management – Grade 12

The MDM4U online course is designed to broaden students’ mathematical knowledge with an emphasis on data application and analysis. Through MDM4U, learners engage in organizing and analyzing extensive datasets, tackling problems with probability and statistics, and conducting a comprehensive culminating investigation that brings together statistical concepts and skills. This exploration not only strengthens their mathematical processes essential for senior mathematics success but also prepares them for university programs in business, social sciences, and humanities. MDM4U stands out for its practical approach to mathematics, an important course for students aiming to navigate the data-centric areas of higher education and professional careers, bridging the gap between theoretical math and its real-world applications.

Course Type: University Preparation

Credit: 1.0

Ontario Curriculum: Grade 12 Mathematics – Data Management

MDM4U Prerequisite: MCR3U – Functions, Grade 11 or MCF3M – Functions and Applications, Grade 11

NCAA Approved Course

The MDM4U online course is designed to broaden students’ mathematical knowledge with an emphasis on data application and analysis. Through MDM4U, learners engage in organizing and analyzing extensive datasets, tackling problems with probability and statistics, and conducting a comprehensive culminating investigation that brings together statistical concepts and skills. This exploration not only strengthens their mathematical processes essential for senior mathematics success but also prepares them for university programs in business, social sciences, and humanities. MDM4U stands out for its practical approach to mathematics, an important course for students aiming to navigate the data-centric areas of higher education and professional careers, bridging the gap between theoretical math and its real-world applications.

MDM4U Course Outline

Unit 1- Counting and Probability
In this unit students will solve probability problems involving discrete sample spaces and problems using
counting principles.
Unit 2 – Probability Distribution
In this unit students will explore and understand probability distributions for discrete random and for
continuous random variables
Unit 3 – Organization of Data for Analysis
In this unit students will explore and understand data concept and collect and organize data.
Unit 4 – Statistical Analysis
In this unit students will analyse one-variable data and two-variable data. In addition, students will evaluate
the validity of the study.
Unit 5 – Culminating Data Management Investigation
In this unit students will design and carry out a culminating investigation. In addition students will be
presenting and critiquing the culminating investigation.

Unit 1
By the end of this course, students will solve problems involving the probability of an event or a combination
of events for discrete sample spaces. Students will solve problems involving the application of permutations
and combinations to determine the probability of an event.

Unit 2
By the end of this course, students will identify a broad range of options for present and future learning,
work, and community involvement. Students will 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. Students will 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.

Unit 3
By the end of this course, students will demonstrate an understanding of the role of data in statistical studies
and the variability inherent in data, and distinguish different types of data. Students will 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.

Unit 4
By the end of this course, students will analyse, interpret, and draw conclusions from one-variable data using
numerical and graphical summaries. Students will analyse, interpret, and draw conclusions from two-variable
data using numerical, graphical, and algebraic summaries; Students will demonstrate an understanding of the
applications of data management used by the media and the advertising industry and in various occupations.

Unit 5
By the end of this course, students will 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. Students
will communicate the findings of a culminating investigation.

In this course, students will experience the following activities.

Presentations with embedded videos are utilized to outline concepts, explain theory with the use of
examples and practice questions, and incorporate multi-media opportunities for students to learn more (e.g.
online simulations, quizzes, etc.).

End of unit conversations and Poodlls are opportunities for students to express their ideas, problem solving,
and thought processes with a teacher who provides timely feedback.

Reflection is an opportunity for students to look back at concepts and theories with new eyes, to relate
theory to practice, and to align learning with their own values and beliefs.

Discussions with the instructor are facilitated through video conferencing, discussing the concepts and skills
being studied. This enables two-way communication between the student and the instructor, to share ideas
and ask questions in dialogue. This also helps to build a relationship between the student and instructor.

Instructor demonstrations (research skills, etc.) are opportunities for the instructor to lead a student through
a concept or skill through video conferencing, videos, or emailing with the student.

Discussion forums are an opportunity for students to summarize and share their ideas and perspectives with
their peers, which deepens understanding through expression. It also provides an opportunity for
peer-to-peer feedback.

Practical extension and application of knowledge are integrated throughout the course. The goal is to help
students make connections between what they learn in the classroom and how they understand and relate to
the world around them and their own lives. Learning becomes a dynamic opportunity for students to be
more aware that their learning is all around them and enable them to create more meaning in their lives.

Individual activities/assignments assessments are completed individually at a student’s own pace and are
intended to expand and consolidate the learning in each lesson. Individual activities allow the teacher to
accommodate interests and needs and to assess the progress of individual students. For this reason, students
are encouraged to discuss IEPs (Individual Education Plans) with their teacher and to ask to modify
assessments if they have a unique interest that they feel could be pursued in the assessment. The teacher
plays an important role in supporting these activities by providing ongoing feedback to students, both orally
and in writing.

Research is an opportunity to apply inquiry skills to a practical problem or question. Students perform
research to gather information, evaluate quality sources, analyse findings, evaluate their analysis, and
synthesize their findings into conclusions. Throughout, students apply both creative thinking and critical
thinking. New questions are also developed to further learning.

Writing as a learning tool helps students to think critically about course material while grasping, organizing,
and integrating prior knowledge with new concepts. Good communication skills are important both in and
out of the classroom.

Virtual simulations are interactive websites that provide students with an opportunity to ask questions, relate
variables, and examine relationships.

Diagrams are visual representations of mathematical ideas and concepts. They provide another perspective
to organize ideas. Visuals are thought to promote cognitive plasticity – meaning, they can help us change our
minds or help us to remember an idea.

Graphs and charts are visual representations of math concepts and analysis. This helps us to see the
relationships within and between sets of data.

Tables involve organizing information in terms of categories (rows and columns). This helps us to understand
the relationships between ideas and data, as well as highlight trends.

Practice problems provide students with a scenario/problem to solve by applying concepts and skills learned
in a context. This helps students to understand the relevance of their learning.

As summarized in Growing Success 2010, 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. 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, 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. All curriculum expectations must be accounted for in instruction, but evaluation focuses on students’ achievement of the overall expectations. A students’ achievement of the overall expectations is evaluated on the basis of his or her achievement of related specific expectations. Teachers will use their professional judgement to determine which specific expectations should be used to evaluate achievement of overall expectations, and which ones will be covered in instruction and assessment but not necessarily evaluated.

In order to ensure that assessment and evaluation are valid and reliable, and that they lead to the improvement of student learning, teachers must use assessment and evaluation strategies that:

● Address both what students learn and how well they learn;
● Are based both on the categories of knowledge and skills and on the achievement level descriptions given in the achievement chart
● Are varied in nature, administered over a period of time, and designed to provide opportunities for students to demonstrate the full range of their learning;
● Are appropriate for the learning activities used, the purposes of instruction, and the needs and experiences of the students;
● Are fair to all students;
● Accommodate students with special education needs, consistent with the strategies outlined in their Individual Education Plan;
● Accommodate the needs of students who are learning the language of instruction;
● Ensure that each student is given clear directions for improvement;
● Promote students’ ability to assess their own learning and to set specific goals
● Include the use of samples of students’ work that provide evidence of their achievement;
● Are communicated clearly to students and parents at the beginning of the school year and at other appropriate points throughout the school year.

The final grade will be determined as follows:

❑ 70% of the grade will be based on evaluation 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 will be given to more recent
evidence of achievement.

❑ 30% of the grade will be based on a final evaluation administered at or towards the end of
the course. This evaluation will be based on evidence from one or a combination of the
following: an examination, a performance, and/or another method of evaluation suitable to
the course content. The final evaluation allows the student an opportunity to demonstrate
comprehensive achievement of the overall expectations for the course.

(Growing Success: Assessment, Evaluation and Reporting in Ontario Schools. Ontario
Ministry of Education Publication, 2010 p.41)

All students can succeed. Some students are able, with certain accommodations, to participate in the regular course curriculum and to demonstrate learning independently. Accommodations allow access to the course without any changes to the knowledge and skills the student is expected to demonstrate. The accommodations required to facilitate the student’s learning can be identified by the teacher, but recommendations from a School Board generated Individual Education Plan (IEP) if available can also be consulted. Instruction based on principles of universal design and differentiated instruction focuses on the provision of accommodations to meet the diverse needs of learners.

Examples of accommodations (but not limited to) include:

• Adjustment and or extension of time required to complete assignments or summative tasks
• Providing alternative assignments or summative tasks
• Use of scribes and/or other assistive technologies
• Simplifying the language of instruction

To learn more go to our Individual Education Plan (IEP) page.

To learn more about this course including tests and exams please visit our FAQ page