What MDM4U focuses on

MDM4U broadens students’ understanding of mathematics as it relates to organizing, analysing, and interpreting data. Students study probability, statistics, data collection, and statistical analysis.

How students apply learning

Students solve probability and statistics problems, analyse large amounts of information, and complete a culminating investigation that integrates the major concepts and skills developed throughout the course.

Counting techniques and event probability

• Identify sample spaces and events in probability experiments.
• Calculate the probability of single events.
• Solve problems involving combinations of events.
• Apply addition and multiplication principles of counting.
• Use permutations to solve counting and probability problems.
• Use combinations to determine the probability of events.
• Apply counting methods to practical and real-world situations.

Discrete, continuous, and normal distributions

• Represent discrete probability distributions numerically.
• Represent discrete probability distributions graphically and algebraically.
• Determine expected values for discrete probability distributions.
• Solve problems involving discrete distributions.
• Develop an understanding of continuous probability distributions.
• Connect continuous and discrete probability distributions.
• Determine and interpret standard deviation.
• Describe the key features of the normal distribution.
• Solve problems involving normal distributions.

Data types, sampling, and primary data collection

• Explain the role of data in statistical investigations.
• Recognize variability within data sets.
• Distinguish between different types of data.
• Describe the characteristics of a representative sample.
• Compare common sampling techniques.
• Identify possible sources of sampling bias.
• Apply principles of primary data collection.
• Collect and organize data to investigate a statistical question.
• Evaluate the reliability and relevance of collected data.

One-variable and two-variable data

• Analyse one-variable data using numerical summaries.
• Represent one-variable data using appropriate graphs.
• Interpret measures of central tendency and spread.
• Draw conclusions from one-variable data.
• Analyse two-variable data using numerical summaries.
• Represent two-variable data graphically.
• Use algebraic models to describe relationships between variables.
• Interpret correlation and trends in data.
• Examine the use of data management in media and advertising.
• Explore statistical applications in different occupations.

Designing and communicating a statistical investigation

• Select a meaningful topic or statistical question.
• Develop a clear investigation plan.
• Select appropriate data-collection and sampling methods.
• Collect, organize, and analyse relevant data.
• Apply probability and statistical concepts from the course.
• Interpret results and draw supported conclusions.
• Communicate findings using written, numerical, and graphical representations.
• Present the completed investigation clearly and effectively.
• Provide constructive feedback on the investigations of others.

How grades are calculated

• 70% — Course work completed throughout the course.
• 30% — Final evaluation, including the culminating investigation and final assessment.
• Knowledge & Understanding: 20%
• Thinking and Inquiry: 20%
• Application: 40%
• Communication: 20%
• Evidence of learning is gathered through products, observations, and conversations.
• Assessment tools may include quizzes, tests, worksheets, investigations, presentations, projects, checklists, and rubrics.

Main course resources

• Advanced Functions 12 — McGraw-Hill Ryerson, 2008.
• Advanced Functions — Nelson Education, 2008.
• Teacher-prepared notes, examples, worksheets, and statistical investigations.
• Spreadsheet software, graphing technology, and statistical tools.
• Selected online mathematics, probability, and statistics resources.

Important supports

Program planning includes varied instructional approaches, accommodations for students with special education needs, environmental education, critical thinking, technology use, career education, literacy, inquiry skills, and academic honesty.

Students learn through direct instruction, discussion, worksheets, investigations, independent work, collaborative activities, presentations, problem solving, technology-supported analysis, and teacher feedback.

Learning activities emphasize accurate interpretation of data, responsible use of information, clear mathematical communication, and real-world applications of probability and statistics.