Curriculum Overview · Ontario Ministry of Education

📋 MDM4U Curriculum Overview

Mathematics of Data Management, Grade 12 University Preparation

Aligned with The Ontario Curriculum, Grades 11 and 12: Mathematics (2007 Revised) · Growing Success (2010)

1. Course Identification

Course Code
MDM4U
Course Title
Mathematics of Data Management
Grade / Type
12 / University (U)
Credit Value
1.0
Scheduled Hours
110
Prerequisite
MCR3U or MCF3M (Grade 11 Functions)
Curriculum Document
2007 Revised
Policy Framework
Growing Success (2010)

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.

2. Strands & Expectations

Strand A — Counting and Probability

Overall Expectations: students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event; and demonstrate an understanding of the role of data in statistical studies.

Key Specific Expectations

  • A1.1 Recognize and describe how probabilities are used to represent the likelihood of a result of an experiment (theoretical, empirical, subjective).
  • A1.2 Describe a sample space as the set of all possible outcomes of an experiment; distinguish between a simple event and a compound event.
  • A1.3 Determine the theoretical probability \( P(A) = \dfrac{n(A)}{n(S)} \) for equally likely outcomes; recognize the additive principle for mutually exclusive events.
  • A1.4 Determine the probability of a compound event using a Venn diagram or the inclusion–exclusion identity \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).
  • A2.1 Solve problems using the additive and multiplicative counting principles.
  • A2.2 Solve problems using factorial notation, including \( P(n,r) = \dfrac{n!}{(n-r)!} \) and identical-item arrangements \( \dfrac{n!}{a!\,b!\cdots} \).
  • A2.3 Solve problems using \( C(n,r) = \binom{n}{r} = \dfrac{n!}{r!(n-r)!} \), Pascal's triangle, and the binomial theorem.
  • A2.4 Solve probability problems involving combinations of events using counting techniques.
  • A3.1 Recognize and describe a discrete random variable; tabulate its probability distribution and verify \( \sum P(X=x) = 1 \).
  • A3.2 Compute the expected value \( E(X) = \sum x_i \, P(X=x_i) \) and apply it to fair-game and decision-making problems.

Strand B — Probability Distributions

Overall Expectations: students will demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, and connect them to real-world applications; demonstrate an understanding of the normal distribution and apply it to model continuous data.

Key Specific Expectations

  • B1.1 Recognize conditions for a binomial distribution and compute \( P(X=k) = \binom{n}{k} p^k (1-p)^{n-k} \); state the mean \( \mu = np \) and standard deviation \( \sigma = \sqrt{np(1-p)} \).
  • B1.2 Recognize conditions for a geometric distribution and compute \( P(X=k) = (1-p)^{k-1} p \); state the mean \( \mu = \tfrac{1}{p} \).
  • B1.3 Recognize conditions for a hypergeometric distribution and compute \( P(X=k) = \dfrac{\binom{r}{k}\binom{N-r}{n-k}}{\binom{N}{n}} \).
  • B1.4 Identify which distribution (binomial, geometric, hypergeometric) models a given experiment.
  • B1.5 Recognize the properties of a normal curve (symmetric, unimodal, bell-shaped, total area 1) and apply the empirical (68–95–99.7) rule.
  • B1.6 Standardize a normal random variable using \( z = \dfrac{x - \mu}{\sigma} \); compute probabilities using a standard-normal table.
  • B1.7 Recognize when the normal distribution can approximate the binomial distribution (when \( np \ge 5 \) and \( n(1-p) \ge 5 \)) and apply the continuity correction.

Strand C — Organization of Data for Analysis

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

Key Specific Expectations

  • C1.1 Recognize and describe the role of data in statistical studies; distinguish between primary and secondary, quantitative and qualitative, continuous and discrete data.
  • C1.2 Describe sampling techniques (simple random, stratified, systematic, cluster, voluntary-response, convenience) and identify potential sources of bias.
  • C1.3 Describe principles of primary data collection (representativeness, validity, reliability, ethics) and design a questionnaire/experiment.
  • C2.1 Compute and interpret measures of central tendency (mean, median, mode) and recognize the effect of outliers and skew.
  • C2.2 Compute and interpret measures of spread (range, IQR, standard deviation, variance) for ungrouped and grouped data.
  • C2.3 Construct and interpret frequency tables, histograms, ogives, and box-and-whisker plots; identify outliers using the 1.5 × IQR rule.
  • C2.4 Recognize and describe the shape of a distribution (symmetric, skewed, bimodal) and explain how it relates to the relationship between mean and median.
  • C3.1 Construct and interpret scatter plots; classify the form, direction, and strength of a linear relationship.
  • C3.2 Compute and interpret the Pearson correlation coefficient \( r \in [-1, 1] \); distinguish correlation from causation.
  • C3.3 Determine the equation of the line of best fit \( \hat{y} = b_0 + b_1 x \) using least squares; interpret slope and intercept in context.
  • C3.4 Compute residuals; recognize when a non-linear model would fit better; interpret \( r^2 \) as the proportion of variability explained.

Strand D — Culminating Data Management Investigation

Overall Expectations: 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; communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.

Key Specific Expectations

  • D1.1 Pose a significant problem of personal interest that requires the organization and analysis of a large amount of data.
  • D1.2 Design a plan to investigate the problem, identifying the variables, the data needed, and the methods of data collection or sources of secondary data.
  • D2.1 Carry out the investigation: collect/find data, organize and analyse it using appropriate techniques (descriptive statistics, two-variable analysis, probability models).
  • D2.2 Interpret, analyse, and summarize the results of the investigation; assess the limitations of the data and the conclusions drawn.
  • D3.1 Communicate the findings of the investigation effectively in a written report and an oral presentation, using appropriate vocabulary, notation, and visuals.
  • D3.2 Critique the investigations of others, including identification of strengths, limitations, and possible extensions.

3. Mathematical Processes

The seven mathematical processes are integrated throughout the course. Students engage in:

Problem SolvingDevelop, select, apply, compare, and adapt strategies to investigate situations and solve data-management problems.
Reasoning & ProvingDevelop and apply reasoning skills to make and investigate conjectures (e.g., independence, correlation vs causation) and to construct/defend arguments.
ReflectingDemonstrate that they are reflecting on and monitoring their thinking to refine arguments and explanations.
Selecting Tools & StrategiesUse a variety of tools (Desmos, GeoGebra, spreadsheets, statistical software, the standard-normal table, scientific calculator).
ConnectingMake connections among counting, probability, and statistics, and between this course and other disciplines (sciences, social sciences, business).
RepresentingCreate numeric, graphical, algebraic, tabular, and verbal representations and translate between them.
CommunicatingCommunicate mathematical thinking orally, visually, and in writing using appropriate vocabulary, notation, and conventions.

4. Achievement Chart

Per Growing Success (2010), each of the four categories carries equal weight (25%) within both term work and the final evaluation.

Knowledge & Understanding
25%

Subject-specific content (knowledge) and comprehension of meaning and significance (understanding). Includes definitions, formulas, computing probabilities, factorials, z-scores, and basic statistics.

Thinking & Inquiry
25%

Use of critical and creative thinking — choosing the correct distribution, planning the culminating investigation, justifying conclusions, identifying bias.

Communication
25%

Conveying meaning through various forms — explanations, oral and written reports, mathematical conventions, vocabulary, and clearly labelled graphs and tables.

Application
25%

Use of knowledge and skills to make connections within and between contexts — real-world data, modelling, transfer of probability and statistical concepts to new situations.

Levels of achievement: Level 4 (80–100%, exceeds standard) · Level 3 (70–79%, provincial standard) · Level 2 (60–69%, approaching) · Level 1 (50–59%, limited) · R (below 50%, insufficient).

5. Evaluation Policy

Final mark = 70% Term Work + 30% Final Evaluation, per Growing Success (2010).

ComponentWeightDescription
Unit Tests (Ch 1–8, Assessment OF Learning)45%Eight chapter unit tests covering all four achievement categories.
Quizzes & Diagnostics (Assessment FOR/AS Learning)10%Formative checks; lowest score dropped.
Performance Tasks & Mini-Investigations10%Modelling, simulations, communication of process.
Pre-Culminating Performance Task5%Cross-strand application due before the final evaluation window.
Subtotal — Term Work70%Reported on the Provincial Report Card
Culminating Data-Management Investigation15%Independent inquiry — research question, data, analysis, written report, and oral presentation.
Final Exam (Ch 1–8 comprehensive, 3 hours, 100 marks)15%Equally weighted across K/U, Thinking, Communication, Application (25 marks each).
Final Course Mark100%One credit toward the OSSD; eligible university prerequisite.
Note on the Culminating Investigation: The Culminating Data-Management Investigation (Strand D) contributes 15% of the 30% Final Evaluation. The remaining 15% is the comprehensive written final exam covering Chapters 1–8. The Investigation is mandatory for the granting of a credit and demonstrates synthesis across all three other strands.

6. Chapter ↔ Strand Mapping

ChapterTitlePrimary StrandSpecific Expectations Addressed
Ch 1Counting & Sample SpacesAA1.1–A1.4, A2.1
Ch 2PermutationsAA2.1, A2.2
Ch 3CombinationsAA2.3, A2.4
Ch 4Probability — Theoretical & EmpiricalAA1.1–A1.4, A3.1, A3.2
Ch 5Discrete Probability DistributionsBB1.1–B1.4
Ch 6The Normal DistributionBB1.5–B1.7
Ch 7Statistics & SamplingCC1.1–C1.3, C2.1–C2.4
Ch 8Correlation, Regression & Culminating InvestigationC, DC3.1–C3.4, D1–D3
← Back to MDM4U Course Page