MDM4U1 (Grade 12 Data Management)

About MDM4U1

MDM4U1 is a grade 12 university preparation Math course, "Mathematics of Data Management," which focuses on the studies of the logic of uncertainty and the art of learning from data.  To practice data management in situations under uncertain conditions, students would first need to identify a question that they want to investigate.  Then, they would need to design and create a statistical experiment or a biased-free survey and then define its scope (i.e., who is their target audience).  After that, they would need to select a sampling method (e.g., simple random sampling, systematic sampling, stratified sampling, cluster sampling, etc.) and collect sample data from the population.  Next, they would analyze the collected data (e.g., calculating the sample mean and standard deviation) and estimate the population statistic(s) (e.g., the confidence interval of the population mean or true proportion) from the sample statistic(s).  In the end, they would make a general conclusion or inference to their question and present their findings.  

This data management course, MDM4U1, covers two closely related concepts: probability and statistics.  Probability refers to the likelihood, or chance, that an event occurs, whereas statistics refers to the art of learning from data, which consists of collecting, analyzing, interpreting, and presenting data so that a general conclusion or inference from the data can be made.  These two concepts are, in fact, inverses of each other.  For probability, we do not have access to the data, and we use the concepts of probability to estimate what kinds of data will likely occur in a situation under uncertain conditions.  On the other hand, for statistics, we have access to the data from either the statistical experiment that we conduct or the survey that we design, give out, and collect, and we are trying to learn from the data and make a general conclusion or inference from the data.

Here are the units of learning in the MDM4U1 course:

• Unit 1: Introduction to Probability

• Unit 2: Permutations

• Unit 3: Combinations

• Unit 4: Probability Distributions for Discrete Variables

• Unit 5: Organization of Data for Analysis

• Unit 6: One-Variable Data Analysis

• Unit 7: Probability Distributions for Continuous Variables

• Unit 8: Two-Variable Data Analysis

In some units of learning in this MDM4U1 course, students will learn how to use Google Sheets (or other spreadsheet programs) to simulate a random experiment with measurable outcomes/properties.  In this type of random experiment, the occurrences of outcomes involve chances and cannot be predicted with certainty.  Examples of such random experiments are the flipping of a fair coin, the tossing of two unloaded dice, and the spinning of a spinner.  

Students will also learn how to use Google Sheets to calculate the sum of entries in a row or along a diagonal in Pascal's triangle and to perform statistical analysis (e.g., calculating mean, median, mode, first and third quartiles, and interquartile range, estimating a line-of-best-fit, and creating a residual plot) on a given set of data that can be downloaded from the website of Statistics Canada or other sources of data.  Furthermore, the students will get hands-on experience in designing a bias-free survey using Google Forms, selecting a sampling method, collecting data based on the selected sampling method, analyzing the data, and presenting the results.

Student Feedback

Mr. Ho's grade 12 Math students said: "Data is the best" and "We will ace data!"

Results of a Survey on Mr. Ho's Teaching Performance

Mr. Ho's MDM4U1 students (i.e., Audrey Senthivel-Davidson, Sophia Faraone, Bowen Zhu, Jayden Breslow-Bardell, and Owen Sabol) conducted a survey that asked a sample of his students from his morning and afternoon MDM4U1 classes how they felt about Mr. Ho's teaching style (whiteboards and thinking classroom) and assessment practice in semester 1 of the 2023-24 school year.  The sampling method that they used was stratified sampling with two strata, one consisting of students in the morning class and the other consisting of students in the afternoon class.  The results are summarized in the following graphs:

Student-Centred Learning: Building Thinking Classrooms

Here are the photos of Mr. Ho's students actively engaged in the in-class activities in the MDM4U1 course:

Technology-Based Learning: Google Sheets Activities
Here are photos of students working in groups and using Google Sheets to simulate experiments in which the occurrences of outcomes involve chances and cannot be predicted with certainty:

Problem-Based Learning (Real-World Problems): COVID-19 & Drug Testing + Social Injustice

Here is a video showing Mr. Ho's students who were engaged in activities that connect data management to social injustice.  This lesson began with a real-life example related to COVID-19.  Mr. Ho then introduced the concept of Bayes' rule, as an enrichment topic, to his students and applied it to solve a COVID-19-related problem.   Then, his students worked in groups to solve a conditional probability problem related to drug testing.  After that, his students used their results to discuss how drug testing might bring social injustice to people in a visible minority group in some countries.  Every student in Mr. Ho's class was engaged, and learning happened throughout the entire class.

Game-Based Learning: Poker Games

Mr. Ho's student teacher, Mr. Eric Huang, taught the MDM4U1 students how to calculate the probabilities of different types of poker hands on Wednesday, October 25th, 2023.  Everyone was having fun playing the poker games in the class and calculating probabilities.

Inquiry-Based Learning: Investigation of a Topic Through Designing a Survey

Here is a video showing Mr. Ho's students exploring and investigating a topic of their choice, designing their own survey using Google Forms, collecting data, analyzing the results, making a conclusion about their topic, and presenting their work in a report:

Kinesthetic Learning: Percentile of Your Height

Here is a video showing Mr. Ho's students measuring their heights and calculating the percentile of their heights:

Students' Work at the End of Mr. Ho's Math Fusion Classroom

Here is a video showing students' work at the end of Mr. Ho's Math Fusion Classroom:

Mr. Ho's MDM4U1 students worked on a culminating project at the end of the course.  One requirement of this culminating project was to have them design and create a game that involves chance.  They needed to calculate the theoretical and experimental winning (or losing) probabilities for their games, and there needed to be at least 10 players to play their games.  Here are short video clips showcasing their work.