Course Title/ Grade/ Course Type: Mathematics of Data Management, Grade 12, University Preparation
Ministry Course Code: MDM4U
Curriculum Document: The Ontario Curriculum, Grades 11 to 12, Mathematics (Revised 2007);
Prerequisite: MCR3U, Functions, Grade 11, University Preparation, or Functions and Applications, Grade 11, University/College Preparation
*If you are a current UMC High School student, please contact your advisor.
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; 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
Outline of Course Content
Unit 1: Section 1 – Permutations and Organized Counting
Throughout this unit, you will learn to solve problems that involve counting the number of outcomes in complex situations. You will learn counting techniques such as listing, tree diagrams, Venn diagrams, and Pascal’s triangle. You will also learn to apply the fundamental counting principles and permutation.
Unit 1: Section 2 – Combinations and The Binomial Theorem
In Unit 1, you used tree diagrams as a tool for counting items when the order of the items was important. This unit introduces a type of diagram that helps you organize data about groups of items when the order of the items is not important. You will also learn how to solve problems involving combinations and to distinguish between a permutation and a combination.
Unit 2: Section 1 – Introduction to Probability
In this unit you will learn basic probability calculations and apply the same concepts to counting problems, independent, dependent, mutually exclusive, and non-mutually exclusive events. You will distinguish between experimental and theoretical probability and determine the relationship between them.
Unit 2: Section 2 – Probability Distribution
This unit involves solving problems involving both dependent and independent events with continuous or discrete probability distributions. You will construct frequency and probability histograms. You will calculate expectation for probability distribution. You will also make connections between the different types of probability distributions.
Unit 3: Section 1 – Probability Distribution for Continuous Variable (MT)
In this unit, you will learn about continuous probability distributions and the role of the standard deviation. You will discover the normal distribution, z-scores and confidence intervals. You will also make connections to discrete random variables.
Unit 3: Section 2 – Organization of Data Analysis
Statistics is the science of conducting studies to collect, organize, summarize, analyze and draw conclusions from data. In this unit, you will learn about the different types of data that can be analyzed and how to go about collecting the data.
Unit 4: Section 1 – One Variable Data Analysis
In this unit, you will develop techniques for analyzing statistics using one variable. This analysis will include graphical analysis such as Box and Whisker Plots as well as mathematical techniques such as Measures of central tendency and measures of spread.
Unit 4: Section 2 – Two Variable Data Analysis
In this unit, you will continue to learn about statistics by investigating two variable statistics. You will learn how to draw conclusions about data by using concepts such as Scatter Plot, Line of Best Fit, Correlation, Residuals, linear Regression, Coefficient of Correlation and Validity of Data. You will also use technology to help in your understanding of two variable statistics.
Unit 5: Culminating Investigations
You will use the concepts you have learned about probability and statistics to design a game of chance and a statistics project. In the game of chance project, you will design a game involving numbered cubes, spinners, cards, or any other reasonable item that introduces an element of chance. You will then collect data, and then conduct analysis for the data. After the analysis is complete it will be presented in a written report and presentation. In the statistics project, you will research a set of data and then conduct analysis for the data. After the analysis is complete it will be presented in a written report and presentation.
Final Mark will be determined following percentages:
70% Determined by the evaluations conducted throughout the duration of the course:
Products – Assignments, Essays, Journals, Portfolio
Observations – Presentations
Conversations – Conferences with the Teacher
30% Final Exam and/or Final Culminating Project