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; apply counting techniques, probability, and statistics in modelling and solving problems; and carry out a data management investigation that integrates the expectations of the course and encourages perseverance and independence. Students planning to pursue university programs in business, the social sciences, or the humanities will find this course of particular interest.
|Unit Titles and Descriptions||Time Allocated|
|Tools for Data Management|
Data Management comprises all the disciplines related to managing data as a valuable resource. Data does not have meaning unless we are able to use it, make decisions and sound judgment based on it. We do this by using tools for managing the data. In this course we will be using spreadsheets and graphing software to perform complex calculations and link, search, sort and graph data. Among other assignments students are introduced in this unit to the Statistics Canada website where they will learn methods of data retrieval and the creation of graphs using CANSIM. This course involves a data management investigative (DMI) that stretches over the first four units. In this unit students will formulate and submit their hypothesis.
To summarize data and recognize the trends, we use tables and graphs. In this unit 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, and collect and organize data to solve a problem; demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations. The DMI continues in this unit and students use statistical skills to appropriately collect and record information.
|Statistics of One Variable|
This unit will focus on the analysis and presentation of one-variable data. Students will process raw data and develop the skills to summarize it in terms of central tendency, spread and distribution. Students will analyze, interpret, and draw conclusions from one-variable data using numerical and graphical summaries and explore methods of describing a single piece of data in the context of a wider data set. Students use a variety of different software to analyze the presentation of data that has been collected and processed by others. They develop the critical thinking skills necessary to interpret and assess the validity of secondary data and conclusions drawn from it, maintaining an awareness of the possibility of bias and misrepresentation, either deliberate or accidental. Students submit the third part of their DMI where they process and analyse their individual data sets.
|Statistics of Two Variables|
Two-variable statistics are the basis for many decisions personally and as a society. Although most two variable statistical tests are beyond the scope of secondary school math, this unit will examine some of the basic topics in two-variable statistics. Two-variable statistics provide methods for detecting relationships between variables and for developing mathematics of these relationships. The visual pattern in a graph or plot can often reveal the nature of the relationship between two variables. In this unit students will analyse, interpret, and draw conclusions from two-variable data using numerical, graphical, and algebraic summaries. Students complete the last part of their DMI where they perform analysis of the relationship between the sets of their information, and use critical thinking skills to formulate a final conclusion relating to their initial hypothesis.
Combinatorics is the branch of mathematics dealing with ideas and methods for counting, especially in complex situations. The techniques and mathematical logic for counting possible arrangements or outcomes are useful for a wide variety of applications. A computer programmer writing software for a game or industrial process would use these techniques, as would a basketball coach planning potential line-ups for a game, or a school board trying to make the most efficient use of its buses. Students will investigate the concepts of combinations and permutations. They will consider situations in which each should be used, and develop the skills to be able to determine which is most appropriate.
Probability was first studied mathematically in the 17th century when Pierre de Fermat and Blaise Pascal attempted to analyze problems associated with gambling. Modern probability theory grew from their correspondence. In this unit 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; 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 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; 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.
|The Normal Distribution|
Students will gain an understanding of continuous distributions, and will investigate different shapes of distribution, considering situations that may generate them. Students will explore the normal distribution in detail, and investigate its many applications. They will make comparisons between the normal and binomial distributions. They will form an understanding of the conditions in which they might be used interchangeably, and develop the skills that will allow them to decide how and when to make use of these properties.
This is a proctored exam worth 30% of your final grade.
Resources required by the student:
Note: This course is entirely online and does not require or rely on any textbook.
- A scanner, smart phone camera, or similar device to digitize handwritten or hand-drawn work,
- A non-programmable, non-graphing, scientific calculator.
- Spreadsheet software (e.g. Microsoft ExcelTM, Mac NumbersTM, or equivalent)
Overall Curriculum Expectations
|A. Counting and Probability|
|A1||solve problems involving the probability of an event or a combination of events for discrete sample spaces;|
|A2||solve problems involving the application of permutations and combinations to determine the probability of an event.|
|B. Probability and Distributions|
|B1||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;|
|B2||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.|
|C. Organization of Data for Analysis|
|C1||demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data;|
|C2||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.|
|D. Statistical Analysis|
|D1||analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries;|
|D2||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.|
|D3||demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.|
|E. Culminating Data Management Investigation|
|E1||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;|
|E2||communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.|
Teaching and Learning Strategies:
The over-riding aim of this course is to help students use the language of mathematics skillfully, confidently and flexibly, a wide variety of instructional strategies are used to provide learning opportunities to accommodate a variety of learning styles, interests, and ability levels. The following mathematical processes are used throughout the course as strategies for teaching and learning the concepts presented:
- Problem solving: This course scaffolds learning by building off of skills learned in each unit. Students will work on a single project across multiple units, applying what they have learned in each unit to further analyze the data they have collected. The course guides students toward recognizing opportunities to apply knowledge they have gained to solve problems.
- Representing: Through the use of examples, practice problems, and solution videos, the course models various ways to demonstrate understanding, poses questions that require students to use different representations as they are working at each level of conceptual development – concrete, visual or symbolic, and allows individual students the time they need to solidify their understanding at each conceptual stage.
- Connecting: Students will connect concepts learned in this course to real-world applications of statistics and probability through investigations and assignments.
- Self-Assessment: Through the use of interactive activities (e.g. multiple choice quizzes, and drag-and-drop activities) students receive instantaneous feedback and are able to self-assess their understanding of concepts.
Assessment, Evaluation and Reporting Strategies of Student Performance:
Our theory of assessment and evaluation follows the Ministry of Education’s Growing Success document, and it is our firm belief that doing so is in the best interests of students. We seek to design assessment in such a way as to make it possible to gather and show evidence of learning in a variety of ways to gradually release responsibility to the students, and to give multiple and varied opportunities to reflect on learning and receive detailed feedback.
Growing Success articulates the vision the Ministry has for the purpose and structure of assessment and evaluation techniques. There are seven fundamental principles that ensure best practices and procedures of assessment and evaluation by Virtual High School teachers. VHS assessments and evaluations,
- are fair, transparent, and equitable for all students;
- support all students, including those with special education needs, those who are learning the language of instruction (English or French), and those who are First Nation, Métis, or Inuit;
- are carefully planned to relate to the curriculum expectations and learning goals and, as much as possible, to the interests, learning styles and preferences, needs, and experiences of all students;
- are communicated clearly to students and parents at the beginning of the course and at other points throughout the school year or course;
- are ongoing, varied in nature, and administered over a period of time to provide multiple opportunities for students to demonstrate the full range of their learning;
- provide ongoing descriptive feedback that is clear, specific, meaningful, and timely to support improved learning and achievement;
- develop students’ self-assessment skills to enable them to assess their own learning, set specific goals, and plan next steps for their learning.
The Final Grade:
The evaluation for this course is based on the student’s achievement of curriculum expectations and the demonstrated skills required for effective learning. The final percentage grade represents the quality of the student’s overall achievement of the expectations for the course and reflects the corresponding level of achievement as described in the achievement chart for the discipline. A credit is granted and recorded for this course if the student’s grade is 50% or higher. The final grade will be determined as follows:
- 70% of the grade will be based upon evaluations conducted throughout the course. This portion of the grade will 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 final evaluations administered at the end of the course. The final assessment may be a final exam, a final project, or a combination of both an exam and a project.
The Report Card:
Student achievement will be communicated formally to students via an official report card. Report cards are issued at the midterm point in the course, as well as upon completion of the course. Each report card will focus on two distinct, but related aspects of student achievement. First, the achievement of curriculum expectations is reported as a percentage grade. Additionally, the course median is reported as a percentage. The teacher will also provide written comments concerning the student’s strengths, areas for improvement, and next steps. Second, the learning skills are reported as a letter grade, representing one of four levels of accomplishment. The report card also indicates whether an OSSD credit has been earned. Upon completion of a course, VHS will send a copy of the report card back to the student’s home school (if in Ontario) where the course will be added to the ongoing list of courses on the student’s Ontario Student Transcript. The report card will also be sent to the student’s home address.
Program Planning Considerations:
Teachers who are planning a program in this subject will make an effort to take into account considerations for program planning that align with the Ontario Ministry of Education policy and initiatives in a number of important areas.
Planning Programs for Students with Special Education Needs, Program Considerations for, English Language Learners, Environmental Education, Healthy Relationships, Equity and, Inclusive Education, Financial Literacy Education, Literacy, Mathematical Literacy, and Inquiry Skills, Critical Thinking and Critical Literacy, The Role of the School Library, The Role of Information and Communications Technology, The Ontario Skills Passport: Making Learning Relevant and Building Skills, Education and Career/Life Planning, Cooperative Education and Other Forms of Experiential Learning, Planning Program Pathways and Programs Leading to a Specialist High Skills Major, Health and Safety, Ethics.
|1. Tools for Data Management|
|Data Analysis Workbook||00:00:00|
|Data Management- A1 Spreadsheet||10, 00:00|
|Data Management- A2||10, 00:00|
|Data Management- A3||10, 00:00|
|MDM4U Test 1||02:00:00|
|TEST- Databases Quiz||02:00:00|
|2. Permutations and Organized Counting|
|4.1-4.3 Organized Counting & Permutations Summary||00:00:00|
|A1- Counting Assignment||10, 00:00|
|A2- Counting Assignment||10, 00:00|
|3. Statistics of 1 Variable|
|1 Variable Data Analysis Workbook||00:00:00|
|A1- Chapter 2 Assignment||10, 00:00|
|A2- Bias in Surveys||10, 00:00|
|A3- Measures of Central Tendency Assignment||10, 00:00|
|A4- Measures of Spread Assignment||10, 00:00|
|4. Statistics of 2 Variable|
|2 Variable Data Analysis Workbook||00:00:00|
|A1- Scatter Plots and Linear Correlation Assignment||10, 00:00|
|A2- Cause and Effect Assignment||10, 00:00|
|A3- Critical Analysis Assignment||10, 00:00|
|L1 VENN DIAGRAM CONCEPTS – Class Notes||00:00:00|
|Venn Diagram – INTRO||00:00:00|
|MDM4U Chapter 5- TEST||02:00:00|
|Mutually Exclusive Events Assignments||10, 00:00|
|DV IV Assignments||10, 00:00|
|Probability Distributions TEST||02:00:00|
|7. The Normal Distribution|
|Distribution Workbook 2||00:00:00|
|A1- The Normal Distribution Assignment||10, 00:00|
|A2- Continuous Probability Distributions||10, 00:00|
|A3- Repeated Sampling and Hypothesis Testing Assignment||10, 00:00|
|A4- Confidence Intervals Assignment||10, 00:00|
|Normal Approximation to the Binomial Distribution Quiz||02:00:00|
|MDM Chapter 1||00:00:00|
|MDM Chapter 2||00:00:00|
|MDM Chapter 3||00:00:00|
|MDM Chapter 4||00:00:00|
|MDM Chapter 5||00:00:00|
|MDM Chapter 6||00:00:00|
|MDM Chapter 7||00:00:00|
|MDM Chapter 8||00:00:00|