Mathematics for Data Management
Grade 12, University Preparation (MDM4U)

 

Course Title : Mathematics for Data Management, Grade 12, University Preparation (MDM4U)
Course Name : Mathematics for Data Management
Course Code : MDM4U
Grade : 12
Course Type : University Preparation
Credit Value : 1.0
Prerequisite : Functions, Grade 11, University Preparation or Functions and Applications – Grade 11, University or College Preparation
Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2010 (Revised)
Course Developer: USCA Academy
Department: Mathematics
Development Date: June 2019
Most Recent Revision Date: June 2019

Course Description


 
This course extends students’ experience with functions. Students will investigate the propertiesof polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidatetheir understanding of mathematics before proceeding to any one of a variety of universityprograms.

Overall Curriculum Expectations

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.

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.

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.

D1. Analyze, interpret, and draw conclusions from one-variable data using numerical and graphical summaries;

D2. Analyze, interpret, and draw conclusions from two-variable data using numerical, graphical, and algebraic summaries;

D3. Demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations.

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.

Outline of Course Content

Unit Titles and Descriptions Time and Sequence
Unit 1 Solving Problems with Matrices 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.

16 hours
Unit 2 Permutations and organized counting

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. 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.

16 hours
Unit 3 Combinations and Binomial Theorem

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. The Binomial Theorem is an important formula giving the expansion of powers of sums. This formula and the triangular arrangement of the binomial coefficients are often attributed to Pascal who described them in the 17th century. This triangle is referred to as Pascal's Triangle. Pascal's method for building his triangle is a simple iterative process similar to those described in Unit 1. Pascal made the triangle famous by finding many applications for it. In this unit students will 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 using the Binomial theorem and Pascal's triangle.

16 hours
Unit 4 Introduction to Probability

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; 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.

24 hours
Unit 5 Probability Distribution

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; 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.

12 hours
Unit 6 Normal Distribution

This unit will cover three discrete probability distributions: 

  • the binomial distribution
  • the normal distribution
  • the standard normal distribution 

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; 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.

15 hours
Culminating Project 8 hours
Final Evaluation

The final assessment task is a three hour exam worth 30% of the student’s final mark.

3 hours
Total 110 hours

Since the over-riding aim of this course is to help students use language skilfully, 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. These include:

Guided Exploration

Problem Solving

Graphing

Visuals

Direct Instruction

Independent Reading

Independent Study

Cooperative Learning

Multimedia Productions

Logical Mathematical Intelligence

Graphing Applications

Problem Posing

Model Analysis

Group discussion

Self-Assessments

Teachers will employ guided exploration, visuals, model analysis, direct instruction, problem posing and self-assessment to enable these student strategies.

Assessment is a systematic process of collecting information or evidence about student learning. Evaluation is the judgment we make about the assessments of student learning based on established criteria. The purpose of assessment is to improve student learning. This means that judgments of student performance must be criterion-referenced so that feedback can be given that includes clearly expressed next steps for improvement. Tools of varying complexity are used by the teacher to facilitate this.

 

The assessment will be based on the following processes that take place in the classroom:

 

 

Assessment FOR Learning

Assessment AS Learning

Assessment OF Learning

During this process the teacher seeks information from the students in order to decide where the learners are and where they need to go.

Conversation Classroom discussion Self-evaluation

Peer assessment

During this process the teacher fosters the capacity of the students and establishes individual goals for success with each one of them.

Conversation Classroom discussion Small group discussion Post-lab conferences

During this process the teacher reports student’s results in accordance to established criteria to inform how well students are learning.

Conversation Presentations of research Debates

Observation

Drama     workshops                (taking direction)

Steps in problem solving

 

Student Products

Reflection journals (to be kept throughout the duration of the course)

Check Lists

Success Criteria

Observation

Group discussions

 

Student Products Practice sheets Socrative quizzes

Observation

Presentations

Group Presentations

 

Student Products

Projects

Poster presentations Tests

In Class Presentations

 

For the more complex evaluations, the criteria are incorporated into a rubric where levels of performance for each criterion are stated in language that can be understood by students.

Strategy

Purpose

Who

Assessment Tool

Self Assessment Quizzes

Diagnostic

Self/Teacher

Marking scheme

Problem Solving

Diagnostic

Self/Peer/Teacher

Marking scheme

Graphing Application

Diagnostic

Self

Anecdotal records

Homework check

Diagnostic

Self/Teacher

Checklist

Teacher/Student Conferencing

Assessment

Self/Teacher

Anecdotal records

Problem Solving

Assessment

Peer/teacher

Marking scheme

Investigations

Assessment

Self/Teacher

Checklist

Problem Solving

Evaluation

Teacher

Marking scheme

Graphing

Evaluation

Teacher

Checklist

Unit Tests

Evaluation

Teacher

Marking scheme

Final Exam

Evaluation

Teacher

Checklist

 

Assessment is embedded within the instructional process throughout each unit rather than being an isolated event at the end. Often, the learning and assessment tasks are the same, with formative assessment provided throughout the unit. In every case, the desired demonstration of learning is articulated clearly and the learning activity is planned to make that demonstration possible. This process of beginning with the end in mind helps to keep focus on the expectations of the course as stated in the course guideline. The evaluations are expressed as a percentage based upon the levels of achievement.

The evaluation of this course is based on the four Ministry of Education achievement categories of knowledge and understanding (25%), thinking (25%), communication (25%), and application (25%). . The evaluation for this course is based on the student's achievement of curriculum expectations and the demonstrated skills required for effective learning.

The 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 for this course 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
  • 30% of the grade will be based on a final exam administered at the end of the The exam will contain a summary of information from the course and will consist of well-formulated multiple choice questions. These will be evaluated using a checklist. 

Textbook

  • McGraw-Hill Ryerson Mathematics of Data Management. 2009
  • Graphing calculator
  • Various internet websites

For the teachers who are planning a program in mathematics must take into account several important areas. The areas of concern to all teachers that are outlined in the policy document of Ontario Ministry of Education, include the following:

  • teaching approaches
  • types of secondary school courses
  • education for exceptional students
  • the role of technology in the curriculum English as a second language (ESL) and English literacy development (ELD)
  • career education
  • cooperative education and other workplace experiences
  • health and safety in mathematics

It is important to ensure that all students, especially those with special education needs, are provided with the learning opportunities and supports they require to gain the knowledge, skills, and confidence needed to succeed in a rapidly changing society. The context of special education and the provision of special education programs and services for exceptional students in Ontario are constantly evolving. Provisions included in the Canadian Charter of Rights and Freedoms and the Ontario Human Rights Code have driven some of these changes. Others have resulted from the evolution and sharing of best practices related to the teaching and assessment of students with special educational needs. Accommodations (instructional, environmental or assessment) allow the student with special education needs access to the curriculum without changes to the course curriculum expectations.

Environmental education teaches students about how the planet's physical and biological systems work, and how we can create a more sustainable future. Good curriculum design following the resource document. This ensures that the student will have opportunities to acquire the knowledge, skills, perspectives and practices needed to become an environmentally literate citizen. The online course should provide opportunities for each student to address environmental issues in their home, in their local community, or even at the global level.

USCA helps students to become environmentally responsible. The first goal is to promote learning about environmental issues and solutions. The second goal is to engage students in practicing and promoting environmental stewardship in their community. The third goal stresses the importance of the education system providing leadership by implementing and promoting responsible environmental practices so that all stakeholders become dedicated to living more sustainably. Environmental education teaches students about how the planet's physical and biological systems work, and how we can create a more sustainable future.

USCA provides a number of strategies to address the needs of ESL/ELD students to accommodate the needs of students who require instruction in English as a second language or English literacy development. Our teacher considers it to be his or her responsibility to help students develop their ability to use the English language properly. Appropriate accommodations affecting the teaching, learning, and evaluation strategies in this course may be made in order to help students gain proficiency in English, since students taking English as a second language at the secondary level have limited time in which to develop this proficiency. School determines the student's level of proficiency in the English Language upon registration. This information is communicated to the teacher of the course following the registration and the teacher then invokes a number of strategies and resources to support the student in the course.

Throughout their secondary school education, students will learn about the educational and career opportunities that are available to them; explore and evaluate a variety of those opportunities; relate what they learn in their courses to potential careers in a variety of fields; and learn to make appropriate educational and career choices. The skills, knowledge and creativity that students acquire through this course are essential for a wide range of careers. Being able to express oneself in a clear concise manner without ambiguity in a second language, would be an overall intention of this course, as it helps students prepare for success in their working lives.

By applying the skills they have developed, students will readily connect their classroom learning to real-life activities in the world in which they live. Cooperative education and other workplace experiences will broaden their knowledge of employment opportunities in a wide range of fields. In addition, students will increase their understanding of workplace practices and the nature of the employer-employee relationship. Teachers should maintain links with community-based businesses to ensure that students have access to hands-on experiences that will reinforce the knowledge they have gained in school.

Every student is entitled to learn in a safe, caring environment, free from violence and harassment. Students learn and achieve better in such environments. The safe and supportive social environment at USCA is founded on healthy relationships between all people. Healthy relationships are based on respect, caring, empathy, trust, and dignity, and thrive in an environment in which diversity is honoured and accepted. Healthy relationships do not tolerate abusive, controlling, violent, bullying/harassing, or other inappropriate behaviours. To experience themselves as valued and connected members of an inclusive social environment, students need to be involved in healthy relationships with their peers, teachers, and other members.

Critical thinking is the process of thinking about ideas or situations in order to understand them fully, identify their implications, make a judgement, and/or guide decision making. Critical thinking includes skills such as questioning, predicting, analysing, synthesizing, examining opinions, identifying values and issues, detecting bias, and distinguishing between alternatives. Students who are taught these skills become critical thinkers who can move beyond superficial conclusions to a deeper understanding of the issues they are examining. They are able to engage in an inquiry process in which they explore complex and multifaceted issues, and questions for which there may be no clear-cut answers.

The school library program in USCA can help build and transform students' knowledge in order to support lifelong learning in our information- and knowledge-based society. The school library program of these schools supports student success across the curriculum by encouraging students to read widely, teaching them to examine and read many forms of text for understanding and enjoyment, and helping them improve their research skills and effectively use information gathered through research. USCA teachers assist students in accessing a variety of online resources and collections (e.g., professional articles, image galleries, videos, databases). Teachers at USCA will also guide students through the concept of ownership of work and the importance of copyright in all forms of media.

Information literacy is the ability to access, select, gather, critically evaluate, and create information. Communication literacy refers to the ability to communicate information and to use the information obtained to solve problems and make decisions. Information and communications technologies are utilized by all Virtual High School students when the situation is appropriate within their online course. As a result, students will develop transferable skills through their experience with word processing, internet research, presentation software, and telecommunication tools, as would be expected in any other course or any business environment. Although the Internet is a powerful learning tool, there are potential risks attached to its use. All students must be made aware of issues related to Internet privacy, safety, and responsible use, as well as of the potential for abuse of this technology, particularly when it is used to promote hatred.

USCA provides varied opportunities for students to learn about ethical issues and to explore the role of ethics in both public and personal decision making. During the inquiry process, students may need to make ethical judgements when evaluating evidence and positions on various issues, and when drawing their own conclusions about issues, developments, and events. Teachers may need to help students in determining appropriate factors to consider when making such judgements. In addition, it is crucial that USCA teachers provide support and supervision to students throughout the inquiry process, ensuring that students engaged in an inquiry are aware of potential ethical concerns and address them in acceptable ways. Teachers will ensure that they thoroughly address the issue of plagiarism with students. In a digital world in which there is easy access to abundant information, it is very easy to copy the words of others and present them as one's own. Students need to be reminded, even at the secondary level, of the ethical issues surrounding plagiarism, and the consequences of plagiarism should be clearly discussed before students engage in an inquiry. It is important to discuss not only dishonest plagiarism but also more negligent plagiarism instances.


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