MDM4U

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 **MDM4U - Mathematics of Data Management ** Grade 12, University Preparation

= Course Description = This course broadens students' understanding of mathematics as it relates to managing information. Students will apply methods for organizing large amounts of information; apply counting techniques, probability, and statistics in modelling and solving problems; and carry out a culminating project 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.  = Prerequisite = Functions, Grade 11, University Preparation (MCR3U) or Functions and Applications, Grade 11, University/College Preparation (MCF3M)  =** Mathematical Processes **= Students' abilities in the following mathematical processes will be fostered through incorporation of appropriate activities throughout the course :
 * Problem Solving
 * Reasoning and Proving
 * Reflecting
 * Selecting Tools and Computational Strategies
 * Connecting
 * Representing
 * Communicating

= Rationale for Organization of Units = The organization and structure of units is based on the OAME course outline found at [|OAME MDM4U]. OAME suggests starting with Counting and Probability in order to establish the course as less algebraic than earlier courses and build on prior experience with probability, which will offer an opportunity for success early in the course. In addition, the formal approach to these topics establishes the course as a university preparation course and will help train students to use complex mathematical processes. Finally, it provides an opportunity to introduce the concepts of variability, which will prepare students for the units on statistical analysis and probability distribution. The Culminating Data Management Investigation strand will be addressed in all units of the course. By having the students carry out several smaller investigations provides more opportunities for early feedback to be incorporated into later projects. Students will have ample time and interaction with the teacher to develop quality projects and all curriculum expectations can be addressed through projects and investigations. This is a more authentic assessment strategy for the content of this course than are traditional tests and exams. = Time allocation to units =
 * < Counting and Probability ||< 20 Periods ||
 * < Organization of data for analysis ||< 11 Periods ||
 * < Statistics ||< 30 Periods ||
 * < Probability distributions ||< 13 Periods ||
 * < Modeling Continuous Data ||< 11 Periods ||

Unit 1: Counting and Probability (20 Periods)
Students will develop skills for counting and determining probabilities using Venn diagrams, simulations, counting principles, factorial notation, permutations, and combinations. They will consider experimental and theoretical probability. [Overall Expectations A1, A2]

For the Culminating Project for this unit, students will choose or create a nursery rhyme or piece of literature that provides the potential for posing and answering problems that involve permutations, combinations, and probability. They will then pose and solve these problems. [Overall Expectations E1, E2]

Unit 2: Organization of Data for Analysis (11 Periods)
Students will be introduced to the role of data in statistical studies. Students will describe the characteristics of a good sample and compare sampling techniques. Students will be introduced to Fathom. Students will learn to find and retrieve credible data from Internet sources, including Statistics Canada (E-STAT). Students will collect their own data gathered through surveys which employ appropriate sampling techniques. Students will learn to organize their own data as well as those gathered from other sources in a manner that facilitates its analysis. [Overall Expectations C1, C2]

Students will identify a topic of interest, begin posing and refining questions, and identify a source of data for their Culminating Investigation. Students will produce a plan for how they will approach completing their Culminating Investigation. [Overall Expectations E1]

Unit 3: Statistics (30 Periods)
Students will use common techniques to explore, analyse, interpret, and draw conclusions from one- and two- variable data. Students will produce, interpret and evaluate the validity of statistical summaries (e.g. graphs, measures of central tendency, equations representing a relationship). [Overall Expectations D1, D2, D3]

Students will carry out their Culminating Investigation by analysing and drawing conclusions from their data in order to produce a report of their research findings. Students will then present a summary of their findings and critique the presentations of their peers. [Overall Expectations E1, E2]

Unit 4: Probability Distributions (13 Periods)
Students will create theoretical probability distributions for discrete random variables. They will carry out simulations to create experimental probability distributions. Students will learn to produce histograms and recognize that the differences between probability frequency histograms may be the result of variability. Students will explore and connect binomial and hypergeometric distributions. [Overall Expectation B1]

Games Fair Culminating Project: Students will create a game of chance with an expected value > 0 for the game provider but that encourages people to play the game. Students will calculate the probability distribution for the game and the expected values. They will then host the game and gather experimental data in order to compare the theoretical and experimental distributions. [Overall Expectation E1, E2]

Unit 5: Modeling Continuous Data (11 Periods)
Students will describe the shapes of distributions of continuous data and extend the concept of a discrete probability distribution to a continuous probability distribution. Students will identify the features of the normal distribution. They will use the normal distribution to describe a population and to make comparisons between one value and the rest of the normal distribution.

For the summative in this unit, students will apply normal distributions to real world situations recognizing the role of variability. [Overall Expectations B2, D1]

= Program Planning Considerations = • Cultural perspectives • Positive reinforcements • Variety of assessment techniques • Flexible group structures • Consideration for Learning Styles || = Assessment Strategies =  All curriculum expectations will be addressed through the assessment of projects and investigations. Both formative and summative assessments will be ongoing throughout the semester. A variety of assessment strategies will be employed to address students’ diverse needs. These may include: =Term Summative Evaluations =  <span style="font-family: arial,helvetica,sans-serif; font-size: 18px; line-height: 27px;">Final Mark Calculation <span style="font-family: Arial,Helvetica,sans-serif;">Calculation of the Mark will be based upon the **//Categories//** of the **//Achievement Chart//**. Final marks will be calculated as follows: <span style="font-family: Arial,Helvetica,sans-serif; font-size: 17px; line-height: 25px;"> ** Summative Evaluations ** = Textbook = Mathematics of Data Management(University Preparation), Nelson (2003) = Resources = = Curriculum documents = The Ontario Curriculum - Mathematics - Grades 11 and 12
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: right;">**Exceptional Students:** || <span style="font-family: Arial,Helvetica,sans-serif;">Additional time will be allowed for evaluations as required. Additional accommodations will be provided in consultation with the Guidance, Special Education and ESL departments. ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: right;">**Technology:** || <span style="font-family: Arial,Helvetica,sans-serif;">Graphing calculators and computers will be utilized for technology-related applications. ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: right;">**Career Education:** || <span style="font-family: Arial,Helvetica,sans-serif;">Links to related fields will be established throughout the course. ||
 * <span style="display: block; font-family: Arial,Helvetica,sans-serif; text-align: right;">**Mathematics Anxiety**: || <span style="font-family: Arial,Helvetica,sans-serif;">Attention will be addressed according to the following:
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Diagnostic assessment
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Performance assessment
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Portfolio assessment
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Rubrics
 * <span style="font-family: Arial,Helvetica,sans-serif;"> Checklists
 * Quizzes, culminating projects and other tasks will occur throughout the academic year at the end of units as outlined in the course summary
 * Students will be provided with reasonable opportunities to master skills relating to the achievement of the curriculum expectations before assessment and evaluation occurs
 * Accommodations will be made for school activities, statutory holidays, cultural days, PD days, sports events and other occurrences that have any impact on the scheduled evaluation. It is the student's responsibility to notify the teacher of such absences in advance and make up the missed work.
 * If a student must miss an evaluation, s/he is expected to: a) see the teacher before the absence to arrange for an alternative date to make up the evaluation; or b) in case of illness or unexpected absence, present a note to the teacher, signed by a parent or guardian, immediately upon their return to explain the absence. An alternate evaluation will then be scheduled at a mutually convenient time.
 * The School Late Policy applies to all assignments and evaluations.
 * Cheating will not be tolerated in any form and will be dealt with appropriately.
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 13px; font-weight: normal; line-height: 19px;"> Knowledge and Understanding: 20%
 * <span style="font-family: Arial,Helvetica,sans-serif;">Thinking and Inquiry: 20%
 * <span style="font-family: Arial,Helvetica,sans-serif;">Application: 35%
 * <span style="font-family: Arial,Helvetica,sans-serif;">Communication: 25%
 * Teacher made worksheets
 * Graphing calculators and computers
 * Dynamic statistics software (e.g. <span style="font-family: Arial,Helvetica,sans-serif;">[|Fathom])
 * <span style="font-family: Arial,Helvetica,sans-serif;">OAME/OMCA Materials found at: <span style="font-family: Arial,Helvetica,sans-serif;">[|www.oame.on.ca/main/staging9.phpcode=grspecres&ph=12&sp=MDM4U]
 * <span style="font-family: Arial,Helvetica,sans-serif;">OCDSB Materials found at: <span style="font-family: Arial,Helvetica,sans-serif;">[|www.ocdsb.edu.on.ca/Secondary_Websites/teacher_res/secondary/tecint/mdm4u.htm]
 * <span style="font-family: Arial,Helvetica,sans-serif;">Data from E-STAT found at: <span style="font-family: Arial,Helvetica,sans-serif;">[]

Cooper, Margaret Dhaliwal, Daljit Dolan, Ross
 * Group Members:**