Mathematics of Data Management: Content and Reporting Targets
Mathematical Processes across all strands: Problem Solving, Reasoning and Proving, Reflecting, Selecting Tools and Computational Strategies, Connecting, Representing, and Communicating.
Unit 1
Counting and Probability
Unit 2
Organization of Data for Analysis
Unit 3
Statistics
Unit 4
Probability Distributions
Unit 5
Modelling Continuous Data
Introducing probability vocabulary and notation in contexts involving simple counting Counting permutations and combinations Using mathematical notation to describe the number of permutations and combinations Solving counting problems Solving probability problems using counting principles
Connecting questions and the data needed to answer them Understanding data concepts
Single-variable data Two-variable data Evaluating validity
Discrete random variables
Continuous random variables
Culminating Projects and Investigations
A: Permutations, Combinations, Probabilities; B: Statistics; C: Probability Distributions
Counting Stories Project
Culminating Investigation
Culminating Investigation
Games Fair Project
Choosing or creating a nursery rhyme or piece of literature that provides the potential for posing and answering connected problems that involve permutations, combinations, and probabilities Posing and solving the connected problems Identifying area of interest and connecting it to probability Posing a problem of interest, finding sources of data, determining relevance of data Designing a plan to study the problem of interest, formulating a research question
Culminating Investigation
Retrieving/ gathering data from various sources, e.g., e-Stat Dealing with/organizing various forms of data Fine-tuning their research question Learning to use data-analysis tools, e.g., Fathom
Interpreting, analysing, and interpreting the data Drawing conclusions from the analysis of data Compiling report, presenting multimedia summary to audience, and answering questions Posing probing questions of presenters Critiquing work of others
Creating a game of chance that has an expected value > 0 for the game provider, and that encourages people to play the game Calculating the probability distribution for the game and the expected values Hosting the game and gathering experimental data Comparing the theoretical probability distribution and the experimental data Critiquing work of others
Mathematics of Data Management (MDM4U) Overview
April 29, 2008
Rationale
Starting with Probability and Counting Helps students understand that this course requires new ways of thinking mathematically that is less algebraic than earlier courses. Due to new pathways producing a more diverse group of students, starting with Probability and Counting trains students to use more complex mathematical processes. Builds on prior experiences with and knowledge of probability to use a more formal mathematical approach, including its vocabulary and notation. Separates the establishment of this formal approach from the introduction to permutations and combinations. Offers an opportunity for success early in the course to students who may not have excelled in more algebraic approaches. Establishes this course as a university preparation course. Provides the opportunity to introduce concepts of variability. Prepares students for statistical analysis and probability distributions. Organization of Data for Analysis (in Unit 2) Provides students with tools for working with data prepares them to begin work on Culminating Investigation B early in the course. Probability Distributions (later in the course) Students benefit from seeing data distributions before applying those concepts to probability distributions. Culminating Projects and Investigations (addressed in all units) Provides time for students to develop quality projects and investigations. Provides time for students to incorporate feedback on Project A into Project and Investigation C Provides time for students to incorporate feedback on various stages of Investigation B into their presentation. Addresses all curriculum expectations through projects and investigations, thereby eliminating the need for an examination. Provides more opportunities for feedback and interactions.
Mathematics of Data Management (MDM4U) Overview
April 29, 2008
Mathematics of Data Management Year Outline Planning Tool
P J T SP Number of pre-planned lessons (including instruction, diagnostic and formative assessments, summative assessments other than summative performance tasks) Number of jazz days of time (instructional or assessment) Total number of days Performance task
Unit 1
Cluster of Curriculum Expectations Counting and Probability Introducing probability
Overall Expectations
SP
vocabulary (e.g., sample space, outcomes, events, trials, discrete, continuous, theoretical probability, experimental probability, mutually exclusive, A1 solve problems involving the random number generator, Venn probability of an event or a diagram, independent and combination of events for discrete dependent events, conditional sample spaces; probability, complement, simulation) and notation (e.g., P(~A), P(A and B), P(A or B), P(A | B)) in contexts involving A2 solve problems involving the simple counting (e.g., where the application of permutations and sample space is given) combinations to determine the Distinguish between and make probability of an event; connections between situations involving the use of permutations and combinations E1 design and carry out a culminating Develop, through investigation investigation that requires the the number of permutations and integration and application of the combinations knowledge and skills related to Using mathematical notation the expectations of this course; n (e.g., n !, P ( n, r ), ) to count r Solving counting problems using counting principles additive, multiplicative Solving probability problems using counting principles Culminating Investigation identifying area of interest and connecting it to probability
15
17
E2 communicate the findings of a culminating investigation and provide constructive critiques of the investigations of others.
Mathematics of Data Management (MDM4U) Overview
April 29, 2008
Unit 2
Cluster of Curriculum Overall Expectations Expectations C1 demonstrate an understanding of Organization of Data for the role of data in statistical Analysis studies and the variability Demonstrate an understanding of the role of data in statistical inherent in data, and distinguish studies different types of data; Describe the characteristics of a good sample and compare C2 describe the characteristics of a sampling techniques good sample, some sampling Design an effective survey and techniques, and principles of collect data primary data collection, and Understand how data is organized collect and organize data to solve Find sources of data, refine topic a problem;
of interest and design a plan in preparation for the Culminating Investigation
SP
11
Statistics Explore, analyse, interpret, and
draw conclusions from onevariable data Explore, analyse, interpret, and draw conclusions from twovariable data Investigate and evaluate validity of statistical summaries Perform a Culminating Investigation - Analyse, interpret, draw conclusions and write a report of their research - Present summary of findings - Critique presentations of their peers
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. D1 analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries; D2 analyse, 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.
18
20
10
Mathematics of Data Management (MDM4U) Overview
April 29, 2008
Unit 4
Cluster of Curriculum Expectations Probability Distributions Understand probability
Overall Expectations
SP
B1 demonstrate an understanding of discrete probability distributions, distributions for discrete random represent them numerically, variables graphically, and algebraically, Explore and connect Binomial determine expected values, and and Hypergeometric distributions solve related problems from a Recognize that the differences variety of applications;
between a probability histogram and a frequency histogram may be the result of variability Complete a Games Fair culminating project
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. D1 analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries; 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.
10
11
Modelling Continuous Data Describe the shapes of
distributions of continuous data Extend the concept of a discrete probability distribution to a continuous probability distribution Understand the features of the normal distribution Apply normal distributions to real-world situations recognizing the role of variability
11
Summative Performance Tasks Total Days
63
71
14 85
The number of prepared lessons represents the lessons that could be planned ahead based on the range of student readiness, interests, and learning profiles that can be expected in a class. The extra time available for instructional jazz can be taken a few minutes at a time within a pre-planned lesson or taken a whole class at a time, as informed by teachers observations of student needs. The reference numbers are intended to indicate which lessons are planned to precede and follow each other. Actual day numbers for particular lessons and separations between terms will need to be adjusted by teachers.
Mathematics of Data Management (MDM4U) Overview
April 29, 2008
