# MDM4U

**Topics:**Probability distribution, Probability theory, Random variable

**Pages:**6 (1431 words)

**Published:**October 18, 2014

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

Unit 2

Unit 3

Unit 4

Unit 5

Counting and Probability

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

Organization of Data for Analysis

Connecting questions and the data needed to answer them

Understanding data concepts

Statistics

Single-variable data

Two-variable data

Evaluating validity

Probability Distributions

Discrete random variables

Modelling Continuous Data

Continuous random variables

Culminating Projects and Investigations

A: Permutations, Combinations, Probabilities; B: Statistics; C: Probability Distributions Counting Stories 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

Culminating Investigation

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

Culminating Investigation

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

Games Fair Project

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

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...

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