MDM4U Grade 12 - University (Mathematics of Data Management)

Authors: Samina, Hailey, Mala (2010), Kevin, Chris (2012)

Ministry Guidelines

Curriculum Document

Key Topics

Table of Contents from McGraw-Hill Ryerson Mathematics of Data Management
  1. Tools for Data Management
  2. Statistics of One Variable
  3. Statistics of Two Variables
  4. Permutations and Organized Counting
  5. Combinations and the Binomial Theorem
  6. Introduction to Probability
  7. Probability Distributions
  8. The Normal Distribution
  9. Culminating Project: Integration of the Techniques of Data Management

Sample Course Outlines

  • MDM4U - Course Outline - Course Outline - Fall 2015 - Carleton Place High School - Upper Canada District School Board
  • MDM4U - Course Outline - Course Outline - Fall 2008 - Merivale High School - Ottawa-Carleton District School Board
  • MDM4U - Course Outline - Fall 2009 - The Bishop Strachan School- `Toronto Catholic District School Board
  • MDM4U - Course Outline - St. Mark High School - Ottawa Catholic School Board
  • MDM4U - Course Outline - Fall 2009 - Jarvis Collegiate Institute - Toronto District School Board
  • MDM4U - Course Outline from Virtual High School Ontario
  • MDM4U - Course Outline - Bayridge Secondary School
  • MDM4U - Course Outline - Ontario Online Academy

Video Podcasts

Statistics of One Variable
Data Analysis with Graphs (2:44)
  • This video discusses the shape of a distribution and how to analyze your data based on what the graph looks like. I found this video helpful and clear.
Sampling Techniques (4:52)
  • This video outlines three sampling techniques: simple random, systematic and stratified. It walks you through a clear example, indicating how you would carry out each and uses pictures to show the example.
Bias in Surveys (5:24)
  • I found this video quite well done. It has a clear title, lists three main types of error that cause bias (data collecting error, data handling error and reporting error). He goes on to give specific, yet easy to understand examples to illustrate each type.
Measures of Central Tendency (3:57)
  • This is a rap video that outlines how to calculate the mean, median and mode. I found it very effective because they would define each measure in a short rhyme and then stop and explain how to calculate. I listened to it once and the words were already stuck in my head. It may not have been the best choice for an instructional video but, as a supplement to help students remember or as a way to represent the information in a cool way, this video could be very useful.
Measures of Spread (12:34)
  • This Khan Academy video explains, in great detail, how to find range, variance and standard deviation. It shows two examples, side by side. One data set is very spread out and the other is close together, but each data set has the same mean. This enables the student to see why the measures of spread are very high for the spread out data and low for the other data set. I thought the examples were well thought out and easy to understand.
Statistics of TwoVariables
Scatter Plots and Linear Correlation (8:09)
  • This video outlines the different types of correlations that can be observed with two variables – negative, positive and no correlation. The provided examples are easy to understand and relatable, where students can easily recall the given scenarios within the classroom.
Linear Regression (5:18)
  • This clip definitely breaks down the components of linear regression analysis from the graph to making observations. The video would be very beneficial amongst the applied classrooms where students would need that well-structured/broken down material to start from.
Calculate Regression (8:29)
  • This link is a second part to the video above – it provides further details into calculating the linear regression using the least square method. So, given a set of independent and dependent variables, the video takes you from plotting the data to forming a linear regression equation. The tutorial is given with proper visuals and labels and is well-paced for the students to follow along.
Cause-and-Effect (6:56)
  • In this clip, different cause and effect relationships are outlined and demonstrated alongside one another for students to visually understand and make their own connections. The material is reviewed in a well-paced manner with appropriate visuals and drawings along the way.
Critical Analysis (4:45)
  • The video may not be as techy as the others, however it is engaging because of the straight-forward pen-to-paper method. Students that refer to this video, would be able to pause and reflect on their own work for instance to learn from their mistakes. I think another positive factor with this video is how he uses the calculator for the viewers to see. Some students have trouble when it comes to plugging in values within brackets on the calculator, so I believe some might find this very useful.
Permutatiions and Organized Counting
Organized counting (9:14)
  • Even though this video is a lesson I think this video will give a clear understanding of organized counting for a teacher in a nutshell.
Permutations(4:31)
  • A clear explanation how to use a calculator to calculate.
Art of Problem Solvings(7:33)
  • Richard Rusczyk explains how to write permutations in terms of factorials.
Pascal's Triangle (3:22)
  • Amazing video from youtube. I just knew how to write a Pascal's triangle but this video just showed me the possibilities. It is short and gives the whole picture. This video can be used as a minds on.
Applying Pascal's Triangle: Binomial Expansion Using Pascal's Triangle (7:37)
  • This video shows how Pascal's triangle can be used in Binomial Expansion. I think this is an amazing tool for students and teachers
Combinations and Binomial Theorem
Introduction to Combinations (10:15)
  • Even though I find the video quite lengthy, it was the best one I could find that explains the differences between permutations and combinations as well as show you some examples of combinations and how to solve for them.
How to Solve Using Equation (3:11)
  • After the amount of explanation from the last video, I think this one is useful for those people who just like to memorize the formula.
Permutation Problem 1 (3:45)
  • This video is useful for those people who do not like the equation way of solving for permutations. It is useful because he makes sure you know that you are going to be solving a permutation and not a combination.
Permutation Problem 2 (2:18)
  • This video is useful for those people who do not like the equation way of solving for permutations. It is useful because he makes sure you know that you are going to be solving a permutation and not a combination.
Combination Problem 1 (7:42)
  • This video is useful because he makes it clear that you are solving for a combination and explains to you exactly why you are using a combination to solve the problem and not a permutation. He also gives you the general formula for combinations that is used in video 5.2 (b).
Combination Problem 2 (5:09)
  • I like this video because it uses a real life situation in the problem. It also extends from the previous problem in that we use probability as well as solving using a combination.
The Binomial Theorem:
Explanation and Example 1 (11:21)
  • He begins by examining the formula and telling you why it is useful. He also gives you a few different ways of coming up with the different variables. He does a thorough overview of the formula and how it is set up. He then goes through a step by step process on how to expand an expression.
Example 2 (5:57)
  • I like this video because he shows you how to solve when the expression has a minus sign in between the variables and not a plus sign. This aspect is often really hard for students to understand when first learning this concept and he does it well.
Pascal's Triangle and the Binomial Coefficients (5:40)
  • I like this video because he makes the connection between Pascal's Triangle and the Binomial Theorem. For some students this may be confusing, but it also gives them a straight forward way of looking at the coefficients of the Binomial Theorem without having to calculate them.
Introduction to Probability
Basic Probability Concepts(8:18) by Khan Academy
Odds (3:16) from TeacherTube
  • Explains definition of odds: The ratio that compares the number of ways an event can occur with sucesses over failures.
Independent & Dependent Events(5:40)
  • Explains how to identify an independent and a dependent event. The video gives exaples of each, as well as explains how to determine probability with each type of event.
Mutually Exclusive Events(3:02)
  • Explains the concept of what a mutually exclusive event is. Aswell gives an example of it in context and solves a problem invovling using probability of mutually exclusive events.(Example of finding probability of getting sent to jail from rolling dice in a game of monopoly)
Normal Distribution
Continuous Probability Distributions(9:58)
  • Went over some sample calculations and noted important points such as probability density function.
Properties of the Normal Distribution(2:59)
  • Listed the 5 properties of normal distribution and used visual aid. This video is straight to the point and easy to understand which is exactly what you want when you're just reviewing a concept.
Normal Approximation to the Binomial Distribution(14:10)
  • Gave a nice introduction of why you want to use normal approximation to the binomial distribution. Bonus is that he has an engaging voice!
Repeated Sampling and Hypothesis Testing (Small Sample Size)(9:04)
Repeated Sampling and Hypothesis Testing (Large Sample Size) (14:30)
  • Went over examples of hypothesis testing for small and large sample sizes.
Confidence Intervals (14:03)
  • Very thorough and easy to understand. Used an example to explain the confidence intervals.

Resources


Teacher Webpages


Lesson Ideas

Technology

Continuous Probability Distributions(9:58) Melissa
Went over some sample calculations and noted important points such as probability density function.
Properties of the Normal Distribution(2:59) Melissa
Listed the 5 properties of normal distribution and used visual aid. This video is straight to the point and easy to understand which is exactly what you want when you're just reviewing a concept.
Normal Approximation to the Binomial Distribution(14:10) Melissa
Gave a nice introduction of why you want to use normal approximation to the binomial distribution. Bonus is that he has an engaging voice!
Repeated Sampling and Hypothesis Testing (Small Sample Size)(9:04) Melissa
Repeated Sampling and Hypothesis Testing (Large Sample Size) (14:30) Melissa
Went over examples of hypothesis testing for small and large sample sizes.
Confidence Intervals (14:03) Melissa
Very thorough and easy to understand. Used an example to explain the confidence intervals.