## Mathematics of Data Management Strands and Subgroups in the Grade 12 Course

• A. COUNTING AND PROBABILITY
- Solving Probability Problems Involving Discrete Sample Space
- Solving Problems Using Counting Principles
• B. PROBABILITY DISTRIBUTIONS
- Understanding Probability Distributions for Discrete Random Variables
- Understanding Probability Distributions for Continuous Random Variables
• C. ORGANIZATION OF DATA FOR ANALYSIS
- Understanding Data Concepts
- Collecting and Organizing Data
• D. STATISTICAL ANALYSIS
- Analysing One-Variable Data
- Analysing Two-Variable Data
- Evaluating Validity
• E. CULMINATING DATA MANAGEMENT INVESTIGATION
- Designing and Carrying Out a Culminating Investigation
- Presenting and Critiquing the Culminating Investigatio

### Chapter 1: Tools for Data Management

1.1: The Iterative Process
1.2: Data Management Software
1.3: Databases
1.4: Simulations
1.5: Graph Theory
1.6: Modelling With Matrices
1.7: Problem Solving With Matrices

### CHAPTER 2: Statistics of One Variable

2.1: Data Analysis With Graphs
2.2: Indices
2.3: Sampling Techniques
2.4: Bias in Surveys
2.5: Measures of Central Tendency

### CHAPTER 3: Statistics of Two Variables

3.1: Scatter Plots and linear Correlation
3.2: Linear Regression
3.3: Non‐Linear Regression
3.4: Cause and Effect
3.5: Critical Analysis

### CHAPTER 4: Permutations and Organized Counting

4.1: Organized Counting
4.2: Factorials and Permutations
4.3: Permutations With Some Identical Elements
4.4: Pascal's Triangle
4.5: Applying Pascal's Method

### CHAPTER 5: Cominations and the Binomial Theorem

5.1: Organized Counting with Venn Diagrams
5.2: Combinations
5.3: Problem Solving With Combinations
5.4: The Binomial Theorem

### CHAPTER 6: Introduction to Probability

6.1: Basic Probability Concepts
6.2: Odds
6.3: Probabilities Using Counting Techniques
6.4: Dependent and Independent Events
6.5: Mutually Exclusive Events
6.6: Applying Matrices to Probability Problems

### CHAPTER 7: Probability Distributions

7.1: Probability Distributions
7.2: Binomial Distributions
7.3: Geometric Distributions
7.4: Hypergeometric Distributions

### CHAPTER 8: Introduction to Probability

8.1: Continuous Probability Distributions
8.2: Properties of the Normal Distribution
8.3: Normal Sampling and Modelling
Technology Extension: Normal Probability Plots 8.4 Normal Approximation to the Binomial Distribution
8.5: Repeated Sampling and Hypothesis Testing
8.6: Confidence Intervals

### CHAPTER 9: Culminating Project: Integration of the Techniques of Data Management

9.1: Defining the Problem
9.3: Developing and Implementing an Action Plan
9.5: Reporting, Presenting, and Critiquing Projects

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### Chapter 1: The Power of Information

1.1: Visual Displays of Data
1.2: Conclusions and Issues
1.3: The Power of Visualizing Data –Trends
1.4: Trends Using Technology (TI-83, spreadsheet)
1.5: The Power of Data – The Media

### CHAPTER 2: In Search of Good Data

2.2: Characteristics of Data
2.3: Collecting Samples
2.6: Secondary Sources (COMPUTER LAB)
2.7: Preparing Data (COMPUTER LAB)
2.4: Creating Questions
2.5: Avoiding Bias

### CHAPTER 3: Tools For Analyzing Data

3.1: Graphical displays of Information(Excel 2nd day)
3.2: Measures of Central Tendency
3.4: Normal Distribution
3.5: Converting Data to the Normal Distribution
3.6: Mathematical Indices

### CHAPTER 4: Introduction To Probability

4.1: Experimental Probability
4.2: Theoretical Probability
4.3: Finding Probability Using Sets
4.4 Conditional Probability
4.5 Tree Diagrams and Outcome Tables
4.6 Permutations
4.7 Combinations

### CHAPTER 5: Probability Distributions & Predictions

5.1 Probability Distributions and Expected Value(TI-83)
5.2 Pascal’s Triangle and the Binomial Theorem
5.3 Binomial/Hypergeometric Distributions
5.4 Normal Approximation to the Binomial Distribution
5.5 Simulations

### CHAPTER 6: Solving Problems with Matrices, Graphs and Diagrams

6.1: Using Diagrams to Represent & Analyze Processes
6.2: Using Diagrams to Represent & Analyze Relationships
6.3: Matrices
6.4 Matrix Multiplication
6.5: Solving Problems with Graphs

# Strictly Ontario Curriculum

Mathematical Processes