Getting Ready for Data Management
Eight tutor-led lessons that turn Grade 11 Functions fluency into the counting, probability, and data-organizing skills Grade 12 Data Management opens with.
Who it's for: Students finishing Grade 11 Functions (MCR3U) and heading into Grade 12 Data Management (MDM4U), in a small tutor-led group of four. MCR3U never touches counting or statistics, so most of this is genuinely new: counting principle, permutations, combinations, probability rules, and organizing data.
The 8-lesson plan
Slides are what your tutor works from in the live lesson. The practice module is homework: do it before the next lesson.
Numbers Behind the Data: Fractions, Percent, Exponents, and Factorial Notation
Rebuild fast fraction, ratio, percent, and exponent arithmetic and introduce factorial notation, the toolkit every counting and probability formula in MDM4U runs on.
The Fundamental Counting Principle: Counting Without Listing Everything
Use the Fundamental Counting Principle, multiplying choices at each stage, to count outcomes for multi-stage events with repetition and restrictions, tying to Lesson 1's factorials.
Permutations: Arranging Distinct Objects in Order
Count ordered arrangements of distinct objects using the permutation formula nPr, derived from Lesson 2's counting principle, distinguishing full arrangements from subsets.
Combinations: Choosing Without Order
Count selections where order does not matter using nCr, derived from nPr, and build the skill of reading a word problem to decide permutation versus combination.
Probability Basics: Sample Spaces, Complements, and the Addition Rule
Define probability as favorable outcomes over total outcomes using the counting tools from Lessons 2-4, then apply the complement and addition rules.
Conditional Probability and Independence
Compute conditional probability P(A given B), test events for independence, apply the multiplication rule, and use tables and tree diagrams for compound-event probability.
Organizing Data: Frequency Tables, Grouped Data, and Central Tendency
Organize raw data into frequency tables and grouped class-interval distributions, and compute mean, median, and mode from both raw and grouped data, opening MDM4U's Organizing Data unit.
Measures of Spread: Variance, Standard Deviation, and Reading Z-Scores
Compute range, variance, and standard deviation by hand for a data set, calculate and interpret z-scores, and take a first look at the normal distribution's empirical rule.