Lesson Notes By Weeks and Term v4 - SHS 1
MAKING PREDICTIONS WITH DATA
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MAKING PREDICTIONS WITH DATA
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Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 18
Grade code: 1.4.2.LI.2
Strand code: 4
Sub-strand code: 2
Content standard code: 1.4.2.CS.1
Indicator code: 1.4.2.LI.2
Theme: HANDLING DATA
Subtheme: MAKING PREDICTIONS WITH DATA
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This lesson introduces the fundamental principles of counting: permutations and combinations. These are powerful mathematical tools used to determine the number of possible outcomes in various situations without having to list them all. In Ghana, we encounter situations that require arrangements and selections daily, from planning events and forming committees to understanding probabilities in games. This lesson will equip learners with the skills to analyse these situations mathematically and solve real-life problems related to arrangements and selections.
A. The Fundamental Counting Principle
This is the foundation of permutations and combinations. Principle: If one event can occur in `m` ways and a second event can occur in `n` ways, then the two events can occur in `m × n` ways.
Example: A student, Kofi, has 2 pairs of trousers (Black, Brown) and 3 shirts (White, Blue, Green). How many different outfits can he wear? Choice of trousers: 2 ways Choice of shirts: 3 ways Total possible outfits = 2 × 3 = 6 outfits. B. Factorial Notation (!)
The factorial of a non-negative integer `n`, denoted by `n!`, is the product of all positive integers less than or equal to `n`. Formula: n! = n × (n - 1) × (n - 2) × ... × 3 × 2 × 1 Example: 5! = 5 × 4 × 3 × 2 × 1 = 120 Special Case: By definition, 0! = 1. C. Permutations (Arrangements - Order Matters)