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: 19
Grade code: 1.4.2.LI.4
Strand code: 4
Sub-strand code: 2
Content standard code: 1.4.2.CS.1
Indicator code: 1.4.2.LI.4
Theme: HANDLING DATA
Subtheme: MAKING PREDICTIONS WITH DATA
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In our daily lives, we often need to count the number of ways things can be done. For example, how many different ways can the regional capitals of Ghana be ranked by population? Or how many different committees of three can be formed from your class to plan a fun day? This lesson introduces two powerful mathematical tools, Permutations and Combinations, that help us answer these questions accurately. These tools are the foundation of probability and help us in making predictions, from planning logistics to understanding games of chance like the national lottery.
Part 1: The Building Block - Factorial Notation (!)
Before we can discuss permutations and combinations, we need to understand the factorial. 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 1: `5! = 5 × 4 × 3 × 2 × 1 = 120` Example 2: `3! = 3 × 2 × 1 = 6` Special Case: By definition, `0! = 1`. This is important for the formulas later. Part 2: Permutations (Arrangements)
A permutation is an arrangement of a set of objects in a specific order. The key phrase to remember is "Order Matters".
Think about choosing a Head Prefect and an Assistant Head Prefect from three students: Ama, Baffour, and Cynthia. Arrangement 1: Ama (Head), Baffour (Assistant) Arrangement 2: Baffour (Head), Ama (Assistant) These are two *different* outcomes because the order/position is different.