Lesson Notes By Weeks and Term v4 - SHS 3
MAKING PREDICTIONS WITH DATA
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MAKING PREDICTIONS WITH DATA
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Subject: Additional Mathematics
Class: SHS 3
Term: 2nd Term
Week: 20
Grade code: 3.4.2.LI.6
Strand code: 4
Sub-strand code: 2
Content standard code: 3.4.2.CS.1
Indicator code: 3.4.2.LI.6
Theme: HANDLING DATA
Subtheme: MAKING PREDICTIONS WITH DATA
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This lesson moves beyond simply calculating permutations and combinations. We will explore how these powerful mathematical tools are the secret engine behind many systems we use every day in Ghana. From the security of our Mobile Money PINs to the logistics of Jumia deliveries and the selection of our beloved Black Stars team, permutations and combinations help bring order, security, and efficiency to our world. Understanding their applications will help you see mathematics not just as a school subject, but as a tool for problem-solving and innovation in business, technology, and industry. This lesson focuses on identifying *where* and *why* these concepts are used to improve systems.
A. Foundational Recap: Permutation vs. Combination
Before we explore applications, let's refresh our memory on the fundamental difference. The key question to always ask is: "Does the order matter?" Permutation (Arrangement) Definition: A permutation is an arrangement of objects in a specific order. The order of the objects is crucial. Keywords: Arrange, Order, Position, Rank, Schedule, Sequence, PIN, Password. Formula: The number of permutations of 'r' objects taken from a set of 'n' distinct objects is: nPr = n! / (n-r)! Simple Analogy: Think of a 100-meter race with 8 runners. The arrangement of the first, second, and third place winners (Gold, Silver, Bronze) is a permutation. Kenzo coming 1st and Afua 2nd is different from Afua 1st and Kenzo 2nd. Order matters. Combination (Selection) Definition: A combination is a selection of objects where the order does not matter. It's about the group you form, not the order in which you pick them. Keywords: Select, Choose, Group, Committee, Team, Sample. Formula: The number of combinations of 'r' objects taken from a set of 'n' distinct objects is: nCr = n! / (r! * (n-r)!) Simple Analogy: Think of forming a committee of 3 students from a class of 10. Selecting Ama, Kofi, and Esi is the *same* committee as selecting Kofi, Esi, and Ama. The final group is what matters, not the order of selection. Order does not matter.
B. Applications in Business, Commerce, and Industry
This is the core of our lesson. Let's see how these concepts are applied in the real world.