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.3
Strand code: 4
Sub-strand code: 2
Content standard code: 1.4.2.CS.1
Indicator code: 1.4.2.LI.3
Theme: HANDLING DATA
Subtheme: MAKING PREDICTIONS WITH DATA
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In our daily lives, we are constantly faced with choices. From selecting a committee for a class project to choosing which subjects to focus on, or even picking players for a school football team. Sometimes, the order in which we choose things matters a lot (like awarding 1st, 2nd, and 3rd prizes). Other times, the order is completely irrelevant (like choosing three friends to form a study group). This lesson explores these two fundamental ways of counting choices: Permutations (where order matters) and Combinations (where order does not matter).
Activity 1: The Core Difference - Arrangement vs. Selection
(Teacher-Led Discussion using Think-Pair-Share)
Let's start with a scenario. Imagine we have three of the best students in our class: Ama, Baffour, and Cynthia (A, B, C). Scenario 1 (Permutation): We need to award prizes for 1st, 2nd, and 3rd place in a quiz competition. If Ama is 1st, Baffour is 2nd, and Cynthia is 3rd, we write this as (A, B, C). Is this the same as (B, A, C)? No! In this case, Baffour is 1st. The order in which we arrange them is very important. Each different order is a unique outcome. This is a PERMUTATION. It is an arrangement. Recall the formula: `nPr = n! / (n-r)!`. The number of ways to arrange 3 students in 3 positions is `3P3 = 3! / (3-3)! = 3! / 0! = 6`. Scenario 2 (Combination): We need to select a 3-person committee to represent the class at a meeting with the Headmaster. We choose Ama, Baffour, and Cynthia. The committee is {A, B, C}. What if we had chosen Baffour, then Cynthia, then Ama? The committee is still {B, C, A}. Is the committee {A, B, C} different from the committee {B, C, A}? No! It's the exact same group of people. Here, the order of selection does not matter. We are only concerned with the final group. This is a COMBINATION. It is a selection or a group.
Key takeaway: Permutation = Position / Arrangement / Order matters. (Think: President, VP, Secretary). Combination = Committee / Group / Selection / Order does not matter. (Think: A group of 3 friends).