Lesson Notes By Weeks and Term v4 - SHS 1
REAL NUMBER SYSTEM
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REAL NUMBER SYSTEM
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Subject: Mathematics
Class: SHS 1
Term: 1st Term
Week: 3
Grade code: 1.1.1.LI.2
Strand code: 1
Sub-strand code: 1
Content standard code: 1.1.1.CS.2
Indicator code: 1.1.1.LI.2
Theme: NUMBERS FOR EVERYDAY LIFE
Subtheme: REAL NUMBER SYSTEM
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In our daily lives in Ghana, from the bustling Makola market to our own classrooms, we are constantly dealing with groups and categories. How many people in our class like both football and basketball? How many households in our community use both MTN and Vodafone? Being able to sort, count, and analyse this kind of information is a powerful skill. While this topic is part of the "Real Number System" sub-strand, it focuses on how we use numbers (specifically, counting numbers) to understand and organize our world.
A. Recap: Two-Set Venn Diagrams Remember that a Venn diagram uses overlapping circles to show relationships between sets. For two sets, A and B, we have four regions: Only A Only B Both A and B (A ∩ B) Neither A nor B B. Introducing the Three-Set Venn Diagram When we have three sets (let's call them A, B, and C), the diagram becomes more interesting. We draw three overlapping circles inside a rectangle that represents the Universal Set (U), which is the total group we are considering.
This creates 8 distinct regions. It is very important to understand what each region represents. Region i (A only): Elements that are in Set A, but NOT in B and NOT in C. Region ii (B only): Elements that are in Set B, but NOT in A and NOT in C. Region iii (C only): Elements that are in Set C, but NOT in A and NOT in B. Region iv (A and B only): Elements in the intersection of A and B, but NOT in C. (A ∩ B ∩ C') Region v (A and C only): Elements in the intersection of A and C, but NOT in B. (A ∩ C ∩ B') Region vi (B and C only): Elements in the intersection of B and C, but NOT in A. (B ∩ C ∩ A') Region vii (A, B, and C): Elements in the intersection of ALL THREE sets. (A ∩ B ∩ C) Region viii (Neither A, B, nor C): Elements within the Universal set but outside all three circles. (A ∪ B ∪ C)' C. The "Inside-Out" Strategy for Solving Problems The most effective way to solve a three-set problem is to start from the centre and work your way outwards. Step 1: The Centre. Find the number that belongs to all three sets (Region vii) and write it in the centre. Step 2: The Two-Set Intersections. Fill in the remaining parts of the intersections (Regions iv, v, vi). Be careful! If a problem says "10 people like A and B", this *includes* the people in the middle who like all three. You must subtract the central number to find the "only" part. Step 3: The "Only" Regions. Fill in the numbers for the large, outer parts of each circle (Regions i, ii, iii). You do this by taking the total for that set and subtracting all the parts you've already filled in within that circle. Step 4: The Outside. Find the number of elements that belong to none of the sets (Region viii). You can do this by adding up all 7 numbers you've filled inside the circles and subtracting that total from the Universal set.