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: 4
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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This lesson introduces students to the use of Venn diagrams to solve problems involving three sets. While part of the Real Number System strand, this topic focuses on the foundational skill of classification and logical organisation, which is essential for understanding relationships between different sets of numbers (e.g., Natural, Integers, Rational). In our daily lives in Ghana, we constantly group and categorise things—from the subjects we study, to the foods we eat, to the languages we speak. Venn diagrams provide a powerful visual tool to understand the overlap and differences between these groups.
A. Recap of Basic Set Concepts (5 mins) Set: A collection of well-defined, distinct objects. Example: V = {a, e, i, o, u} is the set of vowels. Universal Set (U): The set containing all possible elements under consideration. Intersection (A ∩ B): The set of elements that are in both set A and set B. The keyword is "AND". Union (A ∪ B): The set of elements that are in set A or set B or both. The keyword is "OR". Complement (A'): The set of elements in the universal set (U) that are not in set A. B. Understanding the Three-Set Venn Diagram
A Venn diagram with three intersecting sets (let's call them A, B, and C) divides the universal set (U) into 8 distinct regions. It is crucial to understand what each region represents.
Let's use the diagram from the NaCCA exemplar to explain each part. Region (z) - The Central Intersection: Description: Elements that belong to Set A, Set B, AND Set C. Set Notation: A ∩ B ∩ C Example: In a school, students who are in the Debate Club, the Football Team, AND the Science Club. Region (w) - Intersection of A and B only: Description: Elements that belong to Set A and Set B, but NOT Set C. Set Notation: (A ∩ B) ∩ C' Example: Students who like Waakye and Jollof rice, but do NOT like Kenkey. Region (y) - Intersection of A and C only: Description: Elements that belong to Set A and Set C, but NOT Set B. Set Notation: (A ∩ C) ∩ B' Example: Students who speak Twi and Ga, but do NOT speak Ewe. Region (x) - Intersection of B and C only: Description: Elements that belong to Set B and Set C, but NOT Set A. Set Notation: (B ∩ C) ∩ A' Example: Students who use MTN and Vodafone, but do NOT use AirtelTigo. Region (a) - Set A only: Description: Elements that belong to Set A ONLY. They are not in B or C. Set Notation: A ∩ (B' ∩ C') or A only Example: Students who passed Mathematics, but failed both Integrated Science and English. Region (b) - Set B only: Description: Elements that belong to Set B ONLY. Set Notation: B ∩ (A' ∩ C') or B only Example: Students who play Football ONLY (not Volleyball or Basketball). Region (c) - Set C only: Description: Elements that belong to Set C ONLY. Set Notation: C ∩ (A' ∩ B') or C only Example: Students who listen to Afrobeats ONLY (not Highlife or Hiplife). Region (v) - Outside all sets: Description: Elements in the Universal set that do not belong to A, B, or C. Set Notation: (A ∪ B ∪ C)' Example: In a survey about favourite subjects, these are the students who did not choose any of the three options. C. Worked Example: Solving a Three-Set Problem
The Strategy: Always work from the inside out. Start with the central intersection (all three sets). Move to the intersections of two sets. Then calculate the "only" regions. Finally, determine the region outside all three sets.