SHS3 Mathematics · Semester 1, Week 2
Proportional Reasoning
Full lesson notes coming
Notes for this lesson are being prepared. The curriculum details below are complete and ready to use for your planning.
Curriculum details
- Strand
- Numbers for Everyday Life (Strand 1)
- Sub-strand
- Proportional Reasoning (1.2)
- Content standard
- 3.1.2.CS.1 - Demonstrate conceptual understanding of logical reasoning to solve real-life problems. 3.1.2.LO.1 Establish the validity of logical arguments and use it to make relevant decisions in solving problems.
- Indicator
- 3.1.2.LI.2 - Make intelligent guessing to establish valid arguments and draw logical conclusions.
- Suggested placement
-
Semester 1, Week 2
(Week 2 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
- Curriculum reference
- NaCCA curriculum document, p. 303
Exemplars (from the NaCCA curriculum)
In collaborative and gender-responsive groups, learners discuss to establish and analyse arguments using diagrams (truth tables) to carry out investigation on Logical reasoning, including conjunctions. Be conscious of and interpret norms, embrace diversity through collaborative small groups and self-directed
or individualised work in discussion and evaluation, leading to truth, integrity, respect, tolerance, problem-solving skills and making effective judgments.
Example: Use Venn diagrams to represent each of the following. a) A: All my brothers are farmers b) B: Farmers are happy people. c) C: Abu is a farmer but not a brother. d) D: Baba is my brother e) E: Kofi is not happy U= {people}, H= {happy people}, F={farmers}, B={brothers} 𝑎 = 𝐴𝑏𝑢, 𝑎 ∈ 𝐹, 𝑏 = 𝐵𝑟𝑜𝑡ℎ𝑒𝑟𝑠, 𝑏 ∈ 𝐵, 𝑘 = 𝐾𝑜𝑓𝑖, 𝑘 ∉ 𝐹,
Using Problem-based Learning approaches, learners in mixed-ability groups investigate the p ∧ q )" and "or ( p ∨ q )" is used in compound statements, situation where the logical connective "but ( ensuring equity at all stages.
Eg.1. 'She wants to go to school' but 'she wants to go to the party'. Notice this time round, "but" is used in place of "and" to give a different sort of emphasis to the statement. . Let 𝑝 stand for "7 > 5" and 𝑞 stand for "3 < 0." Find the truth value of p ∧ q .
Truth Table for the Conjunction and
T T T T F F F T F F F F Fig. 1: Truth Table for the Conjunction 𝑝 and 𝑞
Truth Table for the disjunction or
T T T T F T F T T F F F Fig. 2: Truth Table for the Conjunction 𝑝 or 𝑞
Teaching and Learning Resources:
- Technology tools:
- Computer, GeoGebra, Google
- Search,
- YouTube videos, etc
- Cardboards,
- measuring instruments
Assessment (3.1.2.AS.2). The document marks no depth-of-knowledge level for this indicator.