Number and Algebraic Patterns

Collaborative Learning: Learners will be working in convenient groups (ability, mixed-ability, mixed gender, or pairs etc.) to establish set identities, set operations, and apply them to solve problems in different contexts.
Talk for Learning Approaches: Learners will brainstorm through think-pairshare/square and debate to discuss set identities and properties of set operations.
Experiential Learning: Learners will collaboratively engage in hands-on activity (learning by doing) to create problems and apply set identities, algebra, and operations to solve.
Activity 1: Set identities and set operations. Use Talk for Learning Approaches (building on what others say, managing Talk for Learning, structuring Talk for Learning), collaborative learning approaches and experiential learning approaches to investigate set identities, set algebra, and set operations and solve related problems.

 Small group discussions/Think-pair-share
- Learners in small convenient groups (for instance, mixed gender, mixed-ability, etc.) investigate and establish set identities and verify these properties.
- Learners use set algebra to verify that for any three Sets 𝐴, 𝐵 and 𝐶:
Example 1: Verify that for any three Sets 𝐴, 𝐵 and 𝐶:
- Commutative Properties : 𝐴 ∪ 𝐵 = 𝐵 ∪ 𝐴 𝐴 ∩ 𝐵 = 𝐵 ∩ 𝐴
- Distributive Properties: 𝐴 ∪ (𝐵 ∩ 𝐶) = (𝐴 ∪ 𝐵) ∩ (𝐴 ∪ 𝐶) 𝐴 ∩ (𝐵 ∪ 𝐶) = (𝐴 ∩ 𝐵) ∪ (𝐴 ∩ 𝐶)
- Associative properties: 𝐴 ∩ (𝐵 ∩ 𝐶) = (𝐴 ∩ 𝐵) ∩ 𝐶 𝐴 ∪ (𝐵 ∪ 𝐶) = (𝐴 ∪ 𝐵) ∪ 𝐶
Activity 2: Use of Venn diagram to verify three set identities/operations.
Small group discussions/Think-pair-share: Learners in small convenient groups (for instance, mixed gender, mixed-ability, etc.) investigate and establish set identities and use Venn diagrams to verify that for any three Sets 𝐴, 𝐵 and 𝐶:
- 𝐴 ∪ 𝐵 = 𝐵 ∪ 𝐴
- 𝐴 ∪ (𝐵 ∩ 𝐶) = (𝐴 ∪ 𝐵) ∩ (𝐴 ∪ 𝐶)
- 𝐴 ∩ (𝐵 ∪ 𝐶) = (𝐴 ∩ 𝐵) ∪ (𝐴 ∩ 𝐶)
Example of illustration of 𝐴 ∩ (𝐵 ∪ 𝐶) = (𝐴 ∩ 𝐵) ∪ (𝐴 ∩ 𝐶) in a Venn diagram

Inter-group competition: Learners from one group create real life problems involving 2 sets whilst the other group applies set algebra, operations, and identities to solve the problems. Group switch roles.
Example: A pharmaceutical company is considering manufacturing new toothpaste. They are considering two charcoal flavours, strawberry and mint. In a sample of 74 people, it was found that 45 liked strawberries, 37 liked mints and 21 liked both types
- Create a Venn diagram to model the information.
- How many liked only strawberries?
- How many liked only mints?
- How many liked exactly one of the two (that is, they liked one but not the other)?
Teaching and Learning Resources:
- Textbooks
- Rectangular paper cut-out
- Addition pyramid
- Curriculum
- Cardboards
- Reading resources
- Colour pens
- Notebook
- Graph sheets
- Mathematical sets
- Technological tools.
Assessment (1.1.1.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 3 Strategic reasoning.
Consider the sets: A={red, green, blue}, B={red, yellow, orange}, C={red, orange, yellow, green, blue, purple} D={yellow, white} and the universal set 𝑈 = 𝐴 ∪ 𝐵 ∪ 𝐶 ∪ 𝐷 a) find 𝐴' ∩ 𝐶 b) find 𝐴 ∪ 𝐶 and 𝐵 - ∩ 𝐴. Strategic Reasoning A survey asks: "Which online social media have you used in the last month: WhatsApp, Facebook, Both". The results show 42% of those surveyed have used WhatsApp, 70% have used Facebook, and 20% have used both. How many people have used neither WhatsApp nor Facebook? Write an expression for the regions outlined in red a) b)