Applications of Algebra

Talk for Learning, Think-Pair-Share, building on what others say.
Learning Experience: Learners, in pairs, discuss statements and the associations in those statements.
Activity 1: Mathematical statements Learners in groups bring out statements for the group to comment whether they are indeed statements and also whether those statements are true or false. A mathematical statement is a sentence which is either true or false. It may contain words and symbols.
Example
- Accra is the capital of Ghana.
- There are three raining seasons in a year in the whole of Ghana.
- Are there factories in every district of Ghana?
Comments: From the example above, sentences a and b are statements, but sentence b is not true. Sentence c, however, is not a statement.
Notation of Statements: In mathematics, statements are denoted by letters such as P, Q and R.
Example P: 7 + 9 = 15, simply means P is the statement 7 + 9 = 15. P is obviously a false statement because 7 + 9 ≠15.
Activity 2: Negation of a Statement Learners in squares discuss and construct negation of a statement and share with the group for comments.
Notes: The negation uses the word no, not. For a statement p, its negation is ~p. The negation of a given statement is the denial of a given statement.
Example 1: Let us take a simple example of the negation of a statement: P: Accra is the capital of Ghana. ~P: Accra is NOT the capital of Ghana.
Example 2: P: The earth is round in shape. ~P: The earth is NOT round in shape.
Activity 3: Learners discuss the difference between the opposite of a statement and the denial of a statement. Learners to come to the conclusion that the negation of a statement is a denial, not the opposite of a given statement.
Example 1 Kofi Yesu is tall. Kofi Yesu is short. (opposite, therefore not a negation statement). Kofi Yesu is not tall. (negation statement).
Activity 4: Statements and Venn Diagrams Learners in convenient groups discuss the representation of statements in Venn diagrams.
Note: Similar to sets, statements can be represented in Venn diagrams. Example: Identify the following from the given statements: 1. Universal set. 2. Subsets. 3. Complement.
Example 1: Represent each of the following statements on a Venn diagram: 1. P: Kofi is a good boy. 2. Q: 4 is a factor of 100, but 3 is not.
Solution U = {boys} A = {Good boys} k = Kofi k {Good boys}

ii. U = {Integers} A = {factors of 100} 4 ∈ factors of 100} A 1 = {3} 

Activity 4: Compound statements Learners in squares discuss and construct compound statements and share them with the group for comments.
Teaching and Learning Resources:
- SHS Curriculum, Graph boards, mathematical set, ICT tools
Assessment (3.1.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.