Lesson Notes By Weeks and Term v4 - SHS 1
NUMBER AND ALGEBRAIC PATTERNS
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NUMBER AND ALGEBRAIC PATTERNS
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Subject: Additional Mathematics
Class: SHS 1
Term: 1st Term
Week: 1
Grade code: 1.1.1.LI.2
Strand code: 1
Sub-strand code: 1
Content standard code: 1.1.1.CS.1
Indicator code: 1.1.1.LI.2
Theme: MODELLING WITH ALGEBRA
Subtheme: NUMBER AND ALGEBRAIC PATTERNS
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In our everyday mathematics, we are very familiar with operations like addition (+), subtraction (-), multiplication (×), and division (÷). We know that 3 + 5 is the same as 5 + 3, but 5 - 3 is not the same as 3 - 5. These "rules" or "properties" are not accidental. Today, we are going to become creators of mathematics. We will define our own new operations and investigate the rules they follow. This branch of mathematics, called abstract algebra, is the backbone of modern technology, including computer programming, internet security (cryptography), and data science. By understanding these properties, we learn to analyse any system of rules, a skill useful in many fields.
What is a Binary Operation?
A binary operation is a rule for combining two elements of a set to produce another element. The word "binary" means two; we always take two elements at a time.
We use symbols like `*`, `∆`, `∇`, `⨀` to represent these new operations. Example: Normal addition `(+)` is a binary operation on the set of Real Numbers (ℝ) because when you add any two real numbers, you get another real number. 5 + 7 = 12.
Let's explore the key properties of these operations. Property 1: Closure