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: 5
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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This lesson focuses on a key algebraic skill: rationalising the denominator of surds. A surd is an irrational number left in root form (like √2 or √7). While we can perform operations with surds, it is considered standard mathematical practice to avoid having a surd in the denominator of a fraction. This process of removing the surd from the denominator is called rationalisation. In Ghana, precision is vital in fields like engineering, architecture, and even in advanced carpentry. Imagine building the frame for a roof; the calculations might involve Pythagoras' theorem, leading to lengths like √5 metres.
A. Recap: What are Surds?
A surd is the irrational root of a rational number. Examples: √2, √3, 5√7. Numbers like √4 = 2 or √9 = 3 are not surds because their roots are rational numbers. Like Surds: Surds with the same number under the root sign (e.g., 2√3 and 5√3). These can be added or subtracted. *Example:* 2√3 + 5√3 = (2+5)√3 = 7√3. Unlike Surds: Surds with different numbers under the root sign (e.g., 2√3 and 5√2). These cannot be added or subtracted directly. B. What is Rationalisation and Why Do We Do It?
Rationalisation is the process of converting a fraction with an irrational denominator into an equivalent fraction with a rational denominator.
Think of it this way: dividing 10 cedis among 2 people is easy (10/2 = 5 cedis each). But dividing 10 cedis among √2 people is abstract and hard to compute. By rationalising `10/√2` to `5√2`, we get a clearer value (5 times approximately 1.414). It is a standard mathematical convention for simplifying expressions. C. Level 1: Rationalising Monomial Denominators (Recap)