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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In our study of numbers, we often encounter irrational numbers like √2 or √5, which are called surds. While they are perfectly valid numbers, having them in the denominator of a fraction is considered 'untidy' in mathematics. It makes further calculations complicated and comparing the size of different fractions difficult. Today's lesson is about a special technique called rationalisation. Specifically, we will learn how to remove a surd from a denominator that has two terms (a binomial denominator). This skill is like simplifying a fraction like 6/8 to 3/4; it is a standard practice that makes our mathematical expressions simpler, more elegant, and easier to work with.
This lesson will be interactive, using Think-Pair-Share to discuss ideas and Collaborative Group Work for practice problems. Part 1: Recap - Why Rationalise? (5 mins)
Remember that a rational number can be written as a fraction p/q, where p and q are integers. An irrational number cannot. A surd is an irrational root.
Consider the fraction `1/√2`. We rationalise it by multiplying the numerator and denominator by `√2`: `1/√2 = (1 × √2) / (√2 × √2) = √2 / 2`
Teacher-led Question: Why is `√2 / 2` considered simpler than `1/√2`? *(Expected response: The denominator is now a rational number (an integer), which is easier to divide by).* Part 2: The Challenge with Binomial Denominators (15 mins)