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: 3
Grade code: 1.1.1.LI.5
Strand code: 1
Sub-strand code: 1
Content standard code: 1.1.1.CS.1
Indicator code: 1.1.1.LI.5
Theme: MODELLING WITH ALGEBRA
Subtheme: NUMBER AND ALGEBRAIC PATTERNS
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This lesson introduces a powerful tool for expanding algebraic expressions called binomials. A binomial is simply an expression with two terms, like `(x + y)` or `(2a - 3)`. We often need to raise these binomials to a power, such as `(x + y)³`. While we could multiply this out manually (`(x+y)(x+y)(x+y)`), it becomes very time-consuming and prone to errors for higher powers like `(x+y)⁷`. In Ghana, understanding patterns is key to solving many problems, from predicting market prices to understanding probability in games of chance. The pattern we will learn today, Pascal's Triangle, provides a quick and elegant shortcut for these expansions.
Phase 1: Starter / Engaging the Learner (10 minutes)
Activity: Think-Pair-Share Think (Individually): "How would you find the value of `(x + y)²`? What about `(x + y)³`?" Give learners 2 minutes to work this out in their notebooks. Pair (In Twos): Learners discuss their methods and answers with a partner. Share (Whole Class): Ask a few pairs to share their results on the board.
*Expected Answers:* `(x + y)² = (x + y)(x + y) = x² + xy + yx + y² = 1x² + 2xy + 1y²` `(x + y)³ = (x + y)(x + y)² = (x + y)(x² + 2xy + y²) = x³ + 2x²y + xy² + x²y + 2xy² + y³ = 1x³ + 3x²y + 3xy² + 1y³`
Teacher's Elicitation: "Well done! Notice the numbers in front of each term, the coefficients. For `n=2`, they are 1, 2, 1. For `n=3`, they are 1, 3, 3, 1. Multiplying out `(x + y)⁵` would be very long! Today, we will learn a shortcut to find these coefficients and the full expansion without tedious multiplication." Phase 2: Explanation of Key Concepts (25 minutes)