Lesson Notes By Weeks and Term v4 - SHS 2

SPATIAL SENSE

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  4. SPATIAL SENSE

Subject: Additional Mathematics

Class: SHS 2

Term: 1st Term

Week: 20

Grade code: 2.2.1.LI.2

Strand code: 2

Sub-strand code: 1

Content standard code: 2.2.1.CS.1

Indicator code: 2.2.1.LI.2

Theme: GEOMETRIC REASONING AND MEASUREMENT

Subtheme: SPATIAL SENSE

Lesson Video

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Performance objectives

Lesson summary

This lesson forms a bridge between the visual world of geometry (shapes) and the symbolic world of algebra (equations). We see circles everywhere in Ghana – from the design of the Kwame Nkrumah Interchange in Accra, to the base of a traditional silo for storing grains, to the ripples formed when a stone is dropped in the Volta Lake. Today, we will learn how to describe any circle perfectly using a single, powerful algebraic equation. We will discover that this equation is not a magic formula, but is built directly from two ideas you already know: the Pythagoras Theorem and the formula for the distance between two points.

Lesson notes

Part A: The Building Blocks (Recap)

Before we build the equation of a circle, let's review our essential tools. The Pythagoras Theorem: In any right-angled triangle, the square of the hypotenuse (the side opposite the right angle, `c`) is equal to the sum of the squares of the other two sides (`a` and `b`). `a² + b² = c²` The Distance Formula: The distance `d` between any two points `(x₁, y₁)` and `(x₂, y₂)` on a Cartesian plane is derived from the Pythagoras theorem.

*Imagine a right-angled triangle where the distance `d` is the hypotenuse.* The length of the horizontal side (`a`) is the difference in the x-coordinates: `|x₂ – x₁|`. The length of the vertical side (`b`) is the difference in the y-coordinates: `|y₂ – y₁|`.

Applying Pythagoras: `d² = (x₂ – x₁)² + (y₂ – y₁)²` Taking the square root of both sides gives us the distance formula: `d = √[(x₂ – x₁)² + (y₂ – y₁)²]`

Evaluation guide