Lesson Notes By Weeks and Term v4 - SHS 1
SPATIAL SENSE
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SPATIAL SENSE
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Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 1
Grade code: 1.2.1.LI.4
Strand code: 2
Sub-strand code: 1
Content standard code: 1.2.1.CS.1
Indicator code: 1.2.1.LI.4
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: SPATIAL SENSE
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This lesson revisits the concept of the gradient (or slope) of a straight line and builds upon it to determine the equation of a line. Understanding the equation of a line is fundamental in mathematics and has numerous practical applications in our daily lives in Ghana. From an architect designing the slope of a roof to withstand our rainy seasons, to an economist plotting the growth of our cocoa exports, or even a driver navigating the hilly roads from Accra to Aburi, the principles of gradient and linear equations are everywhere. This lesson provides the foundational skills to model and analyze such real-world linear relationships.
This section breaks down the core content needed to master the indicator. Part 1: The Gradient of a Line (Recap)
The gradient of a straight line, often denoted by the letter `m`, is a measure of its steepness and direction. It tells us how much the vertical distance (y-value) changes for every one unit of horizontal distance (x-value). A positive gradient means the line slopes upwards from left to right. A negative gradient means the line slopes downwards from left to right. A zero gradient means the line is horizontal. An undefined gradient means the line is vertical.
Formula: Given two points on a line, A(x₁, y₁) and B(x₂, y₂), the gradient `m` is calculated as: ``` m = (Change in y) / (Change in x) = (y₂ - y₁) / (x₂ - x₁) ```