Lesson Notes By Weeks and Term v4 - JHS 2
Patterns and Relations
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Patterns and Relations
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Subject: Mathematics
Class: JHS 2
Term: 2nd Term
Week: 5
Grade code: B8.2.1.1.2
Strand code: 3
Sub-strand code: 1
Content standard code: B8.2.1.1
Indicator code: B8.2.1.1.2
Theme: GEOMETRY AND MEASUREMENT
Subtheme: Patterns and Relations
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This lesson builds on our previous knowledge of plotting points on the Cartesian plane. Today, we will learn a powerful skill: how to use a straight-line graph to find new information that wasn't in our original data. Imagine you are a mobile money vendor. You know the commission for GHS 10, GHS 20, and GHS 50 withdrawals. But what about GHS 35? Or GHS 120? Instead of calculating each time, a graph can give you the answer instantly! This skill is useful for business, science, and making predictions in our everyday lives.
What is a Linear Relation? A linear relation is a relationship between two variables (usually 'x' and 'y') that, when plotted on a graph, forms a perfect straight line. It can be represented by a rule or an equation, such as `y = 3x + 2`. This rule tells us exactly how 'y' is related to 'x'. For every value of 'x' we choose, the rule gives us a corresponding value of 'y'. The Cartesian Plane: A Quick Revision The Cartesian plane is our "graph paper" with two main lines: The x-axis (the horizontal line) The y-axis (the vertical line) They meet at the origin (0,0). A point on the plane is represented by coordinates in the form (x, y). The Core Skill: Using the Graph to Find Missing Values The main purpose of our lesson is to learn that the straight line we draw represents *all possible pairs* of (x, y) values for that relation, not just the few points we plotted. We can use the line to find any missing value. This involves two main actions: Interpolation: Finding a value *between* the points we have already plotted. Extrapolation: Finding a value *beyond* the points we have plotted by extending the line.
Let's go through the entire process step-by-step with an example.