Lesson Notes By Weeks and Term v4 - JHS 3

Lesson Video

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Performance objectives

• Define ratios and proportions.
• Represent proportional relationships using equations.
• Solve problems involving ratios and proportions.
• Apply these concepts to real-life situations.

Lesson summary

This lesson builds on our previous understanding of ratios and proportions. We will learn a powerful way to describe relationships where two quantities increase or decrease together at the same rate. This skill is not just for examinations; it is used every day in Ghana. We see it in cooking when we adjust recipes, in business when calculating profit based on sales, and even in how mobile money charges are calculated. By learning to write these relationships as equations, we can predict outcomes and solve complex problems easily.

Lesson notes

A. What is a Proportional Relationship?

A proportional relationship exists between two quantities when their ratio is always constant. This means that as one quantity changes, the other quantity changes by the same factor.

If we have two quantities, let's call them `x` and `y`, they are in a proportional relationship if the ratio `y/x` is always the same number.

B. The Constant of Proportionality (k)