Lesson Notes By Weeks and Term v4 - SHS 3
PROPORTIONAL REASONING
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PROPORTIONAL REASONING
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Subject: Mathematics
Class: SHS 3
Term: 1st Term
Week: 4
Grade code: 3.1.2.LI.2
Strand code: 1
Sub-strand code: 2
Content standard code: 3.1.2.CS.2
Indicator code: 3.1.2.LI.2
Theme: NUMBERS FOR EVERYDAY LIFE
Subtheme: PROPORTIONAL REASONING
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This lesson extends our understanding of variation beyond the direct and inverse relationships we have studied previously. We will explore joint variation, where a quantity depends on two or more other factors, and partial variation, where a relationship has a fixed starting amount and a variable part. Understanding these concepts is crucial for making informed decisions in many real-life situations in Ghana, from calculating the cost of services like plumbing or taxi rides, to understanding business costs, and even predicting outcomes in agriculture and science.
A. Quick Recap: Direct and Inverse Variation
Before we dive into the new types of variation, let's remember the two basic types: Direct Variation: Two quantities, say *y* and *x*, are in direct variation if they increase or decrease together at the same rate. We write this as `y ∝ x`, which means `y = kx` for some constant *k*. Inverse Variation: Two quantities, *y* and *x*, are in inverse variation if one increases as the other decreases. We write this as `y ∝ 1/x`, which means `y = k/x` for some constant *k*. B. Joint Variation
Definition: Joint variation describes a situation where one quantity varies directly as the product of two or more other quantities.
If a variable `y` varies jointly as `x` and `z`, we write: `y ∝ xz`