Lesson Notes By Weeks and Term v4 - SHS 3
SPATIAL SENSE
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SPATIAL SENSE
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Subject: Mathematics
Class: SHS 3
Term: 2nd Term
Week: 9
Grade code: 3.3.1.LI.3
Strand code: 3
Sub-strand code: 1
Content standard code: 3.3.1.CS.2
Indicator code: 3.3.1.LI.3
Theme: GEOMETRY AROUND US
Subtheme: SPATIAL SENSE
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This lesson introduces the concept of Locus, which is a fundamental idea in geometry. The word "locus" is Latin for "place" or "location." In mathematics, it refers to the path traced by a point as it moves according to a specific rule or condition. Understanding loci is crucial for developing spatial reasoning. In Ghana, we see examples of loci everywhere: the area a goat can graze when tied to a peg, the region covered by a security light at a lorry park, or the path of a surveyor marking a boundary. This lesson will equip learners with the skills to describe, construct, and apply these paths to solve both mathematical and real-world problems.
A. What is a Locus?
A locus is a set of all points that satisfy a given geometric condition or set of conditions. Think of it as a "rule for movement". If a point moves while following a strict rule, the path it creates is its locus. Simple Analogy: Imagine Kofi is told to walk in a field but must always stay exactly 2 meters away from a mango tree. The path Kofi walks will be a perfect circle around the tree. This circle is the locus of Kofi's possible positions. B. The Five Fundamental Locus Theorems
There are five basic types of loci that form the building blocks for solving more complex problems.
Locus Theorem 1: The Circle Condition: The locus of points at a fixed distance, `d`, from a fixed point, `P`. Locus Formed: A circle with centre `P` and radius `d`. Diagram: ```