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: 1st Term
Week: 20
Grade code: 1.2.1.LI.3
Strand code: 2
Sub-strand code: 1
Content standard code: 1.2.1.CS.1
Indicator code: 1.2.1.LI.3
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: SPATIAL SENSE
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In our daily lives, we often need to divide things fairly or precisely—from sharing food among family members to a surveyor marking out plots of land in a new community like East Legon Hills or Appolonia City. This lesson brings the simple idea of sharing in a ratio into the world of geometry and coordinates. We will learn a powerful mathematical method to find the exact coordinates of a point that divides a straight line in any given ratio. This skill is a fundamental building block for advanced topics in coordinate geometry, engineering, computer graphics, and architecture.
Part 1: From Simple Ratios to Geometric Ratios
Let's start with something we already know.
Recall: Imagine two siblings, Ama and Kofi, are asked to share GHC 100 in the ratio 2:3. How do we do this? Total parts: 2 + 3 = 5 parts Value of one part: GHC 100 / 5 = GHC 20 Ama's share (2 parts): 2 × GHC 20 = GHC 40 Kofi's share (3 parts): 3 × GHC 20 = GHC 60
Now, let's apply this same thinking to a line segment. Suppose we have a line segment AB. If we want to find a point P on the line that divides it in the ratio 2:3, it means the length of the segment AP compared to the length of the segment PB is in the ratio 2:3.