Lesson Notes By Weeks and Term v4 - SHS 1

SPATIAL SENSE

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  3. SHS 1
  4. SPATIAL SENSE

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

Lesson Video

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Performance objectives

Lesson summary

This lesson explores how to find the exact coordinates of a point that divides a line segment into a specific ratio. This concept is a fundamental building block in coordinate geometry and has numerous practical applications. In Ghana, this skill is vital in fields like land surveying, where plots of land are often divided among family members or for commercial purposes. It is also used in architecture for structural planning and in computer graphics for creating animations. We will learn how to do this both geometrically (by construction) and algebraically (using a formula).

Lesson notes

Part 1: The Core Idea of Ratio

Before we talk about lines, let's understand ratios with something we all know: money.

Example: Two brothers, Kofi and Kwame, are asked to share GHC 100 in the ratio 2:3. How much does each get? Step 1: Find the total number of parts. The ratio is 2:3. Total parts = 2 + 3 = 5 parts. Step 2: Find the value of one part. The total amount is GHC 100. So, 1 part = GHC 100 / 5 = GHC 20. Step 3: Calculate each person's share. Kofi gets 2 parts: 2 × GHC 20 = GHC 40. Kwame gets 3 parts: 3 × GHC 20 = GHC 60.

Connection to Geometry: Dividing a line segment `AB` in the ratio 2:3 means finding a point `P` on the line such that the length of segment `AP` compared to the length of segment `PB` is exactly 2:3. That is, `AP : PB = 2:3`, or `AP/PB = 2/3`. Part 2: Internal Division of a Line Segment

Evaluation guide