Lesson Notes By Weeks and Term v4 - SHS 1
SPATIAL SENSE
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
SPATIAL SENSE
Download the Lessonotes Mobile Ghana app for faster lesson access on Android and iPhone.
Subject: Additional Mathematics
Class: SHS 1
Term: 2nd Term
Week: 6
Grade code: 1.2.1.LI.3
Strand code: 2
Sub-strand code: 1
Content standard code: 1.2.1.CS.2
Indicator code: 1.2.1.LI.3
Theme: GEOMETRIC REASONING AND MEASUREMENT
Subtheme: SPATIAL SENSE
This page supports the lesson note with a companion video and a short classroom-ready summary.
For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.
This lesson introduces the concept of vectors, which are essential tools for describing quantities that have both magnitude (size) and direction. In our daily lives in Ghana, we encounter vectors all the time. Think about the journey a tro-tro takes from Madina to Circle – it's not just about the distance, but also the specific direction. When a footballer in the Black Stars kicks a ball, the force applied has a strength and a direction. Vectors help us mathematically model and understand this "spatial sense"—our awareness of position, movement, and direction in the world around us.
2.1. Scalars vs. Vectors In mathematics and science, we deal with two types of quantities: Scalar: A quantity that has only magnitude (size or amount). *Examples:* Your age, the price of a ball of kenkey (e.g., GH₵ 3), the temperature in Accra, the distance from Kumasi to Tamale (385 km). Vector: A quantity that has both magnitude and direction. *Examples:* The velocity of a car travelling at 80 km/h *due North*, a force of 15 Newtons pushing a box *to the right*, the displacement of a student who walks 10 metres *towards the classroom door*. 2.2. Representing Vectors Vectors can be represented in two main ways: Geometrically: As a directed line segment (an arrow). The length of the arrow represents the magnitude, and the arrowhead points in the direction. We can denote the vector from point A to point B as `overrightarrow{AB}`. Algebraically: Using components. Column Vector: If a vector moves `x` units horizontally and `y` units vertically, we write it as: a = $\begin{pmatrix} x \\ y \end{pmatrix}$ Unit Vector Notation: We can also write it as a = `xi + yj`, where: i is a unit vector of length 1 in the positive x-direction. j is a unit vector of length 1 in the positive y-direction. 2.3. Magnitude (Modulus) of a Vector The magnitude of a vector is its length. We use the symbol |a| or ||a|| to denote the magnitude of vector a. We find it using Pythagoras' theorem.
If a vector a = $\begin{pmatrix} x \\ y \end{pmatrix}$ or a = `xi + yj`, then its magnitude is: |a| = $\sqrt{x^2 + y^2}$