Lesson Notes By Weeks and Term v4 - SHS 1
SPATIAL SENSE
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SPATIAL SENSE
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Subject: Mathematics
Class: SHS 1
Term: 1st Term
Week: 19
Grade code: 1.3.1.LI.3
Strand code: 3
Sub-strand code: 1
Content standard code: 1.3.1.CS.1
Indicator code: 1.3.1.LI.3
Theme: GEOMETRY AROUND US
Subtheme: SPATIAL SENSE
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Geometry is all around us in Ghana. We see it in the triangular patterns of a Kente cloth, the strong triangular trusses holding up the roofs of our homes and churches, and even in the way a surveyor marks out a piece of land. Today, we are going to learn a powerful rule, or 'theorem', about triangles that helps designers, engineers, and builders to be very precise in their work. This rule, the Exterior Angle Theorem, is a shortcut that makes solving complex angle problems much easier.
(15 mins) - Engage Phase: Activating Prior Knowledge Teacher Activity: Ask learners probing questions to recall previous knowledge. "What is a triangle?" (A three-sided polygon) "What is the sum of the angles inside any triangle?" (180°) "What is the sum of angles on a straight line?" (180°) "What do we call the angles inside a shape?" (Interior angles) Draw a triangle on the board, label its vertices A, B, C, and extend one side (e.g., BC to a point D).
(25 mins) - Explore & Explain Phase: The Exterior Angle Theorem A. Defining the Terms Interior Angles: The angles inside the triangle. In ΔABC, these are ∠BAC, ∠ABC, and ∠BCA. Let's call them a, b, and c. Exterior Angle: The angle formed when one side of the triangle is extended. It is the angle between the extended side and the adjacent side. In our diagram, ∠ACD is the exterior angle. Let's call it e. Adjacent Interior Angle: The interior angle that is next to (forms a linear pair with) the exterior angle. Here, angle c is adjacent to exterior angle e. Interior Opposite Angles (or Remote Interior Angles): The two interior angles that are *not* adjacent to the exterior angle. Here, angles a and b are the interior opposite angles to e. B. Stating the Theorem Teacher Activity: Guide learners, using the "Talk for Learning" strategy. Ask groups to discuss what relationship they think might exist between angle e and angles a and b. After a brief discussion, state the theorem clearly. The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles. In simpler terms: e = a + b C. Proving the Theorem
This proof shows *why* the theorem is true. It is not magic; it is based on rules we already know!
Consider ΔABC: