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: 5
Grade code: 3.3.1.LI.2
Strand code: 3
Sub-strand code: 1
Content standard code: 3.3.1.CS.2
Indicator code: 3.3.1.LI.2
Theme: GEOMETRY AROUND US
Subtheme: SPATIAL SENSE
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This lesson focuses on geometric construction, a fundamental skill in mathematics and many technical fields. Construction is not just about drawing; it is about creating precise geometric figures using only a pair of compasses and a straightedge (ruler). These skills are the foundation for architects designing buildings in Accra, tailors cutting intricate Kente or GTP patterns, carpenters building furniture, and land surveyors demarcating plots. By mastering these techniques, learners develop precision, logical thinking, and an appreciation for the beauty and utility of geometry in our everyday Ghanaian lives.
A. Introduction to Geometric Construction
Geometric construction is the process of drawing shapes, angles, or lines accurately using only two tools: A pair of compasses: Used for drawing circles or arcs and for marking off equal lengths. A straightedge: A ruler without markings, used for drawing straight lines. For our practical purposes in the classroom, we will use our ruler as a straightedge to draw lines, and its markings to measure initial lengths.
The key is that all other lengths and angles are *derived* from the initial given information through construction, not by measuring with a protractor. B. Fundamental Constructions: The Building Blocks
Before we build triangles and quadrilaterals, we must master the basic components. Constructing an Angle of 60° This is the most natural angle for a compass. Step 1: Draw a straight line and mark a point P on it. Step 2: Place the compass point at P and draw a large arc that cuts the line at a point Q. Step 3: Without changing the compass radius, move the compass point to Q and draw another arc that intersects the first arc at a point R. Step 4: Join P to R. The angle ∠RPQ is exactly 60°. Bisecting an Angle This means dividing an angle into two equal parts. Step 1: Place the compass point at the vertex of the angle (e.g., P) and draw an arc that cuts the two arms of the angle at points, say, X and Y. Step 2: Place the compass point at X and draw an arc in the middle of the angle. Step 3: Without changing the radius, move the compass point to Y and draw another arc to intersect the one from Step 2 at a point Z. Step 4: Draw a line from the vertex P through the point Z. This line bisects the original angle. Constructing an Angle of 90° (A Perpendicular) Step 1: Draw a straight line and mark a point P where you want the 90° angle. Step 2: Place the compass point at P and draw a semicircle (a large arc) that cuts the line at two points, A and B. Step 3: Now, increase the compass radius. Place the point at A and draw an arc above P. Step 4: Without changing the radius, move the compass point to B and draw another arc to intersect the one from Step 3 at a point C. Step 5: Join C to P. The line CP is perpendicular to the line AB, so ∠CPA = 90°. C. Constructing Other Angles from the Basics 30°: Construct 60° and then bisect it. 45°: Construct 90° and then bisect it. 120°: Construct a 60° angle. Then, using the new arm of the 60° angle as a base, construct another 60° angle adjacent to it (60° + 60°). 135°: This can be constructed as 90° + 45°. First, construct a 90° angle. Then, bisect the adjacent straight angle (180°) to get another 90° on the other side. Bisect this second 90° angle to get 45°. The total angle will be the first 90° plus the adjacent 45°, which equals 135°. D. Constructing Triangles