SHS3 Mathematics · Semester 2, Week 3

Spatial Sense

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Curriculum details

Strand: Geometry Around Us (Strand 3)
Sub-strand: Spatial Sense (3.1)
Content standard: 3.3.1.CS.2 - Demonstrate knowledge and understanding of geometrical construction, use the knowledge to construct plane shapes and apply these in the world around them. 3.3.1.LO.2 Perform geometric construction of quadrilaterals and given loci.
Indicator: 3.3.1.LI.2 - Construct a triangle or quadrilateral under given conditions.
Suggested placement: Semester 2, Week 3 (Week 23 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Curriculum reference: NaCCA curriculum document, p. 346

Exemplars (from the NaCCA curriculum)

Group discussions: In small groups, learners draw various triangles and quadrilaterals using the appropriate technology tools to enable creative and innovative techniques to construct and verify a triangle or a quadrilateral under given conditions.
Example 1: Construct a triangle ABC with given conditions. (i) AB = 7 cm, AC = 6.5 cm and ∠A = 120°.
Solution

Constructed triangle with AB = 7 cm, angle A = 120 degrees and AC = 6.5 cm, on the ray AX. — A constructed triangle ABC drawn by hand. The base AB is marked 7 cm, the angle at A is marked 120 degrees, the side AC is marked 6.5 cm, and the ray AX runs on beyond C.

Example 2: Construct triangle PQR such that ∠P = 115°, ∠Q = 40° and PQ = 6

Constructed triangle with PQ = 6 cm, angle P = 115 degrees and angle Q = 45 degrees, rays meeting at R. — A constructed triangle PQR drawn by hand. The base PQ is marked 6 cm, the angle at P is 115 degrees and the angle at Q is 45 degrees, and the rays PX and QY meet at R above the base.

Construction steps:
- Step 1: Drawn a line. Marked P and Q on the line such that PQ = 6 cm.
- Step 2: At P, draw O ray PX, making an angle of 115° with PQ.
- Step 3: At Q, draw another ray QY, making an angle of 40° with PQ. Marked the point of intersection of the rays PX and Q Y as R. PQR is the required triangle.

Construction of triangle PQR with angle Q = 90, angle R = 42 and QR = 5.5 cm, with its steps written out. — "Example 3: Construct triangle PQR such that angle Q = 90 degrees, angle R = 42 degrees and QR = 5.5 cm", with the finished construction drawn above and three numbered construction steps below, followed by the opening of Example 4 on a quadrilateral PQRS.

 Example 3: Construct triangle PQR such that ∠Q = 90°, ∠R = 42° and QR = 5.5cm
Construction steps:
- Step 1: Drawn a line. Marked Q and R on the line such that |QR| = 5.5 cm.
- Step 2: At Q, draw a ray |X, making an angle of 90° with QR.
- Step 3: At R, draw another ray RY, making an angle of 42° QR. Marked the point of intersection of the rays QX and RY as P. PQR is the required triangle.
Example 4: Construct a quadrilateral PQRS where |PQ| = 4 cm, |OQ| = 6 cm, |RS| = 5 cm, |PS| = 5.5 cm and |PR|= 7 cm

Constructed quadrilateral PQRS with PR = 7 cm, with its four construction steps written out. — A constructed quadrilateral PQRS drawn by hand with PR marked 7 cm, above four numbered construction steps that draw the triangle PQR by side-side-side, then arcs of radius 5.5 cm from P and 5 cm from R to fix S.

Construction steps:
- Step 1: Draw Δ PQR using SSS construction condition.
- Step 2: With P as the centre, draw an arc of radius 5.5 cm.
- Step 3: With R as the centre, draw an arc of radius 5 cm.
- Step 4: S is the point of intersection of the two arcs. Also, mark S and complete PQRS. PQRS is the required quadrilateral.
Teaching and Learning Resources:
- * Mathematical sets, Graph sheet. * Technology tools such as computers, mobile phones, etc. * Computer software applications like GeoGebra.
Assessment (3.3.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.

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