SHS3 Mathematics · Semester 2, Week 2

Spatial Sense

Full lesson notes coming

Notes for this lesson are being prepared. The curriculum details below are complete and ready to use for your planning.

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.1 - Recall the construction of various angles such as 75°, 105°, 135° and 150°.
Suggested placement: Semester 2, Week 2 (Week 22 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. 345

Exemplars (from the NaCCA curriculum)

Group discussions: In convenient groups, learners discuss and draw various angles using the appropriate mathematical tools and/or technology.
Example: Construct the following angles and verify by measuring them with a protractor: (i) 75° (ii) 105° (iii) 135°
Solution (i) Angle 75° We need to construct two adjacent angles of 60°. The second angle should be bisected twice to get a 15° angle. 75° = 60° + 15° 15° = 30°/2 = (60/2) ÷ 2

Construction of an angle on ray PQ using arcs through points R, S, T, U, V and W. — An angle construction on the ray PQ. Arcs centred at P and at successive intersections cut off points R, S, T, U, V and W, and rays are drawn from P through them; the constructed angle is marked at P.

(ii) Angle 105° We need to construct two adjacent angles of 60°. In the second angle, we need to bisect it to get two 30° angles. The second 30° angle should be bisected again to get a 15° angle. Altogether, we can make an angle of 105°. 105° = 60° + 45° 105°= 60° + 30° + 15°

A second construction on ray PQ, using further arcs and bisections to build a larger angle. — A second angle construction on the ray PQ, with more arcs and bisections than the first, producing points R, S, T, U, V and W and rays from P; the constructed angle is marked at P.

(iii) Angle 135° We need to construct three adjacent angles of 60° each. The third angle should be bisected twice successively to get an angle of 15°. Altogether, we will get an angle of 135°. 135° = 15° + 60° + 60° 15° = (60°/2) ÷ 2

A third angle construction with fine arcs and several rays from the vertex. — A third angle construction on a ray, drawn with fine blue and orange arcs and several rays from the vertex, the constructed angle marked at the vertex.

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.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.

← All lessons this week Full scheme of learning