Fractal Geometry · SHS2 Design And Communication…

Lesson notes

Learning Objectives

Indicator: 2.2.3.LI.4 - Design artefact with loci

By the end of the lesson, learners can:

Define locus, helix, and involute in their own words and distinguish each from the other two types of loci.
Explain the working principles of a helix and an involute, using labelled sketches to support their explanations.
Construct a helix and an involute accurately using drawing instruments, following the step-by-step methods demonstrated.
Design and produce a working model of a car jack that applies the principles of the helix, with correct proportions and smooth, consistent spacing.
Assess their own and peers’ car jack designs against given criteria, including accuracy, neatness, and functionality, and suggest at least one improvement.

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Curriculum details

Strand: Geometry (Strand 2)
Sub-strand: Fractal Geometry (2.3)
Content standard: 2.2.3.CS.1 - 2.2.3.CS.1 Demonstrate knowledge and understanding of fractal geometry in creating fractal designs. 2.2.3.LO.1 Use the understanding of plane and solid geometry to create fractal designs.
Indicator: 2.2.3.LI.4 - Design artefact with loci
Suggested placement: Semester 2, Week 4 (Week 24 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.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

indicator text - printed p.67, in full ink, with a complete assessment cell. All three scope-and-sequence tables give Year 2 Fractal Geometry two learning indicators and the body prints four. This indicator and 2.2.3.LI.3 restate the Plane Geometry indicators 2.2.1.LI.1, LI.2 and LI.3 printed pp.56-57, down to the helix and the car jack, and neither is about fractal geometry. Filed as printed; the ink test measured every code position on the page at 0.1368 or above, so neither is a phantom.
Curriculum reference: NaCCA curriculum document, p. 67

Exemplars (from the NaCCA curriculum)

Discussion, demonstration and problem solving:
1. With the use of pictures, videos and charts, help learners to vividly explain the principles underlying the operations of Helix and Involute as types of loci.
2. Guide learners to accurately design a car jack using the working principles of the helix

Assessment (2.2.3.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.

Teaching and Learning Materials:
- Models
- Charts
- Reference books
- Drawing studio
- Drawing instruments
- Access to internet
- LCD Projector