Spatial Sense · SHS2 Additional Mathematics

Lesson notes

Learning Objectives

Indicator: 2.2.1.LI.1 - Explore the equation a circle and its properties using technological tools, e.g. GeoGebra, Geometer’s sketchpad, paper cutting, Geoboard and other realia.

By the end of the lesson, learners can:

Identify and explain the properties of a circle (centre, radius, diameter, chord, sector, arc, and segment) using a constructed circle in GeoGebra or on a geoboard.
Construct a circle using GeoGebra, drawing instruments, or realia, and describe the geometric relationship between the centre, a point on the circle, and the radius.
State the general algebraic equation of a circle with centre (h, k) and radius r as (x − h)² + (y − k)² = r².
Use GeoGebra to explore how changing the centre (h, k) and radius r changes the equation of a circle, and describe the observed patterns.
Derive the equation of a circle given its centre and radius, and identify the centre and radius from a given equation of a circle.

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Curriculum details

Strand: Geometric Reasoning and Measurement (Strand 2)
Sub-strand: Spatial Sense (2.1)
Content standard: 2.2.1.CS.1 - Demonstrate understanding of loci and their applications. 2.2.1.LO.1 Deduce the equation of a circle and find its centre and radius. 2.2.1.LO.2 Determine the equation of a locus under a given condition.
Indicator: 2.2.1.LI.1 - Explore the equation a circle and its properties using technological tools, e.g. GeoGebra, Geometer's sketchpad, paper cutting, Geoboard and other realia.
Suggested placement: Semester 1, Week 18 (Week 18 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:

exemplars - p.332: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
Curriculum reference: NaCCA curriculum document, p. 332

Exemplars (from the NaCCA curriculum)

Experiential Learning, Think-pair-Share.
Learning Experience: Learners in pairs manipulate a technological tool (GeoGebra) to construct a circle and discover its properties.
Activity 1: Learners in pairs observe a circle, identify its properties and describe them.
- Learners recollect the concept of circles.
- Learners identify and explain the properties of a circle (centre, radius, diameter, chord, sector, arc, and segment).
Activity 2: Learners in pairs construct a circle using GeoGebra and realia. E.g., Learners in pairs construct a circle using GeoGebra/drawing instruments
- Learners in pairs to describe the geometric construction of a circle and state the equation of a circle (algebraic form). In pairs, learners share a variety of circles constructed and present the various equations derived. E.g. 𝑟 ) = (𝑥 − ℎ) ) − (𝑦 − 𝑘) )
Teaching and Learning Resources:
- Worksheets
- Scientific Calculator
- Technological tools, apps, etc.
- SHS Additional Mathematics Curriculum
Assessment (2.2.1.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.