Spatial Reasoning

Curriculum details

Strand

Geometric Reasoning and Measurement (Strand 2)

Sub-strand

Spatial Reasoning (2.1)

Content standard

3.2.1.CS.1 - Demonstrate an understanding of Parabola and its properties. 3.2.1.LO.1 Construct a parabola of a given quadratic equation (𝑦 = 𝑎𝑥 ) + 𝑏 + 𝑐) and explain its key features 3.2.1.LO.2 Sketch a parabola and use it to deduce the relation 𝑦 ) = 4𝑎 3.2.1.LO.3 Sketch a parabola given the directrix Communication: Provide learners the opportunity to engage and and focus. 3.2.1.LO.4 Deduce the equation of the tangent and normal to a parabola

Indicator

3.2.1.LI.4 - Describe a given locus as a parabola.

Suggested placement

Semester 1, Week 11 (Week 11 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. 483

Exemplars (from the NaCCA curriculum)

Think-pair-share, Talk for Learning, and Building on what others will say.
Learning Experience: Learners in mixed-ability groups define a parabola.
Activity 1: Locus describing a parabola Learners brainstorm to define a parabola using their knowledge in locus and explain some keywords.
Definition of Terms in a Parabola
- A parabola is defined as the locus of a point that moves so that it is always the same distance from a fixed point (called the focus) and a given line (called the directrix).
- The focus of a parabola is the fixed point located inside the parabola.
- Directrix of a parabola is a line perpendicular to the axis of symmetry.
Activity 2 Identifying vertex, directrix and focus. Sketch a parabola and identify the vertex, directrix, and focus.

Activity 3 Relationship between focus and directrix Learners in groups brainstorm to discover the relationship between the focus and the directrix.
Expected Response: The distance from the focus to the parabola is the same as the distance from the directrix to the parabola.
Teaching and Learning Resources:
- SHS Curriculum, Graph boards, mathematical set, ICT tools
Assessment (3.2.1.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.