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.11 - Find the point of intersection for a line and a parabola.

Suggested placement

Semester 1, Week 17 (Week 17 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.495: 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
• exemplars - p.496: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page

Curriculum reference

NaCCA curriculum document, p. 495

Exemplars (from the NaCCA curriculum)

Talk for Learning, Group work, and Building on what others say.
Learning Experience: Learners extend knowledge by finding the point of intersection for a line and a parabola.
Activity 1: The intersection of a line and a parabola Learners in groups brainstorm to find the intersection for a line and a parabola.
Example: The line 2𝑦 + 3𝑥 - 6 = 0 intersects the parabola 𝑦 ) = 6𝑥 at K and M respectively.
- Find the coordinates of 𝐾 and 𝑀.
- ) Find the equation of the normal to the parabola at the point i " , 2j.
Solution: i) 2𝑦 + 3𝑥 − 6 = 0 ... . . (1) 𝑦 ) = 4𝑎 ... ... ... ... . (2) /*)A A ! Equation (1)⟹ 𝑥 = and Equation (2)⟹ 𝑥 = " / Since the line and parabola intersect, equation (1)=equation (2) 6 − 2𝑦 𝑦 ) = 3 6 𝑦 + 4𝑦 − 12 = 0 ) 𝑦 = 2 𝑜 6 ) When 𝑦 = 2, 𝑥 = and 𝑦 = −6, 𝑥 = 6 " ) ∴ 𝐾 = i , 2j and 𝑀 = (6, −6) " ii) 2𝑎 − 2𝑎𝑦 ! + 𝑥 ! − 𝑥 ! 𝑦 ! = 0 𝑖 𝑦 ) = 6𝑥
Then 𝑎 = " and the point is i " , 2j, therefore, the equation of the normal is ) )
3 3 2 2 £ ¤ 𝑦 − 2 £ ¤ ∙ 2 + (2)𝑥 − 2 ∙ £ ¤ = 0 2 2 3 9𝑦 + 6𝑥 − 22 = 0
Activity 2: Learners in groups create and pose problems on the intersection of a line and a parabola for other groups to solve.
Teaching and Learning Resources:
- SHS Curriculum, Graph boards, mathematical set, ICT tools
Assessment (3.2.1.AS.11). 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.