Spatial Sense

Curriculum details

Strand

Geometric Reasoning and Measurement (Strand 2)

Sub-strand

Spatial Sense (2.1)

Content standard

1.2.1.CS.2 - Demonstrate knowledge and understanding of spatial sense relating to vectors in two dimensions and perform algebraic operations on vectors and their geometrical interpretations. 1.2.1.LO.1 Describe the properties of lines, including parallel, perpendicular and midpoints. 1.2.1.LO.2 Derive the equation of a line in various forms, find the shortest distance between a point and a line and the perpendicular distance from an external point to a line. 1.2.1.LO.3 Solve problems on acute angles between two intersecting lines. 1.2.1.LO.4 Perform algebraic manipulations of Vectors and resolve vectors using the triangle, parallelogram and polygon laws of addition.

Indicator

1.2.1.LI.3 - Determine the resultant of vectors using triangle and parallelogram laws of addition.

Suggested placement

Semester 2, Week 5 (Week 25 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.161: 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. 161

Exemplars (from the NaCCA curriculum)

Activity 1: In collaborative groups, learners review and calculate the magnitude of vectors.
Example 1: Determine the magnitude of given vectors if 𝐴 «««««⃗ = (3 − 4 ), find ®𝐴 «««««⃗®
«««««⃗® = w3 ) + (−4) ) Solution: ®𝐴
= √25 =5
Activity 2: 1. In collaborative groups, students discuss unit vectors and solve related problems. 2. Learners in groups brainstorm and establish that a unit vector is a vector with a magnitude of 1 unit denoted by, 𝑎¯, and a vector is divided by its magnitude to find the unit vector, i.e. 𝑎¯ = & |&|
Example 1: Find the unit vector for 𝑏 = (−2 1 )
Solution: 𝑏° = (*) ! ) or (−2𝑖 + 𝑗) ! √. √.
Activity 3: Using Collaborative Learning, learners determine a vector 𝑎 in the direction of another vector 𝑏.
For 𝑎 = 𝑏, then |&| = |'| , 𝑎 = |𝑎| × |'| & ' '
Example 1: Given that 𝑚 = (−3 4 ) and 𝑛 = (3 − 5 ), find a vector 𝑟, such that |𝑟| = 25 and 𝑟 in the direction of 2𝑚 + 𝑛.
Solution: 2𝑚 + 𝑛 = 2(−3 4 ) + (3 − 5 ) (3 3 ) ∴ |2𝑚 + 𝑛| = √18 3√2
(" " ) So 𝑟 = 25 × "√) = ).√) (3 3 ) or ).√) (3𝑖 + 3𝑗) / /
Teaching and Learning Resources:
- Graph board or paper
- Compasses
- Mathematical tools
- Dynamic tools like GeoGebra
- Video clips
Assessment (1.2.1.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.