Measurement · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.3.2.LI.3 - Solve problems involving the addition, subtraction, and scalar multiplication of vectors, including problems arising from real-world applications.

By the end of the lesson, learners can:

Translate a real-world problem into a vector diagram using the information given about direction and magnitude.
Apply vector addition, subtraction, and scalar multiplication to find resultant displacement vectors in two dimensions.
Determine the magnitude and direction of a resultant vector using the Pythagorean theorem and inverse trigonometric ratios (tangent).
Interpret the meaning of a resultant vector in the context of the problem and draw conclusions such as whether a journey is possible within given constraints.

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Curriculum details

Strand: Geometry Around Us (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: 2.3.2.CS.1 - Demonstrate knowledge and understanding of measurement with respect to operations on bearings and vectors. 2.3.2.LO.1 Carry out addition, subtraction and scalar multiplication of vectors and investigate with and without technology some properties (e.g., commutative, associative, and distributive properties) of the operations.
Indicator: 2.3.2.LI.3 - Solve problems involving the addition, subtraction, and scalar multiplication of vectors, including problems arising from real-world applications.
Suggested placement: Semester 2, Week 6 (Week 26 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.243: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 242

Exemplars (from the NaCCA curriculum)

Think-pair-share activities: In pairs, learners solve real-world problems on vectors.
Example 1: The Antarctic expedition drives their snowmobiles 185 miles south from their camp. Then, they turn and drive 70 miles west. Now it is time to return to camp. In what direction must they drive, and will they make it on 190 miles worth of fuel?
Solution: Vector Diagram
Note that this is a special case where the resultant vector appears to point backwards.
- This is because that is the path they will need to take back to their base.

Right-angled triangle with base 70 miles, height 185 miles and the angle at the base marked x. — A right-angled triangle with the horizontal side labelled 70 miles and the vertical side labelled 185 miles, with the angle at the left vertex marked x.

𝑐 = √185 2 + 70 2 ⬚ √34225 + 4900 √39125 198 Angle calculation 185 tan −1 = 2.64 = 69.30 70
Final answer 20.8° and, no, they cannot make it on that quantity of fuel, so they will have to walk an additional 8 miles.
Example 2: Michael is running some errands.
- His first stop is 6 km to the east and 3 km to the south from his house.
- His second stop is 2 km to the west and 1 km to the south from the first stop.
- His third stop is 7 km to the west and 5 km to the north from the second stop.
- What is Michael's direction relative to his starting point once he arrives at his third stop?
Teaching and Learning Resources:
- * Mathematical sets. * Technology tools such as computers, mobile phones, etc.
- * Computer software applications like
Assessment (2.3.2.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.