JHS1 Mathematics · Term 3 Week 6: Measurement

Lesson notes

Indicator: B7.3.2.3.5 - Convert vectors in the column (component) form (x, y) to the Magnitude-Bearing form (k, θ) and vice versa

By the end of the lesson, learners can:

Identify the x-component and y-component of a vector written in column form.
Use the Pythagorean theorem to calculate the magnitude (k) of a vector from its column form.
Use the tangent ratio to calculate the direction (θ) of a vector as a bearing, measured clockwise from North.
Convert a vector given in magnitude-bearing form (k, θ) back into column (component) form using sine and cosine.
Interpret the meaning of a vector’s magnitude and direction in practical situations, such as navigation and movement.

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Strand: Geometry and Measurement (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: B7.3.2.3 - Demonstrate understanding of bearings, vector and its components using real life cases.
Indicator: B7.3.2.3.5 - Convert vectors in the column (component) form ( x ) to the y Magnitude-Bearing form (k, θ) and vice versa
Suggested placement: Term 3, Week 6 (Week 30 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:

indicator text - p.71: the column vector is set stacked, x above y, and the flattened line interleaves the words that follow it; read 'Convert vectors in the column (component) form (x, y) to the Magnitude-Bearing form (k, theta) and vice versa'
Curriculum reference: Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 71
Transcribed from the official NaCCA publication. Check this page against the source.

E.g.1 Use the Pythagorean theorem to find the length or the magnitude of a vector.

Eg.2 Find the magnitude and the direction of the following vectors
(i) ⃗ AB =( 12 ) (ii) ⃗ PQ =( 15 ) 15 9