Measurement · JHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: B8.3.2.2.1 - Add, subtract and find the scalar multiplication of vectors in the component form.

By the end of the lesson, learners can:

Identify the component form of a vector, such as (x, y) or a column vector, and state its meaning.
Add two or more vectors written in component form by adding corresponding components, and give the answer as a single vector.
Subtract one vector from another in component form by subtracting corresponding components, and give the answer as a single vector.
Multiply a vector by a scalar by multiplying each component by the scalar, and give the answer as a single vector.
Apply addition, subtraction and scalar multiplication together to simplify expressions like 3q - 2p and q - p + 2r.

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Curriculum details

Strand: Geometry and Measurement (Strand 3)
Sub-strand: Measurement (3.2)
Content standard: B8.3.2.2 - Demonstrate understanding of addition and subtraction of vectors and their applications in solving basic problems
Indicator: B8.3.2.2.1 - Add, subtract and find the scalar multiplication of vectors in the component form.
Suggested placement: Term 3, Week 5 (Week 29 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: Mathematics, Common Core Programme (JHS1-JHS3), 2023, p. 149
Transcribed from the official NaCCA publication. Check this page against the source.

Exemplars (from the NaCCA curriculum)

E.g1 Add vectors using the graphical method.
E.g.2 Add and subtract vectors in their corresponding components. a c
If AB = b and BC = d then AC = AB + BC a c a + c
= b + d = b + d a c
If AB = b and BC = d AC BC
then = AB - a c b d a - c
= - = ( ) b - d
E.g3 Multiply a vector by a scalar k( x )=k( kx ) y ky
E.g.4 If p=( -1 ) , q=( 43 ) , and r=( 3 ), find (i) 3q-2p (ii) r-3p (ii) q-p+2r 2 -2