Applications of Expressions… · SHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: 1.2.1.LI.1 - Construct and interpret formulae for a given task and apply them to problems involving change of subjects.

By the end of the lesson, learners can:

State the meaning of a formula and identify the subject of a given formula in at least three different examples.
Rearrange a given linear formula to make a specified variable the subject, using inverse operations correctly.
Construct a formula from a given worded relationship or real-life situation.
Substitute given values into a formula after changing the subject and compute the required value accurately.
Apply formulae and change of subject to solve at least one real-life problem and explain the steps used.

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Curriculum details

Strand: Algebraic Reasoning (Strand 2)
Sub-strand: Applications of Expressions, Equations and Inequalities (2.1)
Content standard: 1.2.1.CS.2 - Demonstrate knowledge and understanding of equations and inequalities in one variable and apply it in solving real-life problems. 1.2.1.LO.2 Model and solve linear equations and inequalities in one variable, including problems in real life.
Indicator: 1.2.1.LI.1 - Construct and interpret formulae for a given task and apply them to problems involving change of subjects.
Suggested placement: Semester 1, Week 13 (Week 13 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.63: 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. 62

Exemplars (from the NaCCA curriculum)

Group/Collaborative Learning, Problem-based Learning:
Using think-pair-share activity, perform calculations in a change of subject and substitute values into formulae and use it to solve problems. Employ differentiated assessment and ensure values such as tolerance, truth, honesty, respect for others' views, etc., among learners.
Example 1: Change subjects in a given formula. i. Make 𝑐 the subject of the relation y = mx + c
Solution: To make c the subject, subtract 𝑚𝑥 from both sides of the equation. 𝒎𝒙 − 𝒎𝒙 + 𝑐 = 𝑦 − 𝑚𝑥 ∴ 𝒄 = 𝒚 − 𝒎𝒙
ii. From the equation 3c + 2r = md + k, make r the subject.
Solution Given 3c + 2r = md + k, Make 2r the subject: 2r = md + k - 3c Divide both sides by 2. md + k − 3 c r = 2
Example 2: The relation between energy E, mass m, and velocity of light v is given by E = mv 2 . Find the value v when 𝐸 = 20 and 𝑚 = 5
Solution Given that E = mv 2 E v 2 = m
E ∴ v = m
20 𝑣 = √ 5
∴ 𝑣 = 2
Teaching and Learning Resources:
- * Algebraic tiles * Patterns * calculator * technology tools such as
- computer
- mobile phone
- YouTube videos, etc.
- Paper grids
- Maths posters
- YouTube videos
- Whiteboard
- Pan balance
- Videos
- mini whiteboards or laminated white paper
- Dry-erase markers and erasers
Assessment (1.2.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.