SHS1 Additional Mathematics · Semester 1 Week 13: Applications of Algebra

Lesson notes

Learning Objectives

Indicator: 1.1.2.LI.10 - Solve up to three systems of linear equations simultaneously by algebraic manipulations.

By the end of the lesson, learners can:

Solve a system of two linear equations in two unknowns using the elimination method.
Solve a system of two linear equations in two unknowns using the substitution method.
Solve a system of three linear equations in three unknowns by reducing it to a system of two equations and then solving.
Verify solutions by substituting all values back into the original equations.
Apply systems of linear equations to solve realistic problems involving quantities and money.

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Curriculum details

Strand: Modelling with Algebra (Strand 1)
Sub-strand: Applications of Algebra (1.2)
Content standard: 1.1.2.CS.1 - Demonstrate knowledge and understanding of applying algebraic processes and reasoning involving sequence, functions, and linear programming. 1.1.2.LO.1 Examine, analyse, determine and predict other terms in a pattern/sequence. 1.1.2.LO.2 Distinguish among various types of relations, find the domain and range of, and evaluate functions. 1.1.2.LO.3 Show that a function is injective (into) and/or surjective (onto). Find the inverse, describe the relationship between two variables and establish composite functions. 1.1.2.LO.4 Graph linear and quadratic functions and determine the intercepts. 1.1.2.LO.5 Find graphical and algebraic solutions to a system of three linear equations in three variables and apply them to solve real life problems. 1.1.2.LO.6 Perform algebraic manipulations on polynomial functions and graph polynomial functions. 1.1.2.LO.7 Find the domain, range, and zero of a rational function and state when it is undefined. 1.1.2.LO.8 Identify and describe the order of a matrix, the identity matrix and the zero matrix; find the determinant and perform basic arithmetic operations on 2 by 2 matrices (addition and subtraction).
Indicator: 1.1.2.LI.10 - Solve up to three systems of linear equations simultaneously by algebraic manipulations.
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.110: 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. 110

Exemplars (from the NaCCA curriculum)

Activity 2: Solving systems of linear equations.
Collaborative Learning, Experiential Learning, Whole class discussion and Talk for Learning Approaches:
- Collaborative Learning: Learners work in groups/pairs with conventional and personal strategies to solve up to three systems of linear equations involving three unknowns.
- Learners use the elimination and substitution of other appropriate algebraic methods to solve systems of linear equations.
Example 1: solve the equations: 2𝑥 + 𝑦 − 𝑧 = 5; 4𝑦 + 3𝑧 = 5; 𝑦 + 2𝑥 = 7 Example 2: solve the equations 2𝑥 + 𝑦 = 5 and 𝑥 − 𝑦 = 3
Teaching and Learning Resources:
- Cut out shapes of different colours and orientation
- Maths Technology learning apps, tools and devices
- Chalkboard illustrations
- Worksheets
- Cut-out geometrical shapes of different colours and orientation
Assessment (1.1.2.AS.10). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.