Applications of Algebra

Curriculum details

Strand

Modelling with Algebra (Strand 1)

Sub-strand

Applications of Algebra (1.2)

Content standard

1.1.2.CS.2 - Demonstrate knowledge and understanding of algebraic processes and reasoning in relation to matrix operations. 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.2 - Add and subtract matrices (2x2 matrix) and multiply a matrix by a scalar and a matrix by a matrix (2x2 matrices).

Suggested placement

Semester 1, Week 18 (Week 18 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.124: 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. 124

Exemplars (from the NaCCA curriculum)

Activity 1: Discuss matrix addition and subtraction.
Collaborative Learning, Experiential Learning, and Talk for Learning Approaches:
- Learners work in groups/pairs to explore commutative and associative properties of addition.
- Learners recognise the conditions necessary for matrix addition and subtraction.
Learners verify that:
- 𝐴 + 𝐵 = 𝐵 + 𝐴
- 𝐴 + (𝐵 + 𝐶) = (𝐴 + 𝐵) + 𝐶
Activity 2: Discuss matrix multiplication.
Collaborative Learning, Experiential Learning, and Talk for Learning Approaches:
- Learners work in groups/pairs to explore and solve problems related to scalar and matrix multiplication.
- Learners recognise conditions necessary for matrix multiplication.
- Learners carry out scalar multiplication of an m x n matrix.
Investigate the properties of the operations on matrices.
Teaching and Learning Resources:
- Worksheets
- Scientific Calculator
- Technological tools, apps, etc.
- SHS Additional Mathematics Curriculum
Assessment (1.1.2.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 3 Strategic reasoning.