Application of Algebra

Lesson notes

Curriculum details

Strand

Modelling with Algebra (Strand 1)

Sub-strand

Application of Algebra (1.1)

Content standard

2.1.1.CS.4 - Demonstrate the ability to carry out matrix operations, determine the inverse of a linear transformation and represent real life situations in matrix forms. 2.1.1.LO.1 Investigate De Morgan's law on sets algebraically and graphically, formulate and solve real life problems up to three sets. 2.1.1.LO.2 Model sequence recursively and explicitly, and establish the relationship between the two forms, as well as solve real life problems involving linear and exponential sequences and series. 2.1.1.LO.3 Apply indices and logarithms to solve real life problems, including logarithms with different bases, and sketch and interpret logarithmic functions. 2.1.1.LO.4 Formulate and derive appropriate strategies to solve quadratic inequalities. 2.1.1.LO.5 Graph systems of given inequality and identify the region that provides the feasible solution and apply it to real life situations. 2.1.1.LO.6 Determine the set of values for which a rational function is defined and resolve rational functions into partial fractions. 2.1.1.LO.7 Multiply matrices, determine the inverse of a 2 x 2 matrix, find the determinant up to a 3 x 3 matrix and represent matrices in linear transformations.

Indicator

2.1.1.LI.5 - Model and solve problems based on real life situations using matrices.

Suggested placement

Semester 1, Week 17 (Week 17 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.325: 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
• exemplars - p.326: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page

Curriculum reference

NaCCA curriculum document, p. 325

Exemplars (from the NaCCA curriculum)

Collaborative Learning, Experiential Learning, Problem-based Learning, Project-based Learning and Talk for Learning
Activity: Application of Matrices to Simultaneous Equations
Collaborative Learning, Experiential Learning, Whole class discussion, Talk for Learning Approaches and Problem-based Learning.
Work with a partner: Solve problems systems of linear simultaneous equations using matrix properties.
- Solve the following simultaneous equations using matrix methods: 2𝑥 + 3𝑦 = 13 and 5𝑥 + 2𝑦 = 16
Solution: 2 3 𝑥 13 É ÊÉ Ê = É Ê 5 2 𝑦 16
𝑥 2 3 Notice that 𝐴 = É Ê is the matrix of the coefficients, 𝑋 = É 𝑦Ê is a column matrix of the pronumerals x 5 2 13 and y, and 𝐵 = É Ê is a column matrix of the values on the right-hand side of the equations. Using the 16 relation 𝑥 2 3 *! 13 𝐴 *! 𝐵 = 𝑋 = É 𝑦Ê = É Ê × É Ê, so 𝑥 = 2 and 𝑦 = 3 5 2 16 It is worth checking your answers by substituting the values in the original equations.
- Solve 2𝑥 + 𝑦 + 4𝑧 = 17 3𝑥 − 2𝑦 = −6 2𝑥 + 𝑦 + 5𝑧 = 7
- Apply matrix methods to solve real life problems:
There are 5,500 men, women and children altogether at the swimming pool. There are twice as many women as men and four times as many children as women. How many men, women and children are at the swimming pool?
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Teaching and Learning Resources:
- Worksheets
- Scientific Calculator
- Technological tools, apps, etc.
Assessment (2.1.1.AS.5). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.