Applications of Algebra

Lesson notes

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.16 - Recognise a rational function and determine the domain and range.

Suggested placement

Semester 1, Week 16 (Week 16 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.118: 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. 118

Exemplars (from the NaCCA curriculum)

Activity 1: Domain and zeros of rational function.
Collaborative Learning, Experiential Learning, Whole class discussion, Talk for Learning Approaches and Problem-based Learning:
- Learners work in groups/pairs to recall key facts about polynomial functions and recognise that rational function.
- Learners examine different forms of functions and classify rational functions as functions of the form, I(0) 𝑅(𝑥) = J(0) ; 𝑔(𝑥) ≠ 0 (i.e. a ratio of two polynomials for which the divisor is not zero).
- Learners examine and explore graphically and by algebraic means the set of values for which a given rational function will exist (domain of the function).
! Example 1: The domain of the function 𝑦 = 0*) is the set of all real numbers except 𝑥 = 2 i.e., the domain of 𝑦 is {𝑥: 𝑥 ∈ 𝑅, 𝑥 ≠ 2}
)0*! Example 2: State the largest possible domain of the function defined by 𝑓: 𝑥 → )0 ! *20*.
Learners examine and explore graphically and by algebraic means the values of 𝑥 of a function for which the function is zero. 0$" Example 1: The zeros of the function 𝑓: 𝑥 → 0*) is 𝑥 = −3
)0*!
- Example 2: State the zeros of the function defined by 𝑓: 𝑥 → )0 ! *20*.
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.16). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.