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.4 - Use function notation to evaluate functions for inputs in their domain and outputs in the co-domain.

Suggested placement

Semester 1, Week 9 (Week 9 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.99: 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. 99

Exemplars (from the NaCCA curriculum)

Collaborative Learning: Learners will be working in convenient groups (ability, mixed-ability, mixed gender etc.) to solve problems and present answers related to functions and relations.
Talk for Learning Approaches: Learners will brainstorm through Think-Pair-Square and debate and discuss the types and features of functions and relations.
Experiential Learning: Learners will collaboratively engage in hands-on activity (learning by doing) to create functions.
Problem-based Learning: Learners will collaboratively inquire into the domain and range of functions in real life.
Activity 1: Determine the domain and range of functions.
Collaborative Learning, Talk for Learning, Problem-based Learning: Learners work in convenient groups (mixed gender, ability mixed-ability, or pairs) and discuss the domain and range of a function between A and B as a nonempty relation 𝑓 ⊆ 𝐴 × 𝐵 such that if (𝑎, 𝑏) ∈ 𝑓 and (𝑎, 𝑏') ∈ 𝑓, then b = b'. The domain of 'f 'is the set of all first elements of members of f, and the range of 𝑓 is the set of all second elements of members of 𝑓. Symbolically:
Domain 𝑓 = {𝑎: ∃𝑏 ∈ 𝐵 ; (𝑎, 𝑏) ∈ 𝑓} Range 𝑓 = {𝑏: ∃ 𝑎 ∈ 𝐴 ; (𝑎, 𝑏) ∈ 𝑓} For instance, for the function 𝑓(𝑥) = 𝑥 ) , the values 𝑥 = 1,2,3,4, ... are the inputs and the 𝑓(𝑥) = 1,4,9,16,...are the output values:

The set "Out-put values" is referred to as the co-domain of 𝑓. If it happens that the domain of 𝑓 is equal to all of A, then we say 𝑓 is a function from A into B, and we write 𝑓: 𝐴 → 𝐵.
Problem-based Learning: Learners in their various groups investigate the domain of functions such as:
𝑓 = √2𝑥 − 8 and then share findings with the class.
- Learners evaluate functions for output values by substituting giving input values. e.g., Given 𝑓(𝑥) = 2 − 4𝑥 find 𝑓(−3)
Note: Learners recognise that evaluating a polynomial function is just a means of substituting whatever is in the bracket of the 𝑓 of argument for the variable in the function equation.
Example: Evaluate 𝑓(2) for 𝑓(𝑥) = 2𝑥 ) + 2𝑥 − 15
Solution: 𝑓(3) = 2(3) ) + 2(3) − 5 = 18 + 6 − 15 = 9
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.4). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.