Applications of Algebra

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.15 - Draw the graph of a polynomial function with degrees up to 3 by hand and by using technology (e.g., GeoGebra, Demos, PhET Simulations, and Geometer's Sketch Pad) where appropriate.

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.117: 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. 117

Exemplars (from the NaCCA curriculum)

Activity 1: Use graphs of polynomial functions to solve problems.
Collaborative Learning:
- Learners work in groups, pairs, and individually to draw graphs of polynomials up to degree 3 by hand and by leveraging technology.
- Learners review features of graphs of linear functions and quadratic functions.
- Learners draw quadratic and cubic polynomial functions by hand and with the aid of appropriate technology and discuss what happens to the curve as 𝑥 − 𝑣 decreases or increases, the point where the curve touches the 𝑦 − 𝑎, axis of symmetry and turning points etc.
- Learners (working in groups/pairs and independently) use curves of polynomial functions to find the truth set, minimum and maximum turning points, increasing and decreasing intervals and equations of symmetry.

Example: Draw the graph of the relation 𝑓(𝑥) = 𝑥 ) − 4𝑥 + 5 for the interval −2 ≤ 𝑥 ≤ 6. On the same axis, draw the graph of 𝑦 = 𝑥 + 3. Use your graphs to find:
- The equation of the axis of symmetry of the graph 𝑓(𝑥) = 𝑥 ) − 4𝑥 + 5.
- The truth set of 𝑥 ) − 5𝑥 + 2 = 0
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.15). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.