NSW Syllabuses

# Mathematics K–10 - Stage 5.1 - Number and Algebra Non-Linear Relationships

## Outcomes

#### A student:

• MA5.1-1WM

uses appropriate terminology, diagrams and symbols in mathematical contexts

• MA5.1-3WM

provides reasoning to support conclusions that are appropriate to the context

• MA5.1-7NA

graphs simple non-linear relationships

## Content

• Students:
• Graph simple non-linear relations, with and without the use of digital technologies (ACMNA296)
• complete tables of values to graph simple non-linear relationships and compare these with graphs drawn using digital technologies, eg $$y = x^2$$, $$y = x^2 + 2$$, $$y = 2^x$$
• Explore the connection between algebraic and graphical representations of relations such as simple quadraticscircles and exponentials using digital technologies as appropriate (ACMNA239)
• use digital technologies to graph simple quadratics, exponentials and circles, eg
$$\begin{array}{l} y = x^2, \quad y = -x^2, \quad y=x^2 + 1, \quad y = x^2 -1 \\ y=2^x, \quad y = 3^x, \quad y=4^x \\ x^2 + y^2 = 1, \quad x^2 + y^2 = 4 \end{array}$$
• describe and compare a variety of simple non-linear relationships (Communicating, Reasoning)
• connect the shape of a non-linear graph with the distinguishing features of its equation (Communicating, Reasoning)

#### Purpose/Relevance of Substrand

Non-linear relationships, like linear relationships, are very common in mathematics and science. A relationship between two quantities that is not a linear relationship (ie is not a relationship that has a graph that is a straight line) is therefore a non-linear relationship, such as where one quantity varies directly or inversely as the square or cube (or other power) of the other quantity, or where one quantity varies exponentially with the other. Examples of non-linear relationships familiar in everyday life include the motion of falling objects and projectiles, the stopping distance of a car travelling at a particular speed, compound interest, depreciation, appreciation and inflation, light intensity, and models of population growth. The graph of a non-linear relationship could be, for example, a parabola, circle, hyperbola, or cubic or exponential graph. 'Coordinate geometry' facilitates exploration and interpretation not only of linear relationships, but also of non-linear relationships.

### National Numeracy Learning Progression links to this Mathematics outcome

When working towards the outcome MA5.1-7NA the sub-elements (and levels) of Number patterns and algebraic thinking (NPA7) describe observable behaviours that can aid teachers in making evidence-based decisions about student development and future learning.

The progression sub-elements and indicators can be viewed by accessing the National Numeracy Learning Progression.