Outcomes
A student:

 MA5.11WM
uses appropriate terminology, diagrams and symbols in mathematical contexts

 MA5.13WM
provides reasoning to support conclusions that are appropriate to the context

 MA5.17NA
graphs simple nonlinear relationships
Content
 Students:
 Graph simple nonlinear relations, with and without the use of digital technologies (ACMNA296)
 complete tables of values to graph simple nonlinear 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 quadratics, circles 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 nonlinear relationships (Communicating, Reasoning)
 connect the shape of a nonlinear graph with the distinguishing features of its equation (Communicating, Reasoning)
Purpose/Relevance of Substrand
Nonlinear 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 nonlinear 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 nonlinear 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 nonlinear 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 nonlinear relationships.
National Numeracy Learning Progression links to this Mathematics outcome
When working towards the outcome MA5.17NA the subelements (and levels) of Number patterns and algebraic thinking (NPA7) describe observable behaviours that can aid teachers in making evidencebased decisions about student development and future learning.
The progression subelements and indicators can be viewed by accessing the National Numeracy Learning Progression.