## Clarification details

Updated December 2014. This document has been updated to address issues that have arisen from moderation.

The emphasis for this standard is on the use of methods in the process of solving problems rather than simply drawing graphs. Students need to apply graphical methods in solving problems, so the evidence for the standard will most likely be from modelling a situation by graphical models and then using the models to solve the problem.

### Expected evidence for Achieved

For Achieved, the requirements include selecting and using methods. To be used as evidence, a ‘method’ must be relevant to the solution of the problem. The ‘methods’ also need to be at the appropriate curriculum level for the standard.

### Explanatory Note 4

Explanatory Note 4 refers to graphs at curriculum level 7. Further information can be found in the Mathematics and Statistics teaching and learning guide on TKI.

Properties of functions are the attributes which apply to all the functions in a group, for example, all cubics have rotational symmetry, all trigonometric functions are periodic.

Features of graphs apply to a specific function, for example, y = 3sin2x has an amplitude of 3, y = 0.05(x – 4)2 – 7.5 has a line of symmetry at x = 4 and turning point at (4, -7.5).

### Relational thinking

In forming a model to meet some specified criteria and using this model to solve a problem, finding points of intersection, and using these to make recommendations related to given criteria, students are likely to demonstrate relational thinking.

### Extended abstract thinking

This may require students to go beyond the given information. In forming a general rule which could be used to generate families of functions, generalising an equation of a model and using this to determine when specific criteria can be met, or making a decision on a ‘best’ model and giving a detailed explanation for the decision, students are likely to demonstrate extended abstract thinking.

### Communicating solutions

At all grades there is a requirement relating to the communication of the solutions.

At Achieved, communicating the solution is likely to involve providing an appropriate representation of a graph and identifying its features.

At Merit, students need to clearly indicate what they are finding and their solutions need to be linked to the context.

At Excellence, the response needs to be clearly communicated with correct mathematical statements, and students need to explain any decisions they make in the solution of the problem.