# 2.14 Achievement Objectives

### Excellence

• Apply systems of equations in solving problems.

This involves:
- selecting & using methods
- demonstrating knowledge of concepts and terms
- communicating using appropriate representations.

• Apply systems of equations, using relational thinking, in solving problems

This involves:
-selecting and carrying out a logical sequence of steps
- connecting different concepts or representations
- demonstrating understanding of concepts and terms
- forming and using a model;

and also relating findings to a context, or communicating thinking using appropriate mathematical statements.

• Apply systems of equations, using extended abstract thinking, in solving problems.

This involves:
- devising a strategy to investigate or solve a problem
- identifying relevant concepts in context
- developing a chain of logical reasoning, or proof
- forming a generalisation;

and also using correct mathematical statements, or communicating mathematical insight.

Achievement Standard 3.9 #91581 (link to NZQA)

Methods include a selection from those related to
- forming and using a pair of simultaneous equations, one of which is non-linear
- forming and using a system of linear inequations
- connecting different representations of equations or inequations
- interpreting solutions of a system of equations or inequations in context.

Achievement Objectives
- form and use linear and quadratic equations
- form and use pairs of simultaneous equations, one of which may be non-linear

Clarifications
For the award of 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.

For forming a system of equations to provide evidence of a method, one of the equations must be non-linear.

Solving a system of equations is not sufficient as evidence of a method. To provide evidence for the standard the solutions of the system of equations need to be interpreted in context.

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

At Achieved level, students need to indicate what the calculated answer represents.

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

At Excellence level 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.