Nayland College - Mathematics
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Achievement with Merit
Achievement with Excellence
Apply numeric reasoning involves:
• selecting and using a range of methods in solving problems
• demonstrating knowledge of number concepts and terms
• communicating solutions which would usually require only one or two steps.
Relational thinking involves one or more of:
• selecting and carrying out a logical sequence of steps
• connecting different concepts and representations
• demonstrating understanding of concepts
• forming and using a model;
and also relating findings to a context, or communicating thinking using appropriate mathematical statements.
Extended abstract thinking involves one or more of:
• 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.
Problems are situations that provide opportunities to apply knowledge or understanding of mathematical concepts and methods. The situation will be set in a real-life or mathematical context.
The phrase ‘a range of methods’ indicates that evidence of the application of at least three different methods is required.
You need to be familiar with methods related to:
Clarifications (link to NZQA)
For the award of the standard students must apply numeric reasoning in solving problems, therefore students need to be given a problem to solve. Explanatory Note 3 of the standard clarifies what is meant by a problem.
The problem needs to provide sufficient scope for students to demonstrate and develop their own thinking. If there are parts to the problem, all of the parts need to contribute to the solution.
A task with a number of discrete questions based on skills and straightforward calculations is not appropriate for students to demonstrate evidence of the required levels of thinking.
Students need to make their own decisions about what to do and how to solve problems. Where an assessment task has a series of instructions that lead students through a step or a sequence of steps towards the solution, it is likely that the opportunity for students to demonstrate all levels of thinking will be compromised.
Expected evidence for Achieved
For the award of Achieved, the requirements include selecting and using a range of methods. The evidence for this aspect cannot come from a situation where students are told what method to use.
To be used as evidence, ‘methods’ must be relevant to the solution of the problem.
The ‘methods’ also need to be at the appropriate curriculum level for the standard, for example working with everyday fractions like one half, one quarter and one fifth is not at the appropriate curriculum level.
For rounding with decimal places and significant figures, it is likely that there will need to be a holistic judgement on the evidence based on an understanding of rounding across the entire task.
Extended abstract thinking
For the award of Excellence, there needs to be evidence that students are thinking beyond the problem. This could involve considering other identified factors and the effect of them on the solution of the problem. Alternatively, students could consider a change in one of the aspects involved in the solution and explore the consequences of that change on their solution.
At all levels there is a requirement relating to the communication of the solutions.
At Achieved level, the result of a numerical calculation only is insufficient, working is expected and 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.