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Mathematics and Statistics clarifications

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91026: Apply numeric reasoning in solving problems

Updated May 2019. The section describing extended abstract thinking has been renamed ‘Expected evidence for Excellence’.

Solving problems

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 the parts need to contribute to the solution.

A task with several 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 the opportunity for students to demonstrate all levels of thinking will be compromised.

Expected evidence for Achieved

For 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 – 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.

Expected evidence for Excellence

For 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. 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.

Communicating solutions

At all levels there is a requirement relating to the communication of the solutions. At Achieved, the result of a numerical calculation only is insufficient. Working is expected, and students need to indicate what the calculated answer represents.

At Merit, students need to clearly indicate what they are calculating, 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.

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