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### Commentary

## Achieved

91945 Exemplar Achieved (PDF | 143 KB)### Commentary

For Achieved, the student needs to use mathematical methods to explore problems that relate to life in Aotearoa New Zealand or the Pacific.

This involves using mathematical methods that are appropriate to the problems, and communicating accurate mathematical information related to the context of the problems.

This student has used four appropriate mathematical methods across two or more areas. The evidence includes using algebra to find the size of the rectangular shape that optimises the area of the garden bed. The composite volume of the garden bed is calculated, taking into account the volume displaced by the water tower. This provides evidence of a measurement method. Converting the amount of garden mix required to litres is evidence of another appropriate measurement method.

Evidence of a number method (reasoning with a linear proportion) is provided by finding the GST exclusive price of the timber, and when finding the GST exclusive price of the garden mix. The student has correctly communicated mathematical information by showing how they reached their answer and indicating what their calculated answer represents.

The student has made one logical connection linking the composite volume of the garden bed to the volume of soil required in litres. For Merit, the student would need to make a further logical connection linking one process to another as part of a problem or problems. Each part of the connection would need to be completed correctly.

## Merit

91945 Exemplar Merit (PDF | 178 KB)### Commentary

For Merit, the student needs to use mathematical methods to explore problems that relate to life in Aotearoa New Zealand or the Pacific by applying relational thinking.

This involves applying mathematical methods using logical connections, and communicating accurate mathematical information related to the context of the problems using appropriate mathematical statements.

This student has made the required minimum of two logical connections linking one method to another as part of exploring a problem or problems. Each part of the connection is completed correctly, and the methods used are from two or more areas. The first logical connection made by the student occurs when the algebra methods of quadratic tables and graphs are linked to finding optimal solutions.

This student has made a second logical connection by linking the measurement method of using a composite shape to find the volume of garden mix required for the garden to the method of converting the units for the volume of the garden mix from m3 to litres. Mathematical conventions have been followed correctly. Solutions have been appropriately rounded and linked to the context of the problem, with appropriate mathematical statements.

For Excellence, the student would need to extend at least one problem from within the previously chosen mathematical methods. For example, by considering underlying limitation and assumptions and their mathematical impact on any solution found. Mathematical generalisations or predictions, including recommendations for the best model for a garden, would also meet the requirements for Excellence.

## Excellence

91945 Exemplar Excellence (PDF | 251 KB)### Commentary

For Excellence, the student needs to use mathematical methods to explore problems that relate to life in Aotearoa New Zealand or the Pacific by applying extended abstract thinking.

This involves extending mathematical methods using logical, connected sequences to explore or solve a problem by considering limitations, assumptions, generalisations, or predictions.

This student applied extended abstract thinking by further developing at least one problem from within previously chosen mathematical methods. They have explored the garden bed shapes to maximise the area of the garden and find the volume of garden mix that would be needed to fill the garden bed to the required height. This provides evidence of a mathematical generalisation and includes a recommendation for a more suitable model.

The limitations of a circular model for a garden bed, which would be give a greater area, are discussed. Options for purchasing different combinations of lengths of timber for an octagonal garden bed are also explored. Mathematical conventions have been followed correctly. Solutions have been appropriately rounded and linked to the context of the problem.

This annotated exemplar is intended for teacher use only. Annotated exemplars consist of student evidence, with commentary, to explain key parts of a standard. These help teachers make assessment judgements at the grade boundaries.

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Level 1 Mathematics and Statistics assessment resources (external link) - NCEA.education