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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.

Download all exemplars and commentary [PDF, 646 KB]

- NCEA.education

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 problem.

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, which considers the volume displaced by the water tower is calculated. 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.

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 problem using appropriate mathematical statements.

The 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. 

The 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 limitations 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.

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. Mathematical conventions must be used correctly, and solutions should be appropriately rounded and linked to the context of the problem.

The student has applied extended abstract thinking by further developing a previously selected problem. They explored keeping the tiny house鈥檚 floor area, maximum ceiling height, and prism shape the same as in the original problem, while investigating the effect of changing the width of the frontage.

Assumptions were made and explored mathematically in context. The first assumption occurred when the student increased the frontage width to 8 metres and assumed that the vertical height from the roof tip to the horizontal would remain at 1.02 metres. Their calculations showed that maintaining this height would require the roof pitch to become shallower. In a second investigation involving the same frontage width, the student instead assumed that the 9-degree roof pitch would remain constant. This resulted in a greater vertical height from the roof tip to the horizontal, creating potential issues with height clearance for taller people near the lower wall.

The student also made several other relevant observations, although these were not fully communicated mathematically. These included recognising that proportional changes to all dimensions lead to a similar change in surface area, that the lack of wall鈥憌idth measurements introduces uncertainty, and that a square floor plan would likely provide a more compact shape with a lower surface鈥慳rea鈥搕o鈥憊olume ratio.