NCEA

Mathematics - annotated exemplars level 1 AS91026

Apply numeric reasoning in solving problems (1.1)

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This annotated exemplar is intended for teacher use only. The student work shown does not always represent a complete sample of what is required. Selected extracts are used, focused on the grade boundaries, in order to assist assessors to make judgements at the national standard.

Last updated May 2019.

Annotations at Low Excellence, High Merit and Low Merit have been altered to better illustrate the requirements of the standard.

Low Excellence

Commentary

Student response
Student 1 (PDF, 80KB)

For Excellence, the student needs to apply numeric reasoning, using extended abstract thinking, in solving problems.

This 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.

This student’s evidence is a response to the TKI assessment resource ‘Mike and Huia’s Trip to England’.

This student has devised a strategy to investigate the length of time they will need to save for the trip (1). Insight has been shown by considering the maximum possible number of days for the trip (2) and a range of values for the daily spending (3). Correct mathematical statements have been used throughout the response.

For a more secure Excellence, the student could consider other factors which might affect the time required to complete the saving, for example a fluctuation in exchange rates. The student could also provide a fuller explanation for using 92 days for the length of the trip.

High Merit

Commentary

Student response
Student 2 (PDF, 80KB)

For Merit, the student needs to apply numeric reasoning, using relational thinking, in solving problems.

This 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.

This student’s evidence is a response to the TKI assessment resource ‘Mike and Huia’s Trip to England’.

This student has selected and carried out a logical sequence of steps to calculate the savings (1), the cost of the trip (2) and the time to save for the trip (3). The findings have been related to the context and appropriate mathematical statements have been used throughout.

To reach Excellence, the student would need to calculate the cost of the bus trip for two people, determine the correct total cost and investigate factors which might affect the time required to complete the saving.

Low Merit

Commentary

Student response
Student 3 (PDF, 80KB)

For Merit, the student needs to apply numeric reasoning, using relational thinking, in solving problems.

This student’s evidence is a response to the TKI assessment resource ‘Mike and Huia’s Trip to England’.

This student has selected and carried out a logical sequence of steps to calculate the cost of the trip (1), the savings (2) and the time to save for the trip (3). The findings have been related to the context, and appropriate mathematical statements have been used throughout.

For a more secure Merit, the student would need greater accuracy in the decision on the length of time for the trip. The student would also need to deduct the time for the bus trip when calculating the spending money and round the final answer appropriately.

High Achieved

Commentary

Student response
Student 4 (PDF, 93KB)

For Achieved, the student needs to apply numeric reasoning in solving problems.

This involves selecting and using a range of methods, demonstrating knowledge of number concepts and terms, and communicating solutions which would usually require only one or two steps.

This student’s evidence is a response to the TKI assessment resource ‘Mike and Huia’s Trip to England’.

This student has calculated the GST inclusive cost of the insurance (1), converted UK pounds to NZ dollars (2), found a fraction of a quantity (3) and found a percentage of a quantity (4).

To reach Merit, the student would need to calculate the cost of the bus trip for two people, correctly calculate the total daily spending and determine the number of weeks it would take to save the necessary amount.

Low Achieved

Commentary

Student response
Student 5 (PDF, 72KB)

For Achieved, the student needs to apply numeric reasoning in solving problems.

This involves selecting and using a range of methods, demonstrating knowledge of number concepts and terms, and communicating solutions which would usually require only one or two steps.

This student’s evidence is a response to the TKI assessment resource ‘Mike and Huia’s Trip to England’.

The student has found a fraction of a quantity (1), a percentage of a quantity (2) and the cost of the bus trip for one person in NZ dollars (3).

For a more secure Achieved, the student would need to find the cost of the insurance, including GST, and support their conclusions with working and/or explanations.

High Not Achieved

Commentary

Student response
Student 6 (PDF, 58KB)

For Achieved, the student needs to apply numeric reasoning in solving problems.

This involves selecting and using a range of methods, demonstrating knowledge of number concepts and terms, and communicating solutions which would usually require only one or two steps.

This student’s evidence is a response to the TKI assessment resource ‘Mike and Huia’s Trip to England’.

This student has found a fraction of a quantity (1) and a percentage of a quantity (2).

To reach Achieved, the student would need to select and use one further method correctly.