# Mathematics and Statistics - annotated exemplars level 2 AS91260

## Apply network methods in solving problems (2.5)

 Read the STANDARD TKI Mathematics and Statistics Assessment Resources Download all these exemplars and commentary (PDF, 1.1MB)

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 July 2019.

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

### Low Excellence

Commentary
Student work extract

Student 1 (PDF, 438KB)

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

This involves one or more of: devising a strategy to investigate a situation, 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 task ‘Waikato Cycleway’.

The student has identified relevant concepts in context by finding the correct shortest path for the Taupo Club (1), the correct minimum spanning tree for the Hamilton Club (2), the correct maximum spanning tree for the Tirau Club (3), addressing the Tokoroa Club’s question correctly (4) and suggesting an appropriate compromise network (5).

The student has communicated using mathematical insight in constructing and justifying an appropriate compromise network (6).

For a more secure Excellence, the student could strengthen the communication of the strategy used to create a network that satisfies the priorities of the three clubs, for example by communicating fully why the three additional edges were chosen.

### High Merit

Commentary
Student work extract

Student 2 (PDF, 330KB)

For Merit, the student needs to apply network methods, using relational thinking, in solving problems.

This involves one or more of: selecting and carrying out a logical sequence of steps, connecting different concepts or 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 task ‘Waikato Cycleway’.

The student has demonstrated an understanding of concepts by finding the correct shortest path for the Taupo Club (1), by finding and justifying the correct minimum spanning tree for the Hamilton Club (2), the correct maximum spanning tree for the Tirau Club (3) and addressing the question for the Tokoroa Club (4).

The student has communicated using appropriate mathematical statements.

To reach Excellence, the student could fully justify the shortest route for the Taupo club and further develop the recommendation for a compromise network (5).

### Low Merit

Commentary
Student work extract

Student 3 (PDF, 186KB)

For Merit, the student needs to apply network methods, using relational thinking, in solving problems.

This involves one or more of: selecting and carrying out a logical sequence of steps, connecting different concepts or 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 task ‘Waikato Cycleway’.

The student has demonstrated an understanding of concepts by finding the correct shortest path for the Taupo Club (1), the correct minimum spanning tree for the Hamilton Club (2), the correct maximum spanning tree for the Tirau Club (3) and addressing, with justification, the question for the Tokoroa Club (4).

The student has communicated using appropriate mathematical statements.

For a more secure Merit, the student could further explain and justify their solutions for the Taupo, Hamilton and Tirau clubs, for example by showing that they have considered all possible routes from Hamilton to Taupo for the shortest path, and giving the order in which the edges are added into the minimum spanning tree for the Hamilton and Tirau clubs.

### High Achieved

Commentary
Student work extract

Student 4 (PDF, 101KB)

For Achieved, the student needs to apply network methods in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is a response to the TKI task ‘Waikato Cycleway’.

The student has selected and used methods for a shortest path (1), a minimum spanning tree (2) and traversability (3), and communicated using appropriate representations for the cycle paths for the four clubs.

To reach Merit, the student would need to justify their solutions to the cycle paths for the four clubs, for example by explaining how the minimum spanning tree was built up, and providing more information as to how the shortest path was found by trial and error.

### Low Achieved

Commentary
Student work extract

Student 5 (PDF, 74KB)

For Achieved, the student needs to apply network methods in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is a response to the TKI task ‘Waikato Cycleway’.

The student has selected and used methods for a minimum spanning tree (1) and traversability (2), and communicated the solutions using appropriate representations.

For a more secure Achieved, the student could find the correct shortest path between Hamilton and Taupo and provide the correct maximum scenic value.

### High Not Achieved

Commentary
Student work extract

Student 6 (PDF, 97KB)

For Achieved, the student needs to apply network methods in solving problems.

This involves selecting and using methods, demonstrating knowledge of concepts and terms and communicating using appropriate representations.

This student’s evidence is a response to the TKI task ‘Waikato Cycleway’.

The student has selected and used traversability to address the question for the Tokoroa Club (1).

To reach Achieved, the student needs to select and use one further method correctly, for example by finding the shortest path for the Taupo club or the correct minimum spanning tree for the Hamilton club.